SPE 64647

Experimental Study on Friction Pressure Drop for NonNewtonian Drilling Fluids in Pipe
and Annular Flow
R. Subramanian, Process Engineer, Born Inc., Tulsa, Oklahoma and J. J. Azar, McMan Chair Professor, Petroleum
Engineering, University of Tulsa, Tulsa, Oklahoma

Copyright 2000, Society of Petroleum Engineers Inc.

factor that may contribute to the inaccuracies in friction
pressure loss calculation in drilling is the particular
This paper was prepared for presentation at the SPE International Oil & Gas Conference and
Exhibition in China held in Beijing, China, 7-10 November 2000. rheological model used in the development of a given
This paper was selected for presentation by an SPE Program Committee following review of
empirical correlation or theoretical expression. The
information contained in an abstract submitted by the author(s). Contents of the paper, as rheological models that are thought to represent the flow
presented, have not been reviewed by the Society of Petroleum Engineers and are subject to
correction by the author(s). The material, as presented, does not necessarily reflect any behavior of drilling muds are the Bingham Plastic, the power
position of the Society of Petroleum Engineers, its officers, or members. Papers presented at
SPE meetings are subject to publication review by Editorial Committees of the Society of
law and yield power law. Not knowing which model may best
Petroleum Engineers. Electronic reproduction, distribution, or storage of any part of this paper represent a given drilling mud type in the prediction of friction
for commercial purposes without the written consent of the Society of Petroleum Engineers is
prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 pressure loss motivated this study.
words; illustrations may not be copied. The abstract must contain conspicuous
acknowledgment of where and by whom the paper was presented. Write Librarian, SPE, P.O.
Box 833836, Richardson, TX 75083-3836, U.S.A., fax 01-972-952-9435. Literature Review
Many publications appear in the literature that deal with the
Abstract flow of nonNewtonian fluids through pipes and annuli.
An extensive experimental study on friction pressure drop for However, experimental data in regard to these fluids are
nonNewtonian drilling fluids in pipe and annular flow was almost non-existing. Drilling muds are nonNewtonian fluids
conducted. A fully instrumented 350 feet flow loop, and thus several rheological models have been proposed to
consisting of two pipes and two annular flow test sections, was describe their flow behavior. The most commonly used in the
used in the test program. Five different muds were tested, drilling industry are the Bingham plastic model and the power
which included: Bentonite mud, MMH mud, polymer mud, law model. Due to its complexity, the yield power law model
Glycol mud and Petrofree vegetable oil mud. did not receive as much use. Hanks5 et.al. (1963) have
published a paper on flow of fluids with yield stress. He used
The experimental data obtained were used to generate very the Bingham plastic model to predict laminar and turbulent
useful plots of “friction factor” versus “generalized Reynolds transition for fluids with yield stress. They proposed a general
number”. For each of the mud systems, the plots offer a criterion for the onset of turbulence. Hanks9,10 has also
practical and accurate means in determining needed friction published a number of papers on concentric annular flow of
factors for the calculation of pressure drops in pipe and fluids. Langlinais7 et. al. (1985) studied friction pressure
annular flow. In addition, a comparative discussion is losses for gas and drilling mud. They have used different
presented on measured friction pressure drop data, predicted equivalent diameters and their effects on single phase flow of
by correlations such as the power law, Bingham plastic and drilling mud in concentric annulus.
yield power law. The importance of wall roughness on An important contribution to the nonNewtonian fluid in
turbulent flow friction pressure drop calculations is also turbulent flow was done by Metzner and Reed3 (1955). They
investigated. tried to generalize the nonNewtonian fluid to an equivalent
Newtonian fluid. They obtained a generalized Reynolds
Introduction number for the power law fluid. Major work on turbulent
The prediction of friction pressure losses is very important flow for nonNewtonian fluids was done by Dodge and
during drilling operations. The concern is that inaccurate Metzner4 (1959). They developed an empirical friction factor
prediction of the friction pressure loss can cause inaccurate equation based on experimental data and an analytical
engineering decisions that may cause drilling problems such solution for the friction factor of power law fluid in pipes.
as loss of circulation, kicks, improper rig power selection, etc. Although the friction factor correlation was developed for
These problems become more significant in the area of slim smooth pipes, It is found to perform well in most of the power
hole drilling. Generally, when a drilling fluid flow behavior law fluids. Other significant contributions for drilling fluid
deviates from the simple Newtonian, friction pressure loss friction pressure loss predictions are done by Okafor16 et.al.
predictive equations become more complex and less accurate (1992). They conducted experiments with Bentonite mud to
due to many simplifying assumptions. It is believed that one evaluate the Robertson - stiff model, which does not account
2 R. SUBRAMANIAN AND J. J. AZAR SPE 64647

