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Chemical Engineering Research Bulletin 13 (2009) 7-11 Available online at http://www.banglajol.info/index.php/CERB

PREDICTION OF STAND PIPE PRESSURE USING CONVENTIONAL APPROACH

Dipankar Chowdhury∗,1, Pål Skalle1, Mohammed Mahbubur Rahman2

1Department of Petroleum Engineering and Applied Geophysics, Norwegian University of Science and Technology

Trondheim-7491, Norway

2Department of Petroleum and Mineral Resources Engineering, Bangladesh University of Engineering and Technology

Dhaka-1000, Bangladesh

Received 21 June 2009; received in revised form 19 July 2009

Abstract: In rotary drilling operation, the hydraulic circuit typically consists of stand pipe, rotary hose, swivel,

Kelly, drill pipe, drill collar, drill bit, and the annulus between the drillstring and the open hole or the casing.

Stand Pipe Pressure, abbreviated as SPP, is deﬁned as the total frictional pressure drop in the hydraulic circuit.

SPP, an important drilling parameter in selecting proper mud weight, can be calculated using diﬀerent rheological

models. In this paper, the results obtained using the four widely used rheological models namely the Newtonian

model, the Bingham plastic model, the Power law model and the Herschel-Bulkley model are presented. The

rheological data used are collected by performing circulation test while drilling a vertical well in the Po valley,

Italy. The rheological constants associated with each of the four models are calculated using regression analysis,

For the three ﬂow rates used during the circulation test, SPP has been predicted with a maximum error of 1.2%

when compared with the measured values. The Bingham plastic model produces best SPP estimates for all the

three ﬂow rates for the drilling condition considered.

Keywords: SPP, rheological models, frictional pressure drop

DOI:10.3329/cerb.v13i1.2703

1. Introduction

When drilling ﬂuid circulates, pressure drop takes

place due to friction between the ﬂuid and the surface

in contact. The pressure that forces the drilling ﬂuid

to circulate through the hydraulic system is supplied

by the mud pump. The mud pump pressure is partly

used up in overcoming the friction between the ﬂuid,

and the open hole or casing or the surface equipment

used. The remaining pump pressure is consumed as

bit nozzle pressure loss, where the high nozzle speed

is assisting in cuttings removal from the bit and its sur-

roundings. The total pressure drop that occurs due to

ﬂuid friction is termed as Stand Pipe Pressure or SPP.

SPP is an important drilling parameter that must be

known with suﬃcient accuracy for selecting proper jet

bit nozzle size, determining optimum ﬂow rate to en-

sure eﬃcient hole cleaning and selecting proper mud

pump liner. Continuous monitoring of SPP also helps

in identifying downhole problems. For example, too

low SPP can be caused by washed out pipe or bit noz-

zle, loose joint or broken drill string, worn pump pack-

ing or liner, and lost returns due to formation frac-

ture. On the other hand, too high SPP could indicate a

plugged drill bit or an increase in mud density or vis-

cosity. Reliable indication of SPP provides an early

∗Corresponding author Email: dipu049@yahoo.com

warning of circulation problems and thus warns the

driller to make corrections avoiding major problems.

Rheology, the science of ﬂow and deformation of

matter, deals with stress-strain relationships of drilling

ﬂuid. Diﬀerent rheological models are used for char-

acterization of a drilling ﬂuid. Proper determination of

rheological constants is necessary for calculating SPP.

Okafor and Evers [1] performed an experimen-

tal comparison among three rheological models: i)

Robertson-Stiﬀ, ii) Power law and iii) Bingham Plas-

tic model. They used two types of clay-water drilling

ﬂuids. They found that the most accurate frictional

pressure loss was predicted by Robertson-Stiﬀmodel.

They also observed that Robertson-Stiﬀand Power

Law model predicted frictional pressure loss with no

signiﬁcant diﬀerence at typical oil well circulating ve-

locities of 0.061 to 0.24 m/s.

Maglione and Robotti [2] developed a methodol-

ogy to determine the three constants of the Herschel-

Bulkley model using the data from the circulation test

conducted for three ﬂow rates. They calculated SPP

for a drilling well located at the Po valley in Italy us-

ing the same model.

In this paper, the results obtained for four rheo-

logical models are presented. The four models used

are: i) Newtonian model, ii) Bingham plastic model,

iii) Power law model and iv) Herschel-Bulkley model.

The models are tested to ﬁnd out their ability in

providing the best SPP estimate for the water based

c

Bangladesh Uni. of Engg. &Tech.

8 Chemical Engineering Research Bulletin 13(2009) 7-11 /Chowdhury et al.

drilling ﬂuid, drillstring, and the surface equipment

geometry used to drill a vertical well in the Po valley

of Italy [2].

Even though it is well known that drilling muds do

not behave as Newtonian ﬂuids, the Newtonian model

is chosen to investigate about the theoretical pressure

drop if a Newtonian ﬂuid were used. The use of Bing-

ham Plastic model and Power law model is a common

practice for most oil companies. However, these mod-

els tend to represent the drilling ﬂuid behavior inaccu-

rately especially at low and medium shear rate ranges

[3]. The Herschel-Bulkley model is chosen as it in-

corporates the nonlinear shear stress-shear rate rela-

tionship and the yield shear stress exhibited by most

drilling ﬂuids.

