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Predicting Frictional Pressure Loss During Horizontal Drilling for Non-Newtonian FluidsM. Sorguna; M. E. Ozbayoglub

a Petroleum and Natural Gas Engineering Department, Middle East Technical University, Ankara,Turkey b Department of Petroleum Engineering, University of Tulsa, Tulsa, Oklahoma, USA

Online publication date: 13 December 2010

To cite this Article Sorgun, M. and Ozbayoglu, M. E.(2011) 'Predicting Frictional Pressure Loss During Horizontal Drillingfor Non-Newtonian Fluids', Energy Sources, Part A: Recovery, Utilization, and Environmental Effects, 33: 7, 631 — 640To link to this Article: DOI: 10.1080/15567030903226264URL: http://dx.doi.org/10.1080/15567030903226264

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Energy Sources, Part A, 33:631–640, 2011

Copyright © Taylor & Francis Group, LLC

ISSN: 1556-7036 print/1556-7230 online

DOI: 10.1080/15567030903226264

Predicting Frictional Pressure Loss During

Horizontal Drilling for Non-Newtonian Fluids

M. SORGUN1

and M. E. OZBAYOGLU2

1Petroleum and Natural Gas Engineering Department, Middle East Technical

University, Ankara, Turkey2Department of Petroleum Engineering, University of Tulsa, Tulsa,

Oklahoma, USA

Abstract Accurate estimation of the frictional pressure losses for non-Newtoniandrilling fluids inside annulus is quite important to determine pump rates and select

mud pump systems during drilling operations. The purpose of this study is to es-timate frictional pressure loss and velocity profile of non-Newtonian drilling fluids

in both concentric and eccentric annuli using an Eulerian-Eulerian computationalfluid dynamics (CFD) model. An extensive experimental program was performed in

METU-PETE Flow Loop using two non-Newtonian drilling fluids including differentconcentrations of xanthan biopolimer, starch, KCl and soda ash, weighted with barite

for different flow rates and frictional pressure losses were recorded during eachtest. This study aims to simulate non-Newtonian fluids flow through both horizontal

concentric and eccentric annulus and to predict frictional pressure losses using anEulerian-Eulerian computational fluid dynamics (CFD) model. Computational fluid

dynamic simulations were performed to compare with experimental data gathered atthe METU-PETE flow loop and previous studies as well as slot flow approximation

for the annulus. Results show that the computational fluid dynamic model simulationsare capable of estimating frictional pressure drop with an error of less than 10% in

most cases, more accurately than the slot equation.

Keywords computational fluid dynamics, concentric annulus, eccentric annulus,frictional pressure loss, horizontal drilling, non-Newtonian fluids, slot equation

Introduction

Inefficient prediction of pressure drop may give rise to serious drilling problems, such

as stuck pipe, loss circulation, kicks, and improper rig power selection during horizontal

drilling. Numerous studies on the determination of frictional pressure loss have been

conducted using non-Newtonian fluids flow through horizontal concentric and eccentric

annuli. Fredrickson and Bird (1958) solved the Navier-Stokes equation for Power Law

and Bingham Plastic fluids through an annulus and obtained an analytical expression

of flow rate and frictional pressure loss in a laminar regime. Heyda (1959) conducted

an analytical study using bipolar coordinates for determining Newtonian fluid velocity

distribution in eccentric annuli and concluded that eccentricity has a noticeable influence

on the velocity profile of a laminar flowing Newtonian fluid.

Vaughn (1965) obtained a velocity profile of non-Newtonian fluids in an eccentric

annulus using a height slot. Mitsuishi and Aoyagi (1973) carried out experiments using

Address correspondence to Mehmet Sorgun, Petroleum and Natural Gas Department, MiddleEast Technical University, Inonu Blvd., Ankara 06531, Turkey. E-mail: mehmetsorgun@gmail.com

631

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632 M. Sorgun and M. E. Ozbayoglu

high polymer aqueous solutions of CMC, HEC, and MC. Results showed that the pressure

drop for flow in an eccentric annulus decreases as the eccentricity increases at a fixed

flow rate. They observed secondary flows in the eccentric non-Newtonian fluid flow,

which may be due to the viscoelastic effect of the high polymer solution. Iyoho and

Azar (1981) proposed an accurate slot-flow model for power-law fluid flow through

eccentric annuli. Langlinais et al. (1983) conducted an extensive experimental study on

frictional pressure losses for the flow of drilling mud and mud/gas mixtures through

a concentric annulus. Luo and Peden (1990) and Uner et al. (1989) are among the

researchers developing analytical models in order to obtain velocity, volumetric flow

rate, and frictional pressure loss for laminar flowing non-Newtonian fluid in an eccentric

annulus. Also, Uner et al. (1989) emphasized that the eccentricity ratio has a significant

influence on the volumetric flow rate of power-law fluid, especially when the power-law

index, n, is small. Haciislamoglu and Langlinais (1990) numerically solved the governing

equation of flow using finite differences approximation in order to analyze the flow

behavior of non-Newtonian fluids in concentric and concentric annuli. Reed and Pilehvari

(1993) proposed the “effective diameter” concept providing the link between Newtonian

and non-Newtonian flow through a concentric annulus and the method is valid for any

flow regime.