for yield stress. This experimental study was the first in the fluid. The temperature of the fluid was simultaneously
evaluation of rheological models and the pressure loss measured with the ASTM thermometer. A paint cup
correlation for drilling muds. Further studies were conducted pycnometer and a electronic balance(OHAUS-CT600-S) was
by Haccislamoglu and Langlinais15 on non - Newtonian fluids used to measure the mud weight. The pH was also measured
in annular flow. They developed a computer code using and recorded(ORION pH meter SA210 with a Ross pH
numerical simulation for power law fluids. Hanks and Pratt6 electrode). An IBM PC (6MHz AT) based data acquisition
(1967) developed a flow model for Bingham plastic fluid system is used to monitor, collect and display in real time the
through pipes using different non dimensional numbers for flow loop data utilizing the labtech notebook software
transition and turbulent flow regimes. package.
The mud to be tested can be prepared at the location or
Experimental Facility & Test Procedure transported to the tank. As 60% of the total volume of mud is
The experimental facility consists of a series of pipes and present in the pipes of the flow loop, mud is mixed while
annuli joined together to form a "flow loop". The loop allows circulating. The properties of the mud is changed by adding
circulation of the drilling fluids and is instrumented for the proper components while testing. As there are two
measurements of pressure drop, mass flow rate, and compartments in the tank, the mud is kept in one tank and the
temperature. Figure 1 is a schematic diagram of the facility. water in the other tank. Before starting testing with the mud, a
Robbins Myers 6 stage progressing cavity Moyno pump (520 water calibration test is made. The water calibration test is
gpm at a maximum of 500 psi) is powered by a 250 hp AC done to check the pipe roughness in the different pipes used.
motor used to pump fluid through the loop. Initially the loop is flushed with water and circulated until the
The flow loop is made up of the following sections: temperature stabilizes. The following data are recorded for
Two annular sections, one with a fully eccentric geometry and each test section during a water calibration test: mass flow
one with a concentric geometry (outer pipes-5.023” I.D. inner rate, water temperature and differential pressure drop across
pipes-2.375”O.D.), two jointed drill pipe sections with a tool each 50-foot test section. The water viscosity and density
joint midway on each.(4.5" 16.6 lbm / ft grade S & 4.5" 20.0 which are sensitive to the temperatures are calculated from the
lbm / ft grade S) and two non-jointed pipe sections. The flow recorded temperatures using correlations for these properties
loop also has another pipe section with tuboscope pup joints, at atmospheric pressures. The different correlations for the
which was not used for this study. viscosity and density for different temperatures at atmospheric
As can be seen in Fig 1, the fluid leaves the pump and is pressure are given in appendix. The Colebrook-White
routed down through either the concentric or eccentric annular equation for flow of Newtonian fluids in rough pipes is used
sections. The annular sections extend 300 feet from the pump as the reference equation to determine effective pipe diameter
and are joined to the drill pipe sections which are 50 feet long. and sand grain roughness. Once water calibration test is
The fluid leaves the annulus and enters the drill pipe section conducted, the water is displaced with the mud. After
where it passes through the tool joint. At this point the fluid complete displacement, the mud is circulated until the
has reached the turn around point and can be routed directly to temperature is stabilized. Before taking any pressure drop
the pipe sections or can be routed through the jetsub first and readings from the pressure transmitters all pressure taps are
then through the pipe sections. During testing, the fluid is purged. A gear pump is used to purge the pressure taps. The
routed through both. Upon leaving the pipe sections the fluid purging is done to ensure the pressure tap ports are clear and
passes through the mass flow meter and then returns to the differential pressure measured by the transmitters are correct.
circulation tanks. A sample line allows fluid which has just The experimental data are recorded by a computer for each
left the pipe sections to be collected from a "possum belly" in second and stored in different files. The recorded data are
the circulation tank. A jetsub is located at the far end of the analyzed by taking the averages of the readings for different
flow loop. It contains a receiver with four nozzles. The sub is flow rates for 60 seconds. While taking averages, care is
operated with two 14/32 and two 15/32 nozzles. This taken by going through the data file and picking the best data
provided a shear gradient equivalent to that of a drill bit so obtained in the computer. The data for each mud is collected
that shear degradation tests could be conducted on some fluid for different rheology and analyzed. The muds that were used
systems. The additional shear also help with the mixing of for this experimental work were Bentonite, Polymer, MMH,
new muds. Glycol and Petro-free Vegetable oil mud. The test parameters
An EXAC 9000 mass flow meter is used to measure the are five different drilling muds, 20 flow rates, smooth and
fluid circulation rate. The differential pressure is measured rough pipes and concentric annulus. Each mud rheology is
using DP transmitters. Three sets of DP transmitters are used, varied and friction pressure drop data were collected. Thus for
one for each pipe, annulus and tool joint. All DP transmitters each mud around five different rheology data were collected.
are ST3000 smart DP transmitters. The temperature of the
circulating fluid is measured using OMEGA type T Results and Discussion
thermocouples. The temperature is measured at the beginning, The flow loop was tested with water before and after each
middle and end of the loop. The fluid properties were mud test. The water test results were used to determine the
measured during the experiment. A chandler 3500, 12-speed, diameter and roughness of the pipes used in the flow loop.
viscometer was used to measure the viscous properties of the The water viscosity and density are calculated at the recorded
 EXPERIMENTAL STUDY ON FRICTION PRESSURE DROP FOR NONNEWTONIAN DRILLING
SPE 64647 FLUIDS IN PIPE AND ANNULAR FLOW 3

