The Pore Pressure, Bulk Density and Lithology Prediction

By

©Olalere Sunday Oloruntobi

A thesis submitted to the School of Graduate Studies

In partial fulfillment of the requirements for the degree of

Doctor of Philosophy
Faculty of Engineering and Applied Science
Memorial University of Newfoundland
St John’s, Newfoundland, Canada

October 2019

i
 DEDICATION

This work is dedicated to Almighty God who made heaven and earth. Special thanks to my wife

Patience Lucy Oloruntobi who is the solid rock behind my achievement.

ii
 ABSTRACT

The pore and fracture pressures are the two most important parameters required for the effective

well design. In general, the difference between the two parameters at any given depth dictates the

drilling window with no consideration for wellbore stability. While pore pressure prediction

from the drilling parameters started in the mid-nineties, very few improvements have been made

in these areas when compared to other pore pressure prediction techniques such as seismic and

well logs. Pore pressure prediction using the d-exponent method does not consider the effect of

bit hydraulic energy on the rate of penetration (ROP). This limits the application of the d-

exponent to mostly hard rock environments. Under downhole conditions where the bit hydraulic

energy has a significant influence on the ROP (soft rock environments), the d-exponent method

may produce inaccurate results. Hence, the primary goal of this research is to develop new pore

pressure prediction models from the drilling parameters that incorporate the bit hydraulic energy,

making them suitable for any subsurface drilling conditions. The new pore pressure prediction

models use the concept of specific energy to predict the onset of overpressure. The concept of

specific energy is then extended to the real-time identification of subsurface lithology.

Furthermore, overburden pressure is an important input parameter in pore pressure

prediction. Inaccurate prediction of overburden pressure may result in the erroneous prediction

of pore pressure which can lead to well control and process safety incidents. In areas where

density logs are not available, synthetically derived density logs are used for overburden pressure

computations. In this research, an attempt is also made to improve the accuracy of pore pressure

prediction by improving the accuracy of overburden pressure computation via improvement in

density logs prediction. Finally, since pore and fracture pressures are closely related, an attempt

is made to develop a new fracture pressure prediction model for the Niger Delta basin.

iii
 ACKNOWLEDGMENTS

I sincerely express my profound gratitude to my supervisor, Dr. Stephen Butt for his care,

patience and guidance during my doctoral degree program at the Memorial University of

Newfoundland, St John’s, Canada. I count it as a great privilege to have worked under his

supervision. I will like to acknowledge my co-supervisor Dr. Raghu Chunduru of Shell

Exploration and Production Company, Houston, USA for providing great support and

encouragement throughout the research work. I also thankfully acknowledge Shell Petroleum

Development Company, Port Harcourt, Nigeria for granting me leave of absence to complete the

Doctoral degree and providing the necessary field data used in my research. Great appreciation

to the Department of Petroleum Resources, Nigeria for approving the field data used in this

research. Special thanks to Mr. Richard Ebisike of Shell Petroleum Development Company,

Nigeria for his support and mentoring.

iv
 TABLE OF CONTENTS

ABSTRACT..................................................................................................................................................... iii

ACKNOWLEDGMENTS .................................................................................................................................. iv

TABLE OF CONTENTS..................................................................................................................................... v

List of Tables .............................................................................................................................................. viii

List of Figures ............................................................................................................................................... ix

List of Acronyms and Symbols ..................................................................................................................... xi

Chapter 1....................................................................................................................................................... 1

1.0 Introduction and Overview .............................................................................................................. 1

1.1 Formation Pore Pressure.................................................................................................................. 1

1.2 Formation Pore Pressure Regimes .................................................................................................. 2

1.2.1 Compaction Disequilibrium (Under-compaction)................................................................... 4

1.2.2 Tectonic Activities ...................................................................................................................... 5

1.2.3 Clay Diagenesis........................................................................................................................... 6

1.2.4 Aqua-thermal Expansion .......................................................................................................... 6

1.2.5 Hydrocarbon Generation .......................................................................................................... 6

1.3 Pore Pressure Prediction Techniques ............................................................................................. 8

1.3.1 Pore Pressure Prediction from Seismic Data......................................................................... 11

1.3.2 Pore Pressure Prediction from Well Logs ............................................................................. 12

1.3.3 Pore Pressure Prediction from Drilling Parameters............................................................. 21

1.4 Research Objectives ........................................................................................................................ 28

1.5 Connectivity among the Research Papers .................................................................................... 28

1.6 Organization of the Thesis ............................................................................................................. 30

1.7 Reference ......................................................................................................................................... 30

Chapter 2..................................................................................................................................................... 43

2.0 Overpressure Prediction Using the Hydro-Rotary Specific Energy Concept ........................... 43

Preface.................................................................................................................................................... 43
v
 Abstract.................................................................................................................................................. 43

2.1 Introduction ..................................................................................................................................... 44

2.2 Theoretical Background ................................................................................................................. 51

2.3 Methodology .................................................................................................................................... 56

2.4 Field Example .................................................................................................................................. 59

2.5 Discussion......................................................................................................................................... 66

2.6 Conclusions ...................................................................................................................................... 72

2.7 Reference ......................................................................................................................................... 73

Chapter 3..................................................................................................................................................... 79

3.0 Energy-based Formation Pressure Prediction ............................................................................. 79

Preface.................................................................................................................................................... 79

Abstract.................................................................................................................................................. 79

3.1 Introduction ..................................................................................................................................... 80

3.2 Model Development ........................................................................................................................ 92

3.3 Methodology .................................................................................................................................... 96

3.4 Field Example .................................................................................................................................. 97

3.5 Discussion....................................................................................................................................... 102

3.6 Conclusions .................................................................................................................................... 105

3.7 Reference ....................................................................................................................................... 106

Chapter 4................................................................................................................................................... 114

4.0 The New Formation Bulk Density Predictions for Siliciclastic Rocks ..................................... 114

Preface.................................................................................................................................................. 114

Abstract................................................................................................................................................ 114

4.1 Introduction ................................................................................................................................... 115

4.2 Methodology .................................................................................................................................. 120

4.3 Field Examples .............................................................................................................................. 122

4.4 Results and discussions ................................................................................................................. 126

4.5 Conclusions .................................................................................................................................... 137

vi
 4.6 Reference ....................................................................................................................................... 138

Chapter 5................................................................................................................................................... 144

5.0 A New Fracture Pressure Prediction Model for The Niger Delta Basin .................................. 144

Preface.................................................................................................................................................. 144

Abstract................................................................................................................................................ 144

5.1 Introduction ................................................................................................................................... 145

5.2 Field Data....................................................................................................................................... 155

5.3 Model Development ...................................................................................................................... 158

5.4 Model Validation........................................................................................................................... 162

5.5 Conclusion ..................................................................................................................................... 165

5.6 Appendix ........................................................................................................................................ 166

5.7 Reference ....................................................................................................................................... 168

Chapter 6................................................................................................................................................... 174

6.0 Real-time Lithology Prediction Using Hydromechanical Specific Energy .............................. 174

Preface.................................................................................................................................................. 174

Abstract................................................................................................................................................ 174

6.1 Introduction ................................................................................................................................... 175

6.2 Methodology .................................................................................................................................. 179

6.3 Field Example ................................................................................................................................ 184

6.4 Discussion....................................................................................................................................... 191

6.5 Conclusions .................................................................................................................................... 193

6.6 Reference ....................................................................................................................................... 194

Chapter 7................................................................................................................................................... 200

7.0 Summary and Recommendations ................................................................................................ 200

7.1 Summary........................................................................................................................................ 200

7.2 Recommendations ......................................................................................................................... 201

vii
 List of Tables

Table 2. 1 Merits and limitations of pore pressure prediction methods........................................ 46

Table 2. 2 The well data summary. ............................................................................................... 60

Table 2. 3 The bit data summary. ................................................................................................. 62

Table 2. 4 Main differences between HRSE and d – exponent. ................................................... 70

Table 3. 1 The well and bit data summary. ................................................................................... 98

Table 3. 2 Comparison of pore pressure prediction models from drilling parameters. .............. 104

Table 4. 1 The comparison of RMSEs for models under consideration ..................................... 131

Table 5. 1 The pore pressure data for the W 110 well. ............................................................... 163

Table 5. 2 Well data summary .................................................................................................... 166

viii
 List of Figures

Figure 1. 1 The pressure profiles of an onshore well in the Niger Delta. ....................................... 7

Figure 1. 2 The acoustic-depth and resistivity-depth plots (Hottmann and Johnson, 1965). ....... 14

Figure 1. 3 The connectivity among the research papers.............................................................. 29

Figure 2. 1 Illustration of the HRSE method for pore pressure prediction. .................................. 57

Figure 2. 2 The work flow for the proposed methodology. .......................................................... 58

Figure 2. 3 Location map for well A............................................................................................. 59

Figure 2. 4 The well configuration and lithology. ........................................................................ 61

Figure 2. 5 The plots of drilling parameters versus depth for well A. .......................................... 64

Figure 2. 6 The plots of formation bulk densities, overburden pressure and overburden gradient
versus depth for well A. ................................................................................................................ 65

Figure 2. 7 The plots of HRSE, dc – exponent, gamma ray, and shale compressional sonic
velocity versus depth for well A. .................................................................................................. 67

Figure 2. 8 Measured and estimated pore pressure profiles for Well A. ...................................... 71

Figure 3. 1 Location map for Well A. ........................................................................................... 97

Figure 3. 2 The plots of drilling parameters against depth for Well A. ...................................... 100

Figure 3. 3 The formation bulk density and overburden pressure/gradient profiles for Well A. 101

Figure 3. 4 The HMSE and pore pressure profile for well A ..................................................... 103

Figure 4. 1 The location map for Wells A and B. ....................................................................... 123

Figure 4. 2 The well logs for Well A showing the petrophysical properties of penetrated rocks.
..................................................................................................................................................... 124

Figure 4. 3 The well logs for Well B showing the petrophysical properties of penetrated rocks.
..................................................................................................................................................... 125

ix
Figure 4. 4 The comparison of predicted and measured formation bulk density for various
models under consideration (Well A). ........................................................................................ 128

Figure 4. 5 The comparison of predicted and measured formation bulk density for various
models under consideration (Well B). ........................................................................................ 129

Figure 4. 6 The residual-depth plots for Wells A and B showing the error profiles. ................. 130

Figure 4. 7 The histograms of the residuals showing the error distributions for various models
under consideration (Well A)...................................................................................................... 132

Figure 4. 8 The histograms of the residuals showing the error distributions for various models
under consideration (Well B). ..................................................................................................... 133

Figure 4. 9 The overburden gradient profiles using formation bulk density outputs from the new
models for Well A....................................................................................................................... 135

Figure 4. 10 The overburden gradient profiles using formation bulk density outputs from the
Gardner’s and Brocher’s models for Well A. ............................................................................. 136

Figure 5 1: Location map for some wells used in model development. ..................................... 157

Figure 5 2: The plot of formation fracture pressure against depth ............................................. 159

Figure 5 3: Fracture pressure differential versus pore pressure differential. .............................. 161

Figure 5 4: Comparison of predicted and measured fracture pressure for well W110 ............... 164

Figure 6 1: The location map for Well A.................................................................................... 185

Figure 6 2: The plots of drilling parameters and wellbore pressures versus depth for Well A
(Interval 1). ................................................................................................................................. 186

Figure 6 3: The plots of drilling parameters and wellbore pressures versus depth for Well A
(Interval 2). ................................................................................................................................. 187

Figure 6 4: The offset well data used to calibrate ∅o and k. ...................................................... 189

Figure 6 5: The GR-depth, VR-depth and HMSE-depth plots for Well A. ................................ 192

x
 List of Acronyms and Symbols

∅o surface/mudline clay porosity

∆P𝑏 bit pressure drop

∆t m shale matrix compressional transit time with zero porosity

∆t ml mudline compressional transit time

∆t n normal compaction shale travel time at a given depth

∆t O observed shale travel time at a given depth

∆t on observed compressional transit time in the normally pressured intervals

ρb formation bulk density

ρfl saturating fluid density

ρma sand matrix density

ρsh shale matrix density

σe vertical effective stress

σH maximum horizontal stress

σh minimum horizontal stress

σmax vertical effective stress at the onset of unloading

σmax vertical effective stress at the onset of unloading

σ′v vertical effective stress

σ𝑡 horizontal tectonic stress term

∅ formation porosity

∆𝑃 confining/mud pressure minus pore pressure

xi
∆𝑡 shale compressional travel time at a given

Ab bit Area

BHA bottom-hole assembly

BHP bottom-hole pressure

Cb bulk compressibility

Cb bulk compressibility

Cg grain compressibility

Cp pore compressibility

Db bit diameter

dc – exponent corrected d – exponent

dcn dc – exponent from the normal compaction trend at a given depth

dco computed dc – exponent from the measured data at a given depth

ECD equivalent circulating density

Fj jet impact force

FP fracture pressure

FPNPT normally pressured trendline fracture pressure

ft feet

GFP fracture gradient

Gnp normal pore pressure gradient at a given depth

Gob overburden pressure gradient at a given depth

Gpp pore pressure gradient at a given depth

GRlog gamma ray reading

xii
GRmax shale line gamma ray reading

GRmin sand line gamma ray reading

HMSE hydro-mechanical specific energy

HMSEn HMSE from the normal compaction trend at a given depth

HMSEo computed HMSE from the measured data at a given depth

HRSE hydro-rotary specific energy

HRSEn HRSE from the normal compaction trend at a given depth

HRSEo computed HRSE from the measured data at a given depth

IGR gamma ray index

IPmin minimum injection pressure

JSA junk slot area

K hydraulic energy reduction factor

Ki matrix stress ratio

Ko effective stress ratio

LWD logging while drilling

m specific energy (HRSE or HMSE) exponent

MSE mechanical specific energy

MW mud weight

MWD measurement while drilling

N rotary speed

NCT normal compaction trend

NPP normal pore pressure

xiii
NPPG normal pore pressure gradient

o
C degree centigrade

Patm atmospheric pressure

Pc confining pressure

PDC polycrystalline diamond compact

PP pore pressure

PPa actual pore pressure

PPn normal pore pressure

psi pounds per square inch

psi/ft pounds per square inch per foot

Q flow rate

Rn normal compaction trend shale resistivity at a given depth

Ro observed shale resistivity at a given depth

RCB roller cone bit

ROP rate of penetration

STFR speed to flow ratio

Sv overburden pressure

SWD seismic while drilling

T torque on bit

T&D torque and drag

TFA total flow area

TOB torque on bit

xiv
TVD true vertical depth

U unloading parameters

UCS uniaxial compressive strength

v Poisson’s ratio

Vj nozzle/jet velocity

Vmax compressional velocity at the onset of unloading

Vn normal compaction trend shale compressional velocity at a given depth

Vo observed shale compressional velocity at a given depth

Vp compressional wave velocity

Vs shear wave velocity

Vsh shale volume

WOB downhole weight on bit

WOBe effective weight on bit

Z true vertical depth

α Biot’s coefficient

η hydraulic energy reduction factor

μ bit coefficient of sliding friction

𝜃 angle of internal friction

xv
 Chapter 1

1.0 Introduction and Overview

1.1 Formation Pore Pressure

The formation pore pressure is the pressure exerted by the pore fluids on the surrounding rocks.

The pore pressures of sedimentary rocks are extremely important in oil and gas exploration

(Mann and Mackenzie, 1990). At the planning stage, pore pressure is required for well

construction, equipment selection, production forecasting, and reservoir simulation. During the

actual drilling operations, information about the formation pore pressure is required for

improving the drill-ability of the well, maintaining primary well control, reducing the drilling

problems and minimizing formation damage. At the completion phase, accurate knowledge of

pore pressure is required for specifying completion fluid requirements. At the production phase,

information about reservoir pressure is required for well performance analysis, production

forecasting, compaction and subsidence analysis, and determination of reservoir drive

mechanism. During the workover phase, formation pore pressure will dictate the kill fluid

requirements. At the abandonment stage, pore pressure regimes will dictate the isolation

requirements. The formation pore pressure and fracture pressure are considered as the most

important parameters used in well engineering communities. From a safety point of view, it is

necessary to know the subsurface pressure regimes that will be encountered along the well path

before drilling into them. This will help to avoid drilling accidentally into overpressure intervals

which can lead to catastrophic and process safety incidents. Recognizing the existence of

subsurface overpressure conditions is an essential first step in overall well control. The

occurrence of subsurface overpressure conditions poses major problems for safety and cost-

1
effective well design (Gutierrez et al., 2006). In general, the subsurface pressure regimes that

will be encountered while drilling will dictate the overall well cost.

1.2 Formation Pore Pressure Regimes

The formation pore pressure can be described as normal, subnormal and overpressure. The

normal pore pressure can be defined as the pressure exerted by the column of seawater

containing 80,000 ppm total solids (Dickinson, 1953). The normal pore pressure at any given

depth is equal to the vertical height of a column of formation water extending from the surface to

that depth. In the US Gulf Coast, the average normal pore pressure gradient is 0.465 psi/ft

(Harkins and Baugher, 1969). In the North Sea, the average normal pore pressure gradient is

0.452 psi/ft. In the Niger Delta basin, the normal pore pressure gradient varies between 0.433

psi/ft and 0.472 psi/ft. The normal pore pressure gradient is a function of the concentration of

dissolved salts, temperature and content of dissolved gases (Serebryakov et al., 2002). Hence,

there is a variation in the normal pore pressure gradient at different locations and depths. In ideal

environments, pore pressure is expected to be normal from the surface to the depth of interest.

Unfortunately, there are various geological and chemical processes that conspire to produce pore

pressure values that are higher or lower than the normal. In subnormal pressure zones, the

formation pore pressures are lower than the normal at the given depths. In overpressure intervals,

the formation pore pressures are higher than the normal at the given depths.

The origins of subsurface subnormal pressure conditions can be geologic or artificial. The

geologic origins can be tectonic, stratigraphic or geochemical in nature while the artificial origins

are usually related to hydrocarbons withdrawal from porous and permeable rocks. In regions

where erosions have removed a significant amount of the overburden loads, the underlying rocks

2
may relax sufficiently to undergo an increase in pore volume, resulting in the reduction of

formation pore pressure (Barker, 1972; Dickey & Cox, 1977; Serebryakov & Chilingar, 1994).

Many subnormal pressure conditions are artificially induced by reservoir fluids (oil, water, and

gas) withdrawal from subsurface reservoirs during production. For subnormal pressure

conditions to occur, either the reservoirs are completely isolated with no communication with the

surrounding strata or the reservoirs do not operate under active water drive (when the influx rate

of support water is not enough to compensate for the rate of reservoir fluids withdrawal). Drilling

through subnormal pressure intervals can cause severe drilling problems such as lost circulation,

differential sticking and underground blowout. In extremely cases, reduction in reservoir

pressure can lead to compaction and subsidence during production, which can lead to casing

collapse and damage to surface structures (Sulak and Danielsen, 1988; Vudovich et al., 1988;

Wooley and Prachner, 1988; Bickley and Curry, 1992; Bruno, 1992; Schwall et al., 1996;

Schwall and Denney, 1994; Bruno, 2001; Nagel, 2001; Doornhof et al., 2006).

Two conditions must exist for subsurface overpressure conditions to occur: (1) there must

be permeability barriers and (2) there must be mechanisms that generate the overpressure. The

permeability barriers (seals) restrict the movement of the pore fluids such that overburden loads

are partially supported by the pore fluids. The seals are not necessarily impermeable but must be

of low permeability with high capillary entry pressure (Pickering and Indelicato, 1985).

Typically, the processes that generate subsurface overpressure conditions are very similar to

processes involved in the generation, expulsion, migration, accumulation, and entrapment of

hydrocarbons. Subsurface overpressure conditions have been encountered throughout the world

(Fertl, 1972; Bradley, 1975; Carstens, 1978; Singh & Ford, 1982; Hunt, 1990; Kader, 1994;

Gurevich & Chilingar, 1995; Serebryakov & Chilingar, 1995; Swarbrick, 1995; Belonin and

3
Slavin, 1998; Holm, 1998; Heppard et al., 1998; Nashaat, 1998; Wilson et al., 1998; Slavin &

Smirnova, 1998; Schneider, 2000; O’Connor et al., 2012). Several mechanisms have been

proposed as possible causes of overpressure generations in sedimentary basins. The five major

overpressure generation mechanisms are: (1) compaction disequilibrium (under-compaction); (2)

tectonic forces; (3) clay diagenesis; (4) aqua-thermal expansion; and (5) hydrocarbon generation.

There are other minor causes of subsurface overpressure conditions. These include charging,

artesian effects, centroid effects, and buoyancy/gravity effects. Carstens (1978) suggested that

the overpressure conditions found in the argillaceous sediments in the Lower Tertiary of Central

North Sea were caused by a self-sealing mechanism provided by small grain size, clay

mineralogy, discontinuous limestone stingers and presence of gas.

1.2.1 Compaction Disequilibrium (Under-compaction)

Compaction disequilibrium occurs when the rate of deposition of sediments is greater than the

rate of expulsion of interstitial fluids (usually water). The pore fluids become trapped and begin

to support the weight of the overlying sediments (overburden loads), leading to subsurface

overpressure conditions. Compaction disequilibrium is often considered as the chief cause of

subsurface overpressure conditions usually found in young (tertiary) sedimentary basins where

the favorable condition of rapid deposition of sediments containing a large quantity of clay

minerals exists (Hart et al., 1995; Carlin and Dainelli, 1998; Law and Spencer, 1998; Katahara,

2003; Sayers et al., 2005). In most cases, other causes of overpressure generation mechanisms

are generally small compared to compaction disequilibrium (Burrus, 1998). If the rate of

deposition of sediments is equal to the rate of expulsion of interstitial fluids, the excess fluid

pressure created by the increasing overburden loads will be dissipated and normal pore pressure

4
will be maintained throughout the sediments at all depths. The greater the degree of under-

compaction, the higher the porosity, and the lower the vertical effective stresses when compared

to normally pressured intervals at the same depths. Slavin and Smirnova (1998) reported that

with the same magnitude of formation pore pressure, the porosity values of the overpressure

zones caused by compaction disequilibrium are substantially higher than the porosity values of

the overpressure zones caused by post sedimentary or fluid expansion origins

1.2.2 Tectonic Activities

Tectonic activities such as folding, faulting, and diapirism can cause an increase in formation

pore pressure (Dickey et al., 1968; Harkins and Baugher, 1969; Finch, 1969; Law et al., 1998).

Rock compaction takes place when subsurface formation is compressed (folded), leading to pore

fluids being expelled from the formation pore spaces. If the pore fluids cannot escape during the

compression-compaction process, the formation can become over-pressured as the pore fluids

begin to support parts of the compressional and overburden loads. Faulting can create subsurface

overpressure conditions in several ways. The permeable beds can be moved against the

impermeable beds thereby preventing further fluid expulsion with compaction. Faults can create

a leaking pathway for the migration of pore fluids from deeper overpressure intervals to

shallower horizons thereby causing the shallower formations to be over-pressured (charging). A

reverse fault can result in permeable formations being moved up to shallower depths resulting in

subsurface overpressure conditions. Diapirism occurs when salt or shale becomes ductile and

flows like a viscous plastic material under pressure and at elevated temperatures, rising through

the entire thickness of the overlying sediments.

5
1.2.3 Clay Diagenesis

During the sedimentation process, montmorillonite adsorbs water into its lattice structure.

Further burial exposes the montmorillonite to higher temperature and pressure. Clay diagenesis

usually occurs at a temperature between 90 – 150oC. At this temperature range, the

montmorillonite undergoes a transformation and is converted into illite, releasing a large amount

of water in the process (Powers, 1967; Burst, 1969; Rieke and Chilingarian, 1974; Burst, 1976;

Freed & Peacor, 1989; Buryakovsky et al., 1995). Due to the compressive forces resulting from

the increasing depth of burial, formation water can be squeezed and expelled from the shales into

the adjacent porous and permeable rocks, giving rise to subsurface overpressure conditions.

1.2.4 Aqua-thermal Expansion

As the degree of rock compaction increases due to increasing depth of burial, the formation

temperature will increase. This causes the expansion of pore fluids with a subsequent increase in

formation pore pressure. If a normally pressured rock is effectively isolated and then subjected to

a temperature increase, the reservoir fluid pressure will rise above the normal (Lewis & Rose,

1970; Barker, 1972; Magara, 1975; Barkers & Horsfield 1982; Daines, 1982; Sharp Jr, 1983;

Luo and Vasseur, 1992; Miller and Luk, 1993; Chen & Huang, 1996; Polutranko, 1998).

1.2.5 Hydrocarbon Generation

Hydrocarbon generation involves the transformation of kerogen into liquid and gaseous

hydrocarbons. This can result in a significant increase in pore volume leading to subsurface

overpressure conditions (Law & Dickinson, 1985; Spencer, 1987; Holm, 1998; Hunt et al., 1998;

Guo et al., 2010; Tingay et al., 2013). It can also involve thermal cracking of liquid
6
hydrocarbons into gaseous hydrocarbons. Most subsurface overpressure conditions associated

with petroleum source rocks are caused by hydrocarbon generation (Stainforth, 1984).

Nevertheless, field observations have shown that the combination of the above

overpressure generation mechanisms can create subsurface overpressure conditions within the

same sedimentary basin (Plumley, 1980; Kadri, 1991; Luo et al., 1994; Ward et al., 1994; Law et

al., 1998; Freire et al., 2010; Ramdhan and Goulty, 2011; Satti et al., 2015; Liu et al., 2016).

Figure 1.1 shows the pressure profiles of a well located in the onshore region of the Niger Delta.

Pressure gradient (psi/ft)

0.1 0.3 0.5 0.7 0.9 1.1
9000

10000

11000

12000
Depth (ft)

13000

14000

15000
Pore Pressure
16000 Fracture Pressure

Figure 1. 1 The pressure profiles of an onshore well in the Niger Delta.

7
The initial formation pore pressures in the field are normal from the surface down to 14,917 ft

(onset of overpressure) with pore pressure gradient varying between 0.433 psi/ft and 0.472 psi/ft.

The formation pore pressure ramps occur just below 14,917 ft. The formation pore pressure

increases from 0.472 psi/ft at 14,917 ft to 0.828 psi/ft at 15,831 ft (pressure transition zones and

overpressure intervals). No reservoir depletion has ever occurred below the pressure transition

zones. However, fluids withdraw from five reservoirs have caused a reduction in formation pore

pressures below the normal (subnormal). In the subnormal intervals, the formation pore pressure

gradients are less than 0.433 psi/ft. It will be extremely challenging to drill the depleted and

overpressure intervals in the same hole sections with conventional drilling techniques without the

application of stress caging.

1.3 Pore Pressure Prediction Techniques

Most indirect methods of pore pressure detection techniques assume that subsurface overpressure

conditions are associated with under-compaction/compaction disequilibrium. In young, rapidly

subsiding basin, transiting from normal pore pressure regimes to overpressure intervals will

cause changes in the rock geophysical properties and drilling parameters. These changes are

generally seen as reversals in trends when the compaction-dependent geophysical properties are

plotted against depth in a uniform lithology (Bowers, 2002). Shale formations are the preferred

lithology for pore pressure prediction because they are more responsive to effective stresses than

most rock types. Most pore pressure prediction methods require a normal compaction trend

(NCT) of the rock properties to be established. Under normal pore pressure conditions, the

density, resistivity, compressional wave velocity, and degree of rock compaction are all expected

to be increasing with depth while the formation porosity will exponentially decrease with depth.

8
When drilling through the overpressure zones, the rock density, resistivity and compressional

wave velocity are expected to decrease while the formation porosity will increase. However,

lithologic variations can create difficulty in defining the appropriate normal compaction trends

(NCT) (Swarbrick, 2001). Variations in rock bulk and pore compressibility values have been

used to detect the onset of abnormally high formation pressure in carbonate rocks (Atashbari and

Tingay, 2012). Pulsed neutron capture logs can also be used to detect and quantitatively evaluate

overpressure environments, allowing pore pressure depletion to be monitored behind the casing

(Fertl and Chilingarian, 1987). Serebryakov et al. (1995) reported that the natural radioactivity

values in the uniform shale layers can be used to identify the onset of abnormally-high pressured

zones. In normally pressure conditions, gamma ray values will increase with depth. Departures

from the normal compaction trends may signify changes in formation pore pressure regimes

(Zoeller, 1983). Satti and Yusoff (2015) used the acoustic impedance principle to analyze the

origin of overpressure mechanisms in the Malay Basin. Shear wave velocity can also be used to

estimate the formation pore pressure and are more sensitive to pressure variations than the

compressional wave velocity (Ebrom et al., 2002; Ebrom et al., 2004). However, subsurface

overpressure conditions have been reported to occur in rocks with low porosity and high density

especially if the origin of the overpressure mechanism is not compaction disequilibrium.

Carstens and Dypvik (1981) found that the Jurassic overpressure shale from the North Sea

Viking graben was associated with low porosity and high density. Therefore, it is possible not to

have any trend reversal between the normally compacted series and overpressure intervals when

porosity indicators such as resistivity, compressional wave velocity and density are plotted

against depth (Hermanrud et al., 1998; Teige et al., 1999). Most pore pressure prediction

9
techniques currently employed in the oil and gas industry may not be applicable to

unconventional plays (Couzens-Schultz et al., 2013).

All the pore pressure prediction techniques from geophysical and drilling parameters

have their limitations. The formation resistivity is affected by other factors such as rock

permeability, pore fluids, temperature and concentration of dissolved salts. Care must be taken

when using resistivity data to estimate the formation pore pressure as the reversal in resistivity

trend may have nothing to do with subsurface overpressure conditions (Lane and Macpherson,

1976). The compressional wave velocity is affected by the presence of gas and

microcracks/fractures in the formation. The effects of gas and microcracks on compressional

wave velocity are similar to that of overpressure conditions (Gardner et al., 1974; Tatham and

Stoffa, 1976; Ensley, 1985; Williams, 1990; Brie et al., 1995; Hamada, 2004; Kozlowski et al.,

2017). Combining shear and compressional wave velocities will help to differentiate the gas

effect from the overpressure effect (Dvorkin et al. 1999). The shale radioactivity values (gamma

ray) may also be affected by the presence of other minerals in the shales which may have nothing

to do with the overpressure conditions. The drilling parameters are affected by bit hydraulics,

lithologies, bit wears, bit sizes, shocks, and vibrations. The seismic responses are affected by

changes in lithology and pore fluid type. Huffman (2002) summarizes the applications and

limitations of various geophysical methods used for pore pressure predictions. The best approach

to pore pressure prediction is to examine the combination of all the available measured data

(geophysical and drilling parameters) since relying on only one type of data can result in

misinterpretations (Fertl and Timko, 1971). Even direct measurements (repeat formation tester,

modular formation dynamics tester, reservoir characterization explorer, drill stem test, bottom-

hole pressure survey, permanent downhole gauge, and drilling kick) of formation pore pressure

10
have their own limitations. These measurements are usually made only after the well must have

been drilled and possible overpressure zones have been penetrated. Thus, direct measurements

have limitations in terms of real-time monitoring and predicting formation pore pressure ahead

of the bit. A recently developed logging while drilling (LWD) tool (formation pore pressure

while drilling tool) in the bottom-hole assembly (BHA) can measure the reservoir pressures of

penetrated rocks while drilling. This does not still change the fact that the rocks must be

penetrated before taking the pressure measurements since the tool sensor is placed some feet

behind the bit. Direct pore pressure measurements using drilling kick and LWD tool may not be

suitable for low permeability reservoirs because the time required for such reservoirs to reach the

final pressure build up make cause the BHA to get stuck in the hole. The data used to estimate

the formation pore pressure can be classified into three categories: (1) seismic data, (2) well log

data and (3) drilling parameters.

1.3.1 Pore Pressure Prediction from Seismic Data

The seismic reflections are functions of acoustic impedance and they are affected by formation

pore pressure. The formation interval velocity can be obtained from conventional surface

seismic, borehole seismic and seismic while drilling (SWD). The conventional surface seismic

method is the only method available to estimate the formation pore pressure when no drilling

activities have occurred in a field. Pennebaker (1968) was the first to develop a methodology that

uses seismic interval velocity for pore pressure prediction. Dutta and Ray (1997) used the

velocity and acoustic impedance inversion of seismic reflections to obtain the formation pore

pressure. In normally compacted series with no hydrocarbon saturation, seismic wave

propagation velocity will increase with depth in a uniform lithology. Deviation from the

11
increasing velocities with depth to lower values can be directly related to the increase in

formation pore pressure if the rock type and pore fluid remain constant. The quality of the

seismic data will affect its accuracy. Seismic wave velocities can be affected by other factors that

are not related to overpressure conditions. This can make the estimation of formation pore

pressure from seismic sources very difficult. These factors include lithology, degree of rock

cementation and the type of pore fluids (Scott and Thomsen, 1993). Several applications of

seismic data for pre-drill pore pressure predictions have been reported in the literature (Weakley,

1989; Sayers et al., 2000; Dutta et al., 2001; Huffman, 2002; Dutta, 2002; Sayers et al., 2002;

Soleymani & Riahi, 2012; Etminan et al., 2012; Banik et al., 2013). Once the interval velocities

at any given depths are obtained from the seismic data, empirical relationships can be used to

compute the formation pore pressure (Eaton, 1975; Bower, 1995).

1.3.2 Pore Pressure Prediction from Well Logs

Based on the modification to the porosity model proposed by Athy (1930), an exponential

relationship was established between shale porosity and vertical effective stress. This

relationship is given by (Rubey & Hubber, 1959; Flemings et al., 2002):

′
∅ = ∅o e−kσv , (1.1)

where ∅ is the formation porosity (fraction); σ′v is the vertical effective stress (psi); ∅o

surface/mudline clay porosity (fraction); k is the stress compaction constant. The vertical

effective stress is defined by Terzaghi (1927) as the vertical stress minus pore pressure and is

given by:

σ′v = σv − PP, (1.2)

12
where σv is the vertical stress (psi); PP is the pore pressure (psi). Burrus (1998) suggested that

the pore pressure predictions using the vertical effective stress defined by (Biot, 1941) provided

better agreement with the field observations and is given by:

σ′v = σv − αPP, (1.3)

where α is the Biot’s coefficient. The expression for Biot’s coefficient is given by:

Cg
α= 1− , (1.4)
Cb

where Cg is the grain compressibility (psi-1); Cb is the bulk compressibility (psi-1). In normally

compacted series, as vertical effective stress increases, shale porosity will decrease. In pressure

transition and overpressure intervals, a decrease in effective stress will be accompanied by an

increase in shale porosity if the origin of overpressure mechanism is mainly due to compaction

disequilibrium. Mathematical manipulation of equation 1.1 by Hart et al. (1995) is given by:

1 ∅o
PP = σv − [ ln [ ]]. (1.5)
k ∅

Equation 1.5 implies that if shale porosities and vertical stresses at various depths are known, the

pore pressures can be easily determined. The formation porosities and the vertical stresses can

be obtained from density logs. (Burrus, 1998) concluded that the compaction model based on the

vertical effective stress – porosity relation sufficiently explained the overpressure conditions in

rapidly subsiding basins such as Mahakam Delta, Indonesia, and Gulf Coast, U.S.A.

Hottmann and Johnson (1965) were the first to directly correlate well log data (resistivity

and sonic transit time) to subsurface overpressure conditions encountered in the Miocene and

13
Oligocene shales in Upper Texas and Southern Louisiana Gulf Coast. The methodology involves

establishing the normal compaction trend (NCT) that corresponds to the normal pore pressure

regime when shale resistivity or sonic transit time is plotted against depth on the semi-log. The

divergence of observed sonic transit time or resistivity from the NCT is a measure of the

formation pore pressure (Figure 1.2).

Figure 1. 2 The acoustic-depth and resistivity-depth plots (Hottmann and Johnson, 1965).

14
 Based on the shale formation resistivity factor, Foster and Whalen (1966) established a

relationship among pore pressure, depth, and the ratio of normal shale resistivity to observed

shale resistivity for regions with varying salinity. Foster and Whalen’s model is given by:

0.535 Rn
PP = 0.465 ∗ Z + ∗ log [ ], (1.6)
log b Ro

where PP is the formation pore pressure (psi); Z is the true vertical depth (ft); R n is the normal

shale resistivity (ohm-m); Ro is the observed (abnormal) shale resistivity (ohm-m). The log b can

be obtained from the slope of formation factor versus depth plot.

Based on the data presented by Hottmann and Johnson (1965), Gardner et al. (1974)

provided a relationship among vertical effective stress, difference between overburden and

normal pore pressure gradients, interval travel time and depth. Gardner’s model is given by:

1
σv − PP 3 2
[ ] ∗ Z 3 = A − B log e ∆t, (1.7)
Gob − Gnp

where σv is the vertical stress (psi); PP is the pore pressure (psi); Z is the true vertical depth (ft);

Gob is the overburden gradient (psi/ft); Gnp is the normal pore pressure gradient (psi/ft); ∆t is the

interval travel time (μs/ft); A and B are constant parameters. The values of A and B can be

obtained by calibration equation 1.7 to any known normally pressured intervals in the region.

Eaton (1975) developed a correlation that relates formation pore pressure gradient to

overburden gradient, normal pore pressure gradient and resistivity or velocity ratio. Eaton’s

models are given by:

15
 Ro a
Gpp = Gob − {Gob − Gnp } [ ] (1.8)
Rn

and

∆t n b
Gpp = Gob − {Gob − Gnp } [ ] , (1.9)
∆t o

where Gpp is the pore pressure gradient (psi/ft); Gob is the overburden gradient (psi/ft); Gnp is the

normal pore pressure gradient (psi/ft); R o is the observed shale resistivity (ohm-m); R n is the

normal compaction trend shale resistivity (ohm-m); a is the resistivity exponent coefficient

(usually 1.5 but can range from 1.0 – 2.0); ∆𝑡𝑛 is the normal compaction shale travel time

(μs/ft); ∆𝑡𝑜 is the observed shale travel time (μs/ft); b is the sonic exponent coefficient (usually

3.0 but can range from 2.0 – 4.0). The overburden gradient, formation resistivity and interval

travel time are usually obtained from density, resistivity and sonic logs respectively. Eaton’s

models are probably the most widely used empirical models for pore pressure prediction,

especially in under-compacted series.

Eberhart-Phillips et al. (1989) developed empirical relations between measured sonic

velocities, effective stress, porosity, and clay contents for shaly sandstone rocks after conducting

experimental studies on 64 rock samples. Eberhart-Phillips’s models are given by:

′
Vp = 5.77 − 6.94∅ − 1.73√C + 0.446(σ′v − e−16.7σv ) (1.10)

and
′
Vs = 3.70 − 4.94∅ − 1.57√C + 0.361(σ′v − e−16.7σv ), (1.11)

where Vp is the compressional wave velocity (km/s); Vs is the shear wave velocity (km/s); ∅ is

the formation porosity; C is the clay volume (fraction); 𝜎 ′ is the effective pressure (kbar).

16
Equations 1.10 and 1.11 can be adapted for shale by equating the value of clay volume (C) to

one. Given the values of Vp, Vs, and porosity as a function of depth from well logs and/or

seismic data in shale formations, the vertical effective stress (σ′v ) can be determined. Subtracting

the overburden stress from the calculated vertical effective stress at any given depth will give the

corresponding value of the formation pore pressure.

Holbrook et al. (1995) expressed vertical effective stress as a function of formation

porosity given by:

σ′v = A[1 − ∅]B , (1.12)

where σ′v is the vertical effective stress (psi); ∅ is the formation porosity (fraction); A and B are

the fitting parameters relating to the compaction resistance properties of the rocks. The values of

A and B can be obtained by calibrating equation 1.12 to the normally pressured intervals in the

field. The formation pore pressure at any given depth can be obtained from

PP = σv − A[1 − ∅]B , (1.13)

where PP is the formation pore pressure (psi); σv is the vertical stress (psi).

Since, most pore pressure prediction techniques fail to take into account the origins of

overpressure mechanisms, Bowers (1995) proposed new techniques of predicting the formation

pore pressure from compressional sonic velocity based on the principle of effective stress.

Bower’s models consider the excess pore pressure generated by both under-compaction and fluid

expansion mechanisms. The technique involves estimating the vertical effective stress from the

compressional sonic velocity. The pore pressure is then computed by subtracting the overburden

17
pressure from effective stress. Bower’s first relation accounts for normal pore pressure regime

and overpressure conditions caused by under-compaction (virgin curve) and is given by:

V = 5000 + AσBe , (1.14)

where V is the compressional sonic velocity (ft/sec); 𝜎𝑒 is the effective vertical stress (psi); A

and B are virgin curve parameters. The values of A and B can be obtained by calibrating

equation 1.14 to the regional data from the normally pressured intervals. The second Bower’s

relation accounts for overpressure conditions caused by fluid expansion mechanisms (unloading

curve) and is given by:

1 B
σe U
V = 5000 + A [σmax [ ] ] , (1.15)
σmax

1
Vmax − 5000 B
σmax = [ ] , (1.16)
A

where σmax is the effective vertical stress at the onset of unloading (psi); Vmax is the

compressional sonic velocity at the onset of unloading (ft/sec); U is the unloading parameter

which is a measure of how plastic the sediment is. When U is equal to one, there is no permanent

deformation because the unloading curve (equation 1.15) reduces to the virgin curve (equation

1.14). The value of U is obtained by calibrating equation 1.15 to the regional offset well data in

the overpressure intervals. Bower’s models are another widely used empirical relationships and

the models are applicable to many sedimentary basins. However, Bower’s model has been

reported not to be effective for 3D overpressure prediction using seismic velocity in the deep

zones of Malay Basin, Malaysia where fluid expansion mechanism is the dominant cause of

18
overpressure generation (Satti et al., 2016). Bower’s model may also overestimate formation

pore pressure in shallow unconsolidated formations because the velocities in such formations are

very slow (Zhang, 2011).

The combination of compressional and shear wave velocities can be used to estimate the

formation pore pressure (Li et al., 2000; Walls et al., 2000; Ebrom et al., 2006; Kumar et al.,

2006; Saleh et al., 2013; Yu and Hilterman, 2013; Ebrom et al., 2006; Kumar et al., 2006).

Prasad (2002) suggested that the velocity ratio (Vp/Vs) is very sensitive to an increase in

formation pore pressure. Saleh et al., (2013) used the Vp/Vs to predict the pore pressure in subsalt

environments.

A locally calibrated velocity-dependent pore pressure prediction model was proposed by

Shell using the Tau-effective stress concept (Gutierrez et al., 2006) and is given by:

200 − ∆𝑡 𝐵
σ′v = A [ ] (1.17)
∆𝑡 − 50

where σ′v is the vertical effective stress (psi); ∆𝑡 is the compressional transit time (μs/ft); A and

B are fitting constants. The values of A and B can be obtained by calibrating equation 1.17 to the

regional data from the normally pressured intervals. The formation pore pressure at any given

depth can be obtained using:

200 − ∆𝑡 𝐵
PP = σv − A [ ] (1.18)
∆𝑡 − 50

where PP is the formation pore pressure (psi); σv is the vertical stress (psi).