Escudier et al. (2002) investigated numerically the effects of eccentricity and pipe

rotation on frictional pressure loss for Newtonian and non-Newtonian fluids. Singhal

et al. (2005) compared friction pressure predictions from correlations with the data

gathered from computational fluid dynamics (CFD) simulations. They concluded that the

correlation proposed by Reed and Pilehvari (1993) results are in good agreement with the

CFD simulation results. Bilgesu et al. (2007) showed the effects of drilling parameters on

hole cleaning in horizontal and deviated wellbores using CFD. Founargiotakis et al. (2008)

proposed a model predicting pressure drop for laminar, transitional, and turbulent flow of

Herschel-Bulkley fluids in concentric annuli using slot flow approximation. Gallego and

Shah (2009) presented friction pressure correlations for turbulent flow of polymer solu-

tions in straight and coiled tubing. The results show that the frictional pressure correlation

for flow in coiled tubing is in reasonably good agreement with experimental data.

This study aims to simulate frictional pressure loss using the CFD model for non-

Newtonian fluids in both horizontal concentric and eccentric annulus.

Theory

Governing Equation

The equation of continuity is defined as:

@�

@tC r � �v D 0; (1)

for incompressible and steady state condition, � D constant, Eq. (1) reduces to

r � v D 0; (2)

and the equation of continuity may be obtained in rectangular coordinates,

@u

@xC

@v

@yC

@w

@zD 0: (3)

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Predicting Frictional Pressure Loss 633

The equation of motion in terms of � is expressed as:

�Dv

DtD �rp � r � � C �g: (4)

For a power law rheolegical fluid model, shear stress can be defined as:

� D K

�

du

dr

�n

; (5)

where n and K are the power law flow behavior index and consistency index, respectively.

Annular Flow

To represent annular geometry as a narrow slot, it is widely used in the drilling engineer-

ing for practical purposes (Bourgoyne et al., 1991). The slot equation, which is one of the

most used equivalent diameter expressions to represent annular flow, can be calculated

using:

De D 0:816.Do � Di /; (6)

where Do is the wellbore diameter (in.) and Di is the pipe outer diameter (in.).

Frictional pressure gradient inside an annulus using a narrow slot approach is defined

as:

�P

�LD

ff �v2a

21:1.Do � Di /: (7)

Here, �P=�L is the frictional pressure gradient (psi/ft), ff is the fanning friction factor,

� is the fluid density (ppg), and average annular fluid velocity, va (ft/s), is expressed as:

va DQ

2:448.D2o � D2

i /; (8)

where Q is the flow rate (gpm) and the fanning friction factor for laminar regimes is

ff D16

NRe

; (9)

and turbulent regimes is

1p

ff

D4

n0:75log.NRe

f1�

n

2

f / �0:395

n1:2: (10)

Here, NRe, Reynolds number is

NReD

928�vaDe

�eff

; (11)

where effective viscosity for Power Law fluids can be expressed as:

�eff D

�

K.Do � Di /1�n

144v1�n

�

0

B

@

2 C1

n0:028

1

C

A

n

: (12)

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634 M. Sorgun and M. E. Ozbayoglu

Table 1

Fluid and annulus properties

Density,

ppg K, eq-cp n Do, in Di , in

Mud-1 8.4 289 0.514 2.9137 1.8

Mud-2 10 479 0.474 2.9137 1.8

Mud-3 8.8 33 0.807 2.441 1.315

Mud-4 8.8 69 0.784 2.441 1.315

The eccentricity and frictional pressure gradient for eccentric annulus can be calculated

as (Haciislamoglu and Langlinais, 1990):

e D2ı

Do � Di

; (13)

where ı is the distance between centers of inner and outer pipes.

�

�P

�L

�

eccentric

D

�

�P

�L

�

concentric

R (14)

where R is a correction function that depends on the eccentricity, fluid behavior index,

consistency index, outer and inner pipe diameter. In this article (Haciislamoglu and

Langlinais, 1990), correction function is used.