temperature using correlations for these properties at predicted for the different rheologies of the bentonite mud
atmospheric pressure. The viscosity and density are not show that the prediction of the yield power law model is better
sensitive to the pressure in this low pressure range but than the other models. This can be attributed to the fact that
viscosity is very sensitive to the temperature. The equations the friction factor used incorporated the non -Newtonian
used to calculate viscosity and density for different effects and the roughness. The comparison between the
temperatures are given in appendix. The Colebrook - White measured and the predicted pressure drops for the Polymer
equation is used to determine the pipe diameter and sand grain mud show that in the case of pipe flow the models predict
roughness. These are used in subsequent analysis and better for smooth pipe consideration than the rough pipe
calculations for pressure losses in pipes and annuli for the consideration. This is due to the physical property of the
drilling muds which were tested. polymer fluids. The roughness has very little impact on the
The rheological properties of all the muds were flow of polymer fluids in the turbulent flow as they are all
measured using a 12 speed Rheo-chan35 viscometer. The drag reducing fluids. The same behavior is observed in the
different parameters for the rheological models were annulus. The yield power law model predicts the pressure
calculated using a program to fit the viscometer data. losses better than the power law or Bingham plastic models
The friction pressure losses obtained from the for polymer fluids in turbulent flow. It can be seen that the
experiments were then compared with the model predictions. yield power law model predictions are better than the
Since the Reynolds number for the nonNewtonian fluids is not Bingham 3333plastic and power law models for the annular
general for all the models, the analysis was done for the flow. The results for the Glycol mud shows that when the
laminar and turbulent flow predictions separately for all the pipe is considered to be smooth then the predictions are
fluids. As the data obtained were extensive and analysis was comparable to the measured data. This is again attributed to
done on several data, a typical representation of the data is the polymers present in the mud which has a drag reducing
given in this paper. The plots for the five different drilling effect. The yield power law is observed to predict better than
muds are shown for both pipe and annular flow. the Bingham plastic and power law models. The same
behavior is seen in the annulus section also for the Glycol
Frictional Pressure Losses in Laminar Flow. It was mud. The predictions of the Petro-Free vegetable oil mud
observed that the Yield Power Law model prediction has the show that the yield power law model prediction of the
best agreement with the measured experimental data. When pressure drops are better than the Bingham plastic and power
the mud has higher yield point, from this study it was law models.
observed that the Bingham plastic model prediction was as Generalized Reynolds Number (GRE) versus Friction
good as the yield power law. From the comparison between Factor plot for the five different muds are plooted for smooth
the measured and predicted pressure drops for the polymer pipe, rough pipe and concentric annulus. The Petro-free
mud it was observed that, for pipe flow the Bingham plastic vegetable oil mud has less friction pressure drop than the rest
model prediction seems to agree better with the measured than of the muds for the same GRE. The polymer mud shows drag
the power law or the yield power law models. However the reducing charecteristics. These plots can be used to predict
annular flow the trend is reversed. It was observed from the the friction pressure loss for the range of GRE provided in the
experimental data for MMH mud that the yield power law and plots.
power law model predictions are better than the Bingham
plastic model in pipe flow. However the yield power law Conclusions
model predictions are the best for annular flow as in Bentonite From the comparison between existing friction pressure
mud. Also it was observed that MMH mud behaves almost loss model predictions and extensive measured experimental
like Bentonite mud. The results for Glycol mud show that the data for five different drilling muds, the following conclusions
yield power law model prediction is in better agreement with are made.
the measured data. This mud is very sensitive to temperature. 1. The yield power law model predictions were better than
Thus if the temperature effect is incorporated in the the Bingham plastic and the power law models for most of the
rheological parameters, then the yield power law model may muds tested.
predict still better and the error may be reduced. The results 2. For very high yield bentonite mud the Bingham plastic
for Petro-free vegetable oil mud show that the agreement model predictions seems to be in an acceptable agreement
between measured data and predicted is not good. This may with the measured data.
be attributed to the fact that the oil based mud is more 3. For the Polymer mud all model predictions were not in
sensitive to the temperature. good agreement with the measured data. However the
Bingham plastic model seems to predict better than the yield
Frictional Pressure Losses in Turbulent Flow. The analysis power law and power law models for this mud.
of the turbulent flow pressure drops was done by calculating 4. For the turbulent flow the friction factor developed by
the pressure drops for pipe and annular flow using the Reed and Philehvari seems to predict better for the rough pipe
different friction factors for both smooth pipe and rough pipe conditions for bentonite and MMH. muds.
consideration. The measured friction pressure losses and the 5. For the Polymer mud all the models over predict the
4 R. SUBRAMANIAN AND J. J. AZAR SPE 64647

