5/9/2014
Designed & Presented by
Mr. QUANG KHNH, HCMUT
03/2014 Quang Khnh HoChiMinh City University of Technology 1
Email: dqkhanh@hcmut.edu.vn or doquangkhanh@yahoo.com
Content & Agenda
Ref:
Recent Advances In Hydraulic Fracturing, John L. Gidley, Stephen A. Holditch, Dale E.
Nierode & Ralph W. Veatch Jr.,1991
Reservoir Stimulation, 3e Economides & Nolte
Petroleum Production Systems - Economides et al., 1994
Production Operations: Well Completions, Workover, and Stimulation -Thomas O. Allen,
Alan P. Roberts,1984
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Introduction
Objective: to create highly conductive paths some
distance away from the wellbore into the reservoir.
o Execution of a hydraulic fracture involves
the injection of fluids at a pressure sufficiently
high to cause "tensile failure" of the rock.
o At the fracture initiation pressure, often known
as the "breakdown pressure, the rock opens.
o As additional fluids are injected, the opening
is extended and the fracture propagates.
o A properly executed hydraulic fracture results in a "path," connected to the well,
that has a much higher permeability than the surrounding formation.
Introduction
o Minimum hydraulic fracturing candidate well selection screening criteria
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LENGTH, CONDUCTIVITY, & EQUIVALENT SKIN EFFECT
o Every hydraulic fracture can be characterized by its:
length ;
conductivity;
related equivalent skin effect
o In almost all calculations, the fracture length, which must be the conductive length and not the created
hydraulic length, is assumed to consist of two equal halflengths, xf, in each side of the well.
- beside, consider the penetration ratio: Ix = 2 xf / xe.
LENGTH, CONDUCTIVITY, & EQUIVALENT SKIN EFFECT
o The dimensionless fracture conductivity: CfD = kf W / k Xf
= (Ability of fracture to deliver oil/gas to well)/(Ability of formation to deliver gas into the fracture)
> 30 (Infinitely Conductive Fracture)
2 xf
w
o -Related to Prats a (called the relative capacity): CfD = /2a
where:k is the reservoir permeability, k f is the fracture permeability, and w is the propped fracture width.
o Fracture skin effect varying with fracture conductivity
(Cinco-ley and Samaniego, 1981)
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LENGTH, CONDUCTIVITY, & EQUIVALENT SKIN EFFECT
o Equivalent skin effect, sf, & Improve Productivity Index J:
o The equivalent skin effect, sf: the result of a hydraulic fracture of a certain length and conductivity
& can be added to the well inflow equations in the usual manner.=> sf is pseudo skin factor
used after the treatment to describe the productivity:
2kh 1 2kh
J J D
B ln[ re ] 0.75 s B
f
rw
o Prats (1961): the concept of dimensionless effective wellbore radius rwD
in a hydraulically fractured well:
LENGTH, CONDUCTIVITY, & EQUIVALENT SKIN EFFECT
for small values of a, or high conductivity fractures, the rwD is equal to 0.5, leading to rw
= xf /2; which suggests that for these large-conductivity fractures the reservoir drains to a
well with an effective wellbore equal to half of the fracture half-length.
Since the effective wellbore must be as large as possible, values of a larger than unity m
ust be avoided because the effective wellbore radius decreases rapidly.
=> hydraulic fractures should be designed for a < 1 or CfD > 1.6
for large values of a, the slope of the curve is equal to 1, implying a linear relationship
between rw and a that is approximately rw = kf w/4k; Which suggest that for low
conductivity fractures, the increase in rw does not depend on fracture length but instead
on fracture permeability-width product,which must be maximized.
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LENGTH, CONDUCTIVITY, & EQUIVALENT SKIN EFFECT
o What length or fracture permeability is desirable in hydraulic fracturing?
Lowpermeability reservoirs, leading to highconductivity fractures,
would benefit greatly from length.
Moderate to highpermeability reservoirs, naturally leading to
lowconductivity fractures, require good fracture permeability
(good quality proppant and nondamaging fracturing fluid).