Zhang (2011) proposed modified Eaton’s sonic model by using depth-dependent normal

compaction trend equation as given by:

19
 3
∆t m + [∆t ml −∆t m ]e−CZ
Gpp = Gob − {Gob − Gnp } [ ] , (1.19)
∆t o

where Gpp is the pore pressure gradient (psi/ft); Gob is the overburden gradient (psi/ft); Gnp is the

normal pore pressure gradient (psi/ft); ∆𝑡𝑚 is the shale matrix compressional transit time with

zero porosity (approximately 65 μs/ft); ∆𝑡𝑚𝑙 is the mudline compressional transit

time (approximately 200 μs/ft); Z is the true vertical depth below the mudline (ft); C is the

compaction constant; ∆t o is the observed compressional transit time either from the sonic log or

seismic velocity (μs/ft). In Zang’s model, the normal compaction trend decreases exponentially

with depth and this is given by

∆t on = ∆t m + [∆t ml −∆t m ]e−CZ , (1.20)

where ∆t on is the observed compressional transit time in the normally pressured intervals (μs/

ft). The value of C (compaction constant) can be obtained by calibrating equation 1.20 to the

normally pressured intervals. Other modifications to the existing pore pressure prediction models

from geophysical parameters are presented by Zhang (2011).

For carbonate rocks, Atashbari and Tingay (2012) proposed a pore pressure prediction

model based on compressibility attributes. The model is given by

γ
(1 − ∅)Cb σ′v
PP = [ ] , (1.21)
(1 − ∅)Cb − (∅Cp )

20
where PP is the formation pore pressure (psi); ∅ is the formation porosity (fraction); Cb is the

bulk compressibility (psi-1); Cp is the pore compressibility (psi-1); σ′v is the vertical effective

stress (psi); 𝛾 is the empirical constant ranging from 0.9 to 1.0.

Zhang (2013) proposed a pore pressure prediction model for cases without unloading

which relates formation pore pressure to vertical stress, depth and compressional transit times.

This model is given by

σv − αNPP ∆t −∆t
σv − [ ] ln [∆t ml− ∆t m ]
CZ o m
PP = [ ], (1.22)
α

where PP is the formation pore pressure (psi); σv is the vertical stress (psi); NPP is the normal

pore pressure (psi); Z is the true vertical depth below the mudline (ft); ∆𝑡𝑚 is the shale matrix

compressional transit time with zero porosity; ∆𝑡𝑚𝑙 is the mudline compressional transit time; C

is the compaction constant; ∆t o is the observed compressional transit time either from the sonic

log or seismic velocity (μs/ft); α is the Biot’s coefficient. A similar model for unloading

conditions is also available (Zhang, 2013).

1.3.3 Pore Pressure Prediction from Drilling Parameters

This method has the advantage of predicting the formation pore pressure at the bit rather than

behind the bit. Under normal pressure conditions, the rate of penetration (ROP) will gradually

decrease as we drill deeper into the sedimentary basin due to greater rock compaction and

increase in vertical effective stress. In overpressure intervals, the ROP will most likely increase

due to higher rock porosity and decrease in the vertical effective stress from increasing pore

21
pressure. An increase in the formation pore pressure for a given mud weight will cause the ROP

to increase due to reduced back pressure on the formations (Cunningham & Eenink, 1959;

Combs, 1968; Wardlaw. 1969). The results of the experimental studies conducted by Garnier and

Lingen (1959) on permeable rocks of varying strength and permeability showed a reduction in

the drilling rate of penetration due to an increase in rock strength governed by the differential

pressure between the bottom-hole pressure and the formation pore pressure. Black et al. (1985)

conducted experimental studies on four water-saturated sandstone samples using water-based

mud and concluded that increase in the differential pressure across the mud filter cake on the

bottom of the hole will dramatically reduce the penetration rates. From Black’s observations, the

rate of penetration decreased by roughly a factor of 3 as the differential pressure across the filter

cake increased from 0 to 1,000 psi for the specific muds, rock, bit, and conditions tested. Several

other researchers have also reached the same conclusion that the rate of penetration decreases

with an increase in differential pressure between the bottom-hole pressure and formation pore

pressure (Murray & Cunningham, 1955; Lingen, 1962; Maurer, 1965; Vidrine & Benit, 1968;

Wardlaw, 1969; Cheatham et al., 1985). In general, the ROP increases exponentially with a

decrease in differential pressure between the bottom-hole hole pressure and formation pore

pressure. Therefore, the plot of rate of penetration versus depth will most likely follow an ever-

decreasing trend in the normally pressured intervals, and the trend will reverse when entering

into the overpressure zones. Forgotson (1969) suggested that a minimum increase of 200% in the

rate of penetration is required for overpressure detection in shales. However, excessive

overbalance may not show any substantial increase in ROP even with a significant increase in

differential pressure. ROP can also be influenced by many other factors than the differential

pressure. These factors include lithology, formation compaction, weight on bit (WOB), rotary

22
speed, bit size, bit type, hydraulics and bit wear (Bourgoyne and Young, 1973). A sudden

increase in ROP may not necessarily signify drilling into abnormally high-pressured zones.

Therefore, the use of ROP for pore pressure prediction my prove difficult due to several

limitations on its application (Rasmus and Stephens, 1995). Combs (1968) proposed a

mathematical model that relates ROP in shales to differential pressure, WOB, rotary speed, flow

rate, hole size, and bit wear index. Contrary to must publications, Detournay and Atkinson

(2000) suggested that the drilling specific energy does not depend on the virgin formation

pressure in low-permeability formations such as shales. Laboratory drilling studies conducted by

Gray-Stephens et al. (1994) also suggested that differential pressure did not have any strong

influence on the drilling response in hard shales. Bingham (1965) developed a mathematical

relationship between the rate of penetration, weight on bit, rotary speed and the bit diameter

based on the laboratory and field data. Bingham’s model is given by

ROP WOB d
= a[ ] , (1.23)
N Db

where ROP is the rate of penetration (ft/min); N is the rotary speed in revolution per minute

(RPM); WOB is the weight on bit (lbs); Db is the bit diameter (in); a is the matrix strength

constant; d is the formation drill-ability constant. Jorden and Shirley (1966) normalized the

Bingham’s model by correcting for the effects of WOB, rotary speed and hole size on the rate of

penetration resulting in the development of the d-exponent concept. The d-exponent is given by

ROP
log [60N ]
d − exponent = . (1.24)
12WOB
log [ ]
106 D

23
where ROP is the rate of penetration (ft/hr); N is the rotary speed (rpm); WOB is the weight on

bit (lbs); Db is the bit diameter (in). However, the d-exponent proposed by Jorden and Shirley

(1966) did not take into account the hydraulic parameters, mud properties, bit type, bit wear, and

most importantly the effect of mud weight changes. Harper (1969) modified the d-exponent

equation to include the effect of changes in the mud weight/bottom-hole pressure and is given by

Gnp
dc − exponent = d − exponent [ ], (1.25)
ECD

where dc − exponent is the corrected d - exponent; Gnp is the normal pore pressure gradient

(psi/ft or ppg); ECD is the equivalent circulating density (psi/ft or ppg). In the normally

pressured intervals, the plot of the dc - exponent versus depth will show an increasing trend in a

constant lithology. Upon penetrating the transition and overpressure zones, the dc - exponent

values will deviate from the normal trend to lower values due to decrease in rock compaction and

differential pressure. Provided a uniform lithology (100% of clay formation) is being drilled and

the differential pressure is not excessive, the plot of dc - exponent versus depth can be used to

identify the onset of overpressure. The dc - exponent versus depth graph is displayed on the semi-

log to prevent significant variation of dc - exponent with location and geological age. The

vertical axis represents the depth on the linear scale and the horizontal axis represents dc -

exponent on the logarithmic scale (Zamora, 1972). The formation pore pressure can be estimated

from the dc – exponent using Eaton’s model as given by

dco c
Gpp = Gob − {Gob − Gnp } [ ] , (1.26)
dcn

24
where Gpp is the pore pressure gradient (psi/ft); Gob is the overburden gradient (psi/ft); Gnp is the

normal pore pressure gradient (psi/ft); 𝑑𝑐𝑜 is the calculated 𝑑𝑐 from measured data; 𝑑𝑐𝑛 is the

𝑑𝑐 from normal trend line; c is the coefficient (usually 1.2 but can range from 1.0 to 2.0).

The applications of the d-exponent method in the field for pore pressure predictions have

produced mixed results. The major drawback to the application of d – exponent concept to pore

pressure prediction is that it does not consider the effect of bit hydraulic energy on the rate of

penetration (ROP). This greatly limits its application to hard rock environments where bit

hydraulic energy has little or no effect on rock breakage. In hard rock environments, the major

function of the bit hydraulic energy is to clean the bit face and throw the drill cuttings beneath

the bit face into the annulus stream. The bit hydraulic energy becomes important in soft

formations where jetting will make a large contribution to the rate of penetration. Whenever the

bit hydraulic energy changes (due to changes in flow rate, mud weight, and nozzle sizes), or

there is a change in the susceptibility of the formation to jetting (soft rocks), the dc – exponent

will also change. Under downhole conditions where the bit hydraulic energy has a significant

influence on the rate of penetration (unconsolidated sediments), the d – exponent method may

produce inaccurate estimates of formation pore pressure unless the flow rate, mud weight, and jet

velocity can be maintained constant while drilling the transition and overpressure zones.

However, maintaining these parameters constant during drilling operations may not be possible.

Cardona (2011) was the first to apply the mechanical specific energy (MSE) concept to

predict the formation pore pressure in the sub-salt formations in the GOM based on the

adaptation of Eaton (1975) model to include the MSE terms. Teale (1965) defined MSE as the

amount of energy (axial + rotary loads) required to remove a unit volume of rock and is given by

25
 WOB 120 ∗ π ∗ N ∗ T
MSE = + , (1.27)
Ab Ab ∗ ROP

where MSE is the mechanical specific energy (psi); WOB is the downhole weight on bit (lbs); Ab

is the bit area (in2); N is the rotary speed (rpm); T is the torque on bit (lb-ft); ROP is the rate of

penetration (ft/hr). The modified Eaton’s model using MSE parameters is given by

MSEo c
Gpp = Gob − {Gob − Gnp } [ ] , (1.28)
MSEn

where Gpp is the pore pressure gradient (psi/ft); Gob is the overburden gradient (psi/ft); Gnp is the

normal pore pressure gradient (psi/ft); MSEo is the actual MSE calculated using equation 1.28;

MSEn is the hypothetical value of MSE from the normal compaction trend; c is the MSE

coefficient (usually ≤ 1.0).

Akbari et al. (2014) experimentally showed the dependency of MSE on formation pore

pressure. They established a relationship between MSE, differential pressure, and confining

pressure (equation 1.29):

∆P Pc
MSE = UCS + [a + b Pc ] ln , (1.29)
Patm

where MSE is the mechanical specific energy (psi); UCS is the uniaxial compressive strength

(psi); ∆𝑃 is the differential pressure between confining pressure and pore pressure (psi); 𝑃𝑐 is the

confining pressure (psi); 𝑃𝑎𝑡𝑚 is the atmospheric pressure (psi); 𝑎 is the coefficient that is

dependent on rock internal friction angle; 𝑏 is the coefficient that is dependent on rock

permeability, porosity, fluid viscosity, fluid compressibility, rotary speed and depth of the cut.

The last major improvement to pore pressure prediction Majidi et al. (2016) proposed the

26
concept of drilling efficiency and MSE to estimate the formation pore pressure in a sub-salt

deepwater well in the Gulf of Mexico. Majidi’s model involves the application of downhole

drilling parameters and in-situ rock properties. Majidi’s model is given by:

1 − sin θ
PP = ECD − [(DEtrend x MSE) − UCS] [ ], (1.30)
1 + sin θ

DEtrend = a∅bn , (1.31)

USC = 0.43Vp3.2 , (1.32)

θ = 1.532Vp0.5148 , (1.33)

where PP is the pore pressure (psi); ECD is the equivalent circulating density (psi); MSE is the

mechanical specific energy (psi); UCS is the uniaxial compressive strength (psi); 𝜃 is the angle

of internal friction; ∅ is the formation porosity; Vp is the compressional sonic velocity (ft/sec); a

is the coefficient of drilling efficiency trend-line from porosity trend-line; b is the exponent of

drilling efficiency trend-line from porosity trend-line.

While the recent advancement in pore pressure prediction from the drilling parameters

uses the MSE concept (Cardona, 2011; Majidi et al., 2016), the MSE has similar limitations to d

– exponent method because the MSE technique does not consider the effect of bit hydraulic

energy on the ROP. This will certainly make the MSE method to produce erroneous results under

certain drilling conditions where bit hydraulic energy has an effect on ROP. For example, if the

driller decides to increase the flow rate to clean the hole or reduce the flow rate to minimize the

equivalent circulating density while drilling the pressure transition zones in unconsolidated

formations, the MSE may produce inaccurate estimates of formation pore pressure.

27
1.4 Research Objectives

1. To develop a new pore pressure prediction technique from drilling parameters that

incorporates the bit hydraulic energy term based on the concept of total energy consumed

while drilling using downhole measurements.

2. To develop a new pore pressure prediction technique from drilling parameters that

incorporates the bit hydraulic energy term based on the concept of total energy consumed

while drilling using only surface measurements.

3. To improve the accuracy of pore pressure prediction by improving the accuracy of

overburden pressure computation via improvement in density logs prediction.

4. To extend the application of total energy concept to real-time lithology identification.

5. To develop a new fracture pressure prediction model that can be applied to normal and

overpressure intervals in the Niger Delta.

1.5 Connectivity among the Research Papers

The primary objective of this research is to develop hydraulic-dependent pore pressure prediction

models from the drilling parameters using the concept of specific energy. The application of

specific energy to drilling operations is further extended to real-time lithology identification.

Accurate knowledge of overburden pressure is required for pore pressure prediction. Inaccurate

prediction of overburden pressure may lead to erroneous pore pressure estimates. Usually,

overburden pressure is computed from density logs. However, in areas where density logs are not

available, synthetically derived density logs are used. In this research, new formation bulk

density prediction models that can be applied to a wide range of lithologies in siliciclastic

28
environments are proposed. Finally, since pore and fracture pressures are closely related, an

attempt is also made to develop a new fracture pressure prediction model that can be applied to

normal and overpressure intervals in the Niger Delta basin.

Figure 1.3 shows the connectivity among the research papers. The research papers are

highly connected. The pressure-depth and lithology-depth plots form the basis of well design.

Specific energy is required for lithology and pore pressure predictions. Overburden and pore

pressures are required for fracture pressure determination. Formation of bulk density and

overburden pressure are required for pore pressure prediction. Formation bulk density is required

for overburden pressure computation.

Figure 1. 3 The connectivity among the research papers.

29
1.6 Organization of the Thesis

The thesis is prepared in manuscript style and consists of six main chapters. The outlines of the

chapters (research papers) are presented below:

1. Chapter 2 presents an innovative pore pressure prediction technique from drilling

parameters based on the concept of hydro-rotary specific energy using downhole

measurements. This chapter is published in the Journal of Natural Gas Science and

Engineering.

2. Chapter 3 presents a pore pressure prediction method from drilling parameters based on

the hydro-mechanical specific energy concept using only surface measurements. This

chapter is published in the Journal of Petroleum Science and Engineering.

3. Chapter 4 presents the new formation bulk density prediction models that can be applied

to a wide range of lithologies in siliciclastic environments. This chapter is published in

the Journal of Petroleum Science and Engineering.

4. Chapter 5 presents a new fracture pressure prediction model that can be applied to normal

and overpressure intervals in the Niger Delta. This chapter is submitted to the Journal of

Environmental Earth Sciences.

5. Chapter 6 presents a new method of identifying subsurface lithology using specific

energy concept. This chapter is published in the Journal of Petroleum Science and

Engineering.

1.7 Reference

Akbari, B., Miska, S., Yu, M., Ozbayoglu, M., 2014. Experimental Investigations of the Effect of
the Pore Pressure on the MSE and Drilling Strength of a PDC Bit. Soc. Pet. Eng. (SPE

30
 169488). https://doi.org/10.2118/169488-MS
Atashbari, V., Tingay, M.R., 2012. Pore pressure prediction in carbonate reservoirs, in: SPE
Latin America and Caribbean Petroleum Engineering Conference. Society of Petroleum
Engineers.
Athy, L.F., 1930. Density, Porosity, and Compaction of Sedimentary Rocks. Am. Assoc. Pet.
Geol. Bull. 14, 194–200. https://doi.org/10.1306/3D93289E-16B1-11D7-
8645000102C1865D
Banik, N., Koesoemadinata, A., Wagner, C., Inyang, C., Bui, H., 2013. Predrill pore-pressure
prediction directly from seismically derived acoustic impedance. 2013 SEG Annu. Meet.
2905–2909. https://doi.org/10.1190/segam2013-0137.1
Barker, C., 1972. Aquathermal Pressuring--Role of Temperature in Development of Abnormal-
Pressure Zones: GEOLOGICAL NOTES. Am. Assoc. Pet. Geol. Bull. 10, 2068–2071.
https://doi.org/10.1306/819A41B0-16C5-11D7-8645000102C1865D
Barkers, C., Horsfield, B., 1982. Mechanical versus thermal cause of abnormally high pore
pressures in shales. Am. Assoc. Pet. Geol. Bull. 66, 99–100.
https://doi.org/10.1306/2F919760-16CE-11D7-8645000102C1865D
Belonin, M.D., Slavin, V.I., 1998. Abnormally high formation pressures in petroleum regions of
Russia and other countries of the C.I.S. Law, B.E., G.F. Ulmishek, V.I. Slavin eds.,
Abnorm. Press. Hydrocarb. Environ. AAPG Mem. 70, 115–121.
Bickley, M.C., Curry, W.E., 1992. Designing wells for subsidence in the Greater Ekofisk Area,
in: European Petroleum Conference. Society of Petroleum Engineers.
Bingham, M.G., 1965. A New Approach to Interpreting Rock Drillability. Pet. Publ. Co.
Biot, M.A., 1941. General theory of three-dimensional consolidation. J. Appl. Phys. 12, 155–
164. https://doi.org/10.1063/1.1712886
Black, A.D., Dearing, H.L., DiBona, B.G., 1985. Effects of Pore Pressure and Mud Filtration on
Drilling Rates in a Permeable Sandstone. J. Pet. Technol. 37, 1671–1681.
https://doi.org/10.2118/12117-PA
Bourgoyne, J.A.T., Young, J.F.S., 1973. Formation Evaluation and Abnormal Pressure
Detection. SPWLA Fourteenth Annu. Logging Symp. MAY 6-9,.
https://doi.org/10.1016/B978-0-323-04184-3.50079-0
Bowers, G.L., 2002. Detecting high overpressure. Lead. Edge 21, 174–177.
31
Bowers, G.L., 1995. Pore pressure estimation from velocity data: Accounting for overpressure
mechanisms besides undercompaction. SPE Drill. Complet. 10, 89–95.
https://doi.org/10.2118/27488-PA
Bradley, J.S., 1975. Abnormal formation pressure. Am. Assoc. Pet. Geol. Bull. 59, 957–973.
Brie, A., Pampuri, F., Marsala, A.F., Meazza, O., 1995. Shear sonic interpretation in gas-bearing
sands, in: SPE Annual Technical Conference and Exhibition. Society of Petroleum
Engineers.
Bruno, M.S., 2001. Geomechanical analysis and decision analysis for mitigating compaction
related casing damage, in: SPE Annual Technical Conference and Exhibition. Society of
Petroleum Engineers.
Bruno, M.S., 1992. Subsidence-induced well failure. SPE Drill. Eng. 7, 148–152.
Burrus, J., 1998. Overpressure models for clastic rocks, their relation to hydrocarbon expulsion:
a critical re-evaluation. Abnorm. Press. Hydrocarb. Environ. 70, 35–63.
Burst, J., 1969. Diagenesis of Gulf Coast Clayey Sediments and Its Possible Relation To
Petroleum Migration. Am. Assoc. Pet. Geol. Bull. 53, 73–93.
https://doi.org/10.1306/5D25C595-16C1-11D7-8645000102C1865D
Burst, J.F., 1976. Argillaceous Sediment Dewatering. Annu. Rev. Earth Planet. Sci. 4, 293–318.
https://doi.org/10.1146/annurev.ea.04.050176.001453
Buryakovsky, L.A., Djevanshir, R.D., Chilingar, G. V., 1995. Abnormally-high formation
pressures in Azerbaijan and the South Caspian Basin (as related to smectite ??? illite
transformations during diagenesis and catagenesis). J. Pet. Sci. Eng. 13, 203–218.
https://doi.org/10.1016/0920-4105(95)00008-6
Cardona, J., 2011. Fundamental Investigation of Pore Pressure Prediction during Drilling from
the Mechanical Behaviour of Rocks. PhD Thesis, Texas A&M Univ. Mech. Eng.
Carlin, S., Dainelli, J., 1998. Pressure regimes and pressure systems in the Adriatic Foredeep
(Italy). Abnorm. Press. Hydrocarb. Environ. 70, 145–160.
Carstens, H., 1978. Origin Of Abnormal Formation Pressures In Central North Sea Lower
Tertiary Clastics. Log Anal. 19, 24–31.
Carstens, H., Dypvik, H., 1981. Abnormal formation pressure and shale porosity. Am. Assoc.
Pet. Geol. Bull. 65, 344–350.
Cheatham, C.A., Nahm*, J.J., Heitkamp, N.., 1985. Effects of Selected Mud Properties on Rate
32
 of Penetration in Full-Scale Shale Drilling Simulations. Soc. Pet. Eng. (SPE/IADC 13465).
Chen, J., Huang, D., 1996. Formation and mechanism of the abnormal pressure zone and its
relation to oil and gas accummulations in the Eastern Jiuquan Basin, Northwest China. Sci.
China Earth Sci. 39, 194–204.
Combs, D.G., 1968. Prediction o Pore Pressure From Penetration Rate. Soc. Pet. Eng. (SPE
2162).
Couzens-Schultz, B. a., Axon, A., Azbel, A., Hansen, K.S., Haugland, M., Sarker, R., Tichelar,
B., Wieseneck, J.B., Wilhelm, R., Zhang, Z., 2013. IPTC 16849: Pore Pressure Prediction in
Unconventional Resources. Pap. IPTC 16849 Proc. 2013 Int. Pet. Conf. held Beijing, China,
26-28 March. https://doi.org/10.2523/16849-ms
Cunningham, R. a, Eenink, J.G., 1959. Laboratory Study of Effect of Overburden, Formation and
Mud Column Pressures on Drilling Rate of Permeable Formations. Pet. Trans. AIME 217,
9–17.
Daines, S.R., 1982. Aquathermal Pressuring and Geopressure Evaluation: GEOLOGIC NOTES.
Am. Assoc. Pet. Geol. Bull. 66, 931–939.
Detournay, E., Atkinson, C., 2000. Influence of pore pressure on the drilling response in low-
permeability shear-dilatant rocks. Int. J. Rock Mech. Min. Sci. 37, 1091–1101.
https://doi.org/10.1016/S1365-1609(00)00050-2
Dickey, P., Cox, W., 1977. Oil and gas in reservoirs with subnormal pressures. Am. Assoc. Pet.
Geol. Bull. 12, 2134–2142.
Dickey, P.A., Shriram, C.R., Paine, W.R., 1968. Abnormal pressures in deep wells of
southwestern Louisiana. Science (80-. ). 160, 609–615.
Dickinson, G., 1953. Geological Aspects of Abnormal Reservoir Pressures in Gulf Coast
Louisiana. Am. Assoc. Pet. Geol. Bull. 37, 410–432. https://doi.org/10.1306/5CEADC6B-
16BB-11D7-8645000102C1865D
Doornhof, D., Kristiansen, T.G., Nagel, N.B., Pattillo, P.D., Sayers, C., 2006. Compaction and
subsidence. Oilf. Rev. 18, 50–68.
Dutta, N., 2002. Geopressure Detection Using Reflection Seismic Data and Rock Physics
Principles: Methodology and Case Histories From Deepwater Tertiary Clastics Basins. Pap.
SPE 77820 Proc. 2002 SPE Asia Pacific Oil Gas Conf. Exhib. held Melbourne, Aust. 8–10
October. https://doi.org/10.2523/77820-MS
33
Dutta, N., Gelinsky, S., Reese, M., Khan, M., 2001. A New Petrophysically Constrained Predrill
Pore Pressure Prediction Method for the Deepwater Gulf of Mexico: A Real-Time Case
Study. Pap. SPE 71347 Proc. 2001 SPE Annu. Tech. Conf. Exhib. held New Orleans,
Louisiana, 30 Sept. Oct. 2001. https://doi.org/10.2118/71347-MS
Dutta, N.C., Ray, A., 1997. Image of Geopressured Rocks Using Velocity And Acoustic
Impedance Inversion of Seismic Data. 1997 SEG Annu. Meet.
Dvorkin, J., Mavko, G., Nur, A., 1999. Overpressure detection from compressional‐and shear‐
wave data. Geophys. Res. Lett. 26, 3417–3420.
Eaton, B.A., 1975. The Equation for Geopressure Prediction from Well Logs. Soc. Pet. Eng.
(SPE 5544 ). https://doi.org/10.2118/5544-MS
Eberhart-Phillips, D., Han, D., Zoback, M.D., 1989. Empirical relationships among seismic
velocity, effective pressure, porosity, and clay content in sandstone. Geophysics.
https://doi.org/10.1190/1.1442580
Ebrom, D., Albertin, M., Heppard, P., 2006. Subsalt pressure prediction from multicomponent
seismics (and more!). Lead. Edge 25, 1540–1542.
Ebrom, D., Heppard, P., Thomsen, L., 2002. Numerical modeling of PS moveout as a function of
pore pressure, in: SEG Technical Program Expanded Abstracts 2002. Society of
Exploration Geophysicists, pp. 1634–1637.
Ebrom, D., Heppard, P., Thomsen, L., Mueller, M., Harrold, T., Phillip, L., Watson, P., 2004.
Effective stress and minimum velocity trends, in: SEG Technical Program Expanded
Abstracts 2004. Society of Exploration Geophysicists, pp. 1615–1618.
Ensley, R.A., 1985. Evaluation of direct hydrocarbon indicators through comparison of
compressional-wave and shear-wave seismic data - a case study of the Myrnam gas field
Alberta. Geophysics 50, 37–48. https://doi.org/10.1190/1.1441834
Etminan, M., Jamali, J., Riahi, M.A., 2012. Formation Pore Pressure Prediction Using Velocity
Inversion in Southwest Iran. Pet. Sci. Technol. 30, 28–34.
https://doi.org/10.1080/10916461003752538
Fertl, W.H., 1972. Worldwide Occurrence of Abnormal Formation Pressures, Part 1. Pap. SPE
3844 Proc. 1972 Abnorm. Subsurf. Press. Symp. Soc. Pet. Eng. AIME, to be held Bat.
Rouge, La., May 15-16.
Fertl, W.H., Chilingarian, G. V., 1987. Abnormal formation pressures and their detection by
34
 pulsed neutron capture logs. J. Pet. Sci. Eng. 1, 23–38. https://doi.org/10.1016/0920-
4105(87)90012-X
Fertl, W.H., Timko, D., 1971. Parameters for Identification of Overpressure Formations. Pap.
SPE 3223 Proc. 1971 Drill. Rock Mech. Conf. https://doi.org/10.2118/3223-MS
Finch, W., 1969. Abnormal Pressure in the Antelope Field, North Dakota. J. Pet. Technol. 21.
https://doi.org/10.2118/2227-PA
Flemings, P.B., Stump, B.B., Finkbeiner, T., Zoback, M., 2002. Flow focusing in overpressured
sandstones: Theory, observations, and applications. Am. J. Sci. 302, 827–855.
https://doi.org/10.2475/ajs.302.10.827
Forgotson, S.J.M., 1969. Indication of Proximity of High-Pressure Fluid Reservoir, Louisiana
and Texas Gulf Coast. Am. Assoc. Pet. Geol. Bull. 53, 171–173.
Foster, J.B., Whalen, H.E., 1966. Estimation of formation pressures from electrical surveys -
Offshore Louisiana. J. Pet. Technol. 18, 165–171. https://doi.org/10.2118/1200-PA
Freed, R.L., Peacor, D.R., 1989. Geopressured shale and sealing effect of smectite to illite
transition. Am. Assoc. Pet. Geol. Bull. 73, 1223–1232.
Freire, H., Falcão, J.., Silva, C.F., Barghigiani, L.., 2010. Abnormal Pore Pressure Mechanisms
In Brazil. Pap. ARMA 10-407 Proc. 2010 44th US Rock Mech. Symp. 5th U.S.-Canada
Rock Mech. Symp. held Salt Lake City, UT June 27–30,.
Gardner, G.H.., Gardner, L.., Gregory, A.., 1974. Formation Velocity and Density - The
Diagnostic Basic for Stratigraphic Traps. Geophysics 39, 770–780.
Gardner, G.H.F., Gardner, L.W., Gregory, A.R., 1974. Formation Velocity and Density - The
Diagnostic Basics for Stratigraphic Traps. Geophysics 39, 770–780.
Garnier, A.J., Lingen, N.H. van, 1959. Phenomena affecting drilling rates at depth. Pet.
TRANSA CTIONS, A IME (SPE 1097G) 216, 232–239.
Gray-Stephens, D., Cook, J.M., Sheppard, M.C., 1994. Influence of Pore Pressure on Drilling
Response in Hard Shales. SPE Drill. Complet. 9, 263–270. https://doi.org/10.2118/23414-
PA
Guo, X., He, S., Liu, K., Song, G., Wang, X., Shi, Z., 2010. Oil generation as the dominant
overpressure mechanism in the Cenozoic Dongying depression, Bohai Bay Basin, China.
Am. Assoc. Pet. Geol. Bull. 94, 1859–1881.
Gurevich, A.E., Chilingar, G. V., 1995. Abnormal pressures in Azerbaijan: A brief critical
35
 review and recommendations. J. Pet. Sci. Eng. 13, 125–135. https://doi.org/10.1016/0920-
4105(95)00007-5
Gutierrez, M.A., Braunsdor, N.R., Couzens, B.A., 2006. Calibration and ranking of pore-
pressure prediction models. Lead. Edge 25, 1516–1523.
Hamada, G.M., 2004. Reservoir Fluids Identification Using Vp/Vs Ratio. Oil Gas Sci. Technol.
– Rev. IFP 59, 649–654.
Harkins, L.K., Baugher, I.H.., 1969. Geological significance of abnormal formation pressures. J.
Pet. Technol. 961–966. https://doi.org/10.2118/2228-PA
Harper, D., 1969. New Findings From Over Pressure Detection Curves In Tectonically Stressed
Beds. Soc. Pet. Eng. (SPE 2781).
Hart, B.S., Flemings, P.B., Deshpande, A., 1995. Porosity and pressure: Role of compaction
disequilibrium in the development of geopressures in a Gulf Coast Pleistocene basin.
Geology 23, 45–48.
Heppard, P.D., Cander, H.S., Eggertson, E.B., 1998. Abnormal pressure and the occurrence of
hydrocarbons in offshore eastern Trinidad, West Indies. Law, B.E., G.F. Ulmishek, V.I.
Slavin eds., Abnorm. Press. Hydrocarb. Environ. AAPG Mem. 70, 215–246.
Hermanrud, C., Wensaas, L., Teige, G.M.G., Bolas, H.M.N., Hansen, S., Vik, E., 1998. Shale
porosities from well logs on haltenbanken (offshore mid-Norway) show no influence of
overpressuring. Law, B.E., G.F. Ulmishek, V.I. Slavin eds., Abnorm. Press. Hydrocarb.
envi- ronments AAPG Mem. 70, 65–85.
Holbrook, P.W., Maggiori, D.A., Hensley, R., 1995. Real-Time Pore Pressure and Fracture
Gradient Evaluation in All Sedimentary Lithologies. SPE Form. Eval. 10, 215–222.
Holm, G.M., 1998. Distribution and origin of overpressure in the Central Graben of the North
Sea. Law, B.E., G.F. Ulmishek, V.I. Slavin eds., Abnorm. Press. Hydrocarb. Environ.
AAPG Mem. 70, 123–144.
Hottmann, C.E., Johnson, R.K., 1965. Estimation of formation pressures from log-derived shale
properties. J. Pet. Technol. SPE 1110, 717–722. https://doi.org/10.2118/1110-PA
Huffman, a. R., 2002. The future of pore-pressure prediction using geophysical methods. Pap.
OTC 13041 Proc. e 2001 Offshore Technol. Conf. held Houston, Texas, 30 April. May.
Hunt, J.M., 1990. Generation and migration of petroleum from abnormally pressured fluid
compartments. Am. Assoc. Pet. Geol. Bull. https://doi.org/10.1306/0C9B27E5-1710-11D7-
36
 8645000102C1865D
Hunt, J.M., Whelan, J.K., Eglinton, L.B., Cathles, L.M. ll., 1998. Relation of shale porosities,
gas generation, and compaction to deep overpressures in the US. Gulf coast. Law, B.E.,
G.F. Ulmishek, V.I. Slavin eds., Abnorm. Press. Hydrocarb. Environ. AAPG Mem. 70 87–
104.
Jorden, J.R., Shirley, O.J., 1966. Application of Drilling Performance Data to Overpressure
Detection. J. Pet. Technol. 18, 1387–1394. https://doi.org/10.2118/1407-PA
Kader, M.S. Bin, 1994. Abnormal pressure occurrence in the Malay and Penyu basins, offshore
Peninsular Malaysia - a regional understanding. Geol. Soc. Malaysia Bull. 36, 81–91.
Kadri, I.B., 1991. Abnormal Formation Pressures in Post-Eocene Formation, Potwar Basin,
Pakistan. Pap. SPE/IADC 21920 Proc. 1991 SPElIADC Drill. Conf. held Amsterdam, 11-14
March. https://doi.org/10.2523/21920-MS
Katahara, K., 2003. Analysis of overpressure on the Gulf of Mexico Shelf, in: Offshore
Technology Conference. Offshore Technology Conference.
Kozlowski, M., Quirein, J., Engelman, B., Wolanski, K., Ochalik, S., 2017. Quantitative
Interpretation of Sonic Compressional and Shear Logs for Gas Saturation in Medium
Porosity Sandstone, in: SPWLA 58th Annual Logging Symposium. Society of
Petrophysicists and Well-Log Analysts.
Kumar, K.M., Ferguson, R.J., Ebrom, D., Heppard, P., 2006. Pore pressure prediction using an
Eaton’s approach for PS-waves, in: SEG Technical Program Expanded Abstracts 2006.
Society of Exploration Geophysicists, pp. 1550–1554.
Lane, R.A., Macpherson, L.A., 1976. A Review of Geopressure Evaluation From Well Logs -
Louisiana Gulf Coast. J. Pet. Technol. 28, 963–971. https://doi.org/10.2118/5033-PA
Law, B.E., Dickinson, W.W., 1985. Conceptual Model for Origin of Abnormally Pressured Gas
Accumulations in Low-Permeability Reservoirs. Am. Assoc. Pet. Geol. Bull. 69, 1295–
1304. https://doi.org/10.1306/AD462BD7-16F7-11D7-8645000102C1865D
Law, B.E., Shah, S.H. a, Malik, M. a, 1998. Abnormally high formation pressures, Potwar
Plateau, Pakistan. Law, B.E., G.F. Ulmishek, V.I. Slavin eds., Abnorm. Press. Hydrocarb.
Environ. AAPG Mem. 70 247–358. https://doi.org/10.1306/F4C8E6B6-1712-11D7-
8645000102C1865D
Law, B.E., Spencer, C.W., 1998. Abnormal Pressure in Hydrocarbon Environments. Law, B.E.,
37
 G.F. Ulmishek, V.I. Slavin eds., Abnorm. Press. Hydrocarb. Environ. AAPG Mem. 70 1–
11. https://doi.org/10.1016/S0264-8172(99)00059-8
Lewis, C.., Rose, S.., 1970. A theory relating high temeperatures and overpressures. J. Pet.
Technol. 22, 11–16.
Li, Q., Heliot, D., Zhao, L., Chen, Y., 2000. Abnormal pressure detection and wellbore stability
evaluation in carbonate formations of east Sichuan, China, in: IADC/SPE Drilling
Conference (IADC / SPE 59125). Society of Petroleum Engineers.
Lingen, N.H. Van, 1962. Bottom Scavenging-A Major Factor Governing Penetration Rates at
Depth. J. Pet. Technol. (SPE 165) 187–196.
Liu, Y., Qiu, N., Xie, Z., Yao, Q., Zhu, C., 2016. Overpressure compartments in the central
paleo-uplift, Sichuan Basin, southwest China. Am. Assoc. Pet. Geol. Bull. 100, 867–888.
Luo, M., Baker, M.R., LeMone, D. V, 1994. Distribution and generation of the overpressure
system, eastern Delaware Basin, western Texas and southern New Mexico. Am. Assoc. Pet.
Geol. Bull. 78, 1386–1405.
Luo, X., Vasseur, G., 1992. Contributions of compaction and aquathermal pressuring to
geopressure and the influence of environmental conditions (1). Am. Assoc. Pet. Geol. Bull.
76, 1550–1559.
Magara, K., 1975. Importance of aquathermal pressuring effect in Gulf Coast. Am. Assoc. Pet.
Geol. Bull. 59, 2037–2045.
Majidi, R., Albertin, M.L., Last, N., 2016. Method for Pore Pressure Estimation Using
Mechanical Specific Energy and Drilling Efficiency. Pap. IADC/SPE 178842 Proc. 2016
IADC/SPE Drill. Conf. Exhib. held Fort Worth, Texas, USA, 1–3 March.
Mann, D.M., Mackenzie, A.S., 1990. Prediction of pore fluid pressures in sedimentary basins.
Mar. Pet. Geol. 7, 55–65. https://doi.org/10.1016/0264-8172(90)90056-M
Maurer, W.C., 1965. Bit-Tooth Penetration Under Simulated Borehole Conditions. J. Pet.
Technol. 1433–1442.
Miller, T.W., Luk, C.H., 1993. Contributions of compaction and aquathermal pressuring to
geopressure and the influence of environmental conditions: discussion. Am. Assoc. Pet.
Geol. Bull. 77, 2006–2010.
Murray, A.S., Cunningham, R.A., 1955. Effect of Mud Column Pressure on Drilling Rates. Pet.
Trans. AIME 204, 196–204.
38
Nagel, N.B., 2001. Compaction and subsidence issues within the petroleum industry: From
Wilmington to Ekofisk and beyond. Phys. Chem. Earth, Part A Solid Earth Geod. 26, 3–14.
Nashaat, M., 1998. Abnormally high formation pressure and seal impacts on hydrocarbon
accumulations in the Nile Delta and North Sinai basins, Egypt. Law, B.E., G.F. Ulmishek,
V.I. Slavin eds., Abnorm. Press. Hydrocarb. Environ. AAPG Mem. 70 161–180.
O’Connor, S., Swarbrick, R., Hoesni, J., Lahann, R., 2012. Deep Pore Pressure Prediction in
Challenging Areas, Malay Basin, SE Asia. Pap. IPA11 - G - 022 Proceedings, Indones. Pet.
Assoc. 35th Annu. Conv. Exhib. May 2011 15.
Pennebaker, E.., 1968. Detection of Abnormal-pressure Formations from Seismic- Field Data.
Am. Pet. Inst. 184–191.
Pickering, L.A., Indelicato, G.J., 1985. Abnormal formation pressure: a review. Mt. Geol.
Plumley, J.W., 1980. Abnormally High Fluid Pressure: Survey of Some Basic Principles:
ERRATUM. Am. Assoc. Pet. Geol. Bull. 64, 414–422.
Polutranko, A.J., 1998. Causes of Formation and Distribution of Abnormally High Formation
Pressure in Petroleum Basins of Ukraine. Law, B.E., G.F. Ulmishek, V.I. Slavin eds.,
Abnorm. Press. Hydrocarb. envi- ronments AAPG Mem. 70 181–194.
Powers, M.C., 1967. Fluid-release mechanisms in compacting marine mudrocks and their
importance in oil exploration. Am. Assoc. Pet. Geol. Bull. 7, 1240–1254.
Prasad, M., 2002. Acoustic measurements in unconsolidated sands at low effective pressure and
overpressure detection. Geophysics 67, 405–412.
Ramdhan, A.M., Goulty, N.R., 2011. Overpressure and mudrock compaction in the Lower Kutai
Basin, Indonesia: A radical reappraisal. Am. Assoc. Pet. Geol. Bull. 95, 1725–1744.
Rasmus, J.., Stephens, G.D.M.R., 1995. I ; J. SPE Drill. Eng. 177, 1066–1075.
Rieke, H.H., Chilingarian, G. V, 1974. Compaction of argillaceous sediments. Elsevier.
Rubey, W.W., Hubber, K.M., 1959. Role of Fluid Pressure in Mechanics of Overthrust Faulting.
Bull. Geol. Soc. Am. 70, 167–206.
Saleh, S., Williams, K., Rizvi, A., 2013. Predicting Subsalt Pore Pressure with Vp/Vs. Offshore
Technol. Conf. (OTC 24157).
Satti, A.. I., Yusoff, W.W.I., Ghosh, D., 2016. Overpressure in the Malay Basin and prediction
methods. Geofluids 16, 301–313. https://doi.org/10.1111/gfl.12149
Satti, I.A., Ghosh, D., Yusoff, W.I.W., Hoesni, M.J., 2015. Origin of Overpressure in a Field in
39
 the Southwestern Malay Basin. SPE Drill. Complet. 30, 198.
Satti, I.A., Yusoff, W.I.W., 2015. A New Method for Overpressure Mechanisms Analysis. Soc.
Pet. Eng. (SPE 176357).
Sayers, C.M., Boer Den, L.D., Nagy, Z.R., Hooyman, P.J., Ward, V., 2005. Regional trends in
undercompaction and overpressure in the Gulf of Mexico. Seg/houst. 2005 Annu. Meet.
1219–1223.
Sayers, C.M., Johnson, G.M., Denyer, G., 2002. Predrill pore-pressure prediction using seismic
data. Geophysics 67, 1286–1292. https://doi.org/10.1190/1.1500391
Sayers, C.M., Johnson, G.M., Denyer, G., 2000. OTC 11984 Pore Pressure Prediction From
Seismic Tomography. Pap. OTC 11984 Proc. 2000 Offshore Technol. Conf. held Houston,
Texas, 1–4 May.
Schneider, F.J.., 2000. Abnormal Pressures in Hydrocarbon Environments. Mar. Pet. Geol. 17,
559. https://doi.org/10.1016/S0264-8172(99)00059-8
Schwall, G.H., Denney, C.A., 1994. Subsidence induced casing deformation mechanisms in the
Ekofisk field, in: Rock Mechanics in Petroleum Engineering. Society of Petroleum
Engineers.
Schwall, G.H., Slack, M.W., Kaiser, T.M. V, 1996. Reservoir compaction well design for the
Ekofisk field, in: SPE Annual Technical Conference and Exhibition. Society of Petroleum
Engineers.
Scott, D., Thomsen, L., 1993. A global algorithm for pore pressure prediction, in: 55th EAEG
Meeting.
Serebryakov, V.A., Chilingar, G. V., 1995. Abnormal pressure regime in the former USSR
petroleum basins. J. Pet. Sci. Eng. 13, 65–74.
Serebryakov, V.A., Chilingar, G. V., 1994. Investigation of underpressured reservoirs in the
powder river Basin, Wyoming and Montana. J. Pet. Sci. Eng. 11, 249–259.
Serebryakov, V.A., Chilingar, G. V., Katz, S.A., 1995. Methods of estimating and predicting
abnormal formation pressures. J. Pet. Sci. Eng. 13, 113–123. https://doi.org/10.1016/0920-
4105(95)00006-4
Serebryakov, V.A., Robertson Jr, J.O., Chilingarian, G. V, 2002. Origin and prediction of
abnormal formation pressures. Gulf Professional Publishing.
Sharp Jr, J.M., 1983. Permeability controls on aquathermal pressuring. Am. Assoc. Pet. Geol.
40
 Bull. 67, 2057–2061.
Singh, I., Ford, C.., 1982. The occurance, Causes and Detection of Abnormal Pressure in the
Malay Basin. pcocedings offshore South East Asia Conf. 9 - 12 Febr.
Slavin, V.I., Smirnova, E.M., 1998. Abnormally high formation pressures: origin, prediction,
hydrocarbon field development, and ecological problems. Law, B.E., G.F. Ulmishek, V.I.
Slavin eds., Abnorm. Press. Hydrocarb. Environ. AAPG Mem. 70 105–114.
Soleymani, H., Riahi, M.A., 2012. Velocity based pore pressure prediction-A case study at one
of the Iranian southwest oil fields. J. Pet. Sci. Eng. 94–95, 40–46.
Spencer, C.W., 1987. Hydrocarbon Generation as a Mechanism for Overpressuring in Rocky
Mountain Region. Am. Assoc. Pet. Geol. Bull. 71, 368–388.
Stainforth, J.G., 1984. GIFFSLAND HYDROCARBONS-A PERSPECTIVE FROM THE
BASIN EDGE. APPEA J. 24, 91–100.
Sulak, A.M., Danielsen, J., 1988. Reservoir aspects of Ekofisk subsidence, in: Offshore
Technology Conference. Offshore Technology Conference.
Swarbrick, R.E., 2001. Pore-Pressure Prediction: Pitfalls in Using Porosity. Pap. OTC 13045
Proc. 2001 Offshore Technol. Conf. held Houston, Texas, 30 April. May.
Swarbrick, R.E., 1995. Distribution and Generation of the Overpressyre System, Eaastern
Delaware BAsin, Western Texas and Southern New Mexico: Discussion. Am. Assoc. Pet.
Geol. Bull. 12, 1386–1405.
Tatham, R.H., Stoffa, P.L., 1976. V p/V s—A potential hydrocarbon indicator. Geophysics 41,
837–849.
Teale, R., 1965. The Concept of Specific Energy in Rock Drilling. Int. J. Rock Mech. Min. Sci.
2, 57–73. https://doi.org/10.1016/0148-9062(65)90022-7
Teige, G.M.G., Hermanrud, C., Wensaas, L., Bolås, H.M.N., 1999. The lack of relationship
between overpressure and porosity in North Sea and Haltenbanken shales. Mar. Pet. Geol.
16, 321–335.
Terzaghi, K., 1927. No Title. Die Beziehungen zwischen Elastizitat und Inn. Sitzungsbur Akad.
Wiss. Wein. 132 Abt.
Tingay, M.R.P., Morley, C.K., Laird, A., Limpornpipat, O., Krisadasima, K., Pabchanda, S.,
Macintyre, H.R., 2013. Evidence for overpressure generation by kerogen-to-gas maturation
in the northern Malay Basin. Am. Assoc. Pet. Geol. Bull. 97, 639–672.
41
Vidrine, D.J., Benit, E.J., 1968. Field Verification of the Effect of Differential Pressure on
Drilling Rate. J. Pet. Technol. (SPE 1859) 20, 676–682. https://doi.org/10.2118/1859-PA
Vudovich, A., Chin, L. V, Morgan, D.R., 1988. Casing deformation in Ekofisk, in: Offshore
Technology Conference. Offshore Technology Conference.
Walls, J., Dvorkin, J., Mavko, G., Nur, A., 2000. Use of Compressional and Shear Wave
Velocity for Overpressure Detection. Offshore Technol. Conf. (OTC 11912).
Ward, C.D., Coghill, K., Broussard, M.D., 1994. The application of petrophysical data to
improve pore and fracture pressure determination in North Sea Central Graben HPHT wells,
in: SPE Annual Technical Conference and Exhibition. Society of Petroleum Engineers.
Wardlaw, H.W.R., 1969. Drilling Performance Optimization and Identification of Overpressure.
Soc. Pet. Eng. AIME SPE 2388, 67–78.
Williams, D.M., 1990. The acoustic log hydrocarbon indicator, in: SPWLA 31st Annual Logging
Symposium. Society of Petrophysicists and Well-Log Analysts.
Wilson, M.S., Gunneson, B.G., Peterson, K.E., Honore, R., 1998. Abnormal pressures
encountered in a deep wildcat well, southern Piceance Basin, Colorado. Law, B.E., G.F.
Ulmishek, V.I. Slavin eds., Abnorm. Press. Hydrocarb. Environ. AAPG Mem. 70 195–214.
Wooley, G.R., Prachner, W., 1988. Reservoir compaction loads on casings and liners. SPE Prod.
Eng. 3, 96–102.
Yu, H., Hilterman, F.J., 2013. Shear wave sensitivity to pore pressure prediction, in: SEG
Technical Program Expanded Abstracts 2013. Society of Exploration Geophysicists, pp.
600–604.
Zamora, M., 1972. Slide Rule Correlation Aids D-exponent. Oil Gas J. 70, 68–72.
Zhang, J., 2013. Effective stress, porosity, velocity and abnormal pore pressure prediction
accounting for compaction disequilibrium and unloading. Mar. Pet. Geol. 45, 2–11.
Zhang, J., 2011. Pore pressure prediction from well logs: Methods, modifications, and new
approaches. Earth-Science Rev. 108, 50–63. https://doi.org/10.1016/j.earscirev.2011.06.001
Zoeller, W.A., 1983. Pore Pressure Detection From the MWD Gamma Ray. Pap. SPE 12166
Proc. 1983 58th Annu. Tech. Conf. Exhib. held San Fr. CA, Oct. 5-8.