pressure drops than the measured pressure drop when the Application of Drilling Fluid Hydraulics” (1985).
roughness is considered in the friction factor calculations. 3. Metzner, A.B. and Reed, J.C.: “Flow of non-
6. For the Glycol mud the predictions by all the models Newtonian Fluids - Laminar, Transition and Turbu-
were not in good agreement with the measured pressure drops. lent Flow Regions,” AIChEJ (Dec.1955).
7. For the Petro-free vegetable oil mud the agreement 4. Dodge, D.W. and Metzner, A.B.: “Turbulent Flow of
between all model predictions and measured data was not nonNewtonian Systems,” AIChEJ (June 1959).
satisfactory. However, in turbulent flow the yield power law 5. Hanks, R. W. “The Laminar-Turbulent Transition for
model predicts better than the Bingham plastic and power law Fluids with a Yield Stress,” AIChEJ (May 1963).
models. 6. Hanks, R.W. and Pratt, D.R.: “On the Flow of
8. For a concentric annulus the yield power law model Bingham Plastic Slurries in Pipes and Between Parallel
seems to predict better than the Bingham and power law Plates,” SPEJ (Dec. 1967).
models for all the muds. 7. Langlinais, J.P., Bourgoyne, A.T., and Holden, W.R.:
9. Friction pressure losses in eccentric annuli are lower than “Frictional Pressure Losses for Annular Flow of
those for concentric annuli under the same flow conditions for Drilling Mud and Mud-Gas Mixtures,” ASME (March
all muds tested. 1985).
8. Zamora, M and Lord, D.L.: “Practical Analysis of
Nomenclature Drilling Mud Flow in Pipes and Annuli,” SPE4976
∆P Pressure loss across pipes or annuli (1974).
dL Length of the pipes or annuli 9. Hanks, R.W.: “Critical Reynolds Number for
τw The average wall shear stress Newtonian Fluids in Concentric Annuli,” AIChEJ
(Jan. 1980)
γw The average wall shear rate 10. Hanks, R.W.: “The Laminar, Turbulent and
d The inside diameter of the pipes Transition for Flow in Pipes, Concentric Annuli and
d2 The inside diameter of the outer pipe Parallel Plates,” AIChEJ (Jan. 1963).
d1 The outer diameter of the inner pipe 11. Skelland, A.H.P.: “NonNewtonian Flow and Heat
Dhy The hydraulic diameter Transfer,” John Wiley & Sons, Inc. (1967).
Deff The effective diameter 12. Bourgoyne, A.T., et al.: “Applied Drilling Engineering,”
v The average velocity if the fluid flowing in pipe SPE Textbook (1986).
or annulus 13. Govier, G.W., and Aziz, K.: “The Flow of Complex
pv The plastic viscosity for Bingham Plastic Mixtures in Pipes,” Van Nostrand Reinhold Co. (1972).
model 14. Fredrickson, A.G. and Bird, R.B., “NonNewtonian
yp The yield point for the Bingham Plastic Flow in Annuli,” Ind. Engr. Chem. (March 1958).
model 15. Haciislamoglu, M., and Langlinais, J.: “NonNewtonian
K The consistency index for the Power Law Flow in Eccentric Annuli,” ASMEJ (Sept. 1990).
model 16. Okafor, M.N., and Evers, J.F., “Experimental
n The behavior index for the Power Law Comparison of Rheology Models for Drilling Fluids,”
model paper SPE 24086 (1992).
YS The yield stress for the Yield Power Law 17. Metzner, A. B., “ NonNewtonian Fluid Flow,” Ind.
model Engr. Chem. (Sept. 1957).
Ky The consistency index for Yield Power Law 18. Iyoho, A.W., and Azar, J.J.: “ An Accurate Slot-Flow
model Model for nonNewtonian Fluid Flow Through
m The behavior index for the Yield Power Law Eccentric Annuli,” SPEJ (Oct. 1981).
model 19. Terry Hemphill, Wellington Campos and Ali
N Defined for Yield Power Law model for Philevari: “Yield Power Law Model more Accurately
finding effective diameter Predicts Mud Rheology,” Oil & Gas J. (Aug. 1993).
ρ Density of the drilling mud 20. R. Subramanian, MS Thesis, University of Tulsa
µa Apparent viscosity of the drilling fluid (1995).
Re Reynolds Number
f Friction factor for the turbulent flow Appendix
ε Roughness of the pipe or annuli. These rheological models are mathematically represented as:
Bingham plastic model: τ = yp + pv(γ) , A.1
References Power law model: τ = K (γ)n, A.2
1. Reed, T.D. , and Philevari, A.A.: “A New Model for Yield power law model: τ = YS + Ky(γ)m . A.3
Laminar, Transitional and Turbulent Flow of Drilling
Muds,” SPE 25456 (1992). The above mathematical expressions relate the shear stress to
2. Alan Whittaker and EXLOG staff: “Theory and the shear rate and form the basic constitutive equation for
 EXPERIMENTAL STUDY ON FRICTION PRESSURE DROP FOR NONNEWTONIAN DRILLING
SPE 64647 FLUIDS IN PIPE AND ANNULAR FLOW 5