Notation
rw wellbore radius, m (or ft)
r'w Prats equivalent wellbore radius due to fracture,
m (or ft)
xf
f s f ln Cinco-Ley-Samanieggo factor, dimensionless
rw
sf the pseudo skin factor due to fracture,
dimensionless
rw Prats' dimensionless (equivalent) wellbore
xf radius
But JD is the best
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Pseudo-steady state Productivity Index
q Jp
Production rate is proportional to drawdown, defined as average
pressure in the reservoir minus wellbore flowing pressure
Drawdown
2kh
q J D p
B
Circular:
1 Dimensionless
JD Productivity Index
r 3
ln e s
rw 4
Pseudo-skin, equivalent radius, f-factor
2kh 2kh
J J
r or r
B ln 0.472 e s f B ln 0.472 e
rw r 'w
Prats
f (C fD )
2kh 2kh
J
0.472re x 0.472re
B ln s f ln f B ln f
xf rw xf
Cinco-Ley
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Dimensionless Productivity
Index, sf and f and rw
1 1
JD or JD
re re
ln 0.472 sf ln 0.472
rw r 'w
Prats
f (C fD )
1 1
JD
0.472re x 0.472re
f
ln s f ln f ln
xf rw x f
Cinco-Ley
Factor f
(after Cinco-Ley and Samaniego, 1981)
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LENGTH, CONDUCTIVITY, & EQUIVALENT SKIN EFFECT
oExample:
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Proppant placement into formation
We can use the propping
agent to increase fracture
length or width.
Tip screenout (TSO)
techniques:
fracture width can be
increased without
How should we select the optimum fracture length
increasing the fracture
and width under the constraint that the proppant
extent. volume is given?
Fracture half length & CfD,opt
the optimum CfD,opt = 1.6 is a given constant for any reservoir
and any fixed amount of proppant.
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Optimum fracture dimensions
Once we know the volume of proppant that can be placed into one wing of the fracture, Vf, we can
calculate the optimum fracture dimensions as
Moreover, since
and yopt - 0.75 = 0.869, we obtain
Fracture Orientation & In situ stress
Least Principal Stress Least Principal Stress
Horizontal fracture Vertical fracture
The fracture will be oriented at a 90-degree angle to
the least principal stress.
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Fracture Orientation & In situ stress
Role of Formation Properties in Fracturing
The formation properties that are known to influence a fractures
growth pattern, including its height, are:
Young's modulus
Poisson's ratio
Tensile strength
Fracture toughness
Permeability
Porosity
Poroelasticity constant
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Rock Properties
Plane Strain Modulus:
Shear modulus:
Rock Properties
Tensile Strength: The maximum stress that a material can tolerate without rupture in a uniaxial tensile experiment is
the tensile stress.
Fracture Toughness: The critical value of the stress intensity factor, or fracture toughness, characterizes a rocks
resistance to the propagation of an existing fracture.
Permeability: The larger the fluid leakoff, the less driving force is available for fracture growth.
The Poroelastic Constant, , is defined by the relation:
where K is the bulk modulus (ratio of hydrostatic pressure to volumetric strain) of the dry rock material and Ks is the
same measured in a saturated sample.
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Other elasticity constants
Required \ Known E, G, E ,G
Shear modulus, G E G G
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Young's modulus, E E 2G 1 E
E 2G
Poisson ratio,
2G
E 2G
Plane strain modulus, E' 4G 2
1 2 1
4G E
Poroelasticity and Biots constant
p
Total Stress = Effective Stress + a[Pore Pressure]
Grains Force Pore Fluid
Biots constant a ~ 0.7
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Vertical Profile of Minimum Stress
The effective stress, s, is the
absolute stress minus the pore
pressure (p) weighted by the
poroelastic constant (a):
minimum effective horizontal stress
total horizontal stress
1) Poisson ratio changes from layer to layer
2) Pore pressure changes in time
Crossover of Minimum Stress
Depth from original ground surface, m
Ground Surface
-500 0
Current Depth , m
-1000 Critical Depth
-500
977 m
-1500 -1000
-2000 -1500
-2500 -2000
-3000 -2500
0 20x106 40x106 60x106 80x106
Stress, Pa
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Stress Gradients
Overburden gradient gradient
Slope of the Vertical Stress line 1.1 psi/ft
Frac gradient
Basically the slope of the minimum
horizontal stress line 0.4 - 0.9 psi/ft
Extreme value: 1.1 psi/ft or more
STRESS
oExample:
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Fracturing Pressure
Fracture Initiation Pressure or breakdown pressure is the peak value of the pressure appearing
when the formation breaks down and a fracture starts to evolve. Usually it is approximated by
where smin is the minimum horizontal stress, smax is the maximum horizontal stress, T is the tensile
stress of the rock material, a is the poroelasticity constant and po is the pore pressure.