42
 Chapter 2

2.0 Overpressure Prediction Using the Hydro-Rotary Specific Energy Concept

Preface

A version of this chapter has been published in the Journal of Natural Gas Science and

Engineering, 2018. I am the primary author. Co-author Dr. Sunday Adedigba provided much-

needed support in completing the manuscript. Co-author Dr. Faisal Khan reviewed the

manuscript and provided valuable insight into the model development. Co-author Dr. Raghu

Chunduru reviewed the manuscript and provided technical support in model analysis. Co-author

Dr. Stephen Butt reviewed the manuscript and assisted in the development of the concept. I

developed the initial concept and carried out most of the data analysis. I prepared the first draft

of the manuscript and revised the manuscript based on the feedback from the co-authors and

peer review process. The co-authors also helped to refine the concept.

Abstract

Pore pressure predictions from the drilling parameters have experienced little improvement since

the inception of the d-exponent concept. Applications of the d-exponent method to pore pressure

predictions have produced mixed results, especially in deviated wells and under drilling

conditions where bit hydraulic energy has a significant influence on the rate of penetration

(ROP). In this paper, a new energy-based pore pressure prediction technique using the concept of

hydro-rotary specific energy (HRSE) is presented. The HRSE approximates the total energy

required to break and remove a unit volume of rock. Overpressure prediction using the HRSE

method is based on the principle that overpressure intervals with lower effective stress will

43
require less energy to drill than the normally pressured intervals at the same depth. The new

technique is tested using a recently drilled deep vertical exploratory gas well in the Tertiary

Deltaic System in the central swamp region of the Niger Delta in Nigeria. The pore pressure

estimates from the HRSE concept are compared to: (1) the pore pressure estimates derived from

the d-exponent and shale compressional velocity, (2) the actual pore pressure measurements

taken in the reservoir sands of interest. An excellent agreement is observed in magnitude and

trend between the pore pressure estimates derived from the HRSE concept and the actual pore

pressure measurements. This clearly demonstrates the applicability of the HRSE concept in

predicting the onset of overpressure and estimating the formation pore pressure. The HRSE

method of overpressure prediction has the potential to be more accurate in some drilling

environments where the d-exponent method may have produced erroneous results.

Keywords: Pore pressure; Overpressure; Mechanical Specific Energy; Hydro-rotary Specific

Energy, d-exponent; Normal Compaction Trend

2.1 Introduction

The formation pore pressure is of great importance in the oil and gas industry. It provides the

necessary energy required to drive liquid and gaseous hydrocarbons to the surface. It also

represents a potential hazard during drilling, completion, and production if not properly

managed. Accurate knowledge of the formation pore pressure is very useful in all stages of oil

and gas exploration and production. Exploration engineers use pore pressure data to determine

subsurface trap integrity. The occurrence of hydrocarbons in some sedimentary basins is also

believed to be related to the subsurface pore pressure regime (Belonin & Slavin, 1998).

44
Information about the formation pressure helps the reservoir engineers in reservoir modeling.

Production engineers use pore pressure data for well performance analysis. Drilling engineers

use pore pressure data to optimize rig selection, casing depths determination, drilling, and

completion fluid design, wellheads design, casing and tubing design, cement design and material

selection. Facility engineers also use pore pressure data for surface installation designs. From a

business perspective, subsurface pressure regimes will dictate the overall well cost.

The formation pore pressure can be normal (hydrostatic), subnormal or overpressure. It is

normal if it is able to support a continuous column of static formation water from the surface to

the reservoir depth of interest (Swarbrick & Osborne, 1998). The normal pore pressure gradient

varies between 0.433 – 0.515 psi/ft depending on the location, concentration of dissolved salts,

pore fluid type, and temperature. Formations with pore pressure gradient lower than normal pore

pressure gradients are termed subnormal. Overpressure intervals have a pore pressure gradient

greater than the normal pore pressure gradient. Subsurface overpressure conditions and their

origins have been reported in nearly all the hydrocarbon-bearing sedimentary basins around the

world (Plumley, 1980; Spencer, 1987; Hunt, 1990; Swarbrick, 1995; Yassir et al., 1996; Nashaat,

1998; Polutranko, 1998; Slavin & Smirnova, 1998; Holm, 1998; Kumar et al., 2016). The

Normal, subnormal and overpressure conditions can co-exist in a sedimentary basin provided

they are separated by permeability barriers. Conventionally, pore pressure predictions have been

carried out using seismic, drilling and well log data. However, the best approach to pore pressure

prediction is to examine the combination of all the available data. Relying on only one type of

data can lead to misinterpretations. For example, under poor borehole conditions such as

breakouts or washouts, the well log data may produce inaccurate estimates of pore pressure. The

same poor borehole conditions may have little or no effect on the drilling parameters.

45
Table 2. 1 Merits and limitations of pore pressure prediction methods.

Method Merits Limitations

The seismic responses can be affected by

The conventional seismic data can provide pre-
changes in lithology and pore fluid type. The
drill pore pressure predictions for well planning
Seismic
pore pressure prediction accuracy from the
purposes, especially in exploration drilling.
Data
seismic data can be very low. The geology of
Formation pressure can be predicted real-time
the application basin must be known.
ahead of the bit (seismic while drilling).

Well logs can be affected by borehole

Real-time pore pressure prediction using
conditions. Formation pressure is predicted a
logging while drilling (LWD) data. Under
few feet behind the bit for real-time
suitable conditions, pore pressure estimates
Well log applications. They cannot be acquired before
from the well log data provide the most
data the well is drilled. For LWD measurements,
accurate results when compared to other
data quality may be affected by the drilling
methods of pore pressure prediction.
rate. Rock properties can be affected by other

factors than the formation pore pressure.

Not suitable for pre-drill pore pressure

Formation pressure can be estimated real-time
predictions along the well path. Data
at the bit. May provide good pore pressure
Drilling qualities are affected by shocks/vibrations.
estimates under suitable conditions. It is
parameters Drilling parameters are affected by lithology,
relatively inexpensive. Drilling parameter data
rock strength, bit type, bit wear, BHA
are readily available.
sticking and excessive overbalance.

This can make the pore pressure estimates from the drilling parameters to be more accurate than

pore pressure estimates from well logs under such conditions. Similarly, pore pressure estimates

from well log data under excessive bit wear conditions are more likely to be more accurate than

46
the pore pressure estimates derived from the drilling parameters. Table 2.1 summarizes the

merits and limitations of each method.

Hottmann & Johnson (1965) proposed a method for predicting the onset of overpressure

from the resistivity and sonic logs by correlating the amount of deviation from the normal

compaction trend (NCT) at a given depth to the observed pressure in adjacent reservoir

formations. Foster & Whalen (1966) developed a pore pressure prediction model based on the

concept of the shale formation resistivity factor for regions with varying salinity. Pennebaker

(1968) provided a methodology for estimating the formation pore pressure from the seismic data.

Seismic data (velocity and acoustic impedance) have been used in several sedimentary basins for

pre-drill pore pressure predictions (Sayers et al., 2002; Soleymani & Riahi, 2012; Brahma et al.,

2013; El-Werr et al., 2017). Gardner et al. (1974) developed an empirical correlation among

vertical effective stress, depth of burial and interval travel time.

Eaton (1975) proposed three sets of empirical relations based on resistivity, sonic and d-

exponent data. Eaton’s models are given by:

R o 1.2
Gpp = Gob − {Gob − Gnp } [ ] , (2.1)
Rn

Vo 3
Gpp = Gob − {Gob − Gnp } [ ] , (2.2)
Vn

dco 1.2
Gpp = Gob − {Gob − Gnp } [ ] , (2.3)
dcn

where Gpp is the pore pressure gradient (psi/ft); Gob is the overburden gradient (psi/ft); Gnp is the

normal pore pressure gradient (psi/ft); R o is the observed shale resistivity (ohm-m); R n is the

normal compaction trend shale resistivity (ohm-m); Vn is the normal compaction shale
47
compressional velocity (m/s); Vo is the observed shale compressional velocity (m/s); 𝑑𝑐𝑜 is the

calculated 𝑑𝑐 from measured data; 𝑑𝑐𝑛 is the 𝑑𝑐 from the normal trend line. Eaton’s models are

the most widely used pore pressure prediction methods for loading conditions where the main

origin of overpressure mechanism is compaction disequilibrium, especially in young tertiary

sediments.

Bowers (1995) proposed empirical relations between effective stress and compressional

sonic velocity to predict the degree of overpressure generated by compaction disequilibrium and

fluid expansion mechanisms. Bower’s method is applicable to loading and unloading conditions.

Bowers' method is also applicable to many sedimentary basins. However, Bower’s method may

over-predict the formation pore pressure in shallow unconsolidated formations due primarily to

very slow compression sonic velocity in such formations (Zhang, 2011). Zhang (2011) adapted

the Eaton's model for the resistivity and sonic transit time data using depth-dependent normal

compaction equations. Zhang (2013) proposed a theoretical model to estimate the effective stress

and formation pore pressure using porosity and compressional sonic velocity data. Rock

properties such as bulk and pore compressibility (Atashbari & Tingay, 2012), natural

radioactivity (Serebryakov et al., 1995), acoustic impedance (Satti & Yusoff, 2015) and the ratio

of compressional to shear velocities (Li et al., 2000; Walls et al., 2000; Ebrom et al., 2006; Saleh

et al., 2013) have also been used to predict the onset of overpressure and to estimate the

formation pore pressure.

From the field and laboratory observations, the dependency of the ROP on the differential

pressure between the bottom-hole pressure and the formation pore pressure has long been

established (Murray & Cunningham, 1955; Cunningham & Eenink, 1959; Garnier & Lingen,

1959; Vidrine & Benit, 1968; Combs, 1968, Wardlaw, 1969; Black et al., 1985; Cheatham et al.,

48
1985). An increase in the formation pore pressure for a given mud weight will cause the drilling

rate to increase due to reduced back pressure on the formations. This is the main reason why the

driller must stop the drilling operations and perform a flow check any time a positive drilling

break is being observed at the well site and more importantly when drilling exploratory wells.

The d-exponent method was the first empirical method of estimating formation pore pressure

from drilling parameters (Jorden & Shirley, 1966; Harper, 1969; Rehm & Mcclendon, 1971).

The empirical model that relates dc – exponent to drilling parameters is given by:

ROP
log [60N ] Gnp
dc − exponent = ∗[ ], (2.4)
12WOB ECD
log [ 6 ]
10 Db

where dc − exponent is the corrected d – exponent; ROP is the rate of penetration (ft/hr); N is

the rotary speed in revolution per minute (rpm); WOB is the weight on bit (lbs); Db is the bit

diameter (in); Gnp is the normal pore pressure gradient (psi/ft or ppg); ECD is the equivalent

circulating density (psi/ft or ppg). The values of the dc – exponent computed over a uniform

lithological column (100% shale) are plotted against depth on the semi-log. Under normal

pressure conditions, the dc – exponent will increase with depth. In overpressure intervals, the dc –

exponent will undergo a trend reversal and the amount of deviation from the normal compaction

trend (NCT) at any given depth is directly related to the magnitude of overpressure. However,

the d – exponent technique does not consider the effect of hydraulic parameters on the ROP. This

can lead to inaccurate estimates of formation pore pressure under certain drilling conditions (soft

rock environments/unconsolidated formations). The driller can decide to increase the flow rate to

clean the hole or reduce the flow rate to minimize the equivalent circulating density (ECD) while

49
drilling the pressure transition zones. Under these conditions of altering the bit hydraulic energy,

the d – exponent method may fail to detect the onset of overpressure.

The mechanical specific energy (MSE) is the energy required to remove a unit volume of

rock (Teale, 1965). The MSE combines the axial and torsional loads. The MSE is given by:

WOB 120π ∗ N ∗ T
MSE = + , (2.5)
Ab Ab ROP

where MSE is the mechanical specific energy (psi); WOB is the weight on bit (lbs); Ab is the bit

area (in2); N is the rotary speed (rpm); T is the torque on bit (lb-ft); ROP is the rate of penetration

(ft/hr). In the absence of reliable downhole torque measurements, Pessier & Fear (1992)

expressed the downhole torque as a function of WOB, bit diameter and a bit specific coefficient

of sliding friction to eliminate the torque on bit requirement (equation 2.6):

WOB 13.33μ ∗ N ∗ WOB

MSE = + , (2.6)
Ab Db ROP

where MSE is the mechanical specific energy (psi); WOB is the downhole weight on bit (lbs); Ab

is the bit area (in2); N is the rotary speed (rpm); Db is the bit diameter (in); ROP is the rate of

penetration (ft/hr); μ is the bit specific coefficient of sliding friction. For field applications, the

value of bit coefficient of sliding friction is usually assumed to be 0.25 for roller cone bits and

0.5 for PDC bits (Armenta, 2008). However, the bit coefficient of sliding friction will depend on

lithology, rock confined compressive strength, mud weight, bit wear, and depth of cut (Caicedo

et al., 2005). Therefore, using a constant value of bit coefficient of sliding friction for a particular

bit over the entire drilled section may produce erroneous results. Armenta (2008) showed the

importance of bit hydraulic energy on the MSE. Zhou et al. (2017) established a relationship

50
between MSE and depth of cut. Most works on the applications of specific energy to drilling

operations have focused on drilling optimization and identification of downhole drilling

problems such as bit balling, bottom hole balling, bit wear, vibration and hole cleaning issues

(Waughman et al., 2003; Dupriest & Koederitz, 2005; Dupriest, 2006; Bevilacqua et al., 2013;

Abbas et al., 2014; Pinto & Lima, 2016).

The results of the experimental studies performed by Rafatian et al. (2010) on

impermeable and permeable rock samples using a single PDC cutter showed that the MSE

increases with the confining pressure. Similar experimental works by Akbari et al. (2013) on the

Torrey Buff rock samples concluded that the MSE at the underbalanced conditions were

considerably lower than the MSE at the balance conditions. Akbari et al. (2014) established an

empirical relationship among MSE, uniaxial compressive strength (UCS), differential pressure

and confining pressure. Akbari et al. (2014) then concluded that the effect of pore pressure on

MSE is similar to that of confining pressure but to a lesser degree and in the opposite direction.

Attempts have been made in recent times to estimate the formation pore pressure from the

mechanical specific energy (MSE) concept using the field data (Cardona, 2011; Majidi et al.,

2017). However, the applications of the MSE to pore pressure predictions have the same

limitations as the d – exponent method because the MSE approach does not consider the effect of

hydraulic parameters on the ROP. To overcome these limitations, this paper presents a new pore

pressure prediction technique based on the concept of hydro-rotary specific energy (HRSE). It

approximates the total energy required to break and remove a unit volume of rock.

2.2 Theoretical Background

The MSE proposed by (Teale, 1965) does not necessarily represent the total energy expended in

51
breaking and removing a unit volume of rock because it excludes the downhole (bit) hydraulic

energy component. The bit hydraulic energy weakens the formation ahead of the bit (especially

in medium to soft rock environments) and removes the cuttings from the bit face. The hydro-

mechanical specific energy (HMSE) is the actual total energy required to break and remove a

unit volume of rock (Mohan et al. 2015; Wei et al. 2016; Chen et al., 2016). The HMSE

combines the axial, rotary and hydraulic energy (equation 2.7):

Hydraulic Energy
HMSE = MSE + . (2.7)
Rock Volume Drilled

Ideally, not all the jet energy at the bit is available for rock penetration and cuttings removal.

Due to the accelerated fluid entrainment below the bit nozzles, only a fraction of the available jet

energy will reach the bottom of the hole. Therefore, a hydraulic energy reduction factor is

introduced into the hydraulics energy term (equation 2.8):

WOB 120πNT 1154η∆Pb Q

HMSE = + + , (2.8)
Ab Ab ROP Ab ROP

where HMSE is the hydro-mechanical specific energy (psi); WOB is the weight on bit (lbs); Ab

is the bit area (in2); N is the rotary speed (rpm); T is the torque on bit (lb-ft); ROP is the rate of

penetration (ft/hr); η is the hydraulic energy reduction factor; ∆Pb is the bit pressure drop (psi); Q

is the flow rate (gpm). The bit pressure drop can be expressed as a function of mud weight, flow

rate and nozzle total flow area (equation 2.9):

MW Q2
∆Pb = , (2.9)
10858 TFA2

where ∆Pb is the bit pressure drop (psi); MW is the mud weight (ppg); Q is the flow rate (gpm);
52
TFA is the total flow area (in2). The value of η ranges from 25 – 40 % (Warren, 1987).

According to Warren (1987), the actual value of η depends on the ratio of jet velocity to return

fluid velocity (equation 2.10):

−0.122
Jet Velocity
η= 1−[ ] . (2.10)
Return Bit Velocity at Bit Face

However, η can also be expressed as a ratio of bit return flow area to nozzle total flow area since

the flow rate is the same everywhere along the fluid flow path (equation 2.11):

Bit Return Flow Area −0.122

η= 1−[ ] . (2.11)
TFA

For roller cone bits, the bit return flow area is about 15 % of the bit area (in2) (equation 2.12):

0.15 Bit Area −0.122

ηRoller Cone Bit = 1−[ ] . (2.12)
TFA

For PDC bits, the bit area available for fluid return is equal to the junk slot area (equation 2.13):

JSA −0.122
ηPDC Bit = 1−[ ] , (2.13)
TFA

where JSA is the junk slot area (in2); TFA is the total flow area (in2). Equation 2.13 implies that

the amount of PDC bit hydraulic energy that is available at the bottom of the hole will increase

with increasing JSA and decreasing TFA for a given bit size. Therefore, for the roller cone bits,

the HMSE can be obtained by combining equations 2.8, 2.9 and 2.12 (equation 2.14):

0.15 Bit Area −0.122

0.10628 MW Q3 [1 − [ ] ]
WOB 120πNT TFA
HMSE = + + . (2.14)
Ab Ab ROP Ab ROP TFA2
53
Similarly, the HMSE for PDC bits is obtained from equations 2.8, 2.9 and 2.13 (equation 2.15):

JSA −0.122
WOB 120πNT 0.10628 MW Q3 [1 − [TFA] ]
HMSE = + + , (2.15)
Ab Ab ROP Ab ROP TFA2

In this study, the HMSE for PDC bits is considered as the reference case. Changes in the mud

weight/equivalent circulating density (ECD) will result in changes in the values of HMSE.

Excessive overbalance increases the strength of the surrounding rocks and the chip hold down

pressure at the bottom of the hole. This can cause the ROP to reduce and the HMSE to increase

when drilling through the pressure transition and overpressure zones. Hence, the HMSE must be

corrected for the effect of changes in the bottom-hole pressure (equation 2.16):

JSA −0.122
WOB 120πNT 0.10628 MW Q3 [1 − [TFA] ] Gnp
HMSE = + + ∗[ ], (2.16)
Ab Ab ROP Ab ROP TFA2 ECD
[ ]

where Gnp is the normal pore pressure gradient (psi/ft or ppg) and ECD is the equivalent

circulating density (psi/ft or ppg). The contribution of the axial energy due to WOB to the total

energy is less than 1% (Menand & Mills, 2017). The rotary and hydraulic energies make up over

99% of the HMSE term. Also, the rotary energy term in the HMSE equation has indirectly

accounted for the axial energy term because the downhole torque responds in direct proportion to

the WOB (Pessier & Fear, 1992). Hence, the axial energy term in the HMSE equation can be

neglected, leading to the concept of hydro-rotary specific energy (HRSE). The HRSE contains

only the rotary and hydraulic terms (equation 2.17):

54
 JSA −0.122
120πNT 0.10628 MW Q3 [1 − [TFA] ] Gnp
HRSE = + ∗[ ]. (2.17)
Ab ROP Ab ROP TFA2 ECD
[ ]

In normally pressured compacted series, rock density and degree of rock compaction will

increase with depth as pore fluids are being expelled gradually from the underlying sediments.

Under these conditions, rock porosity will decrease and grain – to – grain contact force will

increase with depth due to an increase in effective stress. Hence, the energy (HRSE) required to

remove a unit volume of rock will increase with depth. However, subsurface overpressure

conditions will cause a reversal in the HRSE trend as effective stress decreases. For overpressure

conditions associated with under-compaction, rock density and degree of rock compaction will

decrease as the formation water becomes trapped and begins to support the weights of the

overlying sediments. This will cause the rock porosity to increase and the grain – to – grain

contact force to decrease with a decrease in effective stress. The HRSE can also be applicable to

overpressure conditions caused by fluid expansion mechanisms because the ease of rock removal

is directly related to the differential pressure between the mud pressure and the pore pressure.

For accurate pore pressure prediction, downhole measurements data (torque and rotary

speed) from the measurement while drilling sensor (MWD) sensors should be used to compute

the HRSE. If surface measurements data are used instead, the HRSE will be grossly

overestimated, especially in deviated wells where there can be a significant amount of friction

between the drill string and the borehole walls along the well path. In a vertical well, it may be

possible to use the surface measurements data to compute HRSE because the friction between

the drill string and the borehole walls along the well path is negligible, provided there is no

excessive vibration of the bottom-hole assembly (BHA) and bit while drilling. There are various

ways in which downhole torque can be determined from the surface measurements if the
55
downhole sensors data are not available. The torque on bit (TOB) can be determined from the

difference between the on-bottom and off-bottom torque while drilling in rotary mode. The TOB

can be determined from the WOB value if the coefficient of sliding friction between the bit

cutters and the formation is known (Pessier & Fear, 1992). When drilling with the steerable

system (mud motor), the TOB can be computed from the differential pressure across the mud

motor. The TOB can also be calculated at any given depth using torque and drag (T & D) models

by subtracting the estimated drill string torque from the measured surface torque while drilling.

2.3 Methodology

Below are the steps required to estimate the formation pore pressure using HRSE concept. Figure

2.2 provides a simple workflow for the proposed methodology.

1. Compute the HRSE at various depths from the drilling, bit and well parameters using

equation 2.17. It is recommended that the HRSE be computed over the clean shale

intervals. This will eliminate any lithological effects on the HRSE. However, the HRSE

can also be computed over the entire lithological column that consists of several

stratigraphic units if the effect of lithology on the HRSE is not pronounced (i.e. no wide

variations in HRSE values due to different stratigraphic units being penetrated).

2. Plot the HRSE values against depth on a semi-log (Figure 2.1). Establish the normal

compaction trend (NCT) through the known normally pressured intervals. Under normal

pressure conditions, the HRSE will increase with depth. When the overpressure intervals

are penetrated, the HRSE will start to diminish. The amount of divergence of a given

point from the established NCT is proportional to the magnitude of the overpressure.

Figure 2.1 illustrates the application of the HRSE concept to overpressure prediction.

56
 From 8,000 ft-TVD to 13,000 ft-TVD, the HRSE values exhibit a normal compaction

trend. However, deviation in HRSE values from the normal compaction trend below

13,000 ft-TVD signifies the onset of overpressure.

Figure 2. 1 Illustration of the HRSE method for pore pressure prediction.

3. Compute the pore pressure at a given depth using the modified Eaton’s model given by:

HRSEo m
Gpp = G𝑜𝑏 − {Gob − Gnp } ∗ [ ] , (2.18)
HRSEn

where Gpp is the pore pressure gradient (psi/ft); Gob is the overburden gradient (psi/ft);

Gnp is the normal pore pressure gradient (NPPG) in psi/ft; HRSEo is the actual HRSE
57
 calculated using equation 2.17; HRSEn is the hypothetical value of HRSE from the

normal compaction trend; m is the HRSE exponent. The value of the HRSE exponent

will vary from region to region. The HRSE exponent can be derived by calibrating

equation 2.18 to any known overpressure intervals in the offset wells. It can also be

determined in the well being drilled by calibrating equation 2.18 to any overpressure

intervals predicted by the well log data (shale compressional sonic velocity and

resistivity) preferably while drilling the pressure transition zones.

Figure 2. 2 The work flow for the proposed methodology.

58
2.4 Field Example

To demonstrate the application of the HRSE concept to pore pressure prediction, a recently

drilled deep vertical exploratory gas well (well A) is considered as the case study. The well is

located about 80 km North-West of Port Harcourt in the Tertiary Deltaic System in the central

swamp region of the Niger Delta in Nigeria (Figure 2.3).

Figure 2. 3 Location map for well A.

59
The Niger Delta Basin is an extensional rift basin that consists of Tertiary clastic sediments up to

12 km thick. The Niger Delta sequence stratigraphy consists of three types of formations in

descending order: (1) Benin formations – consist of mainly continental sands, (2) Agbada

formations – consist of alternating sequence of sands and shales, and (3) Akata formations –

consist of marine shales (Short & Stauble 1967; Avbovbo 1978; Adewole et al. 2016). Well A

only penetrates Benin and Agbada formations. The hydrocarbons trapping mechanisms in the

Niger Delta are mainly growth faults associated with rollover structures. The primary cause of

the subsurface overpressure conditions in the Niger Delta is under-compaction (Daukoru 1975;

Ugwu & Nwankwo 2014). The Niger Delta sands have good porosity and permeability. Sands

with more than 25% porosity and permeability in the range of 1 – 5 Darcy are not uncommon.

In this paper, all depths are with respect to the true vertical depth (TVD) below the rotary table

(RT). Table 2.2 and Figure 2.4 provide information about the well configuration, mud type, BHA

type, bit type and the formations that were penetrated.

Table 2. 2 The well data summary.

Hole Size Casing Size Casing Depth Mud

Lithology BHA Bit Type
(inches) (inches) (feet) Type
Piled 30 307 Loose sands N/A N/A N/A

22 18 5/8 4,259 Continental sands WBM Steerable Roller cone

16 13 3/8 10,092 Sand - Shale WBM Steerable Roller cone

RSS &
12 ¼ 9 7/8 15, 224 Sand - Shale SOBM PDC
Steerable
8½ N/A N/A Sand - Shale SOBM RSS PDC

60
Figure 2. 4 The well configuration and lithology.

61
The 30’’ conductor pipe was driven to refusal at 307 ft. After cleaning the conductor pipe, the

22’’ hole was drilled from 307 ft to 4,269 ft. The 18 5/8’’ surface casing was run and cemented

to surface with the shoe at 4,259 ft. The 16’’ hole was drilled from 4,269 ft to 10,099 ft. The 13

3/8’’ intermediate casing was run to 10,092 ft and cemented in place. The 12 ¼’’ hole section

was drilled from 10,099 ft to 15,241 ft. The 9 5/8’’ production casing was run and cemented with

the shoe deep into the pressure transition shale at 15,224 ft to provide the required kick tolerance

to drill the 8 ½’’ hole overpressure intervals. The 8 ½’’ hole section was drilled from 15,241 ft to

15,567 ft and the well was suspended. Table 2.3 provides information about the bits used to drill

the hole sections of interest (12 ¼’’ and 8 ½’’). All the bits used were new bits prior to running

in hole except the 12 ¼’’, HCC, QD 507 FHX, M323 bit that was run as a re-run bit. There was no bit

grading for the last bit because it was lost in hole due to a pipe stuck incident that followed well

killing operations after taking a gas kick from the bottom of the well.

Table 2. 3 The bit data summary.

Drilled Intervals TFA JSA

Bit Data 2
Bit Dull Grade Out
(ft-TVD) (in ) (in2)
12 ¼’’, HCC, Q 506 F, M323 10099 - 15080 1.2824 31.48 2-5-WT-G-X-1-CT-BHA

12 ¼’’, HCC, QD 507 FHX, M323 15080 - 15241 1.2962 21.28 1-2-CT-S-X-1-NO-TD

8 ½’’, HCC, DPD 506, M223 15241 - 16159 0.7777 13.94 1-2-WT-A-X-1-NO-DTF

8 ½’’, HCC, QD 408 FHX, M433 16159 - 16567 0.7823 10.97 N/A

The top-hole sections (22’’ & 16’’) are excluded from the analysis because data acquisitions in

these sections were limited and the sections consist of predominantly unconsolidated sands with

no hydrocarbon-bearing or overpressure intervals. The data analysis is focused on the deeper 12

¼’’ and 8 ½’’ hole sections drilled with mostly rotary steerable system (RSS) assemblies and
62
polycrystalline diamond compact (PDC) bits. These sections consist of hydrocarbon bearing

intervals, normally pressured compacted series, pressure transition zones and overpressure

intervals. The drilling parameters were acquired every 1 ft and out of range (unrealistic) data

were filtered out. Figure 2.5 shows the plots of the actual drilling parameters acquired while

drilling well A. The TOB values were computed from the difference between the measured on-

bottom and off-bottom torque (dark-blue colour) and were validated with the TOB values

estimated from the T & D model (pink colour).

The overburden pressure (Sv ) can be obtained by integrating the formation bulk density

from the surface to the depth of interest and it is given by:

Sv
z
= 0.433 ∫ ρb dz , (2.19)
0

ρb = 0.9526 Z 0.101 , (2.20)

where ρb is the formation bulk density as a function of depth (g/cc); Z is the depth of interest

(ft). In well A, the density log was only acquired in the 12 ¼’’ hole. To obtain the overburden

pressure at each depth of interest, the density log in the 12 ¼’’ hole section of this well was

integrated with the offset well density log to produce the equation of best fit (equation 2.20). The

equation of best fit was then used to compute the formation bulk density values in the intervals

where the density log data were not available. The overburden gradient (Gob) was obtained by

dividing the overburden pressure by the true vertical depth. Figure 2.6 shows the plots of

formation bulk density, overburden pressure and overburden gradient versus depth for well A.

63
Figure 2. 5 The plots of drilling parameters versus depth for well A.

64
Figure 2. 6 The plots of formation bulk densities, overburden pressure and overburden gradient versus depth for well A.

65
2.5 Discussion

The plot of HRSE versus depth is shown in Figure 2.7. The HRSE values are computed across

the sand and shale intervals because the effect of lithology on the HRSE is not pronounced in

this well and the normal compaction trend can be clearly identified. From 11,600 ft to 15,060 ft,

the HRSE increases with depth due to an increase in vertical effective stress. These depth

intervals correspond to the normally pressured compacted series in the field with a pore pressure

gradient of 0.45 psi/ft and they are used to establish the NCT. Below the 15,060 ft (top of

overpressure), the HRSE begins to undergo a departure from the NCT to lower values due to the

presence of subsurface overpressure conditions. As the formation pore pressure increases in the

under-compacted series (decrease in vertical effective stress), the degree of rock compaction

decreases. Under these conditions, the energy required to remove a unit volume of rock (HRSE)

decreases. Hence, the reversal in the HRSE trend can be used to identify the overpressure

intervals. From Figure 2.7, the HRSE clearly identifies the top of overpressure (15,060 ft), the

pressure transition intervals (15,060 – 15,400 ft) and the overpressure zones (>15,400 ft).

Figure 2.7 also shows the plots of dc – exponent, gamma ray (GR) and shale

compressional sonic velocity versus depth. The dc – exponent values are computed using

equation 2.4. In the intervals that correspond to the normally pressured zones, the dc – exponent

and shale compressional sonic velocity increase with depth (similar in trend to HRSE). Below

the top of overpressure at 15,060 ft, the dc – exponent, and shale compressional sonic velocity

start to deviate from the NCT to lower values in the same manner as HRSE. Increase in

formation pore pressure (decrease in vertical effective stress) causes a reversal in the dc –

exponent and shale compressional velocity trends.

66
Figure 2. 7 The plots of HRSE, dc – exponent, gamma ray, and shale compressional sonic velocity versus depth for well A.

67
It is relatively easy to attribute the reversal in the HRSE trend in the 12 ¼’’ hole to a new bit

change. A critical review of the well information suggests otherwise. The first bit (12 ¼’’, HCC,

Q 506 F, M323) penetrated about 20 ft into the pressure transition zones before being pulled out

of hole. The bit was pulled out of hole to change the BHA configuration so that the logging

while drilling (LWD) sensors for pore pressure predictions (GR, sonic and resistivity) could be

placed closer to the bit. The gradual (not sudden) decrease in the HRSE, with the corresponding

decrease in the dc – exponent and shale compressional sonic velocity below 15,060 ft in the 12

¼’’ hole section suggests that the reversal in HRSE trend is most likely due to the presence of

subsurface overpressure conditions rather than the bit change. Finally, a drill bit change that

occurred in the 8 ½’' hole section at 16,159 ft did not produce any corresponding shift in HRSE

and dc – exponent trends. It should be noted that efficient/improved drilling conditions can also

result in the reversal of the HRSE trend. Hence, any reversal in the HRSE trend while drilling

should be investigated especially while drilling the exploratory wells. The gradual reversal in the

HRSE trend, with corresponding reversal in the shale petrophysical properties (compressional

sonic velocity, density and resistivity) will most likely indicate the presence of overpressure. The

sudden reversal in the HRSE trend with no corresponding reversal in the shale petrophysical

properties will most likely indicate efficient/improved downhole drilling conditions.

Figure 2.8 compares the pore pressure estimates derived from the HRSE, dc – exponent,

and shale compressional velocity to the actual pore pressure measurements taken in the reservoir

sands of interest. The actual pore pressure measurements were obtained from the combination of

formation pressure while drilling tool (Tes-Trak), wireline pressure sampling tool (RCX -

reservoir characterization explorer) and gas kick data. The pore pressure estimates from the shale

compressional velocity and dc – exponent are derived from Eaton’s models (equations 2.2 and

68
2.3 respectively). The pore pressure estimates from the HRSE are derived from equation 2.18

with the value of the HRSE exponent (m) equal to 0.32. The HRSE exponent is obtained by

calibrating equation 2.18 to the pore pressure estimates derived from the sonic log data in the

upper sections of the pressure transition zones (15,060 – 15,300 ft). A single constant value of

8.66 ppg (0.45 psi/ft) average equivalent density is used for the normal pore pressure gradient

(NPPG) based on the formation water density/salinity in the region. From Figure 2.8, The HRSE

predicts the formation pore pressure gradient to be normal down to 15,060 ft with an average

value of 0.45 psi/ft. In the transition zones, the HRSE predicts a gradual shift from the normal

pore pressure regime to overpressure regime (the formation pore pressure gradient increases

from 0.45 psi/ft to 0.68 psi/ft). In the overpressure intervals, the formation pore pressure gradient

predicted by HRSE increases further from 0.68 psi/ft at 15,400 ft to 0.81 psi/ft at 16,250 ft. The

formation pore pressure gradient then remains relatively constant at 0.81 psi/ft from 16,250 ft to

the well total depth. There is an excellent agreement in magnitude and trend between the pore

pressure estimates derived from the HRSE concept and the actual pore pressure measurements.

The shale compressional sonic velocity also provides good estimates of the formation pore

pressure. However, the shale compressional sonic velocity is unable to provide the pore pressure

estimates at the well TD because of the offset between the bit and the acoustic sensors. The d –

exponent method provides good estimates in the deeper sections of the well but over-predicts the

formation pore pressure in the intervals immediately below the pressure transition zones,

reaching a formation pore pressure of 0.81 psi/ft just below 15,400 ft. From the drilling

optimization perspective, using the pore pressure estimates derived from the d – exponent

method to design the mud weight (MW) required to drill through the intervals just below the

transition zones with an average actual formation pore pressure of 0.72 psi/ft will create an

69
excessive overbalance, which can result in ROP reduction. If the next casing depth or total depth

is to be called off before drilling through the intervals with formation pore pressure of 0.81 psi/ft,

using the pore pressure estimates derived from the d – exponent method to design the mud

weight may also result in lost circulation and pipe sticking incidents. Although the d – exponent

method over-predicts the formation pore pressures in some overpressure intervals, it is relatively

accurate in this well (in the deeper sections) because the downhole drilling conditions are

suitable to its applications. The well is vertical, the bit hydraulic energy is relatively constant in

each hole section and the rocks are consolidated (shale compressional sonic velocity is greater

than 3,387 m/s above the overpressure intervals). Table 2.4 summarizes the main differences

between HRSE and d – exponent.