developing the laminar flow and turbulent flow friction Power law model2
pressure losses correlations.
Laminar Pipe Flow: Y = 0.37n −0 .14 A.19
Bingham plastic model2 Y
6* pv * v  d1 
β = 1+ A.4 Z = 1− Y 1−   A.20
yp * d  d2 
 ( 3 − Z )n + 1 
z = 3 β2 + β4 − 1 A.5 G = (1 + Z / 2)  A.21
 ( 4 − Z )n 
 1 n
y = 2 1 +  A.6 4KdL  8vG 
 z ∆P =   A.22
( d2 − d1)  ( d2 − d1) 
1  β
8β 
X= y− − y A.7
2  y 
 Yield power law model1

4* dL * yp
∆p = A.8 Y = 0. 37N−0.14 A.23
d* X Y
 d1 
Z =1− Y1−   A.24
Power law model2  d2 
4 * K * dL  2 * v ( 3n + 1)   ( 3 − Z )N + 1 
∆p =   A.9 G = (1 + Z / 2) A.25
d  d* n  
 ( 4 − Z )N 
Yield power law model1
Dhy = d2 − d1 A.26
Concentric Annulus Laminar Flow:
These equations are developed using slot flow assumptions. D hy
The hydraulic diameter concept was used for the diameter. D eff = A.27
G
Bingham plastic model2 m
yp( d2 − d1)  8v 
B= A.15 τ w = ys + K y   A.28
pv * v  D eff 
B τw3
β= A.16 1 / N = −3 +
B+8 ( τ w − ys ) * m * A A.29
2 1 
X = sin sin −1 β 3  A.17
β 3 
( τ w − ys) 2 2ys( τ w − ys ) ys 2
4 * dL * yp A= + +
∆P = A.18 3m + 1 2m + 1 m + 1 A.30
X ( d2 − d1)
τw3
1 / N = −3 + τw * dL * 4
( τ w − ys ) * m * A A.10 ∆P = A.31
D hy