Fracture Propagation Pressure is the stabilized value of the injection pressure for a longer period of
time during which the fracture is evolving.
Detection of formation
breakdown from a step-
rate test
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Fracturing Pressure (MiniFrac)
Fracture Closure Pressure. After a fracture calibration treatment, which is carried out without injecting
proppant material, the fracture volume gradually decreases because of leakoff (and also because of
possible back flow, if the injected fluid is flowed back through the well).
(1) breakdown pressure;
(2) fracture propagation pressure;
(3) instantaneous shut-in pressure;
(4) closure pressure;
(5) fracture reopening pressure;
(6) closure pressure from flow-back;
(7) asymptotic reservoir pressure;
(8) rebound pressure
Leakoff
Fluid leakoff is controlled by a continuous build-up of a thin layer, or filter cake, which
manifests an ever-increasing resistance to flow through the fracture face.
The leakoff velocity, VL , is given by the Carter equation:
CL
uL
t
Where CL is the leakoff coefficient (length/time0.5) and t is the time elapsed since the
start of the leakoff process. The ideas behind Carter's leakoff coefficient are that:
o if a filter-cake wall is building up, it will allow less fluid to pass through a unit area in unit time;
and,
o the reservoir itself can take less and less fluid if it has been exposed to inflow.
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Fluid Loss in Lab
Lost volume per unit surface, m
0.007
0.006
0.005
AL 0.004
0.003
y = 0.0024 + 0.000069x
0.002
Sp 2CL
0.001
CL
uL 0
0 10 20 30 40 50 60
t Square root time, t1/2 (s1/2)
VLost m3
= S p 2CL t CL unit :
m
or
AL s m2 s
units : m mm Sp unit : m
Description of leakoff through flow in porous
media and/or filtercake build-up
CL
Concept of leakoff coefficient uL
t
m m / s1 / 2
1/ 2
s s
Where are those twos coming from?
Integrated leakoff volume:
VL 2 AC L t
Leakoff Width
VL
wL 2CL t
AL
What is the physical meaning? m mm
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Definition of injection rate, fracture area
and permeable height
Width Equations
Perkins-Kern-Nordgren (PKN) Kristianovich-Zheltov-Geertsma-DeKlerk (KGD)
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Comparison of PKN and KGD width equations
The crossover occurs approximately at
the point at which a "square fracture"
has been created, i.e., when
For the small fracture extent, the
physical assumptions behind the KGD
equation are more realistic.
For the larger fracture extent, the PKN
width equation is physically more
sound.
Radial (Penny-shaped) Width Equation
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No-leakoff Behavior of Width Equations
Perkins-Kern-Nordgren model Geertsma and deKlerk model
Types of Fluids
Water-Base Fluids
natural guar gum (Guar)
hydroxypropyl guar (HPG)
hydroxyethyl cellulose (HEC)
carboxymethyl hydroxyethyl cellulose (CMHEC)
Oil-Base Fluids
Lease oil and gelled oils.
Acid-Base Fluids
Used in limestones or dolomitic formations.
Emulsions
Mixtures of oil and an aqueous material (either water or acid).
Gas/Foam Fluids
Specialized emulsions using nitrogen or carbon dioxide gas as the inner phase of an aqueous mixture.
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Fracturing Additives
Bacteria control agents Gypsum inhibitors
Breakers N2and CO2 gases
Clay-stabilizing agents Scale inhibitors
Demulsifying agents Sequestering agents
Dispersing agents Sludge inhibitors
Fluid loss additives Surfactants
Foaming agents Temperature-stabilizing agents
Friction loss reducers Water blockage-control agents
Proppant Pack Permeability & Fracture Conductivity
Proppant duties:
Be capable of holding the fracture faces apart
must be long lasting.
be readily available, safe to handle, and relatively inexpensive.