Table 2. 4 Main differences between HRSE and d – exponent.

HRSE d – exponent

1 Exclude the WOB term Include WOB term

2 Include the torque term Exclude torque term

Excluded the bit hydraulic energy term.

Include the bit hydraulic energy term. Consider
3 Does not consider variations in bit
variations in bit hydraulic energy.
hydraulic energy

Can be applicable to hard and soft rock Mostly suitable for hard rock

4 environments. Soft rocks are more response to environments. Hard rocks are more

rotary speed and bit hydraulics than WOB. response to WOB.

70
Figure 2. 8 Measured and estimated pore pressure profiles for Well A.

71
2.6 Conclusions

A new pore pressure prediction technique based on the amount of energy expended while drilling

is being proposed. This is based on the principle that overpressure intervals with lower effective

stress will require less energy to drill than the normally pressured intervals at the same depth.

Under normal pressure conditions, the HRSE will increase with depth as rock compaction and

effective stress increase. Drilling through the overpressure zones will cause a reversal in the

HRSE trend. The field example presented in this paper demonstrates the applicability of the

HRSE method in predicting the onset of overpressure and estimating the formation pore

pressure. An excellent agreement is observed in magnitude and trend between the pore pressure

estimates derived from the HRSE concept and the actual pore pressure measurements. The

formation pore pressure prediction accuracy from the HRSE concept is also comparable to

compressional sonic velocity. Unlike the d-exponent method, the HRSE method includes the bit

hydraulic energy term, thereby extending its application to some drilling environments (soft rock

environments/unconsolidated formations, varying jet hydraulic energy, etc.) where the d-

exponent method may not work.

However, the ability of the HRSE method to predict the onset of overpressure and its

magnitude will depend greatly on the quality of the input data. TOB measurements from the

bit/BHA subjected to vibrations (axial, torsional/stick-slip, whirl) will produce erroneous results.

Computed TOB from the surface data will produce inaccurate results if the BHA is subjected to

downhole buckling conditions. Excessive bit wear and bit balling can also mask the reversal in

the HRSE trend when drilling through the pressure transition zones. To improve the quality of

the input data, downhole sensors should be properly calibrated before run in hole. Noise should

be minimized in the data transmission system. Shocks and vibrations should be minimized while

72
drilling (optimize BHA design, bit selection, shock sub application for axial vibration, drilling

parameters optimization). Multiple sources of measurements should be made for comparison

purposes. For example, the TOB from the downhole sensors should be compared to surface

derived TOB. If possible, avoid changing from the bit type in the same hole interval (e.g. from

roller cone bit to PDC bit). Compute the HRSE over clean shale intervals only if the effect of

lithology is noticed on the HRSE.

2.7 Reference

Abbas, K.R., Hassanpou, A., Hare, C., Ghadiri, M., 2014. “‘Instantaneous Monitoring of Drill
Bit Wear and Specific Energy as a Criteria for the Appropriate Time for Pulling Out Worn
Bits.’” Soc. Pet. Eng. (SPE 172269).
Adewole, E.O., Macdonald, D.I.M., Healy, D., 2016. Estimating density and vertical stress
magnitudes using hydrocarbon exploration data in the onshore Northern Niger Delta Basin,
Nigeria: Implication for overpressure prediction. J. African Earth Sci. 123, 294–308.
https://doi.org/10.1016/j.jafrearsci.2016.07.009
Akbari, B., Miska, S., Mengjiao, Y., Ozbayoglu, E., 2013. Effect of Rock Pore Pressure on
Mechanical Specific Energy of Rock Cutting Using Single PDC Cutter. Am. Rock Mech.
Assoc. (ARMA 13-205).
Akbari, B., Miska, S., Yu, M., Ozbayoglu, M., 2014. Experimental Investigations of the Effect of
the Pore Pressure on the MSE and Drilling Strength of a PDC Bit. Soc. Pet. Eng. (SPE
169488). https://doi.org/10.2118/169488-MS
Armenta, M., 2008. Identifying Inefficient Drilling Conditions Using Drilling-Specific Energy.
Soc. Pet. Eng. (SPE 116667). https://doi.org/10.2118/116667-MS
Atashbari, V., Tingay, M., 2012. Pore Pressure Prediction in a Carbonate Reservoir. Soc. Pet.
Eng. (SPE 150836).
Avbovbo, A.A., 1978. Tertiary lithostratigraphy of the Niger Delta. Am. Assoc. Pet. Geol. Bull.
62, 295–306.
Belonin, M.D., Slavin, V.I., 1998. Abnormally high formation pressures in petroleum regions of

73
 Russia and other countries of the C.I.S. Law, B.E., G.F. Ulmishek, V.I. Slavin eds.,
Abnorm. Press. Hydrocarb. Environ. AAPG Mem. 70, 115–121.
Bevilacqua, M., Ciarapica, F.E., Marchetti, B., 2013. Acquisition, Processing and Evaluation of
Down Hole Data for Monitoring Efficiency of Drilling Processes. J. Pet. Sci. Res. 2, 49–56.
Black, A.D., Dearing, H.L., DiBona, B.G., 1985. Effects of Pore Pressure and Mud Filtration on
Drilling Rates in a Permeable Sandstone. J. Pet. Technol. 37, 1671–1681.
https://doi.org/10.2118/12117-PA
Bowers, G.L., 1995. Pore pressure estimation from velocity data: Accounting for overpressure
mechanisms besides undercompaction. SPE Drill. Complet. 10, 89–95.
https://doi.org/10.2118/27488-PA
Brahma, J., Sircar, A., Karmakar, G.P., 2013. Pre-drill pore pressure prediction using seismic
velocities data on flank and synclinal part of Atharamura anticline in the Eastern Tripura,
India. J. Pet. Explor. Prod. Technol. 3, 93–103. https://doi.org/10.1007/s13202-013-0055-0
Caicedo, H.U., Calhoun, W.M., Ewy, R.T., 2005. Unique ROP Predictor Using Bit-specific
Coefficient of Sliding Friction and Mechanical Efficiency as a Function of Confined
Compressive Strength Impacts Drilling Performance. Soc. Pet. Eng. (SPE/IADC 92576).
https://doi.org/10.2118/92576-MS
Cardona, J., 2011. Fundamental Investigation of Pore Pressure Prediction during Drilling from
the Mechanical Behaviour of Rocks. PhD Thesis, Texas A&M Univ. Mech. Eng.
Chen, X., Gao, D., Guo, B., Feng, Y., 2016. Real-time optimization of drilling parameters based
on mechanical specific energy for rotating drilling with positive displacement motor in the
hard formation. J. Nat. Gas Sci. Eng. 35, 686–694.
https://doi.org/10.1016/j.jngse.2016.09.019
Combs, D.G., 1968. Prediction o Pore Pressure From Penetration Rate. Soc. Pet. Eng. (SPE
2162).
Cunningham, R. a, Eenink, J.G., 1959. Laboratory Study of Effect of Overburden, Formation and
Mud Column Pressures on Drilling Rate of Permeable Formations. Pet. Trans. AIME 217,
9–17.
Daukoru, J.W., 1975. PD 4(1) Petroleum Geology of the Niger Delta. World Pet. Congr.
Dupriest, F.E., 2006. Comprehensive Drill-Rate Management Process To Maximize Rate of
Penetration. Soc. Pet. Eng. (SPE 102210). https://doi.org/10.2118/102210-MS

74
Dupriest, F.E., Koederitz, W.L., 2005. Maximizing Drill Rates with Real-Time Surveillance of
Mechanical Specific Energy. Soc. Pet. Eng. (SPE/IADC 92194).
https://doi.org/10.2118/92194-MS
Eaton, B.A., 1975. The Equation for Geopressure Prediction from Well Logs. Soc. Pet. Eng.
(SPE 5544 ). https://doi.org/10.2118/5544-MS
Ebrom, D., Heppard, P., Albertin, M., 2006. OTC 18399 Travel-Time Methods of Vp / Vs
Determination for Pore Pressure Prediction Using Lookahead VSPs. Offshore Technol.
Conf. (OTC 18399).
El-Werr, A., Shebl, A., El-Rawy, A., Al-Gundor, N., 2017. Pre-drill pore pressure prediction
using seismic velocities for prospect areas at Beni Suef Oil Field, Western Desert, Egypt. J.
Pet. Explor. Prod. Technol. 7, 1011–1021. https://doi.org/10.1007/s13202-017-0359-6
Foster, J.B., Whalen, H.E., 1966. Estimation of formation pressures from electrical surveys -
Offshore Louisiana. J. Pet. Technol. 18, 165–171. https://doi.org/10.2118/1200-PA
Gardner, G.H.., Gardner, L.., Gregory, A.., 1974. Formation Velocity and Density - The
Diagnostic Basic for Stratigraphic Traps. Geophysics 39, 770–780.
Harper, D., 1969. New Findings From Over Pressure Detection Curves In Tectonically Stressed
Beds. Soc. Pet. Eng. (SPE 2781).
Holm, G.M., 1998. Distribution and origin of overpressure in the Central Graben of the North
Sea. Law, B.E., G.F. Ulmishek, V.I. Slavin eds., Abnorm. Press. Hydrocarb. Environ.
AAPG Mem. 70, 123–144.
Hottmann, C.E., Johnson, R.K., 1965. Estimation of formation pressures from log-derived shale
properties. J. Pet. Technol. SPE 1110, 717–722. https://doi.org/10.2118/1110-PA
Hunt, J.M., 1990. Generation and migration of petroleum from abnormally pressured fluid
compartments. Am. Assoc. Pet. Geol. Bull. https://doi.org/10.1306/0C9B27E5-1710-11D7-
8645000102C1865D
Kumar, A., Gunasekaran, K., Bhardwaj, N., Dutta, J., Banerjee, S., 2016. Technical papers t
Origin and distribution of abnormally high pressure in the Mahanadi Basin , east coast of
India. Interpretation 4, 303–311. https://doi.org/10.1190/INT-2015-0087.1
Li, Q., Heliot, D., Zhao, L., Chen, Y., 2000. Abnormal Pressure Detection and Wellbore Stability
Evaluation in Carbonate Formations of East Sichuan , China. Soc. Pet. Eng. (IADC / SPE
59125).

75
Majidi, R., Albertin, M., Last, N., 2017. Pore-Pressure Estimation by Use of Mechanical Specific
Energy and Drilling Efficiency. 2017 SPE Drill. Complet. J. (SPE 178842).
Menand, S., Mills, K., 2017. Use of Mechanical Specific Energy Calculation in Real-Time to
Better Detect Vibrations and Bit Wear While Drilling. Am. Assoc. Drill. Eng.
Mohan, K., Adil, F., Samuel, R., 2015. Comprehensive Hydromechanical Specific Energy
Calculation for Drilling Efficiency. J. Energy Resour. Technol. 137, 012904.
https://doi.org/10.1115/1.4028272
Nashaat, M., 1998. Abnormally high formation pressure and seal impacts on hydrocarbon
accumulations in the Nile Delta and North Sinai basins, Egypt. Law, B.E., G.F. Ulmishek,
V.I. Slavin eds., Abnorm. Press. Hydrocarb. Environ. AAPG Mem. 70 161–180.
Pennebaker, E.., 1968. Detection of Abnormal-pressure Formations from Seismic- Field Data.
Am. Pet. Inst. 184–191.
Pessier, R.C., Fear, M.J., 1992. Quantifying Common Drilling Problems With Mechanical
Specific Energy and a Bit-Specific Coefficient of Sliding Friction. Soc. Pet. Eng. (SPE
24584). https://doi.org/10.2118/24584-MS
Pinto, C.N., Lima, A.L.P., 2016. Mechanical Specific Energy for Drilling Optimization in
Deepwater Brazilian Salt Environments. Soc. Pet. Eng. (IADC/SPE 180646).
https://doi.org/10.2118/180646-MS
Plumley, J.W., 1980. Abnormally High Fluid Pressure: Survey of Some Basic Principles:
ERRATUM. Am. Assoc. Pet. Geol. Bull. 64, 414–422. https://doi.org/10.1306/2F919409-
16CE-11D7-8645000102C1865D
Polutranko, A.J., 1998. Causes of Formation and Distribution of Abnormally High Formation
Pressure in Petroleum Basins of Ukraine. Law, B.E., G.F. Ulmishek, V.I. Slavin eds.,
Abnorm. Press. Hydrocarb. envi- ronments AAPG Mem. 70 181–194.
https://doi.org/10.1130/0091-7613(1998)026<0911
Rafatian, N., Miska, S., Ledgerwood III, L.W., Ahmed, R., Yu, M., Takach, N., 2010.
Experimental Study of MSE of a Single PDC Cutter Interacting With Rock Under
Simulated Pressurized Conditions. SPE Drill. Complet. 25, 10–18.
https://doi.org/10.2118/119302-MS
Rehm, B., Mcclendon, R., 1971. Measurement of Formation Pressure from Drilling Data. Soc.
Pet. Eng.

76
Saleh, S., Williams, K., Rizvi, A., 2013. Predicting Subsalt Pore Pressure with Vp/Vs. Offshore
Technol. Conf. (OTC 24157).
Satti, I.A., Yusoff, W.I.W., 2015. A New Method for Overpressure Mechanisms Analysis. Soc.
Pet. Eng. (SPE 176357).
Sayers, C.M., Johnson, G.M., Denyer, G., 2002. Predrill pore-pressure prediction using seismic
data. Geophysics 67, 1286–1292. https://doi.org/10.1190/1.1500391
Serebryakov, V.A., Chilingar, G. V., Katz, S.A., 1995. Methods of estimating and predicting
abnormal formation pressures. J. Pet. Sci. Eng. 13, 113–123. https://doi.org/10.1016/0920-
4105(95)00006-4
Short, K.., Stauble, A.., 1967. Outline of Geology of Niger Delta. Am. Assoc. Pet. Geol. Bull.
51, 761–779.
Slavin, V.I., Smirnova, E.M., 1998. Abnormally high formation pressures: origin, prediction,
hydrocarbon field development, and ecological problems. Law, B.E., G.F. Ulmishek, V.I.
Slavin eds., Abnorm. Press. Hydrocarb. Environ. AAPG Mem. 70 105–114.
Soleymani, H., Riahi, M.A., 2012. Velocity based pore pressure prediction-A case study at one
of the Iranian southwest oil fields. J. Pet. Sci. Eng. 94–95, 40–46.
https://doi.org/10.1016/j.petrol.2012.06.024
Spencer, C.W., 1987. Hydrocarbon Generation as a Mechanism for Overpressuring in Rocky
Mountain Region. Am. Assoc. Pet. Geol. Bull. 71, 368–388.
https://doi.org/10.1306/94886EB6-1704-11D7-8645000102C1865D
Swarbrick, R.E., 1995. Distribution and Generation of the Overpressyre System, Eaastern
Delaware BAsin, Western Texas and Southern New Mexico: Discussion. Am. Assoc. Pet.
Geol. Bull. 12, 1386–1405.
Swarbrick, R.E., Osborne, M.J., 1998. Mechanisms that generate abnormal pressures: an
overview. Law, B.E., G.F. Ulmishek, V.I. Slavin eds., Abnorm. Press. Hydrocarb. Environ.
AAPG Mem. 70 13–34.
Teale, R., 1965. The Concept of Specific Energy in Rock Drilling. Int. J. Rock Mech. Min. Sci.
2, 57–73. https://doi.org/10.1016/0148-9062(65)90022-7
Ugwu, S.A., Nwankwo, C.N., 2014. Integrated approach to geopressure detection in the X-field,
Onshore Niger Delta. J. Pet. Explor. Prod. Technol. 4, 215–231.
https://doi.org/10.1007/s13202-013-0088-4

77
Vidrine, D.J., Benit, E.J., 1968. Field Verification of the Effect of Differential Pressure on
Drilling Rate. J. Pet. Technol. (SPE 1859) 20, 676–682. https://doi.org/10.2118/1859-PA
Walls, J., Dvorkin, J., Mavko, G., Nur, A., 2000. Use of Compressional and Shear Wave
Velocity for Overpressure Detection. Offshore Technol. Conf. (OTC 11912).
Wardlaw, H.W.R., 1969. Drilling Performance Optimization and Identification of Overpressure.
Soc. Pet. Eng. AIME SPE 2388, 67–78.
Warren, T.M., 1987. Penetration Rate Performance of Roller Cone Bits. SPE Drill. Eng. 2, 9–18.
https://doi.org/10.2118/13259-PA
Waughman, J.R., Kenner, V.J., Moore, A.R., 2003. Real-Time Specific Energy Monitoring
Enhances the Understanding of When To Pull Worn PDC Bits. SPE Drill. Complet. (SPE
81822) 59–68.
Wei, M., Li, G., Shi, H., Shi, S., Li, Z., Zhang, Y., 2016. Theories and Applications of Pulsed-Jet
Drilling With Mechanical Specific Energy. SPE J. (SPE 174550) 303–310.
Yassir, N., Bell, J., others, 1996. Abnormally high fluid pressures and associated porosities and
stress regimes in sedimentary basins. SPE Form. Eval. 11, 5–10.
https://doi.org/10.2118/28139-PA
Zhang, J., 2013. Effective stress, porosity, velocity and abnormal pore pressure prediction
accounting for compaction disequilibrium and unloading. Mar. Pet. Geol. 45, 2–11.
https://doi.org/10.1016/j.marpetgeo.2013.04.007
Zhang, J., 2011. Pore pressure prediction from well logs: Methods, modifications, and new
approaches. Earth-Science Rev. 108, 50–63. https://doi.org/10.1016/j.earscirev.2011.06.001
Zhou, Y., Zhang, W., Gamwo, I., Lin, J.S., 2017. Mechanical specific energy versus depth of cut
in rock cutting and drilling. Int. J. Rock Mech. Min. Sci. 100, 287–297.
https://doi.org/10.1016/j.ijrmms.2017.11.004

78
 Chapter 3

3.0 Energy-based Formation Pressure Prediction

Preface

A version of this chapter has been published in the Journal of Petroleum Science and

Engineering, 2019. I am the primary author. Co-author Dr. Stephen Butt reviewed the

manuscript and provided technical assistance in the development of the concept. I formulated the

initial concept and carried out most of the data analysis. I prepared the first draft of the

manuscript and revised the manuscript based on the feedback from the co-author and peer

review process. The co-author also helped to refine the concept.

Abstract

Conventionally, pore pressure predictions from the drilling parameters have the advantage of

estimating the formation pressure at the bit at relatively low cost. The limitations on the

application of the d-exponent concept to pore pressure prediction have long been established.

Recent developments in pore pressure prediction from the drilling parameters use the concept of

mechanical specific energy (MSE) and hydro-rotary specific energy (HRSE). These energies are

usually computed from the downhole measurements. However, the majority of readily available

field data in older (offset) and present-day wells are in the form of surface measurements. In this

paper, a new pore pressure prediction technique based on the concept of hydro-mechanical

specific energy (HMSE) is being proposed. The HMSE is the combination of axial, rotary and

hydraulic energies required to break and remove a unit volume of rock. The new technique uses

drilling parameters that are obtained only from surface measurements. Pore pressure prediction

using the concept of HMSE is based on the theory that total energy consumed in breaking and

79
removing a unit volume of rock beneath the bit is a function of effective stress: the higher the

effective stress, the greater the total energy required to break and remove a unit volume of rocks.

Abnormally high formation pressure intervals with lower effective stress will require less energy

to drill than the normally compacted series at the same depth. The new technique is tested using

a recently drilled near-vertical deep High-Pressure High-Temperature (HPHT) exploratory well

in the Tertiary Deltaic System of the Niger Delta basin where the main cause of overpressure

mechanism is under-compaction. The well drilled to a total depth of more than 17,000 ft-TVD,

covers the normally compacted series, pressure transition zones and overpressure intervals. Pore

pressure estimates derived from the HMSE concept are then compared to the actual pore pressure

measurements taken from the formations of interest. There is an excellent agreement between the

predicted and measured formation pore pressure. The new technique can provide a reliable

means of estimating the formation pore pressure from the drilling parameters in the absence of

reliable downhole measurements at relatively low cost.

Keywords: Pore pressure, Effective Stress, Hydro-mechanical Specific Energy, Mechanical

Specific Energy, Normal Compaction Trend.

3.1 Introduction

Pore pressure is the pressure of the formation fluids contained in the pore spaces of rocks.

Accurate knowledge of formation pore pressure is required at all stages of the field development

plan. It is perhaps the single most important input parameter used for well planning and design.

From a well construction point of view, pore pressure data are used for rig sizing, casing depths

determination, cement design, drilling and completion fluid design, wellheads/christmas tree

design, casing and tubing design, and equipment selection. Having accurate knowledge of the

80
formation pore pressure will help to optimize drilling rate, prevent well control incidents

(kicks/blowout), reduce the risk of differential sticking of pipes and minimize formation damage.

Pore pressure data are also used for production forecast/well performance analysis, reservoir

modeling, subsurface trap integrity determination, and geo-mechanical analysis. Pore pressure

prediction is very important to exploration, drilling, and production of oil and gas since

hydrocarbons distribution around the world is directly related to the subsurface pressure and

temperature conditions.

The formation pore pressure is normal if it is able to support a continuous column of

static formation water from surface to formation depth of interest without any losses or excess

surface pressure (Swarbrick and Osborne, 1998). Louden (1972) defined the normal pore

pressure gradient as the lithological gradient for a saltwater basin. The value of the normal pore

pressure gradient varies from region to region depending on pore fluid type, formation

temperature and concentration of dissolved salts in the formation water. Even within the same

geological basin, normal pore pressure gradient may vary from one depth to the other. Generally,

normal pore pressure gradient varies between 0.433 – 0.515 psi/ft. For the North Sea, the average

normal pore pressure gradient is 0.45 psi/ft (Holm, 1998). In the Gulf Coast, the average normal

pore pressure gradient is 0.465 psi/ft (Harkins & Baugher, 1969; Parker, 1973). In the Rocky

Mountain regions in Canada and USA, it is approximately 0.433 psi/ft (Finch, 1969). Intervals

with pore pressure gradient higher or lower than the normal pore pressure gradient are termed

abnormally high (overpressure) or abnormally low (subnormal) respectively.

Subnormal pressure regimes can result from geological and production conditions. The

geological conditions can be tectonic, stratigraphic or geochemical in nature. The production

condition relates to reservoir depletion that results from fluids withdrawal from a rock where the

81
rate of fluid influx into the rock is significantly less than the rate of formation fluids withdrawal.

Barker (1972) suggested that if a reservoir under normal pressure conditions becomes isolated

with permeability barriers and is then subjected to a temperature decrease, the reservoir pressure

will fall below the normal hydrostatic pressure causing subnormal pressure conditions. These

conditions can occur during sediments erosion and upliftment whereby sediments from the

deeper zones are moved to shallower depths. Subnormal pressure conditions have been reported

in some sedimentary basins around the world (Serebryakov & Chilingar, 1994; Bachu &

Underschultz, 1995; Dickey & Cox, 1977). The presence of subnormal pressure conditions in the

subsurface formations can cause drilling problems such as lost circulation, differential sticking,

underground blowout, and a potential surface blowout.

There are five main mechanisms of overpressure generation (Yassir et al., 1996). The

first mechanism is compaction disequilibrium - this occurs when the rate of deposition of

sediments is greater than the rate of expulsion and migration of interstitial fluids (usually water).

The water becomes trapped and begins to support the weights of the overlying sediments since

there is no enough time for the water to escape. This usually occurs when rapid sedimentation

involves large quantities of clay materials (Carlin and Dainelli, 1998). In young sedimentary

basins with thick terrigenous rocks, compaction disequilibrium is the dominant cause of

abnormally high formation pressure (Law and Spencer, 1998; Tingay et al., 2009). Other causes

of overpressure mechanisms are generally small compared to compaction disequilibrium

(Burrus, 1998). Most shallow water flows arising from the overpressure conditions near the mud

line in the offshore Gulf of Mexico (GOM) were attributed to compaction disequilibrium (Sayers

et al., 2005). The second mechanism is tectonic activities – tectonic events such as folding,

faulting and diapirism can result in subsurface overpressure conditions (Law et al., 1998). The

82
third mechanism is clay diagenesis – between 90 – 150oC, montmorillonite undergoes a

transformation and is converted into illite, releasing a large amount of water in the process

(Powers, 1967; Burst, 1969; Burst, 1976, Freed & Peacor, 1989; Buryakovsky et al., 1995). The

threshold temperature requires for clay diagenesis to occur varies from region to region. It ranges

from about 71 °C for Mississippi River sediments in the US to more than 150°C for the Niger

Delta sediments in Nigeria (Bruce, 1984). The fourth mechanism is aqua-thermal expansion –

formation temperature increases as the depth of burial of sediments increases. This causes fluid

expansion with subsequent increase in the formation pore (Barker, 1972; Chen & Huang, 1996;

Barkers & Horsfield, 1982; Sharp, 1983; Polutranko, 1998; Lewis & Rose, 1970). The last major

overpressure mechanism is hydrocarbon generation – thermal cracking of kerogen into liquid and

gaseous hydrocarbons can result in a significant increase in pore volume leading to overpressure

conditions by (Law & Dickinson, 1985; Spencer, 1987; Holm, 1998; Hunt et al., 1998). This is

also applicable to thermal cracking of liquid hydrocarbons into gaseous hydrocarbons. Other

causes of subsurface overpressure conditions include oil and gas occurrence, artesian effect,

centroid effects and charging from other zones. Overpressure generation due to buoyancy effect

can also occur in thick gas-filled reservoirs (Swarbrick and Osborne, 1998; Aadnoy, 2010). The

amount of overpressure within the gas accumulation is a function of the gas gradient and the

height of the gas column.

It should be noted that combination of the above mechanisms can create subsurface

overpressure conditions within the same sedimentary basin (Plumley, 1980; Kadri, 1991; Freire

et al., 2010; Satti et al., 2015; Satti et al., 2016). For example, in a deltaic environment where

sedimentation rate is high, compaction disequilibrium may initially be the cause of abnormally

high formation pressures. As the formation temperature increases from the increasing depth of

83
burial, hydrocarbon generation, clay diagenesis, and aqua-thermal expansion may compliment

compaction disequilibrium as the main cause of overpressure mechanisms. Drilling into

abnormally high formation pressure intervals unexpectedly can lead to catastrophic and process

safety incidents such as surface blowouts. This can result in costly drilling expenses, loss of lives

and properties, loss of reputations and damage to environments. To minimize the risks of a well

blowout, it is therefore extremely important to be able to detect overpressure intervals before

drilling into them. The best approach for the detection and evaluation of overpressure intervals is

to compare the pore pressure estimates derived from various independent sources (seismic, well

logs and drilling parameters) since relying on any single technique can result in

misinterpretations especially when drilling exploratory wells (Fertl & Timko, 1971).

Most pore pressure prediction techniques rely on the hypothesis that overpressure

intervals have higher porosity than normally pressured intervals for any given depth. However,

it is also possible not to have any trend reversal between the normal pressure and overpressure

intervals when porosity indicators (resistivity, compressional sonic velocity, and density) are

plotted against depth (Carstens & Dypvik, 1981; Hermanrud et al., 1998; Teige et al., 1999). In

most cases, pore pressure prediction techniques require a normal compaction trend (NCT) of the

shale petrophysical properties to be established. Deviation from the normal compaction trend

will likely indicate the onset of abnormally high formation pressure. Formation pore pressures

are estimated in shale formations due to distinct variations in the petrophysical properties of

shales with respect to pore pressure. In addition, pore pressure prediction in shale formations will

give early warning of abnormally high formation pressure in the underlying reservoir rocks prior

to drilling into them. Hottmann & Johnson (1965) proposed a method for predicting the onset of

abnormally high formation pressure from petrophysical data (resistivity and compressional sonic

84
travel time) acquired in the Miocene and Oligocene shales in Upper Texas and Southern

Louisiana Gulf Coast. They observed that the plots of shale resistivity and sonic transit time

against depth in zones with normal pore pressures exhibited a distinctive trend called normal

compaction trend (NCT). Reversals in the shale resistivity and sonic transit time were correlated

to the onset of overpressure.

Foster and Whalen (1966) developed an empirical relationship between formation pore

pressure, depth of burial and the ratio of normal shale resistivity to abnormal shale resistivity for

regions with varying salinity (equation 3.1):

0.535 Rn
PP = 0.465 ∗ Z + ∗ log [ ], (3.1)
log b Ro

where PP is the formation pore pressure (psi); Z is the true vertical depth (ft); R n is the normal

shale resistivity (ohm-m); Ro is the observed (abnormal) shale resistivity (ohm-m). The log b can

be obtained from the slope of formation factor versus depth plot. Gardner et al. (1974) proposed

an empirical relationship among vertical effective stress, sonic travel time and depth of burial

based on the data presented by Hottmann and Johnson (1965). Gardner’s model is given by:

1
σv − PP 3 2
[ ] ∗ Z 3 = A − B log e ∆t (3.2)
Gob − Gnp

where σv is the vertical stress (psi); PP is the pore pressure (psi); Z is the true vertical depth (ft);

Gob is the overburden gradient (psi/ft); Gnp is the normal pore pressure gradient (psi/ft); ∆t is the

interval travel time (μs/ft); A and B are constant parameters. The values of A and B can be

obtained by calibration equation 3.2 to any known normally pressured intervals in the region.

Eaton (1975) proposed three sets of pore pressure prediction models based on resistivity

85
measurements, acoustic measurements, and corrected d-exponent computed from drilling

parameters. Eaton’s models are given by:

R o 1.2
Gpp = Gob − {Gob − Gnp } [ ] , (3.3)
Rn

∆t n 3
Gpp = Gob − {Gob − Gnp } [ ] , (3.4)
∆t o

dco 1.2
Gpp = Gob − {Gob − Gnp } [ ] , (3.5)
dcn

where Gpp is the pore pressure gradient (psi/ft); Gob is the overburden gradient (psi/ft); Gnp is the

normal pore pressure gradient (psi/ft); R o is the observed shale resistivity (ohm-m); R n is the

normal compaction trend shale resistivity (ohm-m); ∆𝑡𝑛 is the normal compaction shale travel

time (μs/ft); ∆𝑡𝑜 is the observed shale travel time (μs/ft); 𝑑𝑐𝑜 is the calculated 𝑑𝑐 from

measured data; 𝑑𝑐𝑛 is the 𝑑𝑐 from the normal trend line. Eaton’s models are among the most

widely used pore pressure prediction methods. These models are particularly suitable for

overpressure conditions caused by compaction disequilibrium. Eaton’s models can also be

applicable to other forms of overpressure mechanisms caused by unloading conditions with a

higher exponent coefficient (Satti et al., 2015).

Bowers (1995) proposed pore pressure prediction models based on the principle of

effective stress to predict the degree of overpressure generated by compaction disequilibrium and

fluid expansion mechanisms using the virgin and unloading curves concept. The virgin curve

model for normal pressure and overpressure generated by compaction disequilibrium is given by:

V = 5000 + AσBe , (3.6)

86
where V is the compressional sonic velocity (ft/sec); 𝜎𝑒 is the effective vertical stress (psi); A

and B are virgin curve parameters. The values of A and B can be obtained by calibrating

equation 3.6 to the normally compacted series in the same well or offset wells. The unloading

curve model for overpressure generated by fluid expansion mechanisms is given by

1 B
σe U
V = 5000 + A [σmax [ ] ] , (3.7)
σmax

1
Vmax − 5000 B
σmax = [ ] , (3.8)
A

where σmax is the effective vertical stress at the onset of unloading (psi); Vmax is the

compressional sonic velocity at the onset of unloading (ft/sec); U is the unloading parameter

which measures how plastic the sediment is. The value of U is obtained by fitting equation 3.7 to

the regional offset wells. Under normal and overpressure conditions caused by compaction

disequilibrium, the plot of compressional sonic velocity against effective stress will follow the

virgin curve (equation 3.6). However, subsurface overpressure conditions caused by fluid

expansion mechanisms will trail the unloading curve (equation 3.7).

Most current pore pressure prediction models are not applicable to non-clastic rocks.

Carbonate rocks are stiffer than shales and their porosity related properties may not be affected

by overpressure environments. Atashbari & Tingay ( 2012) proposed a pore pressure prediction

model based on bulk and pore compressibilities for carbonate rocks (equation 3.9):

γ
(1 − ∅)Cb σ′v
PP = [ ] , (3.9)
(1 − ∅)Cb − (∅Cp )

87
where PP is the formation pore pressure (psi); ∅ is the formation porosity (fraction); Cb is the

bulk compressibility (psi-1); Cp is the pore compressibility (psi-1); σ′v is the vertical effective

stress (psi); 𝛾 is the empirical constant ranging from 0.9 to 1.0. There are other popular pore

pressure prediction models that have been developed but these are based mostly on the

modifications to the previous models (Zhang, 2011; Zhang, 2013).

Early application of drilling parameters to pore pressure prediction used the rate of

penetration (ROP) as a principal indicator of subsurface overpressure conditions in a uniform

lithology (Forgotson, 1969). Field and laboratory observations have shown an inverse

relationship between the ROP and differential pressure ( Cunningham & Eenink, 1959; Vidrine

& Benit, 1968; Wardlaw, 1969; Black et al., 1985; Cheatham et al., 1985). In overpressure

formations, the ROP will most likely increase (positive drilling break) due to lower degree of

rock compaction, higher porosity and decrease in vertical effective stress especially if the

primary cause of overpressure mechanism is compaction disequilibrium. However, ROP is

affected by many factors other than the differential pressure. These factors include lithology,

degree of compaction, weight on bit (WOB), rotary speed, bit size, bit type, hydraulics excessive

overbalance and bit wear (Bourgoyne & Young, 1973). From the operational point of view, it is

not always possible to maintain the above factors constant while drilling a well. Hence, a sudden

increase in ROP may not necessarily signify drilling into abnormally pressured zones.

Normalization of ROP for the effects of WOB, rotary speed and bit size led to the development

of d-exponent concept (Jorden &Shirley 1966; Harper 1969; Rehm & McClendon 1971). The dc

– exponent model is given by:

88
 ROP
log [60N ] Gnp
dc − exponent = ∗[ ], (3.10)
12WOB ECD
log [ ]
106 Db

where dc − exponent is the corrected d – exponent; ROP is the rate of penetration (ft/hr); N is

the rotary speed in revolution per minute (rpm); WOB is the weight on bit (lbs); Db is the bit

diameter (in); Gnp is the normal pore pressure gradient (psi/ft or ppg); ECD is the equivalent

circulating density (psi/ft or ppg). The corrected d-exponent (equation 3.10) versus depth graph

is displayed on the semi-log to prevent significant variation of d-exponent with location and

geological age. In normal pressure environments, the corrected d-exponent will show an

increasing trend with depth. In overpressure shales, the corrected d-exponent will deviate from

the normal compaction trend (NCT) to lower values. The amount of deviation from the NCT at a

given depth is correlated to the magnitude of overpressure. One of the major drawbacks to the

application of d – exponent concept to pore pressure prediction is that it does not consider the

effect of bit hydraulic energy on the ROP. This limits its application to hard rock environments.

Traditionally, most works on the applications of specific energy to drilling operations

have been directed at improving the drilling efficiency (drilling optimization) and identification

of abnormal/inefficient drilling conditions (Rabia, 1985; Waughman et al., 2003; Dupriest &

Koederitz, 2005; Koederitz & Weis, 2005; Dupriest, 2006; Armenta, 2008; Amadi & Iyalla,

2012; Bevilacqua et al., 2013; Abbas et al., 2014; Mohan et al., 2015; Pinto & Lima, 2016; Wei

et al., 2016; Zhou et al., 2017). While the results of experimental investigations on rock samples

have shown the dependency of specific energy on confining/differential pressure (Rafatian et al.,

2010; Akbari et al., 2013; Akbari et al., 2014), only few (three) attempts have been made to

apply energy-based concept to pore pressure prediction using field data. Cardona (2011) was the

first to use mechanical specific energy (MSE) concept to estimate the formation pore pressure

89
from the field data. Just like the d-exponent concept, Cardona’s model does not contain the

hydraulic energy term, making it suitable to only hard rock environments. Majidi et al. (2017)

then proposed a methodology to determine the formation pore pressure from the combination of

downhole drilling parameters and in-situ rock properties using the concept of drilling efficiency

and mechanical specific energy (DE-MSE). The formation pressure was expressed as a function

of equivalent circulating density, MSE, uniaxial compressive strength and angle of internal

friction. The Majidi’s model is given by:

1 − sin θ
PP = ECD − [(DEtrend x MSE) − UCS] [ ], (3.11)
1 + sin θ

DEtrend = a∅bn , (3.12)

USC = 0.43Vp3.2 , (3.13)

θ = 1.532Vp0.5148 , (3.14)

where PP is the pore pressure (psi); ECD is the equivalent circulating density (psi); MSE is the

mechanical specific energy (psi); UCS is the uniaxial compressive strength (psi); 𝜃 is the angle

of internal friction; ∅ is the formation porosity; Vp is the compressional sonic velocity (ft/sec); a

is the coefficient of drilling efficiency trend-line from porosity trend-line; b is the exponent of

drilling efficiency trend-line from porosity trend-line. The major drawback to Majidi’s model is

that there are so many variables to be considered including the rock petrophysical properties. The

empirical equations (equations 3.13 and 3.14) that relate uniaxial compressive strength (UCS)

and angle of internal friction to compressional sonic velocity must be validated with core data in

the region of application. More so, Majidi’s model does not provide an independent means of

estimating the formation pore pressure since the compressional sonic velocity which is used to

estimate the UCS and angle of internal friction is also a function of the formation pore pressure.

90
Lastly, Majidi’s model ignores the effect of bit hydraulic energy on the ROP.

Oloruntobi et al. (2018) developed a methodology to estimate the formation pore pressure

using the concept of hydro-rotary specific energy (HRSE). This model is given by:

JSA −0.122
3
120πNT 0.10628 MW Q [1 − [TFA] ] Gnp
HRSE = + 2
∗[ ], (3.15)
Ab ROP Ab ROP TFA ECD
[ ]

where HRSE is the hydro-rotary specific energy (psi); Ab is the bit area (in2); N is the rotary

speed (rpm); T is the torque on bit (lb-ft); ROP is the rate of penetration (ft/hr); Q is the flow rate

(gpm); MW is the mud weight (ppg); JSA is the junk slot area (in2); TFA is the total flow area

(in2); Gnp is the normal pore pressure gradient (psi/ft or ppg) and ECD is the equivalent

circulating density (psi/ft or ppg). Oloruntobi’s model was derived from the combination of

rotary and hydraulic energies with the axial energy being neglected (equation 3.15). While the

model can be applied to consolidated (hard) and unconsolidated (soft) sediments due to the

inclusion of bit hydraulic energy term, accurate knowledge of torque on bit (TOB) is required.

TOB is usually subjected to a lot of fluctuations during drilling and it is perhaps the major source

of errors in the computation of specific energies.

Since most readily available field data in older (offset) and present-day wells are in the

form of surface measurements especially for marginal field operators, there is a need to develop

a pore pressure prediction technique from drilling parameters based on this reality. In this paper,

a new energy-based pore pressure prediction model that uses only surface measurements is being

proposed based on the concept of hydro-mechanical specific energy (HMSE). The HMSE is the

combination of axial, torsional and hydraulic energies required to break and remove a unit

volume of rock. The new technique can provide an excellent means of estimating the formation

91
pore pressure from the drilling parameters in the absence of reliable downhole measurements at

relatively low cost.

3.2 Model Development

Teale (1965) defined mechanical specific energy (MSE) as the amount of energy required to

remove a unit volume of rock. It amounts to the combination of energies due to axial and

torsional loads (equation 3.16):

WOB 120 ∗ π ∗ N ∗ T
MSE = + , (3.16)
Ab Ab ∗ ROP

where MSE is the mechanical specific energy (psi); WOB is the downhole weight on bit (lbs); Ab

is the bit area (in2); N is the rotary speed (rpm); T is the torque on bit (lb-ft); ROP is the rate of

penetration (ft/hr). However, the MSE does not necessarily represent the total energy consumed

in breaking and removing the rock fragments beneath the bit as the bit hydraulic energy term is

omitted in the model. The hydro-mechanical specific energy (HMSE) is the combination of

axial, torsional and hydraulic energies (Mohan et al., 2015; Chen et al., 2016; Wei et al., 2016).

Axial Energy Torsional Energy Hydraulic Energy

HMSE = + + , (3.17)
Rock Volume Drilled Rock Volume Drilled Rock Volume Drilled

The hydro-mechanical specific energy (HMSE) in the expanded form is given by:

WOB 120 ∗ π ∗ N ∗ T 1154 ∗ ∆Pb ∗ Q

HMSE = + + , (3.18)
Ab Ab ∗ ROP Ab ∗ ROP

where WOB is the downhole weight on bit (lbs); Ab is the bit area (in2); N is the rotary speed

(rpm); T is the torque on bit (lb-ft); ROP is the rate of penetration (ft/hr); ∆Pb is the bit pressure

92
drop (psi); Q is the flow rate (gpm). Pessier and Fear (1992) expressed the downhole torque (T)

as a function of weight on bit (WOB), bit specific coefficient of sliding friction (μ) and bit

diameter (Db ) as given by:

μ ∗ Db ∗ WOB
T= . (3.19)
36

Combination of equations 3.18 and 3.19 will lead to equation 3.20:

WOB 13.33 ∗ μ ∗ N ∗ WOB 1154 ∗ ∆Pb ∗ Q

HMSE = + + , (3.20)
Ab Db ∗ ROP Ab ∗ ROP

Excessive overbalance conditions will increase the confinement of rock and cuttings at the bit

face. This can lead to a reduction in ROP and an increase in the amount of energy required to

remove a unit volume of rock. Therefore, the HMSE needs to be corrected for changes in

bottom-hole pressure (equation 3.21):

WOB 13.33 ∗ μ ∗ N ∗ WOB 1154 ∗ ∆Pb ∗ Q Gnp

HMSE = [ + + ]∗[ ], (3.21)
Ab Db ∗ ROP Ab ∗ ROP ECD

where all parameters are as previously defined. This correction follows a similar correction for

the effect of mud weight/equivalent circulating density on d-exponent (Rehm & McClendon

1971). Due to accelerated fluid entrainment immediately below the bit nozzles, not all the

available hydraulic energy at the bit will reach the bottom of the hole. Therefore, the bit

hydraulic energy is converted into the bottom-hole hydraulic energy by introducing a hydraulic

energy reduction factor (η) into the bit hydraulic energy (equation 3.22):

WOB 13.33 ∗ μ ∗ N ∗ WOB 1154 ∗ η ∗ ∆Pb ∗ Q Gnp

HMSE = [ + + ]∗[ ]. (3.22)
Ab Db ∗ ROP Ab ∗ ROP ECD

93
Due to jet impact of the drilling fluid on the formation, an equal and opposite (pump-off) force is

exerted on the bit, leading to a reduction in WOB (equation 3.23):

WOBe 13.33 ∗ μ ∗ N ∗ WOBe 1154 ∗ η ∗ ∆Pb ∗ Q Gnp

HMSE = [ + + ]∗[ ], (3.23)
Ab Db ∗ ROP Ab ∗ ROP ECD

where WOBe is the effective weight on bit (lbs); all other parameters are as previously defined.