(This equation was developed by the author from ref. 13) Thus, the friction pressure losses in turbulent flow are
calculated from the Fanning equation, defined for any fluid
( τ − ys) 2 2ys( τ w − ys ) ys 2
A= w + + model, by:
3m + 1 2m + 1 m + 1 A.11

τ w = ys + K y ( γ w )m A.12 2 * f * dL * ρ * V 2
∆P = . A.32
 3N + 1 8 v d
γw =  A.13
 4N  d
The Fanning equation is empirically derived. This equation
4* dL * τ w forms the basis for calculating friction pressure losses in pipe
∆p = A.14
d and annulus for any fluid model. The friction factor is a
function of the Reynolds number which depends on the
viscosity. Thus, it is difficult to find the viscosity for the
6 R. SUBRAMANIAN AND J. J. AZAR SPE 64647

drilling mud, so an apparent viscosity was used to calculate Yield power law model1
the pressure losses in pipes and annuli. The method used to
τw3
calculate the apparent viscosity and Reynolds number for each 1 / N = −3 +
model is explained below. ( τ w − ys ) * m * A A.40

Bingham plastic model2

The apparent viscosity and Reynolds number are ( τ w − ys) 2 2ys( τ w − ys ) ys 2
calculated as below: A= + +
3m + 1 2m + 1 m + 1 A.41
pv * d
µa = yp + A.33
6*v
τ w = ys + K y ( γ w ) m A.42
ρ*v*d
Re = . A.34
µa  3N + 1 8 v
From the above two parameters the friction factors can γw =  A.43
 4N  d
be calculated for a smooth and rough pipes from the equations
below.
4 Nd
Deff = A.44
For smooth pipe: ( 3N + 1)
0 .0792 τw
f= A.35 µa = A.45
Re0 .25 νw

For rough pipe: ρ * v * D eff

1 ε 1.255 Re = A.46
= −4 log( + ) A.36 µa
f 3.72 * d Re* f
Once the Reynolds number is calculated, we can use the
The friction factors described above were developed friction factor equation of Dodge and Metzner for the smooth
empirically from experiments conducted for Newtonian fluids. pipe and the equation of Reed and Philevari for rough pipe.
From the friction factor, the pressure losses are calculated
using the Fanning equation. For smooth pipe:
1 4 0 .4
Power law model2 = 0 .75 log[Re* ( f ) ( 1− N / 2) ] − 1.2 A.47
For this model, the Reynolds number equation was f N N
developed assuming the apparent viscosity concept. It is
given by: For rough pipe:
−1.2
0 .2488 * ρ * v ( 2 − n ) d* n n 1 0 .27 * ε 1.26 N
Re = ( ) . A.37 = −4 log( + ).
k 2( 3n + 1) −0 .75
f D eff (Re* f ( 1− n / 2) ) N
Once the Reynolds number is calculated, then the
A.48
friction factor is calculated by using the Dodge and Metzner4
equation for smooth pipe and Colebrook-White equation for
rough pipe. They are given by:

For smooth pipe:

1 4 0 .4
= 0 .75 log[Re* ( f ) ( 1− n / 2) ] − 1.2 A.38
f n n

For rough pipe:

1 ε 1.255
= −4 log( + ). A.39
f 3.72 * d Re* f
 EXPERIMENTAL STUDY ON FRICTION PRESSURE DROP FOR NONNEWTONIAN DRILLING
SPE 64647 FLUIDS IN PIPE AND ANNULAR FLOW 7

Figure -1

Bentonite Mud Concentric Annulus Bentonite Mud Concentric annulus (Turbulent)