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Types of Proppants
Two major categories:
Naturally occurring sand
White Sand ("Ottawa" sand)
Manufactured proppants
Sintered Bauxite
Intermediate Strength Proppants
Resin Coated Proppants
A typical proppant selection guide
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Design Logics
Height is known (see height map)
Amount of proppant to place is given (from NPV)
Target length is given (see opt frac dimensions)
Fluid leakoff characteristics is known
Rock properties are known
Fluid rheology is known
Injection rate, max proppant concentratrion is given
How much fluid? How long to pump? How to add proppant?
Key concept: Width Equation
Fluid flow creates friction
Friction pressure is balanced by injection pressure
Net pressure is positive
Fracture width is determined by net pressure and
characteristic dimension (half length or half height)
The combination of fluid mechanics and solid mechanics
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Two approximations:
Perkins-Kern-(Nordgren)
Vertical plane strain
characteristic half-length ( c ) is half height, h/2
elliptic cross section
Kristianovich-Zheltov - (Gertsmaa-deKlerk)
Horizontal plane strain
characteristic half length ( c ) is xf
rectangular cross section
Width Equations (consistent units)
Perkins-Kern-Nordgren PKN
width: w, wo, wwell,o qi x f
1/ 4
ww,0 = 3.27
viscosity: E'
w 0.628ww,0
inj. rate (1 wing): qi
half-length: xf Kristianovich-Zheltov
Geertsma-De-Klerk KGD
plain-strain modulus: E' 1/ 4
qi x 2f
ww = 3.22
height: hf E' h
f
Vf = w(h f x f ) w 0.785ww
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PKN Power-Law Width Equation
With equivalent viscosity at average shear rate, the
maximum width at the wellbore is:
1
n
1 2.14n 2 n 2 2 n 2 qi h f x f 2n2
1 n 1 n 1 n
ww, 0 = 9.15 2n2
3.98 2n2
K
n E'
Power Law fluid
ww,0 K: Consistency (lbf/ft2)sn
n: Flow behavior index
Material balance +Width Equation
Vf = w(h f x f ) 2qi
Vf = w A Vi = qi t e
xf
Vfe = Vi - Vlost
Average
w(xf)
qi
A
hf Lost: spurt +leakoff
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Pumping time, fluid volume, proppant schedule:
Design of frac treatments
Pumping time and fluid volume:
Injected = contained in frac + lost
length reached, width created
Proppant schedule:
End-of-pumping concentration is uniform,
mass is the required
Given:
Mass of proppant, target length, frac height, inj rate, rheology, elasticity
modulus, leakoff coeff, max-possible-proppant-added-conc
Pumping time, slurry volume (1 wing)
1. Calculate the wellbore width at the end of pumping from the PKN (Power Law version)
1
n
1 2.14n 2 n 2 2 n 2 qi h f x f 2n2
1 n 1 n 1 n
ww,0 = 9.15 2n2
3.98 2n2
K
n
E'
2. Convert max wellbore width into average width
we 0.628ww,0
3. Assume a k = 1. 5 and solve the mat balance for inj. time, (selecting sqrt time as the new unknown)
qi
4. Calculate injected volume t 2 C t (we 2S p ) 0
h x L
f f
5. Calculate fluid efficiency Vi qi te
V fe h f x f we
e =
Vi Vi
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Proppant schedule calculation
1 e
1. Calculate the Nolte exponent of the proppant concentration curve
1 e
2. Calculate the pad volume and the time needed to pump it V pad Vi
t pad te
M
3. The required max proppant concentration, ce should be (mass/slurry-volume) ce
eVi
t t pad
4. The required proppant concentration (mass/slurry-volume) curve c ce
t t
e pad
c
5. Convert it to added proppant mass to volume of clean fluid cadded
c
1
propp
(mass/clean-fluid-volume)
Gross and Net Height
2qi
Vi = qi te
Vfe = Vi - Vlost
2D design: hf is given
A
hf
hp Lost: spurt +leakoff
rp= hp /hf
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