The effective weight on bit (WOBe ) is the surface WOB minus the component of jet impact force

that reaches the bottom of the hole (equation 3.24):

WOBe = WOB − η ∗ Fj , (3.24)

where WOB is the surface weight on bit (lbs); (η) is the hydraulic energy reduction factor; Fj is

the bit jet impact force (lbs). Equation 3.25 is obtained by combining equations 3.23 and 3.24:

[WOB − ηFj ] 13.33μN[WOB − ηFj ] 1154η∆Pb Q Gnp

HMSE = [ + + ]∗[ ]. (3.25)
Ab Db ROP Ab ROP ECD

The bit jet impact force is given by:

Fj = 0.000516 ∗ MW ∗ Q ∗ Vj , (3.26)

where MW is the mud weight (ppg); Q is the flow rate (gpm); Vj is the jet velocity (ft/sec). The

jet velocity is given by:

0.32 ∗ Q
Vj = , (3.27)
TFA

where Q is the flow rate (gpm); TFA is the total flow area (in2). For PDC bits, the hydraulic

94
energy reduction factor (η) is expressed as a function of junk slot area and total flow area

(Oloruntobi et al., 2018) and this is given by:

JSA −0.122
ηPDC Bit = 1 − [ ] , (3.28)
TFA

where JSA is the junk slot area (in2); TFA is the total flow area (in2). For roller cone bits, the

model proposed by Warren (1987) provides good estimates and this is given by:

0.15 Bit Area −0.122

ηRoller Cone Bit = 1−[ ] . (3.29)
TFA

The hydraulic energy reduction factor model proposed by Rabia (1989) is more complex and

may not be suitable for applications where there are variations in nozzle sizes within the same

bit. The pressure drop across the bit is given by:

MW Q2
∆Pb = , (3.30)
10858 TFA2

where ∆Pb is the bit pressure drop (psi); MW is the mud weight (ppg); Q is the flow rate (gpm);

TFA is the total flow area (in2). For fixed cutter bits, the value of bit specific coefficient of

sliding friction (μ) will depend on lithology, rock strength, mud weight, blade count, bit wear

and cutter sizes (Caicedo et al. 2005; Guerrero & Kull 2007). However, from field observations,

the value of μ often stays within a narrow range: 0.18 – 0.24 for roller cone bits and 0.5 – 0.8 for

PDC bits under different operating conditions (Wei et al. 2016). To minimize the errors in the

computation of HMSE, it is reasonable to assume average values of 0.21 and 0.65 for roller cone

and PDC bit respectively.

As the depth of burial increases in normally compacted series, the energy (HMSE)

95
required to break and remove a unit volume of rock will also increase. However, subsurface

overpressure intervals with lower vertical effective stress will require less energy to drill than the

normally compacted series at the same depth, leading to the reversal in the HMSE trend.

3.3 Methodology

1. Compute the HMSE at the depth of interest using equations 3.25 – 3.30. If there are wide

variations/fluctuations in HMSE values due to different lithologies being penetrated, the

HMSE should be estimated over clean shale intervals only to remove any lithological

effects on HMSE.

2. Display the plot of HMSE against depth on a semi-log and establish the normal

compaction trend (NCT) over the entire interval.

3. Estimate the formation pore pressure gradient at any given depth using the energy-based

Eaton’s model given as:

HMSEo m
Gpp = Gob − {Gob − Gnp } ∗ [ ] , (3.31)
HMSEn

where Gpp is the pore pressure gradient (psi/ft); Gob is the overburden gradient (psi/ft);

Gnp is the normal pore pressure gradient (NPPG) in psi/ft; HMSEo is the actual HMSE

calculated using equations 3.25 – 3.30; HMSEn is the hypothetical value of HMSE from

the normal compaction trend; m is the HMSE exponent. The value of the specific energy

ratio exponent (m) will vary from one region to another. It can be obtained by calibrating

equation 3.31 to any known overpressure intervals in the offset or current wells. If the

current well being drilled is used as the calibration well, equation 3.30 should be

preferably calibrated to the pressure transition zones where kick intensity is reduced.

96
3.4 Field Example

To demonstrate the applicability of the new pore pressure prediction technique, a recently drilled

High-Pressure High-Temperature exploratory well (Well A) in the tertiary deltaic system of the

Niger Delta is considered as the case study. Well A is located approximately 80 km northwest of

Port Harcourt in the central region of the basin (Figure 3.1).

Figure 3. 1 Location map for Well A.

97
The well is a near-vertical sidetrack well drilled to a total depth of 17,265 ft with a maximum

inclination of 6.8 degrees. The Niger Delta is an extensional rift basin that consists of the

regressive clastic sequence up 12 km in thickness and covers about 75,000 km2 (Evamy et al.,

1978). The detailed geology of the basin can be obtained from the literature (Short and Stauble,

1967; Avbovbo, 1978; Doust and Omatsola, 1990; Reijers, 2011). The growth and development

of the structural and depositional systems in the basin involves a complex interaction of

subsidence, contraction, and extension (Hooper et al., 2002). The structural geology of the area is

characterized by growth faults associated with rollover structures (Daukoru, 1975; Weber, 1987).

The primary mechanism for overpressure generation in the Niger Delta is under-compaction

(Daukoru, 1975; Ugwu & Nwankwo, 2014). In this paper, all depths are referenced to true

vertical depth (TVD) below the rotary table (RT)

Table 3. 1 The well and bit data summary.

BHA Intervals TFA JSA

Hole Size Bit Data Bit Dull Grade
Type (ft) (in2) (in2)
12 ¼’’ PDC Bit
RSS 10099 - 15080 1.2824 31.48 2-5-WT-G-X-I-CT-BHA
(HCC, Q 506 F)
12 ¼’’ PDC Bit
Steerable 15080 - 15193 1.2962 21.28 1-2-CT-S-X-I-NO-TD
(HCC, QD 507 FHX)
8 ½’’ PDC Bit
RSS 15193 - 15601 0.8399 15.55 1-1-WT-S-X-I-NO-DTF
(HCC, DP 506 F)
8 ½’’ PDC Bit
RSS 15601 - 16556 1.0301 15.55 2-2-BU-A-X-I-PN-TD
(HCC, DP 506 F)
5 5/8’’ PDC Bit
Steerable 16556 - 17265 0.8437 4.295 N/A
(HCC, QD 406 FHX)

Table 3.1 provides information about the type of bit and bottom-hole assembly (BHA) used to

drill the hole sections of interest. The dull grade for the bit used to drill the 5 5/8’’ hole was not

available because the bit was lost in hole due to a pipe stuck incident following a well killing

operation. Only the 12 ¼’’, 8 ½’’ and 5 5/8’’ hole sections are under considerations in this paper.

These intervals contain the normally compacted series, pressure transition zones and

98
overpressure formations. The top/big hole sections have been excluded from the analysis because

of limited data acquisitions and the sections contain loose continental sands with no overpressure

or hydrocarbon-bearing intervals. Figure 3.2 displays the plots of the recorded drilling

parameters from surface measurements while drilling the well. Where the bottom hole assembly

(BHA) contains mud motor (steerable), the total rotary speed is obtained using equation 3.32:

Total rotary speed = Surface string rotation + [Q ∗ Motor STFR], (3.32)

where Q is the flow rate (gpm); STFR is the speed to flow ratio (rpm/gpm).

To determine the overburden pressure, the formation bulk density data from the offset

wells were combined with the formation bulk density data from the current well (Well A) to

produce the equation of best fit. The equation of best fit was used to estimate the formation bulk

density values in intervals where formation bulk density logs were not acquired. The formation

bulk density equation of best fit is given by:

ρb = 1.136 Z 0.0833 , (3.33)

where ρb is the formation bulk density as a function of depth (g/cc); Z is the depth of interest

(ft). By integrating the bulk density data, the overburden pressure was computed using:

z
Sv = 0.433 ∫ ρb dz, (3.33)
0

where Sv is the overburden pressure (psi); ρb is the formation bulk density as a function of depth

(g/cc); Z is the depth of interest (ft). The equation of best fit was further constrained by the leak-

off test (LOT) data in the field since the Niger Delta basin operates under normal faulting regime

such that overburden pressure is the maximum principal stress ( Sv > σH > σh ).

99
Figure 3. 2 The plots of drilling parameters against depth for Well A.

100
Figure 3. 3 The formation bulk density and overburden pressure/gradient profiles for Well A.

101
The overburden gradient (Gob) was obtained by dividing the overburden pressure at the depth of

interest by the true vertical depth. The plots of formation bulk density, overburden

pressure/gradient and equation of best fit are displayed in Figure 3.3. Equation 3.33 is an

improvement to the formation bulk density prediction model presented by Oloruntobi et al.

(2018) for the central region of the Niger Delta based on a new set of offset well data.

3.5 Discussion

Figure 3.4A shows the plot of HMSE versus depth for Well A. Since the lithological effect on

the HMSE is minimal in this well, the HMSE values are estimated across the various

stratigraphic units from 10,997 ft to 17,265 ft. From the plot, the normal compaction trend

(NCT) can be visibly identified from 10,997 ft to 15,060 ft. In these intervals, the total energy

required to break and remove a unit volume of rock beneath the bit (HMSE) increases with depth

due to a decrease in rock porosity and an increase in effective stress. Depth intervals that lie on

the NCT correspond to the normally compacted series in the field. Based on the salinity of the

formation waters in the region, the average normal pore pressure in the intervals that lie on the

NCT is 8.66 ppg (0.45 psi/ft). In the intervals just below the 15,060 ft (top of pressure transition

zones), subsurface overpressure conditions cause the HMSE to depart from the NCT to lower

values. The overpressure intervals with lower effective stress consumed less energy to drill than

the normally compacted series at the same depth. The magnitude of overpressure is directly

correlated to the amount of deviation from the NCT.

Figure 3.4B shows the comparison between pore pressure estimates derived from HMSE

concept (equation 3.31) and actual pore pressure measurements. A close agreement exists

between the predicted and measured formation pore pressure.

102
Figure 3. 4 The HMSE and pore pressure profile for well A

The actual pore pressure measurements were obtained from the wireline pressure sampling tool

and drilling kick data at the formations/depths of interest. Since the actual formation pore

pressure in the field is known up to 16,567 ft (from offset wells) prior to drilling the current well,

equation 3.31 is calibrated to these intervals to determine the value of the specific energy ratio

exponent (m). The value of the specific energy ratio exponent (m) is 0.28. The predicted

formation pore pressure is normal from 10,997 ft to 15,060 ft with an average value of 0.45

psi/ft. At the depth just below 15,060 ft (onset of overpressure), the formation pore pressure

103
increases from 0.45 psi/ft to 0.72 psi/ft at 15,630 ft. The formation pore pressure then increases

further from 0.72 psi/ft at 15,630 ft to 0.9 psi/ft at the bottom of the well. The actual formation

pore pressure at the bottom of the well was obtained from a gas kick data. While drilling with a

mud weight (MW) of 0.87 psi/ft at the bottom of the well (17,265 ft), a gas kick was taken with

stabilized shut-in drill pipe pressure (SIDPP) of 530 psi. This results in formation pore pressure

of 0.9 psi/ft. Table 3.2 summarizes the main differences between pore pressure prediction

technique based on HMSE concept and other pore pressure prediction models derived from

drilling parameters.

Table 3. 2 Comparison of pore pressure prediction models from drilling parameters.

Input Drilling
Author Concept Remarks
Parameters

Jorden &Shirley WOB, N, and Empirically derived. It excludes the bit hydraulic
d – exponent
(1966) ROP energy term. Suitable mostly to hard rocks.

Derived from specific energy concept based on the

Cardona WOB, N, T, combination of axial and rotary energies. It excludes
MSE
(2011) and ROP the bit hydraulic energy term. Suitable mostly to
hard rock.

Majidi et al. WOB, N, T, The same as Cardona (2011). It also requires in-situ
DE-MSE
(2017) and ROP rock properties to be known.
Derived from specific energy concept based on the
Oloruntobi et al. N, T, Q, and combination of rotary and hydraulic energies. It
HRSE
(2018) ROP includes the bit hydraulic energy term. Suitable to
soft and hard rocks. It excludes WOB term.
Derived from specific energy concept based on the
WOB, N, Q, combination of axial, rotary and hydraulic energies.
New Method HMSE
and ROP It includes the bit hydraulic energy term. Suitable to
soft and hard rocks. It excludes torque term.

104
3.6 Conclusions

A new methodology to estimate the formation pore pressure from the drilling parameters is being

proposed. The new methodology is based on the concept of total energy (axial, rotary and

hydraulic) required to remove a unit volume of rock using only surface measurements. Since

downhole measurements are not routinely measured as part of normal drilling parameters, the

proposed methodology can provide a reliable means of estimating the formation pore pressure

from the drilling parameters at relatively low cost. The HMSE computed from surface

measurements can provide a reliable means of identifying the onset of overpressure in low

inclination well (inclination < 30 degrees) where there is a good transfer of WOB to the bottom

of the hole. In a high angle well (inclination > 30 degrees), hole drag due to friction loss along

the wellbore may prevent effective transfer of WOB to the bottom of the hole, especially during

sliding operations. In a high angle well, downhole parameters should be used to compute HMSE.

Even if downhole measurements are available, a comparison of HMSE computed from downhole

measurements with HMSE computed from surface measurements along with the compressional

sonic velocity can be useful in identifying the source of a drilling problem. For instance, an

increase in HMSE computed from both surface and downhole measurements with a

corresponding increase in compressional sonic velocity may indicate drilling into a hard

formation for a normal drilling operation. Increase in HMSE computed from both surface and

downhole measurements with no corresponding increase in compressional sonic velocity may

indicate bit related problems for a normal drilling operation. Increase in HMSE computed from

surface measurements with no corresponding increase in HMSE computed from downhole

measurements may indicate wellbore related problems such as stabilizer hanging up and cuttings

accumulation in the annulus (hole inclination > 30 degrees). However, the proposed

105
methodology should be applied with care under excessive bit wear, bit balling conditions,

excessive vibration and mud motor stalling conditions. The above conditions can mask

subsurface overpressure conditions when drilling through the pressure transition zones.

3.7 Reference

Aadnoy, B.S., 2010. Introduction to Geomechanics in Drilling. Mitchell, Robert F Miska, Stefan
Z. Fundam. Drill. Eng. Soc. Pet. Eng. 58–59.
Abbas, R.K., Hassanpour, A., Hare, C., Ghadiri, M., 2014. Instantaneous Monitoring of Drill Bit
Wear and Specific Energy as a Criteria for the Appropriate Time for Pulling Out Worn Bits
(Russian), in: SPE Annual Caspian Technical Conference and Exhibition. Society of
Petroleum Engineers.
Akbari, B., Miska, S., Mengjiao, Y., Ozbayoglu, E., 2013. Effect of Rock Pore Pressure on
Mechanical Specific Energy of Rock Cutting Using Single PDC Cutter, in: 47th US Rock
Mechanics/Geomechanics Symposium. American Rock Mechanics Association.
Akbari, B., Miska, S., Yu, M., Ozbayoglu, M., 2014. Experimental Investigations of the Effect of
the Pore Pressure on the MSE and Drilling Strength of a PDC Bit, in: SPE Western North
American and Rocky Mountain Joint Meeting. Society of Petroleum Engineers.
Amadi, W.K., Iyalla, I., 2012. Application of Mechanical Specific Energy Techniques in
Reducing Drilling Cost in Deepwater Development, in: SPE Deepwater Drilling and
Completions Conference. Society of Petroleum Engineers.
Armenta, M., 2008. Identifying inefficient drilling conditions using drilling-specific energy, in:
SPE Annual Technical Conference and Exhibition. Society of Petroleum Engineers.
Atashbari, V., Tingay, M.R., 2012. Pore pressure prediction in carbonate reservoirs, in: SPE
Latin America and Caribbean Petroleum Engineering Conference. Society of Petroleum
Engineers.
Avbovbo, A.A., 1978. Tertiary lithostratigraphy of the Niger Delta. Am. Assoc. Pet. Geol. Bull.
62, 295–306.
Bachu, S., Underschultz, J.R., 1995. Large-scale underpressuring in the Mississippian-
Cretaceous succession, southwestern Alberta Basin. Am. Assoc. Pet. Geol. Bull. 79, 989–

106
 1004. https://doi.org/10.1306/8D2B21A5-171E-11D7-8645000102C1865D
Barker, C., 1972. Aquathermal Pressuring--Role of Temperature in Development of Abnormal-
Pressure Zones: GEOLOGICAL NOTES. Am. Assoc. Pet. Geol. Bull. 10, 2068–2071.
https://doi.org/10.1306/819A41B0-16C5-11D7-8645000102C1865D
Barkers, C., Horsfield, B., 1982. Mechanical versus thermal cause of abnormally high pore
pressures in shales. Am. Assoc. Pet. Geol. Bull. 66, 99–100.
https://doi.org/10.1306/2F919760-16CE-11D7-8645000102C1865D
Bevilacqua, M., Ciarapica, F.E., Marchetti, B., 2013. Acquisition, processing and evaluation of
down hole data for monitoring efficiency of drilling processes. J. Pet. Sci. Res.
Black, A.D., Dearing, H.L., DiBona, B.G., 1985. Effects of Pore Pressure and Mud Filtration on
Drilling Rates in a Permeable Sandstone. J. Pet. Technol. 37, 1671–1681.
https://doi.org/10.2118/12117-PA
Bourgoyne Jr, A.T., Young Jr, F.S., 1973. The Use of Drillability Logs for Formation Evaluation
and Abnormal Pressure Detection, in: SPWLA 14th Annual Logging Symposium. Society
of Petrophysicists and Well-Log Analysts.
Bowers, G.L., 1995. Pore pressure estimation from velocity data: Accounting for overpressure
mechanisms besides undercompaction. SPE Drill. Complet. 10, 89–95.
https://doi.org/10.2118/27488-PA
Bruce, C.H., 1984. Smectite Dehydration-Its Relation to Structural Development and
Hydrocarbon Accumulation in Northern Gulf of Mexico Basin. Am. Assoc. Pet. Geol. Bull.
68, 673–683. https://doi.org/10.1306/AD461363-16F7-11D7-8645000102C1865D
Burrus, J., 1998. Overpressure models for clastic rocks, their relation to hydrocarbon expulsion:
a critical re-evaluation. Abnorm. Press. Hydrocarb. Environ. 70, 35–63.
Burst, J., 1969. Diagenesis of Gulf Coast Clayey Sediments and Its Possible Relation To
Petroleum Migration. Am. Assoc. Pet. Geol. Bull. 53, 73–93.
https://doi.org/10.1306/5D25C595-16C1-11D7-8645000102C1865D
Burst, J.F., 1976. Argillaceous Sediment Dewatering. Annu. Rev. Earth Planet. Sci. 4, 293–318.
https://doi.org/10.1146/annurev.ea.04.050176.001453
Buryakovsky, L.A., Djevanshir, R.D., Chilingar, G. V., 1995. Abnormally-high formation
pressures in Azerbaijan and the South Caspian Basin (as related to smectite ??? illite
transformations during diagenesis and catagenesis). J. Pet. Sci. Eng. 13, 203–218.

107
 https://doi.org/10.1016/0920-4105(95)00008-6
Caicedo, H.U., Calhoun, W.M., Ewy, R.T., 2005. Unique ROP Predictor Using Bit-specific
Coefficient of Sliding Friction and Mechanical Efficiency as a Function of Confined
Compressive Strength Impacts Drilling Performance. Soc. Pet. Eng. (SPE/IADC 92576).
https://doi.org/10.2118/92576-MS
Cardona, J., 2011. Fundamental Investigation of Pore Pressure Prediction during Drilling from
the Mechanical Behaviour of Rocks. PhD Thesis, Texas A&M Univ. Mech. Eng.
Carlin, S., Dainelli, J., 1998. Pressure regimes and pressure systems in the Adriatic Foredeep
(Italy). Abnorm. Press. Hydrocarb. Environ. 70, 145–160.
Carstens, H., Dypvik, H., 1981. Abnormal formation pressure and shale porosity. Am. Assoc.
Pet. Geol. Bull. 65, 344–350.
Cheatham, C.A., Nahm*, J.J., Heitkamp, N.., 1985. Effects of Selected Mud Properties on Rate
of Penetration in Full-Scale Shale Drilling Simulations. Soc. Pet. Eng. (SPE/IADC 13465).
Chen, J., Huang, D., 1996. Formation and mechanism of the abnormal pressure zone and its
relation to oil and gas accummulations in the Eastern Jiuquan Basin, Northwest China. Sci.
China Earth Sci. 39, 194–204.
Chen, X., Gao, D., Guo, B., Feng, Y., 2016. Real-time optimization of drilling parameters based
on mechanical specific energy for rotating drilling with positive displacement motor in the
hard formation. J. Nat. Gas Sci. Eng. 35, 686–694.
Cunningham, R. a, Eenink, J.G., 1959. Laboratory Study of Effect of Overburden, Formation and
Mud Column Pressures on Drilling Rate of Permeable Formations. Pet. Trans. AIME 217,
9–17.
Daukoru, J.W., 1975. PD 4(1) Petroleum Geology of the Niger Delta. World Pet. Congr.
Dickey, P., Cox, W., 1977. Oil and gas in reservoirs with subnormal pressures. Am. Assoc. Pet.
Geol. Bull. 12, 2134–2142.
Dupriest, F.E., 2006. Comprehensive Drill-Rate Management Process To Maximize Rate of
Penetration. Soc. Pet. Eng. (SPE 102210). https://doi.org/10.2118/102210-MS
Dupriest, F.E., 2006. Comprehensive Drill Rate Management Process To Maximize ROP, in:
SPE Annual Technical Conference and Exhibition. Society of Petroleum Engineers.
Dupriest, F.E., Koederitz, W.L., 2005. Maximizing drill rates with real-time surveillance of
mechanical specific energy, in: SPE/IADC Drilling Conference. Society of Petroleum

108
 Engineers.
Eaton, B.A., 1975. The Equation for Geopressure Prediction from Well Logs. Soc. Pet. Eng.
(SPE 5544 ). https://doi.org/10.2118/5544-MS
Evamy, B.D., Haremboure, J., Kamerling, P., Knaap, W.A., Molloy, F.A., Rowlands, P.H., 1978.
Hydrocarbon habitat of Tertiary Niger delta. Am. Assoc. Pet. Geol. Bull. 62, 1–39.
Fertl, W.H., Timko, D.J., 1971. Parameters for identification of overpressure formations, in:
Drilling and Rock Mechanics Conference. Society of Petroleum Engineers.
Finch, W., 1969. Abnormal Pressure in the Antelope Field, North Dakota. J. Pet. Technol. 21.
https://doi.org/10.2118/2227-PA
Forgotson, S.J.M., 1969. Indication of Proximity of High-Pressure Fluid Reservoir, Louisiana
and Texas Gulf Coast. Am. Assoc. Pet. Geol. Bull. 53, 171–173.
Foster, J.B., Whalen, H.E., 1966. Estimation of formation pressures from electrical surveys -
Offshore Louisiana. J. Pet. Technol. 18, 165–171. https://doi.org/10.2118/1200-PA
Freed, R.L., Peacor, D.R., 1989. Geopressured shale and sealing effect of smectite to illite
transition. Am. Assoc. Pet. Geol. Bull. 73, 1223–1232. https://doi.org/10.1306/44B4AA0A-
170A-11D7-8645000102C1865D
Freire, H., Falcão, J.., Silva, C.F., Barghigiani, L.., 2010. Abnormal Pore Pressure Mechanisms
In Brazil. Pap. ARMA 10-407 Proc. 2010 44th US Rock Mech. Symp. 5th U.S.-Canada
Rock Mech. Symp. held Salt Lake City, UT June 27–30,.
Gardner, G.H.., Gardner, L.., Gregory, A.., 1974. Formation Velocity and Density - The
Diagnostic Basic for Stratigraphic Traps. Geophysics 39, 770–780.
Guerrero, C.A., Kull, B.J., 2007. Deployment Of An SeROP Predictor Tool For Real-Time Bit
Optimization. SPE/IADC Drill. Conf. https://doi.org/10.2118/105201-MS
Harkins, L.K., Baugher, I.H.., 1969. Geological significance of abnormal formation pressures. J.
Pet. Technol. 961–966. https://doi.org/10.2118/2228-PA
Harper, D., 1969. New Findings from Over Pressure Detection Curves in Tectonically Stressed
Beds, in: SPE California Regional Meeting. Society of Petroleum Engineers.
Hermanrud, C., Wensaas, L., Teige, G.M.G., Bolas, H.M.N., Hansen, S., Vik, E., 1998. Memoir
70, Chapter 4: Shale Porosities from Well Logs on Haltenbanken (Offshore Mid-Norway)
Show No Influence of Overpressuring.
Holm, G.M., 1998. Distribution and origin of overpressure in the Central Graben of the North

109
 Sea. Law, B.E., G.F. Ulmishek, V.I. Slavin eds., Abnorm. Press. Hydrocarb. Environ.
AAPG Mem. 70, 123–144.
Hooper, R.J., Fitzsimmons, R.J., Grant, N., Vendeville, B.C., 2002. The role of deformation in
controlling depositional patterns in the south-central Niger Delta, West Africa. J. Struct.
Geol. 24, 847–859.
Hottmann, C.E., Johnson, R.K., 1965. Estimation of formation pressures from log-derived shale
properties. J. Pet. Technol. 17, 717–722.
Hunt, J.M., Whelan, J.K., Eglinton, L.B., Cathles, L.M. ll., 1998. Relation of shale porosities,
gas generation, and compaction to deep overpressures in the US. Gulf coast. Law, B.E.,
G.F. Ulmishek, V.I. Slavin eds., Abnorm. Press. Hydrocarb. Environ. AAPG Mem. 70 87–
104.
Jorden, J.R., Shirley, O.J., 1966. Application of drilling performance data to overpressure
detection. J. Pet. Technol. 18, 1–387.
Kadri, I.B., 1991. Abnormal Formation Pressures in Post-Eocene Formation, Potwar Basin,
Pakistan. Pap. SPE/IADC 21920 Proc. 1991 SPElIADC Drill. Conf. held Amsterdam, 11-14
March. https://doi.org/10.2523/21920-MS
Koederitz, W., Weis, J., 2005. A Real-Time Implementation of MSE, American Association of
Drilling Engineers. AADE-05-NTCE-66.
Law, B.E., Dickinson, W.W., 1985. Conceptual Model for Origin of Abnormally Pressured Gas
Accumulations in Low-Permeability Reservoirs. Am. Assoc. Pet. Geol. Bull. 69, 1295–
1304. https://doi.org/10.1306/AD462BD7-16F7-11D7-8645000102C1865D
Law, B.E., Shah, S.H. a, Malik, M. a, 1998. Abnormally high formation pressures, Potwar
Plateau, Pakistan. Law, B.E., G.F. Ulmishek, V.I. Slavin eds., Abnorm. Press. Hydrocarb.
Environ. AAPG Mem. 70 247–358. https://doi.org/10.1306/F4C8E6B6-1712-11D7-
8645000102C1865D
Law, B.E., Spencer, C.W., 1998. Abnormal Pressure in Hydrocarbon Environments. Law, B.E.,
G.F. Ulmishek, V.I. Slavin eds., Abnorm. Press. Hydrocarb. Environ. AAPG Mem. 70 1–
11. https://doi.org/10.1016/S0264-8172(99)00059-8
Lewis, C.., Rose, S.., 1970. A theory relating high temeperatures and overpressures. J. Pet.
Technol. 22, 11–16.
Louden, L.R., 1972. Origin and maintenance of abnormal pressures, in: Abnormal Subsurface

110
 Pressure Symposium. Society of Petroleum Engineers.
Majidi, R., Albertin, M., Last, N., 2017. Pore-Pressure Estimation by Use of Mechanical Specific
Energy and Drilling Efficiency. SPE Drill. Complet. 32, 97–104.
Mohan, K., Adil, F., Samuel, R., 2015. Comprehensive Hydromechanical Specific Energy
Calculation for Drilling Efficiency. J. Energy Resour. Technol. 137, 012904.
https://doi.org/10.1115/1.4028272
Oloruntobi, O., Adedigba, S., Khan, F., Chunduru, R., Butt, S., 2018. Overpressure prediction
using the hydro-rotary specific energy concept. J. Nat. Gas Sci. Eng. 55, 243–253.
Parker, C.A., 1973. Geopressures in the deep Smackover of Mississippi. J. Pet. Technol. 25,
971–979.
Pessier, R.C., Fear, M.J., 1992. Quantifying common drilling problems with mechanical specific
energy and a bit-specific coefficient of sliding friction, in: SPE Annual Technical
Conference and Exhibition. Society of Petroleum Engineers.
Pinto, C.N., Lima, A.L.P., 2016. Mechanical Specific Energy for Drilling Optimization in
Deepwater Brazilian Salt Environments. Soc. Pet. Eng. (IADC/SPE 180646).
https://doi.org/10.2118/180646-MS
Plumley, J.W., 1980. Abnormally High Fluid Pressure: Survey of Some Basic Principles:
ERRATUM. Am. Assoc. Pet. Geol. Bull. 64, 414–422. https://doi.org/10.1306/2F919409-
16CE-11D7-8645000102C1865D
Polutranko, A.J., 1998. Causes of Formation and Distribution of Abnormally High Formation
Pressure in Petroleum Basins of Ukraine. Law, B.E., G.F. Ulmishek, V.I. Slavin eds.,
Abnorm. Press. Hydrocarb. envi- ronments AAPG Mem. 70 181–194.
https://doi.org/10.1130/0091-7613(1998)026<0911
Powers, M.C., 1967. Fluid-release mechanisms in compacting marine mudrocks and their
importance in oil exploration. Am. Assoc. Pet. Geol. Bull. 7, 1240–1254.
Rabia, H., 1989. Rig Hydraulics Entrac Software.
Rabia, H., 1985. Specific energy as a criterion for bit selection. J. Pet. Technol. 37, 1225–1229.
https://doi.org/10.2118/12355-PA
Rafatian, N., Miska, S.Z., Ledgerwood, L.W., Yu, M., Ahmed, R., Takach, N.E., 2010.
Experimental study of MSE of a single PDC cutter interacting with rock under simulated
pressurized conditions. SPE Drill. Complet. 25, 10–18.

111
Rehm, B., McClendon, R., 1971. Measurement of formation pressure from drilling data, in: Fall
Meeting of the Society of Petroleum Engineers of AIME. Society of Petroleum Engineers.
Reijers, T., 2011. Stratigraphy and sedimentology of the Niger Delta. Geologos 17, 133–162.
Satti, A.. I., Yusoff, W.W.I., Ghosh, D., 2016. Overpressure in the Malay Basin and prediction
methods. Geofluids 16, 301–313. https://doi.org/10.1111/gfl.12149
Satti, I.A., Ghosh, D., Yusoff, W.I.W., Hoesni, M.J., 2015. Origin of Overpressure in a Field in
the Southwestern Malay Basin. SPE Drill. Complet. 30, 198.
Sayers, C.M., Boer Den, L.D., Nagy, Z.R., Hooyman, P.J., Ward, V., 2005. Regional trends in
undercompaction and overpressure in the Gulf of Mexico. Seg/houst. 2005 Annu. Meet.
1219–1223.
Serebryakov, V.A., Chilingar, G. V., 1994. Investigation of underpressured reservoirs in the
powder river Basin, Wyoming and Montana. J. Pet. Sci. Eng. 11, 249–259.
https://doi.org/10.1016/0920-4105(94)90044-2
Sharp, J.M., 1983. Permeability Controls on Aquathermal Pressuring. Am. Assoc. Pet. Geol.
Bull. 67, 2057–2061.
Short, K.., Stauble, A.., 1967. Outline of Geology of Niger Delta. Am. Assoc. Pet. Geol. Bull.
51, 761–779.
Spencer, C.W., 1987. Hydrocarbon Generation as a Mechanism for Overpressuring in Rocky
Mountain Region. Am. Assoc. Pet. Geol. Bull. 71, 368–388.
https://doi.org/10.1306/94886EB6-1704-11D7-8645000102C1865D
Swarbrick, R.E., Osborne, M.J., 1998. Mechanisms that generate abnormal pressures: an
overview. Law, B.E., G.F. Ulmishek, V.I. Slavin eds., Abnorm. Press. Hydrocarb. Environ.
AAPG Mem. 70 13–34.
Teale, R., 1965. The Concept of Specific Energy in Rock Drilling. Int. J. Rock Mech. Min. Sci.
2, 57–73. https://doi.org/10.1016/0148-9062(65)90022-7
Teige, G.M.G., Hermanrud, C., Wensaas, L., Bolås, H.M.N., 1999. The lack of relationship
between overpressure and porosity in North Sea and Haltenbanken shales. Mar. Pet. Geol.
16, 321–335.
Tingay, M.R.P., Hillis, R.R., Swarbrick, R.E., Morley, C.K., Damit, A.R., 2009. Origin of
overpressure and pore-pressure prediction in the Baram province, Brunei. Am. Assoc. Pet.
Geol. Bull. 93, 51–74.

112
Ugwu, S.A., Nwankwo, C.N., 2014. Integrated approach to geopressure detection in the X-field,
Onshore Niger Delta. J. Pet. Explor. Prod. Technol. 4, 215–231.
https://doi.org/10.1007/s13202-013-0088-4
Vidrine, D.J., Benit, E.J., 1968. Field Verification of the Effect of Differential Pressure on
Drilling Rate. J. Pet. Technol. (SPE 1859) 20, 676–682. https://doi.org/10.2118/1859-PA
Wardlaw, H.W.R., 1969. Drilling Performance Optimization and Identification of Overpressure.
Soc. Pet. Eng. AIME SPE 2388, 67–78.
Warren, T.M., 1987. Penetration Rate Performance of Roller Cone Bits. SPE Drill. Eng. 2, 9–18.
https://doi.org/10.2118/13259-PA
Waughman, J.R., Kenner, V.J., Moore, A.R., 2003. Real-Time Specific Energy Monitoring
Enhances the Understanding of When To Pull Worn PDC Bits. SPE Drill. Complet. (SPE
81822) 59–68.
Weber, K.J., 1987. Hydrocarbon distribution patterns in Nigerian growth fault structures
controlled by structural style and stratigraphy. J. Pet. Sci. Eng. 1, 91–104.
Wei, M., Li, G., Shi, H., Shi, S., Li, Z., Zhang, Y., 2016. Theories and applications of pulsed-jet
drilling with mechanical specific energy. SPE J. 21, 303–310.
Yassir, N., Bell, J., others, 1996. Abnormally high fluid pressures and associated porosities and
stress regimes in sedimentary basins. SPE Form. Eval. 11, 5–10.
https://doi.org/10.2118/28139-PA
Zhang, J., 2013. Effective stress, porosity, velocity and abnormal pore pressure prediction
accounting for compaction disequilibrium and unloading. Mar. Pet. Geol. 45, 2–11.
https://doi.org/10.1016/j.marpetgeo.2013.04.007
Zhang, J., 2011. Pore pressure prediction from well logs: Methods, modifications, and new
approaches. Earth-Science Rev. 108, 50–63. https://doi.org/10.1016/j.earscirev.2011.06.001
Zhou, Y., Zhang, W., Gamwo, I., Lin, J.-S., 2017. Mechanical specific energy versus depth of
cut in rock cutting and drilling. Int. J. Rock Mech. Min. Sci. 100, 287–297.

113
 Chapter 4

4.0 The New Formation Bulk Density Predictions for Siliciclastic Rocks

Preface

A version of this chapter has been published in the Journal of Petroleum Science and

Engineering, 2019. I am the primary author. Co-author Dr. Stephen Butt reviewed the

manuscript and provided technical assistance in the development of the concept. I formulated the

initial concept and carried out most of the data analysis. I prepared the first draft of the

manuscript and revised the manuscript based on the feedback from the co-author and peer

review process. The co-author also helped to refine the concept.

Abstract

Accurate determination of the overburden pressure obtained by integrating the formation bulk

densities from surface to the depth of interest is very critical to pore pressure prediction. When

information about the formation bulk density is not available, the current practice is to estimate

the formation bulk density from compressional wave velocity using empirical relationships.

There is no single formation bulk density prediction model that considers lithologic variation in

siliciclastic settings. This imposes severe limitations on the application of the existing empirical

relationships to any lithological column that consists of several stratigraphic units and/or non-

clean intervals. In this paper, attempt is made to develop the new formation bulk density

prediction models that can be applied to a wide range of lithologies in siliciclastic environments.

The new models are validated using wireline log data acquired from two wells in the tertiary

deltaic system of the Niger Delta basin. In the new models, formation bulk density is expressed

114
as a function of compressional wave velocity and shale volume factor. The accuracy of the new

models is quantified using statistical analysis. When compared to the existing models, the new

models outperform the most widely used empirical relationships. The new models produce the

lowest root mean square errors (5 - 6%), excellent error distributions and lowest residual values.

Unlike any of the existing empirical relationships, the new formation bulk density prediction

models can be applied to clean sands, clean shales and formations that contain a mixture of sands

and shales in any proportion. In general, the applications of the new models show an excellent

agreement between the predicted and measured formation bulk density.

Keywords: Formation bulk density, Compressional velocity, Empirical relationship, Lithology.

4.1 Introduction

Accurate determination of the rock mechanical properties is very essential for reducing the risks

associated with drilling, completion and production operations (Onalo et al., 2018). In addition to

compressional and shear wave velocity data, formation bulk density is an important input

parameter required to estimate the rock mechanical properties (Tixier et al., 1975; Coates and

Denoo, 1980; Onyia, 1988; Potter and Foltinek, 1997; Ohen, 2003; Chang et al., 2006; Fjar et al.,

2008; Ameen et al., 2009; Khair et al., 2015; Xu et al., 2016; Najibi et al., 2015; Feng et al.,

2019). These properties are required for geo-mechanical analyses such as compaction and

subsidence, wellbore stability prediction, perforation strategy, hydraulic fracturing, sand

production prediction and reservoir characterization. Formation bulk density data are also

required for porosity estimation, lithology determination, pore fluid identification and

overburden pressure prediction. Information about the formation bulk density and its derivative

115
in clean shales can be very useful in estimating the formation pore pressure and predicting the

origin of overpressure (Burrus, 1998; Bowers, 2001; Swarbrick, 2001; Zhang, 2011; Zhang,

2013; Hoesni, 2004; Satti et al., 2015). In seismic reflection analysis, information about the

formation bulk density is required in determining the elastic impedance of an interface.

Although density logs are among the common well logs acquired while drilling a well or

after the well has been drilled, there are several occasions when formation bulk density

predictions from other well log data may be required. First and foremost, density logs are usually

not run in all the intervals from surface/seabed to well total depth (Zoback, 2010). In most cases,

these logs (density) are run only in the intervals of interest (such as intervals that contain

hydrocarbon-bearing sands) for a selected number of wells in a certain field. Furthermore,

density logs are usually not run in the top/big hole sections (greater than 16 inches) because of

the difficulty of acquiring such logs in large diameter boreholes that are prone to excessive

washout and the fact that these sections do not normally contain hydrocarbon-bearing sands.

Even if density logs are run in a well, comparison with its prediction from other well logs can be

a useful quality control tool, especially in a rugose wellbore. More so, it is possible that density

tool may fail while drilling or logging at great depth (greater than 17,000 feet) in an offshore

environment with a floating rig. Under this condition of extremely high operating cost, operators

will not likely pull out of hole to re-run the density tool if other well logs that can be used to

accurately predict formation bulk density are available. Finally, accurate determination of

overburden pressure for pre-drill pore/fracture pressure predictions and wellbore stability

analyses requires information about the formation bulk density over the entire penetrated

intervals from surface to the depth of interest. Since density logs are not usually acquired over

the entire drilled intervals from surface to the depth of interest, prediction of this property is

116
highly required in the intervals that do not contain density logs. In general, lack of continuous

formation bulk density measurements along the well path necessitates its prediction for

overburden pressure estimation. Other possible reasons for the absence of density logs in most

wells/intervals may include economic reasons (especially marginal operators) and the risk of

losing a radioactive source in the well. In formations/intervals where density logs are not

acquired, empirical relationships have been developed to estimate the formation bulk density

from the compressional wave velocity. Equations of best fit through the intervals that do not

contain formation bulk density data should be used with caution and only if formation bulk

density values cannot be predicted due to unavailability of other well log data. In this paper,

unless otherwise stated, the compressional velocity and formation bulk density are expressed in

kilometers per second (km/s) and grams per cubic centimeter (g/cm3 or g/cc) respectively.

The relationship between the formation bulk density and compressional wave velocity

has long been established. In non-fractured rocks, the formation bulk density is a function of

compressional wave velocity (Lobkovsky et al., 1996). Birch (1961) established a linear

relationship between the formation bulk density (ρb ) and compressional wave velocity (Vp ) for

igneous and metamorphic rocks based on laboratory measurements. The empirical model

proposed by Birch (1961) is given by:

ρb = AVp + B, (4.1)

where A and B are empirical constants. Anderson (1967) then extended and modified Birch’s

model to be in accordance with theoretical predictions. For most volcanic and granitic rocks,

Carroll (1969) concluded that the relationship between formation bulk density and compressional

wave velocity is also linear. Based on a large number of laboratory and field observations of

117
different brine-saturated rock types (excluding evaporites) from a wide variety of basins and

depths, Gardner et al. (1974) proposed the most widely used exponential relationship between

the formation bulk density (ρb ) and compressional velocity (Vp ). Gardner’s relation is given by:

0.25
ρb = 1.74[𝑉𝑝 ] . (4.2)

Gardner’s model is one of the most important empirical relationships used in seismic prospecting

(Castagna and Backus, 1993). The model is most reliable when the rocks are well consolidated,

water-saturated and under substantial effective stress. Gardner’s model and its modifications

have been applied to several sedimentary basins around the world (Dey and Stewart, 1997; Potter

and Stewart, 1998; Potter, 1999; Quijada and Stewart, 2007; Ojha and Sain, 2014; Nwozor et al.,

2017; Akhter et al., 2018). In most cases, Gardner’s model tends to overestimate formation bulk

density in sandstones and underestimate formation bulk density in shales (Wang, 2001). Lindseth

(1979) established an empirical relationship between acoustic impedance (ρb Vp ) and

compressional velocity (Vp ) based on Gardner et al. (1974) data set (equation 4.3):

Vp = 0.308ρb Vp + 3460, (4.3)

where the compressional wave velocity is expressed in feet per second (ft/s). Although

Christensen and Mooney (1995) proposed both linear and nonlinear relationships between

formation bulk density (ρb ) and compressional wave velocity (Vp ) for crystalline rocks, they

concluded that the nonlinear relationship provides the best correlation. The non-linear model

proposed by Christensen and Mooney (1995) is given by:

K
ρb = G + , (4.4)
Vp

118
where G and K are empirical constants that depend on the depth at which the rocks are found.