(Laminar) 7
6
6
5 Experiment DP
Pressure Drop PSI
Pressure Drop PSI

Yield Power LawDP 5 Experiment DP

BinghamPlastic DP YieldPower lawDP

4 4
Power LawDP BinghamPlastic DP

3 Power LawDP
3

2
2
1
1
0
0 100 200 300 400 500 600
0
0 50 100 150 200 250 300 350 400 FlowRateGPM
FLowRate, GPM
8 R. SUBRAMANIAN AND J. J. AZAR SPE 64647

Bentonite Mud Rough Pipe

Bentonite Mud Rough Pipe (Laminar) 60
(Turbulent)
3
E x p e rim e nt D P
50 E x p e rim e n t D P
Pressure Drop PSI

Pressure Drop PSI

2 .5 Y ie ld P o w e r L aw D P
Y ie ld P o w e r L aw D P
B ing ham P las t ic D P 40
2 B in g ham P las t ic D P
P o w e r L aw D P
30
1 .5 P o w e r L aw D P

20
1

0 .5 10

0 0
0 20 40 60 80 100 120 0 100 200 300 400 500 600

Flow Rate GPM

Flow Rate in GPM

Glycol Mud Concentric Annulus Glycol Mud Concentric Annulus

(Laminar) (Turbulent)

2
E x p e rim e n t D P 6 E xp eriment D P
1 .8
Y ie ld P o w e r L a w D P Y ield P o w er L aw D P
5
Pressure Drop PSI

1 .6
Pressure Drop PSI

B in g h a m P la s t ic D P
1 .4 B ing ham P las tic D P
P o w e r L aw D P 4
1 .2
P o w er L aw D P
1 3
0 .8
2
0 .6

0 .4 1
0 .2

0 0
0 50 100 150 200 250 300 350 0 100 200 300 400 500 600

Flow Rate GPM Flow Rate GPM

Glycol Mud Rough Pipe (Laminar) Glycol Mud Rough Pipe

1 .4 (Turbulent)
60
E x p e rim e n t D P E x p e rim e n t D P
1 .2
Y ie ld P o w e r L aw D P 50 Y ie ld P o w e r L a w D P
Pressure Drop PS
Pressure Drop PSI

1
B in g ham P las t ic D P
B in g h a m P la s t ic D P
P o w e r L aw D P 40
0 .8
P o w e r L aw D P
30
0 .6

0 .4 20

0 .2 10

0
0
0 10 20 30 40 50 60 70 80
0 100 200 300 400 500 600
Flow Rate GPM
Flow Rate GPM
 EXPERIMENTAL STUDY ON FRICTION PRESSURE DROP FOR NONNEWTONIAN DRILLING
SPE 64647 FLUIDS IN PIPE AND ANNULAR FLOW 9

Polymer Mud Rough Pipe Polymer Mud Concentric Annulus

(Turbulent) (Turbulent)
7
60
E x p e rim e n t D P

Pressure Drop PSI

6 E x p erim ent D P
50
Pressure Drop

Y ie ld P o w e r L aw D P 5 Y ield P o w er L aw D P
40 B in g ham P las t ic D P
4 B ing ham P las tic D P
PSI

30 P o w e r L aw D P P o w er L aw D P
3
20 2
10 1

0 0
0 100 200 300 400 500 600 0 100 200 300 400 500 600
Flow Rate in GPM Flow Rate in GPM

Polymer Mud Concentric Annulus Petro-Free Vegetable Oil Mud Rough

3 .5 (Laminar) Pipe (Turbulent)
70
3
60 E x p e rim e n t D P
Pressure Drop PSI

Pressure Drop PSI

2 .5
Y ie ld P o w e r L aw D P
50
2 B in g ham P las t ic D P
40
E x p e rim e n t D P
1 .5 P o w e r L aw D P
30
Y ie ld P o w e r L a w D P
1 20
B in g h a m P la s t ic D P

0 .5 P o w e r L aw D P 10

0 0
0 100 200 300 400 500 600 0 100 200 300 400 500 600
Flow Rate in GPM Flow Rate GPM