CFD

CFD simulations have been performed to investigate frictional pressure losses of non-

Newtonian fluids in both horizontal concentric and eccentric annulus. Navier-Stokes fluid

dynamics equation with a numerical method is solved using CFD component of the

package for laminar and turbulent flow. Concentric and eccentric annuli were created

and meshed using commercial CFD software Ansys Workbench (ANSYS, Inc.) and

simulations were solved using Ansys CFX 10.0. Ansys CFX is a general purpose CFD

code, combining an advanced solver with powerful pre- and post-processing capabilities.

In this study, simulations were conducted for four different power law fluids (Table 1),

both concentric and eccentric annulus and two horizontal wellbore sections (2.91–1.8 in.,

2.441–1.315 in.). Fluids and pipe geometries were taken from Langlinais et al. (1983) and

experiments conducted on METU-PETE flow loop. Also, frictional pressure loss results

of a finite element simulator were compared with them. For all of the cases, the geometry

was divided approximately 2:8 � 106 tetrahedral mesh and the flow was assumed to be

steady, incompressible, isothermal, and k-" model used for turbulent flow. Figure 1 shows

a tetrahedral meshing sample for fully eccentric annulus.

Experimental Work

Flow Loop

Extensive experimental in horizontal fully eccentric annuli were carried out in a METU-

PETE flow loop using mud-1 and mud-2. The inner pipe is subjected to sagging; therefore,

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Predicting Frictional Pressure Loss 635

Figure 1. Tetrahedral meshing sample (fully eccentric).

more realistic annulus representation is achieved. Experiments were conducted using non-

Newtonian fluids for demonstrating drilling mud flow conditions through horizontal fully

eccentric annulus. A schematic view of the flow loop is presented in Figure 2. The test

section is 12 ft long and made of acrylic casing and steel drillpipe. 2.91 in ID acrylic

casing—1.8 in O.D drillpipe annular geometrical configuration is used. A centrifugal

pump is mounted with a flow capacity of 250 gpm, and the flow rate is controlled and

measured using a magnetic flow meter and a pneumatic flow controller, respectively.

During the flow tests, pressure drop is also measured at a fully developed section on the

test section using a digital pressure transducer.

Figure 2. METU-PETE flow loop.

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636 M. Sorgun and M. E. Ozbayoglu

Figure 3. Comparison of CFD simulation, slot equation, and mud 1 experimental data for fully

eccentric annuli.

Results and Discussion

The CFD model frictional pressure gradient predictions, the slot flow approximation

results, and experimental data gathered at the METU-PETE flow loop for frictional

pressure losses are presented in Figures 3 and 4. Also, the model is compared with

Langlinais et al.’s (1983) experimental results in Figures 5 and 6. As seen from these

figures, the CFD model can estimate the frictional pressure losses with a high accuracy

for most cases and more accurately than the slot equation. The performance of the model

can be examined by investigating Figure 7. Solid lines in Figure 7 represent the perfect

match between the experimental and calculated values, and the dashed lines present

˙15% error margin. As can be seen from this figure, most of the predicted values fall

into ˙15% error margin. An error analysis is performed and the results are presented

in Figure 8. As seen from Figure 8, CFD model can estimate the frictional pressure

loss of non-Newtonian fluids for both laminar and turbulent flow regimes with an error

of less than 10% and only four data points showed a deviation in excess of 20% and

maximum deviation of 25.6%. These results show that frictional pressure predictions of

CFD simulations are in very good agreement with the experimental data.

Conclusion

CFD simulations of non-Newtonian fluids flowing through horizontal concentric and

eccentric annulus were performed using an Eulerian–Eulerian numerical model in order

to evaluate capability CFD and to predict frictional pressure losses of drilling fluids. It

has been observed that the CFD model can estimate pressure drop better than slot flow

equations when compared with experimental data. Frictional pressure loss distribution

and fluid velocity profile of non-Newtonian fluids in concentric and eccentric annulus

can be easily obtained by using CFD software.

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Predicting Frictional Pressure Loss 637

Figure 4. Comparison of CFD simulation, slot equation, and mud 2 experimental data for fully

eccentric annuli.

Figure 5. Comparison of CFD simulation, slot equation, and mud 3 experimental data for

concentric annuli.

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638 M. Sorgun and M. E. Ozbayoglu

Figure 6. Comparison of CFD simulation, slot equation, and mud 4 experimental data for

concentric annuli.

Figure 7. Comparison of experimental and calculated frictional pressure drop.

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Predicting Frictional Pressure Loss 639

Figure 8. Comparison of the performance CFD model as a function of error distribution.

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