Brocher (2005) proposed a nonlinear (polynomial) relationship between formation bulk density

(ρb ) and compressional velocity (Vp ) based on the data provided by Ludwig et al. (1970) for all

rock types except mafic crustal and calcium-rich rocks. The model is valid for compressional

velocity between 1.5 km/s and 8.5 km/sec (Brocher 2008). Brocher’s model is another widely

used empirical relationship given by:

ρb = 1.6612Vp − 0.4721Vp 2 + 0.0671Vp 3 − 0.0043Vp 4 + 0.000106Vp 5 . (4.5)

Khandelwal (2013) presented another linear relationship between formation bulk density (ρb )

and compressional wave velocity (Vp ) for representative rock mass samples of igneous,

sedimentary, and metamorphic rocks. Khandelwal’s correlation is given by:

ρb = 0.202Vp − 1794.7, (4.6)

where the compressional wave velocity and formation bulk density are expressed in m/s and

kg/m3 respectively. Attempts have also been made to estimate the formation bulk density from

the combination of compressional and shear wave velocities (Ursenbach, 2001; Ursenbach,

2002a; Ursenbach, 2002b).

Most of the existing empirical relationships between the formation bulk density and

compressional wave velocity were developed mainly for clean formations and they do not

consider variations in lithology. Empirical relationships that work very well for clean sandstone

formations may perform poorly in clean shale/shaly-sandstone formations and vice versa. In fact,

the most recent formation bulk density prediction models proposed by Akhter et al. (2018) are

still limited to clean formations containing less than 10 % shale by volume. Based on the

119
experimental data presented by Han et al. (1986) at 40 MPa differential pressure, Miller &

Stewart (1991) determined that the relationships between compressional wave velocity and

formation bulk density were scattered for rocks that contain a mixture of sand and shale.

However, they observed that the relationships improved significantly when the data were

categorized by clay content based on Vernik & Nur (1992) classification. This is the basis of the

new formation bulk density predictions. In this paper, an attempt is made to develop new

formation density prediction models that can be applied to a wide range of lithologies in

siliciclastic environments. The new models intend to consider lithologic variation by

incorporating a shale volume factor term. The addition of the shale volume term will normalize

the new models for lithology effects.

4.2 Methodology

Laboratory investigations have shown that compressional wave velocity (Vp ) can be expressed as

functions of effective porosity (∅) and clay volume (Vsh ) (Tosaya 1982; Tosaya and Nur 1982;

Kowallis et al., 1984; Castagna et al. 1985; Han et al. 1986). This relationship is given by:

VP = A − B∅ − CVsh , (4.7)

where A, B and C are regression coefficients. For liquid-filled non-clean formations in

siliciclastic settings, effective porosity (∅) can be expressed as functions of formation bulk

density (ρb ), sand matrix density (ρma ), shale matrix density (ρsh ), saturating fluid density (ρfl )

and shale volume fraction (Vsh ) as given by:

ρma 1 ρma − ρsh

∅= [ ]− [ ] ρb − [ ]V . (4.8)
ρma − ρfl ρma − ρfl ρma − ρfl sh

120
To a large extent, the quantities in the parentheses in equation 4.8 are approximately constant for

liquid-filled porous rocks. The saturating fluid density (ρfl ) is usually approximated as the

density of mud filtrate. Hence, equation 4.8 will reduce to equation 4.9:

∅ = M − Nρb − XVsh , (4.9)

where M, X and N are constant parameters. Combination of equations 7 and 9 will lead to:

ρb = QVp + ZVsh + P, (4.10)

where Q, Z and P are the new coefficients. When applied over clean formations where shale

volume factor is zero, equation 4.10 will reduce to Birch’s model (equation 4.1). Hence, equation

4.10 is referred to as modified Birch’s model. Since Gardner’s model is the most widely used

empirical relationship, a shale volume factor term is also added to Gardner’s model to account

for variations in lithology. The modified Gardner’s model is given by:

𝑚
ρb = k[𝑉𝑝 + GVsh ] , (4.11)

where k, G and m are constant parameters. To determine the values of the constant parameters Q,

Z, P, G, k and m, equations 4.10 and 4.11 are calibrated to the experimental data provided by

Han et al. (1986). Han et al. (1986) conducted laboratory ultrasonic experiments on brine

saturated sandstone cores obtained from quarries in USA and Gulf of Mexico wells. Han’s data

are selected for calibration because the laboratory experiments were conducted on both clean and

non-clean formations with the volume of shale in the core samples ranging from 0 to 51%. By

calibrating equations 4.10 and 4.11 to the compressional wave velocity, formation bulk density

and shale volume data provided by Han et al. (1986) for the entire 75 samples at 40 MPa

121
differential pressure, the values of the constant parameters Q, Z, P, G, k and m are determined to

be 0.222, 0.361, 1.431, 1.650, 1.351 and 0.390 respectively. Hence, the new formation bulk

density prediction model (Model I) based on equation 4.10 is given by:

ρb = 0.222Vp + 0.361Vsh + 1.431. (4.12)

Likewise, the new density prediction (Model II) based on equation 4.11 is given by:

0.390
ρb = 1.350[𝑉𝑝 + 1.651Vsh ] . (4.13)

4.3 Field Examples

To demonstrate the applicability of the new bulk density prediction models, two wells from the

tertiary deltaic system in the Niger Delta basin are considered as the case studies. The Niger

Delta is an extensional rift basin system that consists of clastic sediments up to 12 km in

thickness and covers an area of about 75,000 km2 (Doust and Omatsola, 1990; Evamy et al.,

1978). The Tertiary Niger Delta consists of three types of formations that represent the pro-

grading depositional facies of sands and shales. These formations in descending order are: Benin

formation, Agbada formation and Akata formation (Short and Stauble, 1967; Ejedawe et al.,

1984; Avbovbo, 1978; Matava et al., 2003; Adewole et al., 2016). The Benin formation consists

mainly of continental loose sands. The Agbada formation consists of alternating sands and

shales. The hydrocarbon accumulations of the Niger Delta basin are generally confined to

various levels of the Agbada formation (Ejedawe, 1981). The Akata formation at the base of the

delta consists of thick marine shales (potential source rock), turbidite sand (potential reservoirs in

deep water environments), and minor amounts of clay and silt (Abbey et al., 2018).

122
Figure 4. 1 The location map for Wells A and B.

The primary trapping mechanisms in the basin are growth faults associated with rollover

structures (Daukoru, 1975; Weber, 1987). At depth shallower than 12,000 ft, the Niger Delta

sands have good porosity and permeability (porosity in excess of 20% and permeability in the

darcy range). The detailed geology and hydrocarbon system of the Tertiary Niger Delta is

presented by Evamy et al. (1978). Figure 4.1 shows the location map of the two wells. Well A is

an onshore appraisal well located about 71 km northwest of Port Harcourt. Well B is a shallow

offshore exploratory well located about 94 km southeast of Port Harcourt in 215 ft water depth.

123
Wells A and B only penetrated the Benin and Agbada formations. In this paper, all depths are

referenced to true vertical depth below the mean sea level.

Figure 4. 2 The well logs for Well A showing the petrophysical properties of penetrated rocks.

124
Figure 4. 3 The well logs for Well B showing the petrophysical properties of penetrated rocks.

Figures 4.2 and 4.3 display the wireline log data acquired in the two wells. The measured

data include gamma ray, compressional wave velocity, formation bulk density, caliper, neutron

porosity, and deep resistivity. Although all the necessary environmental corrections (borehole

125
size, tool stand-off, mud cake thickness, mud type, mud weight, borehole salinity, pressure,

temperature, etc.) have been applied to the log data, the inclusion of the caliper logs will help to

identify the likely regions of poor borehole conditions which may result in poor data acquisition.

The caliper logs indicate that data acquisitions were carried out in good borehole conditions.

Further quality checks on the log data were performed using the compression velocity of

seawater (1.61 km/s), compressional velocity of sandstone matrix (5.49 km/s) and shale matrix

density in the Niger Delta (2.68 g/cc). The well log data cover a wide range of lithologies (clean

sands, clean shales, and a mixture of sands and shales) in siliciclastic environments.

4.4 Results and discussions

Figures 4.4 and 4.5 show the comparison of predicted and measured formation bulk density for

the two wells under consideration. The formation bulk density values are computed using

equation 4.12 (new model I), equation 4.13 (new model II), equation 4.2 (Gardner’s model) and

equation 4.5 (Brocher’s model). Since Gardner’s and Brocher’s models are the most widely used

empirical relationships developed for a wide range of lithologies, formation bulk density values

are also computed using these models for comparison purposes. For tertiary clastic sediments in

the Niger Delta basin, field observations have shown that shale volume (Vsh ) is linearly related to

gamma ray index (IGR ). Hence, shale volume (in fraction) is computed using equation 4.14:

GR log − GR min
Vsh = IGR = , (4.14)
GR max − GR min

where GRlog is the gamma ray reading at any given depth; GRmin is the sand line gamma ray

reading; GRmax is the shale line gamma ray reading. However, there are other non-linear

126
empirical responses between shale volume and gamma ray index depending on the geographic

area or formation age (Larionov, 1969; Stieber, 1970; Clavier et al., 1971; Assaad, 2008).

Figures 4.4 and 4.5 clearly highlight the limitations in applying any empirical relationship

that is based solely on compressional wave velocity to estimate the formation bulk density. For

both wells, the newly developed models (model I and model II) provide accurate estimates of

formation bulk density across various stratigraphic units. Reasonable estimates are obtained in

clean sands, clean shales, and formations that contain a mixture of sands and shales in any

proportion. The addition of the shale volume factor normalizes the new models for lithology

effects. Unlike the new models, Gardner’s and Brocher’s models fail to provide good estimates

across all the stratigraphic units. Gardner’s model slightly overestimates formation bulk density

in clean sands and underestimates formation bulk density in clean shales. Gardner’s model

provides formation bulk density estimates that fall between the clean sands and clean shales.

Gardner’s model slightly overestimates bulk density in clean sands because the relationship is

basically an average of the fits for sandstones, shales, and carbonates. It also underestimates

formation bulk density in clean shales due to lack of shaliness term in the model. While the

Brocher’s model provides reasonable estimates in clean sand intervals, it underestimates

formation bulk density in intervals that contain clean shales due to lack of shaliness term in the

model. In clean sands, the accuracy of Brocher’s model is higher than that of Gardner’s, while in

clean shales, the opposite is the case. When applied over a lithological column that consists of

several stratigraphic units in siliciclastic environments, any empirical relationship that expresses

formation bulk density as a function of only compressional velocity will most likely produce

inaccurate estimates in some intervals.

127
Figure 4. 4 The comparison of predicted and measured formation bulk density for various models under consideration (Well A).

128
Figure 4. 5 The comparison of predicted and measured formation bulk density for various models under consideration (Well B).

129
Figure 4. 6 The residual-depth plots for Wells A and B showing the error profiles.

In order to compare the accuracy of various methods under consideration, the residual-depth

plots are shown in Figure 4.6. The residual value is computed from the difference between

measured and predicted value. For all lithologies, the values of residual obtained from the new

130
models stay close to zero (dotted red line). However, the Gardner’s and Brocher’s models

produce larger residual values especially in clean shale formations. To properly show the error

distributions associated with various estimation techniques, the histograms of the residuals are

displayed in Figures 4.7 and 4.8. The histograms show that the new models produce lower

maximum deviations and better error distributions than the Gardner’s and Brocher’s models. In

Well A, over 92% of the data points fall between the residual range of -0.1g/cc and +0.1g/cc

using the new models, whereas less than 22% of the data points fall between the same residual

range when Gardner’s and Brocher’s models are used. In Well B, over 95% of the data points

fall between the residual range of -0.1g/cc and +0.1g/cc using the new models, whereas less than

45% of the data points fall between the same residual range when Gardner’s and Brocher’s

models are used.

Table 4. 1 The comparison of RMSEs for models under consideration

Model Well A Well B

New model I 5% 6%
New model II 6% 6%

Gardner et al. 1974 16% 15%

Brocher 2005 21% 17%

Table 4.1 shows the comparison of root mean square errors (RMSE) obtained from various

models. The new models produce lower RMSE than the most widely used empirical

relationships. The statistical analysis clearly shows that the performance of the new models is

superior to Gardner’s and Brocher’s models. The addition of shale volume improves the

accuracy of the prediction.

131
Figure 4. 7 The histograms of the residuals showing the error distributions for various models
under consideration (Well A).

132
Figure 4. 8 The histograms of the residuals showing the error distributions for various models
under consideration (Well B).

If density logs are not available, one has to use synthetically derived formation bulk densities for

overburden pressure computation (Kenda et al., 1999; Aminzadeh et al., 2002). Since the

133
magnitude of overburden pressure is obtained by integrating the formation bulk density values

from surface to the depth of interest along the well path (Christman, 1973; Zoback et al., 2003;

Aadnoy, 2010; Oloruntobi et al., 2018; Oloruntobi and Butt, 2019), care should be taken in using

any model that estimates formation bulk density based solely on compressional wave velocity

for overburden pressure computation in areas where the density logs are not available. The

knowledge of the overburden pressure is very critical to effective well design. Inaccurate

prediction of overburden pressure may result in erroneous prediction of pore pressure, fracture

pressure and vertical stress. This in turn can lead to well control, lost circulation and wellbore

stability incidents during actual drilling operations especially in very deep wells. To demonstrate

the effect of various estimation techniques on overburden gradient computation, Well A is

considered as the case study. To estimate the overburden gradient for Well A, a reasonable

assumption needs to be made about the average formation bulk density value from surface to the

depth where the well log data start (5,627 ft). Based on the overburden gradient curve provided

by Oloruntobi et al. (2018) for the onshore region of the Niger Delta, an average sediment bulk

density value of 2.08 g/cc is assumed between the ground level and the start of well log data. The

overburden pressure (Sv) is computed using:

z
Sv = 0.433 ∫ ρb dz, (4.15)
0

where ρb is the formation bulk density as a function of depth (g/cc); Z is the depth of interest

(ft). The overburden gradient at the depth of interest is obtained by dividing the overburden

pressure at any given depth by the true vertical depth. Figures 4.9 and 4.10 compare predicted

and measured overburden gradient profiles for the well under consideration along with gamma

ray logs. The plots clearly show the limitation of using Gardner’s and Brocher’s models to

134
compute formation bulk density values for overburden gradient prediction. While the outputs

from the new models provide good estimates of overburden gradient across the entire intervals,

the outputs from the Gardner’s and Brocher’s models underpredict the overburden gradient at the

well total depth.

Figure 4. 9 The overburden gradient profiles using formation bulk density outputs from the new
models for Well A.

135
Figure 4. 10 The overburden gradient profiles using formation bulk density outputs from the
Gardner’s and Brocher’s models for Well A.

Between 6,627ft and 6,250ft, the outputs from Brocher’s model provide accurate estimates of

overburden gradient because the lithologies in these intervals are mostly sands. Below 6,250ft

where most lithologies are shales, the outputs from Brocher’s model grossly underestimate the

overburden gradient. Between 6,627ft and 7,260ft, the outputs from Gardner’s model provide

reasonable estimates of overburden gradient because the amount of overprediction in sand

136
intervals negates the amount of underprediction in shale intervals. Below 7,260ft, the outputs

from Gardner’s model underpredict the overburden gradient because there are no enough sand

intervals to negate the massive shale intervals. The accuracy of Gardner’s model to estimate

formation bulk density for overburden gradient prediction will depend on the shale-to-sand ratio.

Outputs from Gardner’s model will underpredict the overburden gradient in sedimentary basins

that have a very high shale-to-sand ratio. For depositional environments with very low shale-to-

sand ratio, outputs from Gardner’s model will overpredict the overburden gradient.

4.5 Conclusions

Core samples and well logs from different basins (Gulf of Mexico and Niger Delta) have been

used to develop and validate the new formation bulk density prediction models. The new models

incorporate the shale volume term, making it suitable for clean and non-clean formations. The

application of the new models clearly demonstrates that the existing empirical relationships are

simply inadequate for accurate prediction of formation bulk density over a lithological column

that consists of several stratigraphic units. For petrophysical evaluations, both Gardner’s and

Brocher’s models are not suitable for formation bulk density prediction. Application of

Brocher’s model should be limited only to clean sand intervals. Gardner’s model provides

formation bulk density estimates that fall between the clean sands and clean shales. The outputs

from Brocher’s model should not be used for overburden gradient computation except the entire

lithological column is sand. The outputs from Gardner’s model should not be used for

overburden gradient computation in sedimentary basins where shale-to-sand ratio is very high or

very low. However, the outputs from Gardner’s model will provide reasonable estimates of

137
overburden gradient in sedimentary basins where shale-to-sand ratio approaches unity because

the amount of overprediction in sands may negate the amount of underprediction in shales.

Just like all the existing empirical relationships, the new models may not be applicable to

gas-filled formations or rocks that contain microcracks/fractures. In consolidated formations that

contain microcracks, changes in effective stress will cause substantial changes in compressional

wave velocity with little or no changes in formation bulk density until all the microcracks are

closed. To be applicable to gas-filled rocks, the generalized forms of the new models are

calibrated to any known gas intervals in the regional/field. Although the new models should be

applicable to siliciclastic rocks in most sedimentary basins, it will be prudent to calibrate the

generalized forms of these models (modified Birch’s – equation 4.10 and modified Gardner’s –

equation 4.11) to regional/field data. In general, a close agreement exists between the predicted

and measured formation bulk density using the new models. When compared to the most widely

used empirical relationships, the new models produce lower RMSEs, lower residuals, and better

error distributions.

The new models are developed primarily for liquid-saturated siliciclastic rocks which

include sandstones, siltstones, shales and formations that contain a mixture of sands and shales in

any proportion. The models do not cover carbonate and evaporite environments. However, the

generalized forms of the new models can be calibrated to carbonate and evaporite rocks to obtain

the new set of models for these environments.

4.6 Reference

Aadnoy, B.S., 2010. Introduction to Geomechanics in Drilling. Mitchell, Robert F Miska, Stefan
Z. Fundam. Drill. Eng. Soc. Pet. Eng. 57.
Abbey, C.P., Okpogo, E.U., Atueyi, I.O., 2018. Application of rock physics parameters for

138
 lithology and fluid prediction of ‘TN’field of Niger Delta basin, Nigeria. Egypt. J. Pet.
Adewole, E.O., Macdonald, D.I.M., Healy, D., 2016. Estimating density and vertical stress
magnitudes using hydrocarbon exploration data in the onshore Northern Niger Delta Basin,
Nigeria: Implication for overpressure prediction. J. African Earth Sci. 123, 294–308.
https://doi.org/10.1016/j.jafrearsci.2016.07.009
Akhter, G., Khan, Y., Bangash, A.A., Shahzad, F., Hussain, Y., 2018. Petrophysical relationship
for density prediction using Vp & Vs in Meyal oilfield, Potwar sub-basin, Pakistan. Geod.
Geodyn. 9, 151–155.
Ameen, M.S., Smart, B.G.D., Somerville, J.M., Hammilton, S., Naji, N.A., 2009. Predicting rock
mechanical properties of carbonates from wireline logs (A case study: Arab-D reservoir,
Ghawar field, Saudi Arabia). Mar. Pet. Geol. 26, 430–444.
Aminzadeh, F., Chilingar, G. V, Robertson Jr, J.O., 2002. Seismic methods of pressure
prediction, in: Developments in Petroleum Science. Elsevier, pp. 169–190.
Anderson, D.L., 1967. A seismic equation of state. Geophys. J. Int. 13, 9–30.
Assaad, F.A., 2008. Field methods for petroleum geologists: A guide to computerized
lithostratigraphic correlation charts case study: Northern Africa. Springer Science &
Business Media.
Avbovbo, A.A., 1978. Tertiary lithostratigraphy of the Niger Delta. Am. Assoc. Pet. Geol. Bull.
62, 295–306.
Birch, F., 1961. The velocity of compressional waves in rocks to 10 kilobars: 2. J. Geophys. Res.
66, 2199–2224.
Bowers, G.L., 2001. Determining an appropriate pore-pressure estimation strategy, in: Offshore
Technology Conference. Offshore Technology Conference.
Brocher, T.M., 2008. Key elements of regional seismic velocity models for long period ground
motion simulations. J. Seismol. 12, 217–221.
Brocher, T.M., 2005. Empirical Relations between Elastic Wavespeeds and Density in the
Earth’s Crust. Bull. Seismol. Soc. Am. 95, 2081–2092. https://doi.org/10.1785/0120050077
Burrus, J., 1998. Memoir 70, Chapter 3: Overpressure models for clastic rocks, their relation to
hydrocarbon.
Carroll, R.D., 1969. The determination of the acoustic parameters of volcanic rocks from
compressional velocity measurements, in: International Journal of Rock Mechanics and

139
 Mining Sciences & Geomechanics Abstracts. Elsevier, pp. 557–579.
Castagna, J.P., Backus, M.M., 1993. Offset-dependent reflectivity—Theory and practice of AVO
analysis. Society of Exploration Geophysicists.
Castagna, J.P., Batzle, M.L., Eastwood, R.L., 1985. Relationships between compressional‐wave
and shear‐wave velocities in clastic silicate rocks. Geophysics 50, 571–581.
Chang, C., Zoback, M.D., Khaksar, A., 2006. Empirical relations between rock strength and
physical properties in sedimentary rocks. J. Pet. Sci. Eng. 51, 223–237.
Christensen, N.I., Mooney, W.D., 1995. Seismic velocity structure and composition of the
continental crust: A global view. J. Geophys. Res. Solid Earth 100, 9761–9788.
Christman, S.A., 1973. Offshore Fracture Gradients. J. Pet. Technol. 25, 910–914.
Clavier, C., Hoyle, W., Meunier, D., 1971. Quantitative interpretation of thermal neutron decay
time logs: part I. Fundamentals and techniques. J. Pet. Technol. 23, 743–755.
Coates, G.R., Denoo, S.A., 1980. Log derived mechanical properties and rock stress, in: SPWLA
21st Annual Logging Symposium. Society of Petrophysicists and Well-Log Analysts.
Daukoru, J.W., 1975. PD 4(1) Petroleum Geology of the Niger Delta. World Pet. Congr.
Dey, A.K., Stewart, R.R., 1997. Predicting density using Vs and Gardner’s relationship.
CREWES Res. Rep. 9.
Doust, H., Omatsola, E., 1990. Niger Delta, in: Divergent / Passive Margin Basins. pp. 201–238.
Ejedawe, J.E., 1981. Patterns of incidence of oil reserves in Niger Delta Basin. Am. Assoc. Pet.
Geol. Bull. 65, 1574–1585.
Ejedawe, J.E., Coker, S.J.L., Lambert-Aikhionbare, D.O., Alofe, K.B., Adoh, F.O., 1984.
Evolution of oil-generative window and oil and gas occurrence in Tertiary Niger Delta
Basin. Am. Assoc. Pet. Geol. Bull. 68, 1744–1751.
Evamy, B.D., Haremboure, J., Kamerling, P., Knaap, W.A., Molloy, F.A., Rowlands, P.H., 1978.
Hydrocarbon habitat of Tertiary Niger delta. Am. Assoc. Pet. Geol. Bull. 62, 1–39.
Feng, C., Wang, Z., Deng, X., Fu, J., Shi, Y., Zhang, H., Mao, Z., 2019. A new empirical method
based on piecewise linear model to predict static Poisson’s ratio via well logs. J. Pet. Sci.
Eng. 175, 1–8.
Fjar, E., Holt, R.M., Raaen, A.M., Risnes, R., Horsrud, P., 2008. Petroleum related rock
mechanics. Elsevier.
Gardner, G.H.., Gardner, L.., Gregory, A.., 1974. Formation Velocity and Density - The

140
 Diagnostic Basic for Stratigraphic Traps. Geophysics 39, 770–780.
Han, D., Nur, A., Morgan, D., 1986. Effects of porosity and clay content on wave velocities in
sandstones. Geophysics 51, 2093–2107. https://doi.org/10.1190/1.1442062
Hoesni, M.J., 2004. Origins of overpressure in the Malay Basin and its influence on petroleum
systems. (Doctoral Diss. Durham Univ.
Kenda, W.P., Hobart, S., Doyle, E.F., 1999. Real-time geo-pressure analysis reduces drilling
costs. Oil Gas J. 97, 52–59.
Khair, E.M.M., Zhang, S., Abdelrahman, I.M., 2015. Correlation of Rock Mechanic Properties
with Wireline Log Porosities through Fulla Oilfield - Mugllad Basin -Sudan. SPE North
Africa Tech. Conf. Exhib. https://doi.org/10.2118/175823-MS
Khandelwal, M., 2013. Correlating P-wave velocity with the physico-mechanical properties of
different rocks. Pure Appl. Geophys. 170, 507–514.
Kowallis, B.J., Jones, L.E.A., Wang, H.F., 1984. Velocity-porosity-clay content systematics of
poorly consolidated sandstones. J. Geophys. Res. Solid Earth 89, 10355–10364.
Larionov, V. V, 1969. Radiometry of boreholes. Nedra, Moscow 127.
Lindseth, R.O., 1979. Synthetic sonic logs—A process for stratigraphic interpretation.
Geophysics 44, 3–26.
Lobkovsky, L.I., Ismail-Zadeh, A.T., Krasovsky, S.S., Kuprienko, P.Y., Cloetingh, S., 1996.
Gravity anomalies and possible formation mechanism of the Dnieper-Donets Basin.
Tectonophysics 268, 281–292.
Ludwig, W.., Nafe, J.., Drake, C.., 1970. No Title. Seism. Refract. Sea, A. E. Maxwell Vol. 4,
53–84.
Matava, T., Rooney, M.A., Chung, H.M., Nwankwo, B.C., Unomah, G.I., 2003. Migration
effects on the composition of hydrocarbon accumulations in the OML 67–70 areas of the
Niger Delta. Am. Assoc. Pet. Geol. Bull. 87, 1193–1206.
Miller, S.L.M., Stewart, R.R., 1991. The relationship between elastic-wave velocities and density
in sedimentary rocks: A proposal. Crewes Res. Rep. 260–273.
Najibi, A.R., Ghafoori, M., Lashkaripour, G.R., Asef, M.R., 2015. Empirical relations between
strength and static and dynamic elastic properties of Asmari and Sarvak limestones, two
main oil reservoirs in Iran. J. Pet. Sci. Eng. 126, 78–82.
Nwozor, K.K., Onuorah, L.O., Onyekuru, S.O., Egbuachor, C.J., 2017. Calibration of Gardner

141
 coefficient for density–velocity relationships of tertiary sediments in Niger Delta Basin. J.
Pet. Explor. Prod. Technol. 7, 627–635.
Ohen, H.A., 2003. Calibrated Wireline Mechanical Rock Properties Model for Predicting and
Preventing Wellbore Collapse and Sanding., in: SPE European Formation Damage
Conference. Society of Petroleum Engineers.
Ojha, M., Sain, K., 2014. Velocity-porosity and velocity-density relationship for shallow
sediments in the Kerala-Konkan basin of western Indian margin. J. Geol. Soc. India 84,
187–191.
Oloruntobi, O., Adedigba, S., Khan, F., Chunduru, R., Butt, S., 2018. Overpressure prediction
using the hydro-rotary specific energy concept. J. Nat. Gas Sci. Eng. 55, 243–253.
Oloruntobi, O., Butt, S., 2019. Energy-based formation pressure prediction. J. Pet. Sci. Eng.173,
955–964
Onalo, D., Oloruntobi, O., Adedigba, S., Khan, F., James, L., Butt, S., 2018. Static Young’s
modulus model prediction for formation evaluation. J. Pet. Sci. Eng. 171, 394–402.
Onyia, E.C., 1988. Relationships between formation strength, drilling strength, and electric log
properties, in: SPE Annual Technical Conference and Exhibition. Society of Petroleum
Engineers.
Potter, C.C., 1999. Relating density and elastic velocities in clastics: an observation. CREWES
1999 Res. Rep. 11.
Potter, C.C., Foltinek, D.S., 1997. Formation elastic parameters by deriving S-wave velocity
logs. Consort. Res. Elastic Wave Explor. Seismol. Res. Rep. 9, 1–13.
Potter, C.C., Stewart, R.R., 1998. Density predictions using V p and V s sonic logs. CREWES
Res 10, 1–10.
Quijada, M.F., Stewart, R.R., 2007. Density estimations using density-velocity relations and
seismic inversion. CREWES Res Rep 19, 1–20.
Satti, I.A., Ghosh, D., Yusoff, W.I.W., Hoesni, M.J., 2015. Origin of Overpressure in a Field in
the Southwestern Malay Basin. SPE Drill. Complet. 30, 198.
Short, K.., Stauble, A.., 1967. Outline of Geology of Niger Delta. Am. Assoc. Pet. Geol. Bull.
51, 761–779.
Stieber, S.J., 1970. Pulsed neutron capture log evaluation-louisiana gulf coast, in: Fall Meeting
of the Society of Petroleum Engineers of AIME. Society of Petroleum Engineers.

142
Swarbrick, R.E., 2001. Pore-Pressure Prediction: Pitfalls in Using Porosity, in: Offshore
Technology Conference. Offshore Technology Conference.
Tixier, M.P., Loveless, G.W., Anderson, R.A., 1975. Estimation of Formation Strength From the
Mechanical-Properties Log (incudes associated paper 6400). J. Pet. Technol. 27, 283–293.
Tosaya, C., Nur, A., 1982. Effects of diagenesis and clays on compressional velocities in rocks.
Geophys. Res. Lett. 9, 5–8. https://doi.org/10.1029/GL009i001p00005
Tosaya, C.A., 1982. Acoustical Properties of Clay-Bearing Rocks. PhD Thesis, Stanford Univ.
Ursenbach, C.P., 2002a. Generalized Gardner relation for gas-saturated rocks. CREWES 2002
Res. Rep. 14, 1–6.
Ursenbach, C.P., 2002b. Generalized Gardner Relations. 2002 SEG Annu. Meet.
Ursenbach, C.P., 2001. A generalized Gardner relation. CREWES 2001 Res. Rep. 13, 77–82.
Vernik, L., Nur, A., 1992. Petrophysical classification of siliciclastics for lithology and porosity
prediction from seismic velocities (1). Am. Assoc. Pet. Geol. Bull. 76, 1295–1309.
Wang, Z., 2001. Fundamentals of seismic rock physics. Geophysics 66, 398–412.
Weber, K.J., 1987. Hydrocarbon distribution patterns in Nigerian growth fault structures
controlled by structural style and stratigraphy. J. Pet. Sci. Eng. 1, 91–104.
Xu, H., Zhou, W., Xie, R., Da, L., Xiao, C., Shan, Y., Zhang, H., 2016. Characterization of rock
mechanical properties using lab tests and numerical interpretation model of well logs. Math.
Probl. Eng. 2016.
Zhang, J., 2013. Effective stress, porosity, velocity and abnormal pore pressure prediction
accounting for compaction disequilibrium and unloading. Mar. Pet. Geol. 45, 2–11.
Zhang, J., 2011. Pore pressure prediction from well logs: Methods, modifications, and new
approaches. Earth-Science Rev. 108, 50–63. https://doi.org/10.1016/j.earscirev.2011.06.001
Zoback, M.D., 2010. Reservoir geomechanics. Cambridge University Press.
Zoback, M.D., Barton, C.A., Brudy, M., Castillo, D.A., Finkbeiner, T., Grollimund, B.R., Moos,
D.B., Peska, P., Ward, C.D., Wiprut, D.J., 2003. Determination of stress orientation and
magnitude in deep wells. Int. J. Rock Mech. Min. Sci. 40, 1049–1076.

143
 Chapter 5

5.0 A New Fracture Pressure Prediction Model for The Niger Delta Basin

Preface

A version of this chapter has been submitted to the Journal of Environmental Earth Sciences,

2019. I am the primary author. Co-author Omolola Falugba reviewed the manuscript and

provided much-needed support in data acquisition. Co-author Oluchi Ekanem-Attah reviewed

the manuscript and provided much-needed support in data acquisition. Co-author

Chukwunweike Awa reviewed the manuscript and provided much-needed support in data

acquisition. Co-author Dr. Stephen Butt reviewed the manuscript and assisted in the

development of the concept. I developed the initial concept and carried out most of the data

analysis. I prepared the first draft and subsequently revised the manuscript based on the

feedback from the co-authors.

Abstract

Accurate knowledge of formation fracture pressure is very essential to optimizing well design at

all stages of the field development. However, erroneous prediction of formation fracture pressure

can lead to process safety incidents such as surface and underground blowouts. While fracture

pressure prediction models have been developed for some sedimentary basins, it is difficult to

transfer these models to areas beyond the regions of study. In the Niger Delta basin, few fracture

pressure prediction models have been developed. However, these models were developed

primarily from leak-off test data acquired from the normally pressured intervals. Basically, the

existing Niger Delta fracture pressure prediction models lack the leak-off test measurements in

144
the overpressure intervals because such data are not available. In this paper, a new fracture

pressure prediction model that can be applied to normally pressured intervals and overpressure

zones is being proposed. Model development is based on establishing a relationship between

fracture pressure, true vertical depth, and magnitude of overpressure using several leak-off test

data acquired from over 100 wells in various fields scattered across the basin. Unlike the

previous models, the newly developed model incorporates leak-off test measurements from the

overpressure intervals in the basin. In general, the newly proposed model can be used with a high

degree of confidence to predict the formation fracture pressure required for safe and economical

well planning across the entire basin.

Keywords: Pore pressure, Fracture pressure, Normally pressured, Overpressure, Leak-off test.

5.1 Introduction

Fracture pressure is the pressure required to initiate a crack in a formation. The fracture pressure

and pore pressure data are the most important input parameters required for well planning and

design. The difference between formation fracture pressure and pore pressure (drilling window)

will dictate the overall drilling and completion strategies for the field. Fracture pressure

determinations are usually performed as part of pre-drill and wellsite tasks. Pre-drill fracture

pressure predictions are very essential for well planning purposes at the ‘’select’’ and ‘’define’’

phases of a field development plan. Wellsite fracture pressure determinations are very important

for operational decisions. The operational decisions at the wellsite following a formation

integrity test (leak-off test, formation break-down test or limit test) may include: (1) performing

squeeze cementing jobs; (2) optimizing the flow rate to minimize the annular pressure loss; (3)

145
reducing the rate of penetration (ROP) to minimize cuttings concentration in the annulus; (4)

optimizing tripping in strategy to minimize surge pressure; (5) determining the maximum

permissible drilling depth based on the amount of influx (kick tolerance) that can be taken in the

open hole sections for a specific kick intensity and circulated out with a Driller’s method of well

control without fracturing the weakest formations. Decisions can also be made to apply wellbore

strengthening/stress caging techniques following a formation integrity test at the wellsite

(Alberty & McLean 2004; Aston et al. 2004; Song & Rojas 2006; Bybee 2008; Wang et al. 2009;

Kumar et al. 2010; Contreras et al. 2014; Savari et al. 2014; Chellappah et al. 2015; Zhang et al.

2016; Feng & Gray 2017; Chellappah et al. 2018). From well engineering point of view,

information about the formation fracture pressures can be used to: (1) determine the maximum

allowable equivalent circulating density (ECD) required to drill a well; (2) establish the bottom-

hole pressure required for squeeze jobs and hydraulic fracturing; (3) establish the injection

pressure required for casing design and equipment selection; (4) select optimum mud properties

and additives; and (5) determine the maximum allowable annular surface pressure (MAASP)

required to prevent formation breakdown in the event of a kick; (6) establish the bottom-hole

pressure required for cuttings reinjection (CRI). From an exploration standpoint, formation

fracture pressure data are used for subsurface trap integrity analysis, prospect evaluation and

hydrocarbon migration analysis. In intervals where formation pore pressures are greater than the

fracture pressures, subsurface traps are likely to leak. Failure to accurately predict the formation

fracture pressure can lead to lost circulation and well control incidents (surface and underground

blowouts). In general, information about the magnitude of formation fracture pressure is very

vital to achieving the overall well objective, especially when drilling into high pressured zones.

146
 To geomechanics specialists, formation fracture pressure is referred to as the minimum

principal stress. In well engineering community, formation fracture pressure is referred to as the

bottom-hole leak-off pressure (LOP): the bottom-hole pressure at which drilling fluid starts to

invade the formation and the relation between mud pressure and volume starts to deviate from

linearity (Edwards et al., 1998; Altun et al., 2001; Couzens-Schultz and Chan, 2010). The leak-

off test measurements can be conventional or dynamic. Conventional leak-off tests are usually

conducted after drilling a few feet of the new formation below the casing shoe. Dynamic leak-off

tests can be performed at any depth in the open hole by determining the equivalent circulating

density (ECD) required to leak off drilling mud into the formation using the pressure while

drilling (PWD) sensors. During the dynamic leak-off tests, bottom-hole pressure (BHP) can be

increased either by increasing the flow rate to increase the annular pressure loss or by increasing

the annular backpressure while drilling in managed pressure drilling (MPD) mode. However, the

magnitude of the minimum principal stress (usually horizontal in the normal faulting regime) can

only be determined from micro-fracturing/mini-fracturing/extended leak-off test/lost circulation

incidents (Daneshy et al., 1986; De Bree and Walters, 1989; Kunze and Steiger, 1992; Thiercelin

et al., 1996; Raaen et al., 2006; Li et al., 2009; Li et al., 2009; Wang et al., 2011; Chan et al.,

2015; Feng and Gray, 2016). From field observations, comparison of LOT and hydraulic

fracturing (micro-frac/mini-frac/extended leak-off test) data for non-fractured rocks have shown

that vast majority of leak-off pressures exceed the minimum principal stresses by an average of

10 - 15%. In this paper, fracture pressure is referred to as the bottom-hole leak-off pressure

(pressure at which the pressure versus volume curve starts to deviate from a straight line). The

formation fracture pressure is dependent on several factors including formation type, rock

strength, permeability, magnitude of the principal stresses, formation pore pressure, wellbore

147
inclination and azimuth, orientation of the plane of weakness and formation temperature. In most

cases, fracture pressures in shale formations are generally higher than that of sand formations.

Field experience has shown that increasing water depth reduces the overburden pressure (vertical

stress) which can lead to a reduction in apparent fracture pressure (Christman, 1973). Although

not in the same proportion, an increase in pore pressure will result in an increase in fracture

pressure and a decrease in pore pressure will lead to a decrease in fracture pressure (Salz, 1977;

Engelder and Fischer, 1994; Yassir et al., 1998). The magnitude of fracture pressure is affected

by wellbore inclination and azimuth (Rai et al., 2014). Generally, fracture pressure reduces as

wellbore inclination increases (Aadnoy and Chenevert, 1987). Heating a formation above its

undisturbed value (bottom-hole static temperature) will result in higher formation fracture

pressure and cooling a formation below its undisturbed temperature will cause a decrease in

formation fracture pressure (Perkins & Gonzalez 1984; Gonzalez et al. 2004; Hettema et al.

2004; van Oort & Vargo 2008; Zoback, 2010). The effects of anisotropic elasticity parameters on

formation fracture pressure are usually very small Aadnoy, (1988).

When drilling in areas where there are limited or no LOT data (especially rank wildcat)

theoretical and empirical relationships have been developed to estimate the formation fracture

pressure. Hubbert & Willis (1957) proposed an approximate expression for the minimum

injection pressure required to extend a fracture under normal-faulting stress regime (equation

5.1):

1
IPmin = [σv − PP] + PP, (5.1)
3

where IPmin is the Minimum injection pressure (psi); σv is the vertical stress (psi); PP is the pore

pressure (psi). By solving popular Kirch’s equation for vertical well at the wellbore wall with no

148
consideration for temperature effect, Haimson & Fairhurst (1967) suggested that the wellbore

pressure required to initiate a fracture in elastic rocks with smooth wellbore wall for non-

penetrating wellbore fluid (impermeable case) is a function of the two horizontal principal

stresses, the rock tensile strength and the formation pore pressure and it is given by:

FP = 3σh − σH − PP + To , (5.2)

where FP is the fracture pressure (psi); σh is the minimum horizontal stress (psi); σH is the

maximum horizontal stress (psi); PP is the pore pressure (psi); To is the tensile strength (psi). For

porous and permeable rocks, Haimson & Fairhurst (1967) then introduced poroelastic constants

into the formation breakdown pressure model to account for the wellbore fluid pressure

penetration effect (equation 5.3):

3σh − σH + To
FP = [ ] − PP, (5.3)
1 − 2v
2−α( 1−v )

where FP is the fracture pressure (psi); σh is the minimum horizontal stress (psi); σH is the

maximum horizontal stress (psi); PP is the pore pressure (psi); To is the tensile strength (psi); v is

the Poisson’s ratio; α is the Biot’s coefficient. When a formation breaks down, the fractures

created will propagate in the direction perpendicular to the least principal stress. While

theoretical models are helpful, they are difficult to apply in the field (Taylor and Smith, 1970).

Matthews and Kelly (1967) proposed a correlation that incorporated a depth-dependent matrix

stress coefficient to estimate the fracture pressure of sedimentary formations (equation 5.4).