Petro-Free Vegetable Oil Mud Petro-Free Vegetable Oil Mud

9 Rough Pipe (Laminar) Cocentric Annulus (Turbulent)
9
8
8 E x p e rim e nt D P
Pressure Drop PS

7
Y ie ld P o w e r L aw D P
Pressure Drop PSI

7
6 B in g ham P las t ic D P
6 P o w e r L aw D P
5
5
4
E xp eriment D P
4
3 Y ield P o w er L aw D P
3
2 B ing ham P las tic D P
2
1 P o w er L aw D P
1
0
0
0 50 100 150 200
0 100 200 300 400 500 600
Flow Rate GPM Flow Rate GPM
10 R. SUBRAMANIAN AND J. J. AZAR SPE 64647

MMH MudConcentric Annulus MMH MudConcentric Annulus

1 .6
(Laminar) 6
1 .4
(Turbulent)
5

Pressure Drop PSI

E x p erim ent D P
Pressure Drop PSI

1 .2
Y ield P o w er L aw D P
1 4
B ing ham P las tic D P
E x p e rim e nt D P
0 .8 3
P o w er L aw D P
Y ie ld P o w e r L aw D P
0 .6
2
0 .4 B in g ham P las t ic D P

P o w e r L aw D P 1
0 .2

0 0
0 50 100 150 200 250 0 100 200 300 400 500 600
Flow Rate GPM Flow Rate GPM

60
MMH Mud Rough Pipe (Turbulent) MMH Mud Rough Pipe (Laminar)
2
1 .8
50 E xp eriment D P E x p erim ent D P
Pressure Drop PSI

Pressure Drop PSI 1 .6

Y ie ld P o w e r L aw D P
Y ield P o w er L aw D P 1 .4
40 B ing ham P las t ic D P
B ing ham P las tic D P 1 .2 P o w er L aw D P
30 1
P o w er L aw D P
0 .8
20 0 .6
0 .4
10
0 .2

0 0
0 20 40 60 80 100 120
0 100 200 300 400 500 600
Flow Rate GPM
Flow Rate GPM

Friction Factor Vs Generalized Reynolds Number

(Concentric Annulus)
0 .8 0 0

0 .7 0 0 F r i c t i o n F a c t o r F o r B e n t o n it e M u d

F r ic tio n F a c to r F o r p o ly m e r M u d
0 .6 0 0
F r ic tio n F a c to r F o r M M H M u d
Friction Factor

0 .5 0 0
F r ic tio n F a c to r F o r G ly c o l M u d

0 .4 0 0 F r i c t i o n F a c t o r F o r P e t r o - F r e e V e g e t a b le O i l M u d

0 .3 0 0

0 .2 0 0

0 .1 0 0

0 .0 0 0
0 2000 4000 6000 8000 10000 12000 14000 16000
G e n e r a l iz e d R e y n o ld s N u m b e r
 EXPERIMENTAL STUDY ON FRICTION PRESSURE DROP FOR NONNEWTONIAN DRILLING
SPE 64647 FLUIDS IN PIPE AND ANNULAR FLOW 11

F r ic t io n F a c t o r V s G e n e r a liz e d R e y n o ld s N u m b e r ( R o u g h
P ip e )
1 .8 0 0

1 .5 0 0 F r i c ti o n F a c to r F o r B e n to n i te M u d

F r i c ti o n F a c to r F o r P o ly m e r M u d

F r i c ti o n F a c to r F o r M M H M u d
1 .2 0 0
Friction Factor

F r i c ti o n F a c to r F o r G ly c o l M u d

F r i c ti o n F a c to r F o r P e tr o - F r e e V e g e ta b le O i l M u d
0 .9 0 0

0 .6 0 0

0 .3 0 0

0 .0 0 0
0 10000 20000 30000 40000 50000 60000 70000 80000 90000 100000 110000

G e n e r a liz e d R e y n o ld s N u m b e r

F r ic tio n F a c to r V s G e n e r a liz e d R e y n o ld s N u m b e r
(S m o o th P ip e )
1.800

F r i c ti o n F a c to r F o r B e n to n i te M u d

1.500 F r i c ti o n F a c to r F o r P o ly m e r M u d

F r i c ti o n F a c to r F o r M M H M u d
1.200
Friction Factor

F r i c ti o n F a c to r F o r G ly c o l M u d

F r i c ti o n F a c to r F o r P e tro - F r e e V e g e ta b le O i l M u d
0.900

0.600

0.300

0.000
0 10000 20000 30000 40000 50000 60000 70000 80000 90000 100000 110000

G e n e r a li z e d R e y n o l d s N u m b e r