σv − PP PP
FP = K i [ ]+ , (5.4)
Z Z

149
where FP is the fracture pressure (psi); σv is the vertical stress (psi); Ki is the matrix stress

coefficient; PP is the pore pressure (psi); Z is the true vertical depth (ft). Pennebaker (1968)

expressed formation fracture gradient as a function of overburden gradient, pore pressure

gradient and effective stress ratio for formations in the US Gulf Coast (Equation 5.5):

GFP = K o [GOB − GPP ] + GPP , (5.5)

where GFP is the fracture pressure gradient (psi/ft); GOB is the overburden gradient (psi/ft); GPP is

the pore pressure gradient (psi/ft); Ko is the effective stress ratio. While Pennebaker (1968)

recognized the dependency of effective stress ratio on the elastic constant of the rock (Poisson’s

ratio), effective stress ratio was expressed as a function of depth. The value of effective stress

ratio can also be obtained by calibrating equation 5.5 to actual fracture pressure and pore

pressure measurements in the field/region. Eaton (1969) modified Hubbert and Willis’s model by

incorporating the Poisson’s ratio. Eaton’s model is given by:

v
GFP = [G − GPP ] + GPP , (5.6)
1 − v OB

where GFP is the fracture pressure gradient (psi/ft); GOB is the overburden gradient (psi/ft); GPP is

the pore pressure gradient (psi/ft); v is the Poisson’s ratio. Although initially developed for the

US Gulf Coast area, Eaton’s model is the most widely used empirical correlation to estimate the

formation pressure (Parriag, 1976). Eaton’s model allows the effect of lithology to be considered

on formation fracture pressure. The Poisson’s Ratio is usually back-calculated from the

fracture/LOT data from the offset wells. Anderson et al. (1973) expressed formation fracture

pressure as a function of overburden pressure (vertical stress), pore pressure, Poisson’s ratio and

Biot’s constant for US Gulf Coast sands (equation 5.7):

150
 2v
FP = [ ] [σ − αPP] + αPP, (5.7)
1−v v

where FP is the fracture pressure (psi); σv is the vertical stress (psi); PP is the pore pressure (psi);

v is the Poisson’s ratio; α is the Biot’s coefficient. Salz (1977) proposed an exponential

relationship between fracture propagation gradient and pore pressure gradient based on

instantaneous shut-in pressure data obtained during hydraulic fracture treatments performed on

partially depleted and overpressure intervals for the Vicksburg formation in South Texas. Salz’s

model is given by:

GFP = 0.75e(0.57Gpp) . (3.8)

Daines (1982) introduced a superposed horizontal tectonic stress term into the fracture pressure

prediction model proposed by Eaton (equation 5.9):

v
FP = σt + [ ] [σ − PP] + PP, (5.9)
1−v v

where FP is the fracture pressure (psi); σv is the vertical stress (psi); PP is the pore pressure (psi);

v is the Poisson’s ratio; σt is the horizontal tectonic stress term (psi). Using hydraulic fracturing

data from various sedimentary basins, Breckels & Van Eekelen (1982) proposed empirical

relationships between minimum horizontal stress and depth for US Gulf Coast (equation 5.10:

for D < 11,500 ft and equation 5.11 for D > 11,500 ft), Venezuela (equation 5.12: for 5,900 ft <

D < 9,200 ft) and Brunei (equation 5.13 for D < 10,000 ft). These models are given by:

σh = 0.197Z1.145 + 0.46[OP], (5.10)

151
σh = 1.167Z − 4596 + 0.46[OP], (5.11)

σh = 0.210Z1.145 + 0.56[OP], (5.12)

σh = 0.227Z1.145 + 0.49[OP], (5.13)

where σh is the minimum horizontal stress (psi); OP is the overpressure (psi). Overpressure is the

difference between the formation pore pressure and the normal pore pressure. The normal pore

pressure gradient can vary between 0.433 – 0.515 psi/ft depending on pore fluid type, formation

temperature and concentration of dissolved salts in the formation water (Oloruntobi et al., 2018;

Oloruntobi and Butt, 2019). The normal pore pressure corresponds to a gradient of 0.452 psi/ft

in the North Sea (Holm, 1998). In the US Gulf Coast, the normal pore pressure corresponds to a

gradient of 0.465 psi/ft (Harkins and Baugher, 1969). The normal pore pressure gradient is

approximately 0.433 psi/ft in the Rocky Mountain regions in Canada and USA (Finch, 1969). A

formation is said to be overpressure if it has a pore pressure gradient higher than the normal pore

pressure gradient. Several Mechanisms that generate subsurface overpressure conditions have

been reported in the literature ( Dickey 1976; Swarbrick 1995, Swarbrick & Osborne 1998).

Constant & Bourgoyne (1988) extended Eaton's work to deepwater settings by exponentially

fitting effective stress ratio to depth for formations in the US Gulf Coast (equation 5.14):

FP = [1 − Ae(B∗Z) ][σv − PP] + PP, (5.14)

where FP is the fracture pressure (psi); σv is the vertical stress (psi); PP is the pore pressure (psi);

Z is the true vertical depth (ft); A and B are constant parameters. Avasthi et al. (2000) then

152
introduced Biot’s poroelastic constant into the fracture pressure model proposed by Eaton (1969)

using the concept of uniaxial strain model (equation 5.15):

v
FP = [ ] [σ − αPP] + αPP, (5.15)
1−v v

where FP is the fracture pressure (psi); σv is the vertical stress (psi); PP is the pore pressure (psi);

v is the Poisson’s ratio; α is the Biot’s coefficient. Zhang and Zhang (2017) modified Avasthi’s

model to include minimum stress coefficient based on the generalized Hooke's law with coupling

stresses and pore pressure (equation 5.16):

v c
FP = [ ] [σv − αPP] + αPP + [ ]σ , (5.16)
1−v 1−v v

where FP is the fracture pressure (psi); σv is the vertical stress (psi); PP is the pore pressure (psi);

v is the Poisson’s ratio; α is the Biot’s coefficient; c is the minimum stress coefficient. The

minimum stress coefficient (c) can be obtained by calibrating equation 5.16 to the in-situ

measured fracture/LOT data from the correlating offset wells. Zhang & Yin (2017) developed a

fracture gradient model based on LOT data obtained from offshore wells in several sedimentary

basins (equation 5.17):

B
GFP = [A + ] [GOB − GPP ] + GPP , (5.17)
eZ/C

where GFP is the fracture pressure gradient (psi/ft); GOB is the overburden gradient (psi/ft); GPP is

the pore pressure gradient (psi/ft); Z is the true vertical depth (ft). The model incorporates a

depth-dependent effective stress ratio and the variables A, B and C can be obtained by

calibrating equation 5.17 to the fracture/LOT data obtained from the offset wells. There are other

153
popular fracture pressure prediction models in the literature that are not specific to the Niger

Delta basin (Berry and Macpherson, 1972; Althaus, 1977; Brennan and Annis, 1984; Holbrook,

1989; Vuckovic, 1989; Schmitt and Zoback, 1989; Aadnoy and Larson, 1989; Akinbinu, 2010;

Zhang, 2011).

Lowrey and Ottesen (1995) proposed an empirical correlation to estimate the in-situ

minimum horizontal stress for offshore Niger Delta based on fracture closure pressures obtained

from extended leak-off tests (equation 5.18):

FP = 0.1779Z1.1586 , (5.18)

where FP is the fracture pressure (psi); Z is the true vertical depth (ft). Equation 5.18 is limited to

normally pressured intervals and does not account for the effect of overpressure on fracture

pressure. Ajienka and Nwokeji (1988) proposed a fracture gradient correlation for the onshore

region of the Niger Delta basin based on 135 LOT measurements acquired from 93 onshore well

covering a depth range of 2,159 ft to 13,070 ft (equation 5.19):

GFP = 14.57595 + 0.0002193[Z] − 16.16777[GOB ] − 0.270395[K i ] + 0.6665068[GPP ], (5.19)

K i = 0.135726 + 0.0000366[Z], (5.20)

where GFP is the fracture pressure gradient (psi/ft); GOB is the overburden gradient (psi/ft); GPP is

the pore pressure gradient (psi/ft); Z is the true vertical depth (ft); Ki is the stress ratio. The stress

ratio (Ki) is expressed as a function of depth (Ajienka et al. 2009). Considering that Niger Delta

basin operates under normal faulting regime where Sv > σH > σh , Ajienka and Nwokeji’s model

is fundamentally flawed because they suggested that formation fracture pressure decreases as

overburden pressure increases. Hence, this model should not be used in predicting the formation

154
fracture pressure in the Niger Delta basin. Reginald-Ugwuadu et al. (2014) proposed the most

calibrated fracture pressure prediction model for the Niger Delta sediments based on combined

LOT data obtained from onshore, swamp and shallow offshore wells (equation 5.21):

FP = 0.000029[𝑍 2 ] + 0.46Z, (5.21)

where FP is the fracture pressure (psi); Z is the true vertical depth (ft). However, the model fails

to capture the effect of overpressure on fracture pressure. This limits its application to normally

pressured intervals. Reginald-Ugwuadu’s model was built from LOT measurements acquired at

various wellbore inclinations and azimuths.

While few empirical models have been developed for the Niger Delta basin, none of the

models were developed to work in High-Pressure High-Temperature (HPHT) environments. In

fact, no fracture pressure prediction model exists in the Niger Delta that incorporates LOT

measurements from the hard overpressure environments (pore pressure gradient > 0.70 psi/ft).

The existing models were developed primarily from LOT measurements acquired from the

normally and mildly pressured intervals. In this paper, an attempt is made to develop a new

fracture pressure prediction model that can be applied to normal and overpressure intervals in the

onshore, swamp and shallow offshore regions of the Niger Delta basin.

5.2 Field Data

The Niger Delta basin is an extensional rift basin located in the Niger Delta and the Gulf of

Guinea along the west of central Africa. The basin covers an area of about 75,000 km 2 and

consists of clastic sediments up to 12 km thick (Doust and Omatsola 1990; Evamy et al. 1978).

The basin consists of three types of formations in descending order: Benin formations, Agbada

155
formations and Akata formations (Short and Stauble 1967; Avbovbo 1978a; Adewole et al.

2016). The Benin formations consist primarily of continental loose sands. The Agbada

formations consist of an alternating sequence of sands and shales. The Akata formations consist

of thick marine overpressure shales. The geothermal gradient varies across the Niger Delta basin

between 1.2 – 3.0oF per 100 feet (Avbovbo, 1978b). The structural trapping mechanisms in the

basin are growth faults associated with rollover structures and the basin operates under normal

faulting regime (Daukoru 1975; Weber 1987). The primary mechanism of subsurface

overpressure conditions in the Niger Delta basin is compaction disequilibrium (Ugwu and

Nwankwo, 2014; Oloruntobi et al., 2018; Oloruntobi and Butt, 2019).

For data analysis, all depths and pressures are referenced to a true vertical depth below

the mean sea level. Figure 5.1 shows the location map for most of the wells used to build the new

fracture pressure prediction model. Due to a large number of wells involved (> 100 wells), only

53 wells are displayed on the location map just to show the area extent of the LOT data. All other

wells not shown on the map are scattered across the basin. Table 5.2 in the appendix provides a

well data summary. A total of 141 LOT measurements from 109 wells were used to develop the

new model. The well data cover the land, swamp and shallow offshore regions of the basin. The

shallow offshore regions of the basin are limited to 500 ft water depth. The LOT data also cover

a wide range of depth between 885 ft and 16,478 ft. The formation pore pressure gradient ranges

between 0.433 psi/ft and 0.826 psi/ft. No existing fracture pressure prediction model in the Niger

Delta covers this pore pressure range. Note that the normal pore pressure gradient in the Niger

Delta ranges between 0.433 psi/ft to 0.472 psi/ft. In Table 5.2, any pore pressure value

designated as ‘’normal’’ will have a pore pressure gradient in this range. The fracture gradient

ranges between 0.479 psi/ft and 1.018 psi/ft. Unexpectedly, the LOT measurements in the deep

156
overpressure zones have shown that fracture gradient can exceed 1.0 psi/ft in the Niger Delta.

Most of the LOT data at depths shallower than 5000 ft were acquired in continental sands while

LOT measurements at depths deeper than 5000 ft were mostly acquired in shale formations.

Figure 5 1: Location map for some wells used in model development.

To elimination/minimize the effect of well inclination and azimuth on formation fracture

pressure, only LOT measurements acquired in mostly vertical wells are considered with only few
157
slightly deviated wells. In the few slightly deviated wells, the wellbore inclinations at which

LOT measurements were acquired are less than 18 degrees, thereby making the effect of well

inclination and azimuth on formation fracture pressure insignificant in these wells. It should be

noted that limit-test measurements across the Niger Delta basin are excluded from the data used

to develop the new fracture pressure prediction model because they do not really provide any

quantitative information about the formation strength

5.3 Model Development

To develop a single equation that can be used to describe the formation fracture pressure in

normal and overpressure intervals, the LOT measurements acquired in overpressure intervals

must be normalized for the effect of pore pressure. The procedures used to derive the new model

are highlighted below.

• Measured fracture pressure data were plotted against depth.

• Trends corresponding to normal and overpressure intervals were identified.

• A model was fitted through the fracture pressure data acquired in normally pressured

intervals. This is called normally pressured trendline model.

• Fracture pressure differentials were obtained across the overpressure intervals by

computing the difference between the actual fracture pressure measurements and fracture

pressure values estimated from the normally pressured trendline model.

• Pore pressure differentials were obtained across the overpressure intervals by computing

the difference between the actual pore pressure and normal pore pressure.

• Fracture pressure differentials were plotted against the pore pressure differentials in the

overpressure intervals to generate the new fracture pressure prediction model.

158
Figure 5.2 shows the plot of fracture pressure against depth using the LOT data presented in

Table 5.2. While the pressure data are reported in gradient equivalent, pore and fracture pressure

values are obtained by multiplying the pressure gradients by the corresponding vertical depth.

20000
LOT (Normally Pressured)
18000 LOT (Overpressure)
Power (Normally pressured)
16000

14000
Fracture Pressure (psi)

12000

10000

y = 0.0682x1.2662
8000
R² = 986
6000

4000

2000

0
0 3000 6000 9000 12000 15000 18000

Depth (ft)

Figure 5 2: The plot of formation fracture pressure against depth

Although two distinct trends can be clearly identified from the plot (Figure 5.2), remarkable non-

scattered trends are observed for each pressure regime despite the LOT measurements being

acquired from various fields across the basin. A power law trend is observed between fracture

pressure and depth for normally pressured intervals while a linear trend is observed for the

overpressure intervals. As expected, formation fracture pressure values are higher in

159
overpressure intervals than the normally pressured intervals at the same depth. For instance, at

the depth of 11,890 ft, the fracture pressure values in normally pressured and overpressure

intervals are 9,854 psi and 10,986 psi respectively. This is an increase of 1,132 psi in formation

fracture pressure when pore pressure increases by 2,378 psi from the normal. Likewise, at the

depth of 14,122 ft, the formation fracture pressure values in normally pressured and overpressure

intervals are 12,252 psi and 13,908 psi respectively. This is an increase of 1,657 psi in formation

fracture pressure when pore pressure increases by 4,053 psi from the normal. These data indicate

that formation fracture pressure increases at a rate proportional to but less than the rate of pore

pressure increase. From Figure 5.2, at pore pressure value corresponding to a gradient of 0.515

psi/ft, the formation fracture pressure values for the normally pressured and overpressure

intervals almost overlap. For non-depleting formations, overpressure has little effect on

formation fracture pressure when pore pressure gradient falls below 0.515 psi/ft. A normally

pressured trendline (NPT) is obtained by fitting a power-law model through the fracture pressure

data acquired in the normally pressured intervals (equation 5.22). The formation fracture

pressure in equation 5.22 is only a function of depth with no pore pressure term.

FPNPT = 0.06817[D]1.2662 (5.22)

Figure 5.3 shows the plot of fracture pressure differential (measured fracture pressure minus the

corresponding fracture pressure computed from equation 5.22) versus the pore pressure

differential (actual pore pressure (PPa) minus normal pore pressure (PPn)) in the overpressure

intervals. Note that for all the normally pressured intervals, pore pressure differential will be

zero. A normal pore pressure (PPn) value with a gradient of 0.433 psi/ft with respect to mean sea

level is used to derive the new model. From Figure 5.3, a polynomial relationship exists between

160
the fracture pressure differential and pore pressure differential (equation 5.23). The plot shows a

good trend despite the overpressure LOT measurements were obtained from different fields.

2500
y = -0.0000486x2 + 0.6050968x
R² = 0.9892827
Fracture pressure differential (psi)

2000

1500

1000

500

0
0 2000 4000 6000 8000 10000 12000

Pore pressure differential (psi)

Figure 5 3: Fracture pressure differential versus pore pressure differential.

By rearranging equation 5.23 and substituting for the normally pressured trendline fracture

pressure (equation 5.22), a new fracture pressure prediction model for the Niger Delta is obtained

(equation 5.25). When operating in normally pressured intervals, the overpressure/pore pressure

differential (PPa − PPn) term will go to zero and equation 5.25 will reduce to equation 5.22.

∆FP = 0.6051[∆PP] − 0.0000486[∆PP]2 (5.23)

161
FP − FPNPT = 0.6051[PPa − PPn ] − 0.0000486[PPa − PPn ]2 (5.24)

FP = 0.06817[D]1.2662 + 0.6051[PPa − PPn ] − 0.0000486[PPa − PPn ]2 (5.25)

PPn = 0.433[𝐷] (5.26)

5.4 Model Validation

To demonstrate the applicability of the new fracture pressure prediction technique, a recently

drilled high-pressure high-temperature (HPHT) exploratory gas well (W 110) is considered as

the case study. The well is located approximately 82 km northwest of Port Harcourt in the central

region of the basin. The well is a slightly deviated well drilled to a total depth of 16,809 ft with a

maximum inclination of 14.56°. The formation integrity tests were conducted at the 13

3/8’’casing, 9 5/8’’ casing and 7’’ liner shoes. The 13 3/8’’casing, 9 5/8’’ casing and 7’’ liner

shoes were set at 9,382 ft, 15,087 ft and 16,404 ft respectively. The wellbore inclinations at the

13 3/8’’casing, 9 5/8’’ casing and 7’’ liner shoes are 11o, 12o and 3o respectively. The types of

formation integrity test performed at the 13 3/8’’ and 9 5/8’’ casing shoes were limit tests (no

leak-off). The type of formation integrity test performed at the 7’’ liner shoe was the leak-off

test. Although limit test measurements are not considered in the new model because they will

not provide any quantitative information about the formation strength, they are included in this

well to serve as control/calibrating data. The bottom-hole limit test pressure gradient at the 13

3/8’’ and 9 5/8’’ casing shoes are 0.717 psi/ft and 0.917 psi/ft respectively. The formation

fracture gradient (bottom-hole leak-off pressure gradient) at the 7’’ liner shoe is 1.009 psi/ft.

Table 5.1 shows the pore pressure data for the W 110 well. The formation pore pressures were

obtained from the combination of formation pressure while drilling tool, wireline pressure

162
sampling tool, sonic logs and drilling kick data. The formation pore pressure is normal from

9,200 ft to 14,805 ft (onset of overpressure). The formation pore pressure gradient then increases

gradually from 0.471 psi/ft at 14,805 ft to 0.856 psi/ft at 16,445 ft. Therefore, from 9,200 ft to

14,805 ft (normally pressured intervals), equation 5.25 will be used to estimate the formation

fracture pressures with the overpressure/pore pressure differential (PPa − PPn ) term being equal

to zero. From 14,805 ft to 16,445 ft (overpressure intervals), full components of Equation 5.25

will be used to estimate the formation fracture pressure. Note that pore and fracture pressure

terms are calculated by multiplying pressure gradient by depth.

Table 5. 1 The pore pressure data for the W 110 well.

Depth PP Depth PP Depth PP Depth PP

S/N S/N S/N S/N
(ft) (psi/ft) (ft) (psi/ft) (ft) (psi/ft) (ft) (psi/ft)
1 9200 0.432 7 10600 0.433 13 14235 0.462 19 15867 0.797

2 9382 0.432 8 11200 0.432 14 14546 0.470 20 15930 0.812

3 9562 0.432 9 12115 0.464 15 14805 0.471 21 16105 0.812

4 9722 0.432 10 12309 0.463 16 15087 0.610 22 16181 0.849

5 9943 0.435 11 12947 0.463 17 15122 0.665 23 16404 0.852

6 9988 0.433 12 13658 0.462 18 15407 0.722 24 16445 0.856

Figure 5.4 shows the comparison of predicted and measured fracture pressures for well W 110

using the new model and the most calibrated existing model for the Niger Delta basin (equation

5.21). At the 7’’ liner shoe (16,404 ft) where the actual leak-off test was conducted, a good

agreement exists between the predicted and measured fracture pressure in overpressure interval.

The newly proposed model predicts the formation fracture pressure within an accuracy of ±125

psi which is typically less than the trip margin (200 psi) normally applied to formation fracture

pressure as a safety factor. At the 13 3/8’’ and 9 5/8’’ casing shoes where limit tests were
163
conducted, the new model predicts fracture pressure values higher than the bottom-hole limit test

pressures because limit tests are usually stopped prior to reaching the point where drilling fluid

starts to invade the formation (leak-off point).

Figure 5 4: Comparison of predicted and measured fracture pressure for well W110

By using Reginald-Ugwuadu’s model (equation 5.21), fairly accurate estimates of formation

fracture pressures are observed in the normally pressured intervals (9,200 – 14,805 ft). However,

in the transition and overpressure intervals, the model completely breaks down and underpredicts

164
the formation fracture pressures. At the 7’’ liner shoe, Reginald-Ugwuadu’s model underpredicts

the formation fracture pressure by 1,199 psi. Even at the 9 5/8’’ casing shoe, Reginald-

Ugwuadu’s model wrongly predicts the fracture pressure value that is less than the bottom-hole

limit test pressure. Using such only depth-dependent model for pre-drill fracture pressure

predictions in overpressure intervals will lead to expensive drilling campaign (more casing

strings may be required than necessary).

5.5 Conclusion

A new robust fracture pressure prediction model that can be applied to a wide range of depths

and subsurface pressure regimes (normal to very hard overpressure) has been developed. The

new model establishes a relationship between fracture pressure, depth, and overpressure. The

model covers land, swamp and shallow offshore sections of the Niger Delta basin. It is the first

model to incorporate LOT measurements acquired in overpressure environments in the Niger

Delta. The proposed model can form the new Niger Delta guideline for: (1) performing the limit

tests at the wellsite during the actual drilling operations; (2) determining the pre-dill formation

fracture pressure for well planning and design; and (3) establishing the injection pressure

required for hydraulic fracturing. Although only one operator is currently drilling HPHT wells in

the Niger Delta, the new model will find a useful application as more operating companies plan

to embark on exploration drilling campaigns into the deeper HPHT sections of the basin.

165
5.6 Appendix

Table 5. 2 Well data summary

Depth FP PP Depth FP PP
Well Location Well Location
(ft) (psi/ft) (psi/ft) (ft) (psi/ft) (psi/ft)
W1 Land 4395 0.560 Normal 3951 0.607 Normal
W 27 Swamp
W2 Land 4398 0.532 Normal 10641 0.804 Normal
1988 0.527 Normal W 28 Offshore 3183 0.566 Normal
7275 0.615 Normal W 29 Offshore 2334 0.598 Normal
W3 Land
11339 0.879 0.560 W 30 Offshore 2202 0.610 Normal
13614 0.972 0.690 W 31 Land 3353 0.614 Normal
W4 Land 4378 0.691 Normal W 32 Land 9849 0.732 Normal
W5 Land 4945 0.538 Normal W 33 Swamp 4448 0.570 Normal
W6 Swamp 4952 0.524 Normal W 34 Swamp 3942 0.522 Normal
W7 Swamp 4946 0.635 Normal 4692 0.501 Normal
W8 Land 4958 0.561 Normal 7406 0.614 Normal
W 35 Swamp
W9 Swamp 4741 0.718 Normal 11557 0.786 Normal
W 10 Swamp 5741 0.556 Normal 13957 0.833 Normal
W 11 Swamp 2452 0.622 Normal 5261 0.580 Normal
W 36 Swamp
1982 0.495 Normal 10962 0.763 Normal
W 12 Land 7947 0.798 0.515 W 37 Swamp 8433 0.757 Normal
10489 0.894 0.620 W 38 Land 3861 0.698 Normal
W 13 Land 9934 0.786 Normal 6214 0.683 Normal
W 39 Land
W 14 Swamp 11950 0.776 Normal 11741 0.784 Normal
W 15 Swamp 5947 0.575 Normal W 40 Land 7709 0.794 Normal
W 16 Swamp 6448 0.597 Normal W 41 Land 16478 1.018 0.828
W 17 Swamp 5921 0.581 Normal 12183 0.804 Normal
W 42 Land
W 18 Swamp 5943 0.598 Normal 14890 0.904 Normal
1962 0.575 Normal 6743 0.613 Normal
W 19 Swamp
5963 0.590 Normal W 44 Offshore 1912 0.548 Normal
4940 0.582 Normal W 45 Offshore 1156 0.666 Normal
W 20 Swamp
8504 0.677 Normal W 46 Offshore 1400 0.740 Normal
W 21 Swamp 3941 0.640 Normal W 47 Land 3924 0.530 Normal
W 22 Swamp 9965 0.709 Normal 3065 0.626 Normal
W 48 Land
W 23 Swamp 8255 0.760 Normal 5101 0.687 Normal
W 24 Swamp 10940 0.778 Normal W 49 Land 8165 0.786 Normal
2409 0.631 Normal W 50 Offshore 902 0.745 Normal
W 25 Offshore
5542 0.715 Normal W 51 Offshore 2412 0.539 Normal
W 26 Land 1954 0.560 Normal W 52 Offshore 1433 0.548 Normal

166
 Depth FP PP Depth FP PP
Well Location Well Location
(ft) (psi/ft) (psi/ft) (ft) (psi/ft) (psi/ft)
2681 0.549 Normal W 83 Swamp 10943 0.733 Normal
W 53 Offshore
5340 0.593 Normal W 84 Swamp 3955 0.576 Normal
W 54 Offshore 4999 0.771 Normal W 85 Land 4793 0.532 Normal
6022 0.607 Normal W 86 Land 4922 0.570 Normal
W 55 Land
11826 0.836 Normal 7951 0.669 Normal
W 56 Land 14122 0.985 0.720 W 87 Land 10004 0.813 Normal
4585 0.518 Normal 10912 0.928 0.660
W 57 Land 10341 0.832 Normal W 88 Land 4430 0.545 Normal
11890 0.924 0.633 W 89 Offshore 980 0.662 Normal
W 58 Offshore 10786 0.816 Normal 1542 0.648 Normal
5931 0.645 Normal W 90 Offshore 6430 0.738 Normal
W 59 Offshore
11670 0.789 Normal 11867 0.823 Normal
W 60 Swamp 5955 0.610 Normal W 91 Offshore 885 0.670 Normal
W 61 Swamp 5970 0.632 Normal W 92 Swamp 4446 0.500 Normal
W 62 Land 9531 0.744 Normal W 93 Land 10051 0.754 Normal
W 63 Land 5754 0.603 Normal W 94 Offshore 6440 0.677 Normal
W 64 Land 10580 0.799 Normal W 95 Land 7833 0.714 Normal
W 65 Land 1926 0.560 Normal W 96 Land 7046 0.705 Normal
W 66 Land 4439 0.694 Normal W 97 Land 10970 0.760 Normal
W 67 Land 5746 0.608 Normal W 98 Land 3876 0.589 Normal
W 68 Land 5752 0.628 Normal W 99 Land 4872 0.674 Normal
W 69 Swamp 3946 0.577 Normal 3023 0.479 Normal
W 70 Swamp 3945 0.600 Normal W 100 Swamp 7451 0.645 Normal
W 71 Swamp 4491 0.617 Normal 12988 0.824 Normal
W 72 Swamp 3948 0.524 Normal W 101 Swamp 10352 0.761 Normal
W 73 Swamp 5739 0.616 Normal 9452 0.724 Normal
W 102 Swamp
W 74 Land 10810 0.739 Normal 4447 0.566 Normal
W 75 Land 4908 0.557 Normal 5932 0.571 Normal
W 103 Swamp
W 76 Land 4990 0.596 Normal 11967 0.790 Normal
W 77 Land 5981 0.592 Normal W 104 Offshore 6925 0.769 Normal
W 78 Land 14945 0.860 Normal W 105 Land 7951 0.760 Normal
W 79 Land 4324 0.641 Normal 1501 0.600 Normal
W 106 Offshore
W 80 Land 5259 0.751 Normal 5605 0.768 Normal
W 81 Land 4184 0.526 Normal W 107 Swamp 8109 0.763 Normal
W 82 Land 4690 0.530 Normal W 109 Land 5510 0.585 Normal

167
5.7 Reference

Aadnoy, B.S., 1988. Modeling of the Stability of Highly Inclined Boreholes in Anisotropic Rock
Formations (includes associated papers 19213 and 19886 ). SPE Drill. Eng. 3, 259–268.
https://doi.org/10.2118/16526-PA
Aadnoy, B.S., Chenevert, M.E., 1987. Stability of Highly Inclined Boreholes (includes
associated papers 18596 and 18736 ). SPE Drill. Eng. 2, 364–374.
https://doi.org/10.2118/16052-PA
Aadnoy, B.S., Larson, K., 1989. Method for Fracture-Gradient Prediction for Vertical and
Inclined Boreholes. SPE Drill. Eng. 4, 99–103. https://doi.org/10.2118/16695-PA
Adewole, E.O., Macdonald, D.I.M., Healy, D., 2016. Estimating density and vertical stress
magnitudes using hydrocarbon exploration data in the onshore Northern Niger Delta Basin,
Nigeria: Implication for overpressure prediction. J. African Earth Sci. 123, 294–308.
https://doi.org/10.1016/j.jafrearsci.2016.07.009
Ajienka, J.., Nwokeji, B.., 1988. Evaluating the performance of onshore fracture pressure
gradient correlations in the Niger Delta. University of Port Harcourt.
Ajienka, J., Egbon, F., Onwuemena, U., 2009. Deep Offshore Fracture Pressure Prediction in the
Niger Delta - A New Approach. Niger. Annu. Int. Conf. Exhib.
https://doi.org/10.2118/128339-MS
Akinbinu, V.A., 2010. Prediction of fracture gradient from formation pressures and depth using
correlation and stepwise multiple regression techniques. J. Pet. Sci. Eng. 72, 10–17.
Alberty, M.W., McLean, M.R., 2004. A Physical Model for Stress Cages. SPE Annu. Tech.
Conf. Exhib. https://doi.org/10.2118/90493-MS
Althaus, V.E., 1977. A New Model For Fracture Gradient. J. Can. Pet. Technol. 16, 12.
https://doi.org/10.2118/77-02-10
Altun, G., Langlinais, J., Bourgoyne Jr., A.T., 2001. Application of a New Model To Analyze
Leak-Off Tests. SPE Drill. Complet. 16, 108–116. https://doi.org/10.2118/72061-PA
Anderson, E.M., 1951. The Dynamics of Faulting and Dyke Formation with Applications to
Britain. Edinburgh, Oliver Boyd.
Anderson, R.A., Ingram, D.S., Zanier, A.M., 1973. Determining Fracture Pressure Gradients
From Well Logs. J. Pet. Technol. 25, 1259–1268. https://doi.org/10.2118/4135-PA

168
Aston, M.S., Alberty, M.W., McLean, M.R., de Jong, H.J., Armagost, K., 2004. Drilling Fluids
for Wellbore Strengthening. IADC/SPE Drill. Conf. https://doi.org/10.2118/87130-MS
Avasthi, J.M., Goodman, H.E., Jansson, R.P., 2000. Acquisition, Calibration, and Use of the In
Situ Stress Data for Oil and Gas Well Construction and Production, in: SPE Rocky
Mountain Regional/Low-Permeability Reservoirs Symposium and Exhibition. Society of
Petroleum Engineers.
Avbovbo, A.A., 1978a. Tertiary lithostratigraphy of the Niger Delta. Am. Assoc. Pet. Geol. Bull.
62, 295–306.
Avbovbo, A.A., 1978b. Geothermal gradients in the southern Nigeria basin. Bull. Can. Pet. Geol.
26, 268–274.
Berry, L.N., Macpherson, L.A., 1972. Prediction of Fracture Gradients from Log Derived Elastic
Moduli. Log Anal. 13.
Breckels, I.M., Van Eekelen, H.A.M., 1982. Relationship between horizontal stress and depth in
sedimentary basins. J. Pet. Technol. 34, 2–191.
Brennan, R.M., Annis, M.R., 1984. A New Fracture Gradient Prediction Technique That Shows
Good Results in Gulf of Mexico Abnormal Pressure. SPE Annu. Tech. Conf. Exhib.
https://doi.org/10.2118/13210-MS
Bybee, K., 2008. Wellbore Strengthening in Shale. J. Pet. Technol. 60, 71–72.
https://doi.org/10.2118/0108-0071-JPT
Chan, A.W., Ekbote, S., Hows, M.P., Wong, G.K., 2015. In Situ Stress Measurements during
Well Abandonment. 49th U.S. Rock Mech. Symp.
Chellappah, K., Kumar, A., Aston, M., 2015. Drilling Depleted Sands: Challenges Associated
With Wellbore Strengthening Fluids. SPE/IADC Drill. Conf. Exhib.
https://doi.org/10.2118/173073-MS
Chellappah, K., Majidi, R., Aston, M., Cook, J., 2018. A Practical Model for Wellbore
Strengthening. IADC/SPE Drill. Conf. Exhib. https://doi.org/10.2118/189589-MS
Christman, S.A., 1973. Offshore Fracture Gradients. J. Pet. Technol. 25, 910–914.
https://doi.org/10.2118/4133-PA
Constant, D.W., Bourgoyne Jr, A.T., 1988. Fracture-gradient prediction for offshore wells. SPE
Drill. Eng. 3, 136–140.
Contreras, O., Hareland, G., Husein, M., Nygaard, R., Al-saba, M.T., 2014. Experimental

169
 Investigation on Wellbore Strengthening In Shales by Means of Nanoparticle-Based
Drilling Fluids. SPE Annu. Tech. Conf. Exhib. https://doi.org/10.2118/170589-MS
Couzens-Schultz, B.A., Chan, A.W., 2010. Stress determination in active thrust belts: An
alternative leak-off pressure interpretation. J. Struct. Geol. 32, 1061–1069.
Daines, S.R., 1982. Prediction of Fracture Pressures for Wildcat Wells. J. Pet. Technol. 34, 863–
872. https://doi.org/10.2118/9254-PA
Daneshy, A.A., Slusher, G.L., Chisholm, P.T., Magee, D.A., 1986. In-Situ Stress Measurements
During Drilling. J. Pet. Technol. 38, 891–898. https://doi.org/10.2118/13227-PA
Daukoru, J.W., 1975. PD 4(1) Petroleum Geology of the Niger Delta. World Pet. Congr.
De Bree, P., Walters, J. V, 1989. Micro/Minifrac test procedures and interpretation for in situ
stress determination, in: International Journal of Rock Mechanics and Mining Sciences &
Geomechanics Abstracts. Elsevier, pp. 515–521.
Doust, H., Omatsola, E., 1990. Niger Delta, in: Divergent / Passive Margin Basins. pp. 201–238.
Eaton, B.A., 1969. Fracture Gradient Prediction and Its Application in Oilfield Operations. J.
Pet. Technol. 21, 1353–1360. https://doi.org/10.2118/2163-PA
Edwards, S.T., Meredith, P.G., Murrell, S.A.F., 1998. An investigation of leak-off test data for
estimating in-situ stress magnitudes: application to a basinwide study in the North Sea, in:
SPE/ISRM Rock Mechanics in Petroleum Engineering. Society of Petroleum Engineers.
Engelder, T., Fischer, M.P., 1994. Influence of poroelastic behavior on the magnitude of
minimum horizontal stress, S h in overpressured parts of sedimentary basins. Geology 22,
949–952.
Evamy, B.D., Haremboure, J., Kamerling, P., Knaap, W.A., Molloy, F.A., Rowlands, P.H., 1978.
Hydrocarbon habitat of Tertiary Niger delta. Am. Assoc. Pet. Geol. Bull. 62, 1–39.
Feng, Y., Gray, K.E., 2017. Review of fundamental studies on lost circulation and wellbore
strengthening. J. Pet. Sci. Eng. 152, 511–522.
Feng, Y., Gray, K.E., 2016. A comparison study of extended leak-off tests in permeable and
impermeable formations, in: 50th US Rock Mechanics/Geomechanics Symposium.
American Rock Mechanics Association.
Finch, W., 1969. Abnormal Pressure in the Antelope Field, North Dakota. J. Pet. Technol. 21.
Gonzalez, M.E., Bloys, J.B., Lofton, J.E., Pepin, G.P., Schmidt, J.H., Naquin, C.J., Ellis, S.T.,
Laursen, P.E., 2004. Increasing Effective Fracture Gradients by Managing Wellbore

170
 Temperatures. IADC/SPE Drill. Conf. https://doi.org/10.2118/87217-MS
Haimson, B., Fairhurst, C., 1967. Initiation and extension of hydraulic fractures in rocks. Soc.
Pet. Eng. J. 7, 310–318.
Harkins, L.K., Baugher, I.H.., 1969. Geological significance of abnormal formation pressures. J.
Pet. Technol. 961–966. https://doi.org/10.2118/2228-PA
Hettema, M.H.H., Bostrøm, B., Lund, T., 2004. Analysis of Lost Circulation During Drilling in
Cooled Formations. SPE Annu. Tech. Conf. Exhib. https://doi.org/10.2118/90442-MS
Holbrook, P.W., 1989. A New Method for Predicting Fracture Propagation Pressure From MWD
or Wireline Log Data. SPE Annu. Tech. Conf. Exhib. https://doi.org/10.2118/SPE-19566-
MS
Holm, G.M., 1998. Distribution and origin of overpressure in the Central Graben of the North
Sea. Law, B.E., G.F. Ulmishek, V.I. Slavin eds., Abnorm. Press. Hydrocarb. Environ.
AAPG Mem. 70, 123–144.
Hubbert, M.K., Willis, D.G., 1957. Mechanics Of Hydraulic Fracturing.
Kumar, A., Savari, S., Whitfill, D., Jamison, D.E., 2010. Wellbore Strengthening: The Less-
Studied Properties of Lost-Circulation Materials. SPE Annu. Tech. Conf. Exhib.
Kunze, K.R., Steiger, R.P., 1992. Accurate In-Situ Stress Measurements During Drilling
Operations. SPE Annu. Tech. Conf. Exhib. https://doi.org/10.2118/24593-MS
Li, G., Lorwongngam, A., Roegiers, J.-C., 2009. Critical Review Of Leak-Off Test As A
Practice For Determination Of In-Situ Stresses. 43rd U.S. Rock Mech. Symp. 4th U.S. -
Canada Rock Mech. Symp.
Lowrey, J.P., Ottesen, S., 1995. An Assessment of the Mechanical Stability of Wells Offshore
Nigeria. SPE Drill. Complet. 10, 34–41. https://doi.org/10.2118/26351-PA
Matthews, W.R., Kelly, J., 1967. How to predict formation pressure and fracture gradient from
electric and sonic logs. Oil Gas.
Oloruntobi, O., Adedigba, S., Khan, F., Chunduru, R., Butt, S., 2018. Overpressure prediction
using the hydro-rotary specific energy concept. J. Nat. Gas Sci. Eng. 55, 243–253.
Oloruntobi, O., Butt, S., 2019. Energy-based formation pressure prediction. J. Pet. Sci. Eng. 173,
955–964.
Parriag, E.R., 1976. Prediction of Fracture Gradients in Samaan Field, in: SPE Petroleum and
Exposition Conference. Society of Petroleum Engineers.

171
Pennebaker, E.S., 1968. An Engineering Interpretation of Seismic Data. Fall Meet. Soc. Pet.
Eng. AIME. https://doi.org/10.2118/2165-MS
Perkins, T.K., Gonzalez, J.A., 1984. Changes in Earth Stresses Around a Wellbore Caused by
Radially Symmetrical Pressure and Temperature Gradients. Soc. Pet. Eng. J. 24, 129–140.
https://doi.org/10.2118/10080-PA
Raaen, A.M., Horsrud, P., Kjørholt, H., Økland, D., 2006. Improved routine estimation of the
minimum horizontal stress component from extended leak-off tests. Int. J. Rock Mech. Min.
Sci. 43, 37–48.
Rai, U.B., Ghodke, N., Schutjens, P., Shete, K., 2014. Fracture Gradient From Leakoff Test:
Pitfalls of Using LOT Data From Nonvertical Wells. IADC/SPE Drill. Conf. Exhib.
https://doi.org/10.2118/167963-MS
Reginald-Ugwuadu, O.G., Alabi, T.I., Eze, J.O., Ebisike, R.C., 2014. Fracture Gradient
Estimation in the Niger Delta - A Practical and Statistical Approach. SPE Niger. Annu. Int.
Conf. Exhib. https://doi.org/10.2118/172481-MS
Salz, L.B., 1977. Relationship Between Fracture Propagation Pressure And Pore Pressure. SPE
Annu. Fall Tech. Conf. Exhib. https://doi.org/10.2118/6870-MS
Savari, S., Whitfill, D.L., Jamison, D.E., Kumar, A., 2014. A Method to Evaluate Lost
Circulation Materials - Investigation of Effective Wellbore Strengthening Applications.
IADC/SPE Drill. Conf. Exhib. https://doi.org/10.2118/167977-MS
Schmitt, D.R., Zoback, M.D., 1989. Poroelastic effects in the determination of the maximum
horizontal principal stress in hydraulic fracturing tests—a proposed breakdown equation
employing a modified effective stress relation for tensile failure, in: International Journal of
Rock Mechanics and Mining Sciences & Geomechanics Abstracts. Elsevier, pp. 499–506.
Short, K.., Stauble, A.., 1967. Outline of Geology of Niger Delta. Am. Assoc. Pet. Geol. Bull.
51, 761–779.
Song, J., Rojas, J.C., 2006. Preventing Mud Losses by Wellbore Strengthening. SPE Russ. Oil
Gas Tech. Conf. Exhib. https://doi.org/10.2118/101593-MS
Swarbrick, R.E., 1995. Distribution and Generation of the Overpressyre System, Eaastern
Delaware BAsin, Western Texas and Southern New Mexico: Discussion. Am. Assoc. Pet.
Geol. Bull. 12, 1386–1405.
Swarbrick, R.E., Osborne, M.J., 1998. Mechanisms that generate abnormal pressures: an

172
 overview. Law, B.E., G.F. Ulmishek, V.I. Slavin eds., Abnorm. Press. Hydrocarb. Environ.
AAPG Mem. 70 13–34.
Taylor, D.B., Smith, T.K., 1970. Improved Facture Gradient Estimates in Offshore Drilling
Operations, in: Drilling and Production Practice. American Petroleum Institute.
Thiercelin, M.J., Plumb, R.A., Desroches, J., Bixenman, P.W., Jonas, J.K., Davie, W.A.R., 1996.
A New Wireline Tool for In-Situ Stress Measurements. SPE Form. Eval. 11, 19–25.
https://doi.org/10.2118/25906-PA
Ugwu, S.A., Nwankwo, C.N., 2014. Integrated approach to geopressure detection in the X-field,
Onshore Niger Delta. J. Pet. Explor. Prod. Technol. 4, 215–231.
van Oort, E., Vargo, R.F., 2008. Improving Formation-Strength Tests and Their Interpretation.
SPE Drill. Complet. 23, 284–294. https://doi.org/10.2118/105193-PA
Vuckovic, V., 1989. Prediction of Fracture Gradients Offshore Australia. SPE Asia-Pacific Conf.
Wang, H., Soliman, M.Y., Shan, Z., Meng, F., Towler, B.F., 2011. Understanding the effects of
leakoff tests on wellbore strength. SPE Drill. Complet. 26, 531–539.
Wang, H., Soliman, M.Y., Towler, B.F., 2009. Investigation of Factors for Strengthening a
Wellbore by Propping Fractures. SPE Drill. Complet. 24, 441–451.
Weber, K.J., 1987. Hydrocarbon distribution patterns in Nigerian growth fault structures
controlled by structural style and stratigraphy. J. Pet. Sci. Eng. 1, 91–104.
Yassir, N.A., Addis, M.A., Hennig, A., 1998. Relationships between pore pressure and stress in
different tectonic settings.
Zhang, J., 2011. Pore pressure prediction from well logs: Methods, modifications, and new
approaches. Earth-Science Rev. 108, 50–63.
Zhang, J., Alberty, M., Blangy, J.P., 2016. A Semi-Analytical Solution for Estimating the
Fracture Width in Wellbore Strengthening Applications. SPE Deep. Drill. Complet. Conf.
Zhang, J., Yin, S.-X., 2017. Fracture gradient prediction: an overview and an improved method.
Pet. Sci. 14, 720–730.
Zhang, Y., Zhang, J., 2017. Lithology-dependent minimum horizontal stress and in-situ stress
estimate. Tectonophysics 703, 1–8.
Zoback, M.D., 2010. Reservoir geomechanics. Cambridge University Press

173
 Chapter 6

6.0 Real-time Lithology Prediction Using Hydromechanical Specific Energy

Preface

A version of this chapter has been published in the Journal of Petroleum Science and

Engineering, 2019. I am the primary author. Co-author Dr. Stephen Butt reviewed the

manuscript and provided technical assistance in the development of the concept. I formulated the

initial concept and carried out most of the data analysis. I prepared the first draft of the

manuscript and revised the manuscript based on the feedback from the co-author.

Abstract

The previous applications of specific energy to drilling operations have focused mainly on

drilling optimization and identification of inefficient drilling conditions. Recent advances in

specific energy extend its applications to overpressure detection and pore pressure prediction. In

this paper, an attempt is made to further extend the application of specific energy to real-time

identification of subsurface lithology. The concept is based on the principle that the total energy

required to break and remove a unit volume of rock is a function of lithology. The proposed

methodology is tested using a recently drilled exploratory gas well in the tertiary deltaic system

of the Niger Delta basin. In general, an excellent agreement is observed in trend between the

traditional lithology identifiers (gamma ray and sonic velocity ratio) and the total energy

consumed in breaking and removing the penetrated rocks. Unlike the logging while drilling

(LWD) technique commonly employed in the industry (including the application of near bit

sensors placed few feet behind the bit), the proposed methodology can provide a reliable means

174
of picking formation tops and identifying subsurface lithology at the bit with no extra cost since

drilling parameters are routinely recorded at the wellsite during the drilling of a well. The

proposed methodology will assist the drilling engineers and geologists in determining the casing

setting depths and coring points without having to drill too deep into the formation of interest.

Keywords: Hydromechanical specific energy, Lithology, Rate of penetration, Drilling, Bit.

6.1 Introduction

Traditionally, real-time detection of lithological boundary and identification of lithology is

performed at the wellsite during the drilling of a well using the logging while drilling (LWD)

tools. However, there are some critical subsurface drilling conditions where the application of

conventional LWD may prove inadequate. For instance, using the conventional LWD tools to

determine the coring point of a thin reservoir. Under this condition, a large proportion of the

reservoir thickness may be unknowingly penetrated before the conventional LWD is able to

identify the formation top of interest, thereby jeopardizing the entire coring operations. The

application of near bit LWD allows lithology identification a few feet behind the bit at an

extremely high cost. In most cases, the high cost of the near bit sensors may be prohibitive to

operating companies, especially the marginal operators. Moreover, while drilling at a great depth

in an offshore environment with a floating rig, there is a possibility that the LWD tools may fail

when approaching the casing setting depth or coring point with only a few feet remaining to be

drilled before calling off the current operations. Under this prohibitive condition of extremely

high operating cost, the drilling engineers and geologists will not likely pull out of hole to

replace the LWD tools if subsurface lithology can be predicted from readily recorded drilling

parameters except for the purpose of reservoir evaluation other than lithology identification. The

175
applications of cutting descriptions by mud loggers for lithology identification also have their

limitations. The associated lag time required to move the drill cuttings from the bottom of the

hole to surface and the possibility that the drill cuttings obtained at the shale shakers may not be

coming from the bottom of the hole but rather somewhere higher up in the well (especially in

unstable wellbore) can make the cutting descriptions unsuitable for determining the casing

setting depths and coring points. At best, cutting descriptions are mostly used in conjunction with

LWD for confirmation purposes.

Previous attempts to use drilling-related parameters (ROP and d-exponent) to identify

subsurface lithology have produced mixed results. The ROP is influenced by several factors

which include: the degree of rock compaction, lithology, rotary speed, bit type, weight on bit

(WOB), bit size, bit wear, torque, bit hydraulics energy and differential pressure (Bourgoyne and

Young, 1973). From an operational point of view, it may not always be possible to maintain the

above factors constant during the drilling of a well (Oloruntobi and Butt, 2019a). Therefore,

changes in ROP may not necessarily signify changes in subsurface lithology. Although the d-

exponent is normalized for the effects of rotary speed, WOB and bit diameter on the ROP

(Jorden and Shirley, 1966), one of its major limitations is that the model does not consider the

effect of bit hydraulic energy on the ROP. This limits the application of d-exponent to hard rocks

and makes it unsuitable to most unconsolidated sediments where the bit hydraulic energy assists

in breaking the rock ahead of the bit. There are also instances when the driller decides to increase

the flow rate for hole cleaning, reduces the flow rate to minimize loss circulation incidents,

change the nozzle sizes for drilling optimization purposes or change the mud weight for well

control and wellbore stability purposes. Under such circumstances of fluctuating bit hydraulic

energy, the use of d-exponent for lithology identification may lead to wrong interpretation.

176
 The mechanical specific energy was first defined by Teale (1965) as the amount of

energy required to remove a unit volume of rock (the sum of axial and rotary energies):

WOB 120πNT
MSE = + (6.1)
Ab Ab ROP

where MSE is the mechanical specific energy (psi); WOB is the downhole weight on bit (lbs); Ab

is the bit area (in2); N is the rotary speed (rpm); T is the torque on bit (lb-ft); ROP is the rate of

penetration (ft/hr). Because the majority of the field data are recorded by the surface sensors

under normal circumstances, Pessier and Fear (1992) proposed a relationship among the

downhole torque, bit diameter (Db ) and WOB:

μ ∗ Db ∗ WOB
T= , (6.2)
36

where T is the downhole torque (lb-ft); Db is the bit diameter (in); WOB is the weight on bit

(lbs); μ is the bit specific coefficient of sliding friction. The bit coefficient of sliding friction

depends on several factors which include rock confined compressive strength, lithology, depth of

cut, mud weight, cutter density/blade count (for PDC bits), cutter sizes and bit wear (Caicedo et

al. 2005; Guerrero & Kull 2007). Pessier and Fear combined equations 6.1 and 6.2 to produce

equation 6.3:

WOB 13.33μNWOB
MSE = + . (6.3)
Ab Db ROP

The real-time application of MSE is a valuable tool for both drillers and drilling engineers

(Koederitz and Weis, 2005). The MSE surveillance has proved to be an effective tool in

identifying downhole drilling problems and optimizing drilling operations (Dupriest et al., 2005;

177
Dupriest, 2006; Amadi & Iyalla, 2012; Bevilacqua et al., 2013; Pinto & Lima, 2016). Rabia

(1985) used the concept of modified specific energy for bit selection. Waughman et al. (2003)

also used the specific energy concept to determine when to pull worn poly polycrystalline

diamond compact (PDC) bit in oil-based mud. To improve the usefulness of MSE surveillance in

field operations, the original mechanical specific energy equation as derived by Teale (1965) was

adjusted to include a mechanical drilling efficiency factor (Dupriest & Koederitz, 2005).

Armenta (2008) showed the importance of including the bit hydraulic energy term into the MSE

model. The results of extensive experimental studies conducted by Rajabov et al. (2012) on three

different rock types (Carthage marble, Mancos shale, and Torrey Buff sandstone) showed that

the mechanical specific energy of PDC cutters increases with increasing back rake angle at both

atmospheric and confining pressure conditions. Abbas et al. (2014) combined the bit dullness

model (dimensionless torque and dimensionless rate of penetration) and MSE to determine the

downhole drill bit conditions where torque data is unavailable. Abbott (2015) used the

mechanical specific energy ratio (MSER) to optimize real-time drilling performance for under-

reaming operations. Menand and Mills (2017) used the combination of MSE and MSE-DS

(drilling strength) ratio to detect vibration, bit balling, and bit wear. Wei et al. (2016) used the

MSE plus hydraulic energy to identify abnormal conditions for pulsed-jet drilling. Zhou et al.

(2017) proposed a model that relates MSE to the depth of cut for a circular cutter. Laboratory

investigations have shown the dependency of MSE on differential/confining pressure (Rafatian

et al. 2010; Akbari et al. 2013). Akbari et al. (2014) established a relationship among MSE,

uniaxial compressive strength, differential pressure, and confining pressure:

∆P Pc
MSE = UCS + [a + b Pc ] ln , (6.4)
Patm

178
where MSE is the mechanical specific energy (psi); UCS is the uniaxial compressive strength

(psi); ∆𝑃 is the differential pressure between confining pressure and pore pressure (psi); 𝑃𝑐 is the

confining pressure (psi); 𝑃𝑎𝑡𝑚 is the atmospheric pressure (psi); 𝑎 is the coefficient that is

dependent on rock internal friction angle; 𝑏 is the coefficient that is dependent on rock

permeability, porosity, fluid viscosity, fluid compressibility, rotary speed and depth of the cut.

The dependency of specific energy on differential pressure has been explored for pore

pressure predictions (Cardona, 2011; Majidi et al., 2017; Oloruntobi et al., 2018).

Currently, the applications of specific energy to drilling operations can be classified into

three categories: (1) drilling optimization; (2) identification of drilling problems; (3) pore

pressure prediction. In this paper, an attempt is made to extend the application of specific energy

to real-time detection of lithological boundaries and identification of subsurface lithology.

6.2 Methodology

The mechanical drilling efficiency factor (MDEF) is defined as the ratio between the rock’s

confined compressive strength (CCS) and the MSE:

CCS
MDEF = (6.5)
MSE

The value of MDEF is typically between 0.3 and 0.4 for most drilling conditions (Dupriest &

Koederitz, 2005). Based on the Mohr-Coulomb criterion, the CCS is given by:

1 − sin θ
CCS = UCS + ∆P [ ] (6.6)
1 + sin θ

where UCS is the unconfined compressive strength (psi); ∆P is the differential pressure between

179
the bottom-hole pressure and formation pore pressure (psi); θ is the angle of internal friction

(degrees). Equations 6.5 and 6.6 can be combined to obtain equation 6.7:

1 1 − sin θ
MSE = [UCS + ∆P [ ]] (6.7)
MDEF 1 + sin θ

Equation 6.7 clearly demonstrates that the drilling response (specific energy) is a function of

rock properties (UCS and θ) which are lithology dependent, differential pressure (∆P) and bit

conditions (MDEF). Therefore, changes in specific energy can be used to identify changes in

lithology if the drilling environment is known or changes in lithological boundary if the drilling

environment is not known. Note that changes in lithological boundary will also indicate variation

in the stratigraphic unit. Moreover, changes in specific energy can also be used to identify

downhole bit conditions and subsurface pressure regimes.

However, the MSE does not necessarily represent the total energy consumed in removing

a unit volume of rock because it excludes the bit hydraulic energy (Oloruntobi et al., 2018). In

soft rock environments, the bit hydraulic energy contributes to the total energy required to

remove a unit volume of rock by weakening the rocks ahead of the bit. The hydromechanical

specific energy (HMSE) is the total energy consumed during the drilling of a well (Mohan et al.

2015; Chen et al. 2016; Wei et al., 2016; Oloruntobi and Butt, 2019). The HMSE is the

combination of the axial, rotary, and hydraulic energies (equation 6.8):

HMSE = Axial Energy + Rotary Energy + Hydraulic Energy (6.8)

HMSE = MSE + Hydraulic Energy (6.9)

In the expanded form, the hydromechanical specific energy is given by:

180
 WOB 120πNT 1154η∆Pb Q
HMSE = + + (6.10)
Ab Ab ROP Ab ROP

where WOB is the downhole weight on bit (lbs); Ab is the bit area (in2); N is the rotary speed

(rpm); T is the torque on bit (lb-ft); ROP is the rate of penetration (ft/hr); ∆Pb is the bit pressure

drop (psi); Q is the flow rate (gpm); η is the hydraulic energy reduction factor. Due to

accelerated fluid entrainment immediately below the jet nozzles during drilling, only a portion

(25 – 40%) of the available bit hydraulic energy actually reaches the bottom of the hole (Warren,

1987). The hydraulic energy reduction factor converts the jet hydraulic energy into the bottom-

hole hydraulic energy. For polycrystalline diamond compact (PDC) bits, the hydraulic energy

reduction factor (ηPDC Bit ) can be expressed as a function of the junk slot area and total flow area

(Oloruntobi et al., 2018):

JSA −0.122
ηPDC Bit = 1−[ ] (6.11)
TFA

where JSA is the junk slot area (in2); TFA is the total flow area (in2). For roller cone bits (RCB),

the hydraulic energy reduction factor is expressed as a function of bit area and total flow area

Warren (1987):

0.15 Bit Area −0.122

ηRCB = 1−[ ] (6.12)
TFA

The pressure drop at the bit nozzle is expressed as a function of circulating fluid density,

volumetric flow rate, and nozzle total flow area:

MW Q2
∆Pb = , (6.13)
10858 TFA2
181
where ∆Pb is the bit pressure drop (psi); MW is the mud weight (ppg); Q is the flow rate (gpm);

TFA is the total flow area (in2). The hydromechanical specific energy consumed while drilling

with PDC bits can be obtained by combining equations 6.10, 6.11 and 6.13:

JSA −0.122
WOB 120πNT 1154 MW Q3 [1 − [TFA] ]
HMSEPDC = + + (6.14)
Ab Ab ROP 10858 Ab ROP TFA2

The hydromechanical specific energy consumed while drilling with roller cone bits can be

obtained by combining equations 6.10, 6.12 and 6.13:

3 0.15 Bit Area −0.122

1154 MW Q [1 − [ ] ]
WOB 120πNT TFA
HMSERCB = + + (6.15)
Ab Ab ROP 10858 Ab ROP TFA2

It is acknowledged that the HMSE may be affected by several factors other than subsurface

lithology. These factors include rock compaction, bit wear, bit type and the differential pressure

between the bottom-hole pressure (dictated by equivalent circulating density: ECD) and the

formation pore pressure. In normally pressured intervals, rock compaction typically increases

with depth due to an increase in effective stress. Hence, the energy required to break and remove

a unit volume of rock will also increase with depth. Generally, bit wear will cause an increase in

the HMSE due to reduction in the rate of penetration. The application of different bit type in the

same hole section will produce different HMSE signature due to variation in cutting structure.

An increase in the strength of the surrounding rocks due to an increase in the downhole

differential pressure will result in an increase in the HMSE. The effect of differential pressure on

the ROP (hence, HMSE) is more pronounced at low values of overbalance than at high values of

overbalance (Vidrine and Benit, 1968; Black et al. 1985; Bourgoyne et al., 1986). Although

lithology is the major factor controlling the HMSE changes, if the effects of other factors on the

182
HMSE can be minimized, changes in the HMSE can be directly attributed to lithological changes

due to changes in drillability corresponding to different rocks types.

Based on Athy (1930) porosity compaction model (equation 6.16), the HMSE can be

normalized for rock compaction effect (equations 6.16 and 6.17):

∅ = ∅o e−k𝑍 (6.16)

JSA −0.122
WOB 120πNT 1154 MW Q3 [1 − [TFA] ]
HMSEPDC = + + ∅o e−k𝑍 (6.17)
Ab Ab ROP 10858 Ab ROP TFA2
[ ]

0.15 Bit Area −0.122

1154 MW Q3 [1 − [ ] ]
WOB 120πNT TFA
HMSERCB = + + ∅o e−k𝑍 (6.18)
Ab Ab ROP 10858 Ab ROP TFA2
[ ]

where ∅o is the surface/mudline porosity (fraction); Z is the true vertical depth (ft); k is the

compaction coefficient (1/ft). The value of ∅o ranges between 0.40 and 0.70, depending on the

lithology and environment of deposition (Meade, 1966; Burrus, 1998; Swarbrick and Osborne,

1998; Zoback, 2010). It is widely known that different lithologies will compact at different rates

and from contrasting surface/mudline porosities (Swarbrick, 2001). Therefore, a line of best fit

through an offset well data that consists of several stratigraphic units can be used to calibrate the

compaction coefficient and surface/mudline porosity.

For practical purposes, the effects of bit wear and bit type on the HMSE can be

minimized by analyzing the HMSE over short intervals drilled with a single bit. The short

intervals will ensure that the bit dulling is within tolerable range and the single bit will ensure the

effect of bit type on the HMSE is eliminated. Interval of analysis to minimize bit wear effect

should be obtained from the offset data. Therefore, over the intervals where the bit dulling is

183
within an acceptable range, any changes in the HMSE trend will either indicate changes in

lithology or changes in differential pressure. The changes caused by differential pressure are

more gradual: gradual decrease in the HMSE may indicate drilling through the pressure

transition zones as formation pore pressure increases while the gradual increase in the HMSE

may indicate the amount of overbalance is becoming excessive. However, the changes caused by

lithology are typically abrupt and easily identified. Since lithology identification is the objective;

any sudden changes in the HMSE trend will indicate changes in lithology. When plotted against

depth on semi-log, the HMSE computed using equation 6.17 or 6.18 should be able to identify

the various stratigraphic units being penetrated.

If available, downhole measurements of torque and WOB from the measurement while

drilling (MWD) tools should be used to estimate the HMSE. Using the drilling parameters

obtained from surface measurements to estimate the HMSE can introduce significant errors

especially in moderately to highly deviated wells (> 20o inclination) due to the presence of

friction between the drill string and the borehole walls. The application of drilling data obtained

from surface measurements to compute the HMSE is possible in vertical wells since the friction

between the drill string and the walls of the borehole is usually negligible.

6.3 Field Example

To demonstrate the usefulness of the proposed methodology, an exploratory gas well (Well A)

located approximately 83 km northwest of Port Harcourt in the central swamp region of the

Niger Delta basin is considered as the case study. Well A is a slightly deviated well with a

maximum inclination of 14.6o. Figure 6.1 shows the location of the well under consideration.

The Niger Delta is an extensional rift basin system that consists of three types of formations in

184
descending order: (1) Benin formation – this formation consists of mostly continental loose

sands, (2) Agbada formation – this formation consists of alternating sequence of sands and shales

where commercial accumulation of hydrocarbons are found, and (3) Akata formation – this

formation consists of thick marine shales. (Oloruntobi and Butt, 2019b; Oloruntobi et al., 2019;

Yusuf et al., 2019). The detailed geology and hydrocarbon system of the basin can be obtained

from the literature (Short and Stauble, 1967; Burke, 1972; Daukoru 1975; Avbovbo, 1978;

Evamy et al., 1978; Nwachukwu and Chukwura, 1986; Weber 1987; Doust, 1990; Doust and

Omatsola, 1990; Reijers 2011).

Figure 6 1: The location map for Well A.

185
Figure 6 2: The plots of drilling parameters and wellbore pressures versus depth for Well A (Interval 1).

186
Figure 6 3: The plots of drilling parameters and wellbore pressures versus depth for Well A (Interval 2).

187
 Figures 6.2 and 6.3 display the recorded drilling parameters and wellbore pressures for

two separate intervals in Well A. The recorded data include torque, rotary speed, flow rate, rate

of penetration (ROP), weight on bit (WOB), equivalent circulating density (ECD), mud weight

(MW) and pore pressure (PP). The bottom-hole pressure (BHP) is obtained from the ECD. The

recorded drilling parameters were obtained from surface measurements. These data were then

checked for identification and elimination of outliers. The errors associated with using the

drilling data obtained from surface measurements to compute the HMSE in this well may be

negligible because the well maximum inclination is low (< 15o), the intervals under consideration

are short (≤ 2000 ft), the kick-off point is deep (7,878 ft) and the dogleg severities (DLS) do not

exceed 1.50/100 ft anywhere across the intervals. Over short intervals in low inclination wells at

low DLS, changes in friction forces between the drill string and the borehole walls can be

negligible.

In interval 1 (Figure 6.2), the recorded drilling parameters were acquired in the 16’’ hole

section drilled with a single roller cone (milled tooth) bit from 8,695 ft to 9,420 ft. The interval

was drilled with water-based mud and the total flow area (TFA) of the roller cone bit is 1.1689

in2. The formation pore pressure is normal across all the penetrated rocks with an average

gradient of 0.435 psi/ft. In interval 2 (Figure 6.3), the recorded drilling parameters were acquired

in the 12 ¼’’ hole section drilled with a single PDC bit from 9,690 ft to 11,690 ft. The total flow

area (TFA) of the PDC bit is 1.2003 in2 and its junk slot area (JSA) is 21.28 in2. The interval was

drilled with oil-based mud and the formation pore pressure varies across the penetrated rocks

between 0.254 psi/ft and 0.455 psi/ft. This interval consists of both normally pressured zones and

two depleted sands.

188
Figure 6 4: The offset well data used to calibrate ∅o and k.

To obtain the rock compaction coefficient (k) and the surface porosity (∅o ), equation 6.16

is calibrated to an offset well in the basin. Figure 6.4B shows the plot of porosity against depth.

189
The red dotted line corresponds to the shale compaction trend (equation 6.19). The yellow dotted

line corresponds to the sand compaction trend (equation 6.20). The black dotted line corresponds

to a line of best fit through the various stratigraphic units (equation 6.21).

∅ = 0.60e−0.00018∗Z (6.19)

∅ = 0.448e−0.00004∗𝑍 (6.20)

∅ = 0.54e−0.0001∗Z (6.21)

In this paper, equation 6.21 is used to normalize the HMSE for rock compaction effect for all the

lithologies with the rock compaction coefficient and the surface porosity being 0.0001 1/ft and

0.54 (fraction) respectively. Using equation 6.21 to normalize the HMSE for all the lithologies

will only introduce small error which can be acceptable. The formation porosity (∅) is estimated

using equation 6.22:

ρma 1 ρma − ρsh

∅= [ ]− [ ] ρb − [ ]V (6.22)
ρma − ρfl ρma − ρfl ρma − ρfl sh

where ∅ is the formation porosity (fraction); ρma is the sand matrix density (g/cc); ρsh is the

shale matrix density (g/cc); ρfl is the saturating fluid density which is typically assumed to be

1.00 g/cc; ρb is the measured formation bulk density (g/cc) Vsh is the shale volume (fraction). In

the Niger Delta, the values of sand matrix density and shale matrix density are 2.65 g/cc and 2.68

g/cc respectively. For the Niger Delta sediments, field observations have shown that a linear

relationship exists between shale volume and gamma ray index (IGR ). Therefore, shale volume is

obtained using equation 6.23:

190
 GR log − GR min
Vsh = IGR = (6.23)
GR max − GR min

where GRlog is the gamma ray reading at any given depth; GRmin is the sand line gamma ray

reading; GRmax is the shale line gamma ray reading. However, other non-linear empirical

responses between shale volume and gamma ray index exist depending on the formation age and

geographic area (Larionov, 1969; Stieber, 1970; Clavier et al., 1971; Assaad, 2008).

6.4 Discussion

Figure 6.5A shows the GR-depth and HMSE-depth plots for interval 1. The HMSE is computed

using equation 6.18 because the interval was drilled with a roller cone bit. An excellent

agreement in trend is observed between the gamma ray (GR) and the HMSE. This clearly

demonstrates the applicability of the HMSE to lithology identification. Abrupt changes in the

HMSE trend indicate lithological changes. In shale formations as indicated by high GR, higher

specific energy is consumed in removing the rocks. However, in sand formations as indicated by

low GR, lower specific energy is consumed in removing the rocks. A shale baseline drawn

through the interval indicates that the shale formation between 8,695 ft and 8,826 ft required

lower energy to drilled than the remaining deeper shale formations. This is probably due to bit

dulling effects on the HMSE.

Figure 6.5B shows the GR-depth, velocity ratio-depth and HMSE-depth plots for interval

2. The velocity ratio is derived from the ratio of compressional to shear velocities. Note that the

display unit of velocity ratio is in 1/100 for ease of interpretation.

191
Figure 6 5: The GR-depth, VR-depth and HMSE-depth plots for Well A.

192
The HMSE is computed using equation 6.17 because the interval was drilled with PDC bit. A

good agreement exists between the conventional lithology identifiers and the HMSE. In shale

formations as indicated by high GR and high velocity ratio, lower specific energy is consumed in

breaking the rocks. In sand formations as indicated by low GR and low velocity ratio, higher

specific energy is consumed in breaking the rocks The formation tops are clearly visible with

abrupt changes in the HMSE. Remarkably, the HMSE is able to identify the very tiny sands

(minor reservoirs), confirming the accuracy of the proposed methodology. The HMSE values in

the shale intervals trail the shale baseline except at depths greater than 11,600 ft where the

HMSE values in the bottom shale interval begin to shift from the shale baseline possibly due to

bit dulling effects. If the longer interval of analysis is considered, the effects of bit dulling on the

HMSE may be more pronounced, making evaluations more complex and difficult. The

conflicting responses of roller cone and PDC bits in the same lithology are mainly due to their

cutting actions. Each bit type drills hole in a different manner. The roller cone bit crushes the

formations while the PDC bit shears the formations. The abrupt changes in the HMSE at the

formation tops indicate that the effect of lithology on the HMSE dominates the drilling process.

6.5 Conclusions

In addition to drilling optimization and identification of drilling problems, the applications of

HMSE have been extended to real-time identification of lithology. Lithology identification using

the HMSE concept is based on observing trend changes. Any abrupt change in the HMSE trend

can be directly attributed to lithological change. The proposed methodology can provide a

reliable means of picking formation tops and identifying the various stratigraphic units being

penetrated at a relatively low cost. The proposed methodology can serve as an excellent
193
correlation tool in wells where petrophysical data are either not available or poorly acquired. To

ease interpretation, the drill bit responses (HMSE signatures) in different lithologies may be

predicted in advance by applying the HMSE concept to the offset data. Since PDC and roller

cone bits produce different HMSE responses, intervals drilled with two different types of bits

should not be analyzed together. The HMSE-depth plot for each bit run should be entirely

separated from the other bit runs.

The ability of the proposed methodology to be able to accurately identify subsurface

lithology will depend on the quality of the input data. Computation of HMSE using drilling

parameters that are subjected to severe vibrations will produce inaccurate results. The quality of

the input data can be improved in several ways: (1) measured parameters should be compared to

model parameters; (2) surface/downhole sensors should be calibrated before use; (3) If possible,

measurements should be taken using different sensors for comparison purposes; (4) Noise in the

data transmission system should be minimized; (5) Shocks and vibrations can be controlled by

incorporating the shock sub into the bottom-hole assembly (BHA), optimizing drilling

parameters (weight on bit and rotary speed) and selecting the right bit/BHA.

6.6 Reference

Abbas, K.R., Hassanpou, A., Hare, C., Ghadiri, M., 2014. “‘Instantaneous Monitoring of Drill
Bit Wear and Specific Energy as a Criteria for the Appropriate Time for Pulling Out Worn
Bits.’” Soc. Pet. Eng. (SPE 172269).
Abbott, A., 2015. The MSE Ratio: The New Diagnostic Tool to Optimize Drilling Performance
in Real-Time for Under-Reaming Operations. SPE Annu. Tech. Conf. Exhib.
https://doi.org/10.2118/178724-STU
Akbari, B., Miska, S., Mengjiao, Y., Ozbayoglu, E., 2013. Effect of Rock Pore Pressure on
194
 Mechanical Specific Energy of Rock Cutting Using Single PDC Cutter, in: 47th US Rock
Mechanics/Geomechanics Symposium. American Rock Mechanics Association.
Akbari, B., Miska, S., Yu, M., Ozbayoglu, M., 2014. Experimental Investigations of the Effect of
the Pore Pressure on the MSE and Drilling Strength of a PDC Bit. Soc. Pet. Eng. (SPE
169488). https://doi.org/10.2118/169488-MS
Amadi, W.K., Iyalla, I., 2012. Application of Mechanical Specific Energy Techniques in
Reducing Drilling Cost in Deepwater Development, in: SPE Deepwater Drilling and
Completions Conference. Society of Petroleum Engineers.
Armenta, M., 2008. Identifying Inefficient Drilling Conditions Using Drilling-Specific Energy.
Soc. Pet. Eng. (SPE 116667). https://doi.org/10.2118/116667-MS
Assaad, F.A., 2008. Field methods for petroleum geologists: A guide to computerized
lithostratigraphic correlation charts case study: Northern Africa. Springer Science &
Business Media.
Athy, L.F., 1930. Density, Porosity, and Compaction of Sedimentary Rocks. Am. Assoc. Pet.
Geol. Bull. 14, 194–200. https://doi.org/10.1306/3D93289E-16B1-11D7-
8645000102C1865D
Avbovbo, A.A., 1978. Tertiary lithostratigraphy of the Niger Delta. Am. Assoc. Pet. Geol. Bull.
62, 295–306.
Bevilacqua, M., Ciarapica, F.E., Marchetti, B., 2013. Acquisition, processing and evaluation of
down hole data for monitoring efficiency of drilling processes. J. Pet. Sci. Res.
Black, A.D., Dearing, H.L., DiBona, B.G., 1985. Effects of Pore Pressure and Mud Filtration on
Drilling Rates in a Permeable Sandstone. J. Pet. Technol. 37, 1671–1681.
https://doi.org/10.2118/12117-PA
Bourgoyne, A.T., Millheim, K.K., Chenevert, M.E., Young, F.S., 1986. Applied Drilling
Engineering (SPE Textbook Series, Vol. 2). Soc. Pet. Eng. Richardson, TX.
Bourgoyne, J.A.T., Young, J.F.S., 1973. Formation Evaluation and Abnormal Pressure
Detection. SPWLA Fourteenth Annu. Logging Symp. MAY 6-9,.
https://doi.org/10.1016/B978-0-323-04184-3.50079-0
Burke, K., 1972. Longshore drift, submarine canyons, and submarine fans in development of
Niger Delta. Am. Assoc. Pet. Geol. Bull. 56, 1975–1983.

195
Burrus, J., 1998. Memoir 70, Chapter 3: Overpressure models for clastic rocks, their relation to
hydrocarbon.
Caicedo, H.U., Calhoun, W.M., Ewy, R.T., 2005. Unique ROP Predictor Using Bit-specific
Coefficient of Sliding Friction and Mechanical Efficiency as a Function of Confined
Compressive Strength Impacts Drilling Performance. Soc. Pet. Eng. (SPE/IADC 92576).
https://doi.org/10.2118/92576-MS
Cardona, J., 2011. Fundamental Investigation of Pore Pressure Prediction during Drilling from
the Mechanical Behaviour of Rocks. PhD Thesis, Texas A&M Univ. Mech. Eng.
Chen, X., Gao, D., Guo, B., Feng, Y., 2016. Real-time optimization of drilling parameters based
on mechanical specific energy for rotating drilling with positive displacement motor in the
hard formation. J. Nat. Gas Sci. Eng. 35, 686–694.
Clavier, C., Hoyle, W., Meunier, D., 1971. Quantitative interpretation of thermal neutron decay
time logs: part I. Fundamentals and techniques. J. Pet. Technol. 23, 743–755.
Daukoru, J.W., 1975. PD 4(1) Petroleum Geology of the Niger Delta. World Pet. Congr.
Doust, H., 1990. Petroleum geology of the Niger Delta. Geol. Soc. London, Spec. Publ. 50, 365.
Doust, H., Omatsola, E., 1990. Niger Delta, in: Divergent / Passive Margin Basins. pp. 201–238.
Dupriest, F.E., 2006. Comprehensive Drill-Rate Management Process To Maximize Rate of
Penetration. Soc. Pet. Eng. (SPE 102210). https://doi.org/10.2118/102210-MS
Dupriest, F.E., Koederitz, W.L., 2005. Maximizing drill rates with real-time surveillance of
mechanical specific energy, in: SPE/IADC Drilling Conference. Society of Petroleum
Engineers.
Dupriest, F.E., Witt, J.W., Remmert, S.M., 2005. Maximizing ROP with real-time analysis of
digital data and MSE, in: International Petroleum Technology Conference. International
Petroleum Technology Conference.
Evamy, B.D., Haremboure, J., Kamerling, P., Knaap, W.A., Molloy, F.A., Rowlands, P.H., 1978.
Hydrocarbon habitat of Tertiary Niger delta. Am. Assoc. Pet. Geol. Bull. 62, 1–39.
Guerrero, C.A., Kull, B.J., 2007. Deployment Of An SeROP Predictor Tool For Real-Time Bit
Optimization. SPE/IADC Drill. Conf. https://doi.org/10.2118/105201-MS
Jorden, J.R., Shirley, O.J., 1966. Application of Drilling Performance Data to Overpressure
Detection. J. Pet. Technol. 18, 1387–1394. https://doi.org/10.2118/1407-PA

196
Koederitz, W., Weis, J., 2005. A Real-Time Implementation of MSE, American Association of
Drilling Engineers. AADE-05-NTCE-66.
Larionov, V. V, 1969. Radiometry of boreholes. Nedra, Moscow 127.
Majidi, R., Albertin, M., Last, N., 2017. Pore-Pressure Estimation by Use of Mechanical Specific
Energy and Drilling Efficiency. SPE Drill. Complet. 32, 97–104.
Meade, R.H., 1966. Factors influencing the early stages of the compaction of clays and sands--
review. J. Sediment. Res. 36.
Menand, S., Mills, K., 2017. Use of Mechanical Specific Energy Calculation in Real-Time to
Better Detect Vibrations and Bit Wear While Drilling. Am. Assoc. Drill. Eng.
Mohan, K., Adil, F., Samuel, R., 2015. Comprehensive Hydromechanical Specific Energy
Calculation for Drilling Efficiency. J. Energy Resour. Technol. 137, 012904.
https://doi.org/10.1115/1.4028272
Nwachukwu, J.I., Chukwura, P.I., 1986. Organic matter of Agbada Formation, Niger Delta,
Nigeria. Am. Assoc. Pet. Geol. Bull. 70, 48–55.
Oloruntobi, O., Adedigba, S., Khan, F., Chunduru, R., Butt, S., 2018. Overpressure prediction
using the hydro-rotary specific energy concept. J. Nat. Gas Sci. Eng. 55, 243–253.
Oloruntobi, O., Butt, S., 2019a. Energy-based formation pressure prediction. J. Pet. Sci. Eng.
173, 955–964.
Oloruntobi, O., Butt, S., 2019b. The New Formation Bulk Density Predictions for Siliciclastic
Rocks. J. Pet. Sci. Eng. 180, 526–537.
https://doi.org/https://doi.org/10.1016/j.petrol.2019.05.017
Oloruntobi, O., Onalo, D., Adedigba, S., James, L., Chunduru, R., Butt, S., 2019. Data-driven
shear wave velocity prediction model for siliciclastic rocks. J. Pet. Sci. Eng. 106293.
https://doi.org/https://doi.org/10.1016/j.petrol.2019.106293
Pessier, R.C., Fear, M.J., 1992. Quantifying Common Drilling Problems With Mechanical
Specific Energy and a Bit-Specific Coefficient of Sliding Friction. Soc. Pet. Eng. (SPE
24584). https://doi.org/10.2118/24584-MS
Pinto, C.N., Lima, A.L.P., 2016. Mechanical Specific Energy for Drilling Optimization in
Deepwater Brazilian Salt Environments. Soc. Pet. Eng. (IADC/SPE 180646).
https://doi.org/10.2118/180646-MS

197
Rabia, H., 1985. Specific energy as a criterion for bit selection. J. Pet. Technol. 37, 1225–1229.
https://doi.org/10.2118/12355-PA
Rafatian, N., Miska, S.Z., Ledgerwood, L.W., Yu, M., Ahmed, R., Takach, N.E., 2010.
Experimental study of MSE of a single PDC cutter interacting with rock under simulated
pressurized conditions. SPE Drill. Complet. 25, 10–18.
Rajabov, V., Miska, S.Z., Mortimer, L., Yu, M., Ozbayoglu, M.E., 2012. The Effects of Back
Rake and Side Rake Angles on Mechanical Specific Energy of Single PDC Cutters with
Selected Rocks at Varying Depth of Cuts and Confining Pressures. IADC/SPE Drill. Conf.
Exhib. https://doi.org/10.2118/151406-MS
Reijers, T., 2011. Stratigraphy and sedimentology of the Niger Delta. Geologos 17, 133–162.
Short, K.., Stauble, A.., 1967. Outline of Geology of Niger Delta. Am. Assoc. Pet. Geol. Bull.
51, 761–779.
Stieber, S.J., 1970. Pulsed neutron capture log evaluation-louisiana gulf coast, in: Fall Meeting
of the Society of Petroleum Engineers of AIME. Society of Petroleum Engineers.
Swarbrick, R.E., 2001. Pore-Pressure Prediction: Pitfalls in Using Porosity, in: Offshore
Technology Conference. Offshore Technology Conference.
Swarbrick, R.E., Osborne, M.J., 1998. Memoir 70, Chapter 2: Mechanisms that Generate
Abnormal Pressures: an Overview.
Teale, R., 1965. The Concept of Specific Energy in Rock Drilling. Int. J. Rock Mech. Min. Sci.
2, 57–73. https://doi.org/10.1016/0148-9062(65)90022-7
Vidrine, D.J., Benit, E.J., 1968. Field Verification of the Effect of Differential Pressure on
Drilling Rate. J. Pet. Technol. (SPE 1859) 20, 676–682. https://doi.org/10.2118/1859-PA
Warren, T.M., 1987. Penetration Rate Performance of Roller Cone Bits. SPE Drill. Eng. 2, 9–18.
https://doi.org/10.2118/13259-PA
Waughman, J.R., Kenner, V.J., Moore, A.R., 2003. Real-Time Specific Energy Monitoring
Enhances the Understanding of When To Pull Worn PDC Bits. SPE Drill. Complet. (SPE
81822) 59–68.
Weber, K.J., 1987. Hydrocarbon distribution patterns in Nigerian growth fault structures
controlled by structural style and stratigraphy. J. Pet. Sci. Eng. 1, 91–104.
Wei, M., Li, G., Shi, H., Shi, S., Li, Z., Zhang, Y., 2016. Theories and applications of pulsed-jet

198
 drilling with mechanical specific energy. SPE J. 21, 303–310.
Yusuf, B., Oloruntobi, O., Butt, S., 2019. The formation bulk density prediction for intact and
fractured siliciclastic rocks. Geod. Geodyn.
https://doi.org/https://doi.org/10.1016/j.geog.2019.05.005
Zhou, Y., Zhang, W., Gamwo, I., Lin, J.S., 2017. Mechanical specific energy versus depth of cut
in rock cutting and drilling. Int. J. Rock Mech. Min. Sci. 100, 287–297.
https://doi.org/10.1016/j.ijrmms.2017.11.004
Zoback, M.D., 2010. Reservoir geomechanics. Cambridge University Press.

199
 Chapter 7

7.0 Summary and Recommendations

7.1 Summary

The works presented in this manuscript have demonstrated the application of specific energies

(HRSE and HMSE) to pore pressure prediction. The new techniques allow the formation pore

pressure to be reliably predicted at the bit at relatively low cost. The field data required for the

computation of these energies allow the formation pore pressure to be monitored real-time.

Unlike the previous pore pressure prediction models from the drilling parameters, the inclusion

of the bit hydraulic energy term in the new models allows accurate prediction of formation pore

pressure under any subsurface drilling conditions (soft and hard rock environments). Pore

pressure prediction from the new methods is based on the concept that overpressure intervals

with lower effective stress will require less energy to drill than the normally pressured intervals

at the same depth. In normally pressured intervals, the values of the specific energy computed

over a uniform stratigraphic unit will increase with depth due to an increase in rock density and

degree of rock compaction. In overpressure intervals, the specific energy values start to gradually

deviate from the normal compaction trend to lesser values. The amount of deviation from the

normal compaction trend at any given depth is generally related to the magnitude of

overpressure. The higher the deviation, the greater the formation pore pressure. The concept of

specific energy has also been extended to real-time identification of subsurface lithology. The

accuracy of formation pore pressure prediction can be improved by improving the accuracy of

overburden pressure computation via improvement in formation bulk density prediction. This

thesis also presents a novel, simple and accurate techniques of estimating the formation bulk

200
density in areas where density logs are unavailable or unreliable. The new bulk density prediction

models can be applied to a wide range of lithologies in siliciclastic environments. Finally, since

pore and fracture pressures are closely related, this thesis presents a new fracture pressure

prediction model that can be applied to normal and overpressure intervals in the Niger Delta

basin. The main contributions of this thesis are highlighted below:

1. The development of a new pore pressure prediction technique from drilling parameters

that incorporates the bit hydraulic energy term based on the concept of total energy

consumed while drilling using downhole measurements.

2. The development of a new pore prediction technique from drilling parameters that

incorporates the bit hydraulic energy term based on the concept of total energy consumed

while drilling using only surface measurements.

3. The development of the new bulk density prediction models for siliciclastic rocks.

6. The application of specific energy concept to real-time lithology identification.

7. The development of a new fracture pressure prediction model for the Niger Delta.

7.2 Recommendations

Although the works in this thesis present new techniques of predicting pore pressure, fracture

pressure (Niger Delta), bulk density and lithology, many knowledge gaps still exist, and future

works can be used to address some of these gaps. These include but not limited to:

1. Excessive bit wear can mask the reversal in the specific trend when drilling through the

overpressure and pressure transition zones. Therefore, specific energy models that

incorporate wear factor term can be developed.

201
2. Just like the previous empirical relationships, the newly proposed formation bulk density

prediction models in this thesis may not be applicable to rocks that contain

microcracks/fractures. In consolidated formations that contain microcracks, changes in

effective stress will cause substantial changes in compressional wave velocity with little

or no changes in formation bulk density until all the microcracks are closed. The newly

proposed models should be extended to rocks that contain microcracks/fractures by

incorporating an additional parameter (shear sonic velocity) that will negate the effect of

microcracks/fractures on compressional sonic velocity.

3. The newly proposed formation bulk density prediction models do not cover carbonate

and evaporite environments. Similar models should be developed for these environments.

202