2. The Rheological Models

A rheological model describes the relationship be-

tween shear stress and shear rate when a ﬂuid ﬂows

through a circular section or an annulus. Among the

various rheological models, this paper considers the

four most widely considered rheological models.

2.1. Newtonian model

It describes a ﬂuid considering a linear relationship

between shear stress (τ) and shear rate (γ). Graph-

ically this is represented by a straight line passing

through the origin with a slope equal to the dynamic

viscosity (µ) of the ﬂuid. This can be expressed as

τ=µγ (1)

This linear relation is valid only as long as the ﬂuid

ﬂow is laminar [4]. Laminar ﬂow occurs at low shear

rates. At high shear rates, the ﬂow pattern changes

from laminar to turbulent. For a Newtonian ﬂuid, vis-

cosity is constant and is only inﬂuenced by changes in

temperature and pressure [5].

2.2. Bingham plastic model

It is used to approximate the pseudoplastic behav-

ior (i.e. decrease of apparent viscosity with increasing

shear rate) of drilling ﬂuids and cement slurries [4].

The Bingham plastic model is deﬁned as

τ=µpγ+τy(2)

The above mathematical expression is valid only for

laminar ﬂow [4]. The Bingham plastic ﬂuid requires

the applied shear stress to exceed a certain minimum

value so that the ﬂuid can ﬂow. This minimum value

is called the yield point (τy). Once the yield point is

exceeded, changes in shear stress are proportional to

changes in shear rate. The constant of proportionality

is called the plastic viscosity (µp). The plastic viscos-

ity depends on pressure and temperature. The Bing-

ham plastic model works well for higher shear rates

but gives a signiﬁcant error at low shear rates. It also

may predict a non-physical yield point [6].

2.3. Power law model

It is used to approximate the pseudoplastic behavior

of drilling ﬂuids and cement slurries [4]. This model

is deﬁned as

τ=Kγm(3)

This model uses two parameters for ﬂuid

characterization- the consistency index (K) and

the ﬂow behavior index (m). When m=1, the above

equation reduces to the Newtonian model. Besides,

the Power law model can be used to represent a

pseudoplastic ﬂuid (m<1) and also a dilatant ﬂuid

(m>1).

Kdescribes the thickness of the ﬂuid and is analo-

gous to apparent viscosity of the ﬂuid. Large values of

Kmean that the ﬂuid is very thick. The value of min-

dicates the degree of Non-Newtonian behavior of the

ﬂuid. The shortcoming of Power law model is that it

underestimates the shear stresses at medium and low

shear rate ranges [3]. The Power law model is also

known as the Ostwald-de Walle model.

2.4. Herschel-Bulkley model

It is also known as the yield Power law model, as

it is a hybrid of the Bingham Plastic and the Power

law models [7]. The Power law model does not con-

sider the yield point while the Herschel-Bulkley model

takes the yield point into account. This model is de-

ﬁned as

τ=τy+Kγm(4)

The Herschel-Bulkley model is reduced to the

Power law model when τy=0 and to the Bingham

plastic model when m=1. It is to be noted that

this model can yield mathematical expressions that are

not readily solved analytically but can be solved using

non-linear regression [7].

A graphical representation of the four rheological

models is presented in Figure 1.

Figure 1: Graphical comparison of the four rheological models

Chemical Engineering Research Bulletin 13(2009) 7-11 /Chowdhury et al. 9

3. Field Data and Operational Conditions

SPP has been measured for three diﬀerent ﬂow rates

while performing a circulation test in the 17 1/2"sec-

tion of the well at a depth of 798 m. During the test,

the following conditions are maintained:

•The drilling ﬂuid is circulated with the bit oﬀbot-

tom while making a run in hole trip.

•During the test, the drill string is not rotated.

•The mud logging unit monitored the stand pipe

pressure readings.

•The mud sample used for rheological measure-

ment is taken from the shale shaker outlet during

the circulation test.

Figure 2shows the geometrical dimensions of the

cased and open hole sections. The casing and hole di-

mensions, the mud rheology measurements, the drill-

string dimensions, and the measured SPPs alongwith

the corresponding ﬂow rates are presented in Tables 1,

2, 3 and 4 respectively in the Appendix and adopted

from Maglione and Robotti [2].

Figure 2: Casing and hole dimensions

4. SPP Prediction

The following steps are used for predicting SPP for

the three ﬂow rates used during the circulation test:

4.1. Determination of the rheological constants

The initial estimates of the rheological constants are

determined using the ﬁeld approach. In this approach,

the Fann viscometer readings for 600 and 300 rpm are

used. These intial estimates are then used for get-

ting the ﬁnal values of the rheological constants us-

ing regression analysis. The regression analysis is per-

formed over all the six readings of the Fann viscome-

ter. For regression analysis, MS Excel has been used.

A detail of the approach used can be found in literature

[8].

4.2. Prediction of SPP

A Fortran 95 code is developed to predict SPP for

the drilling condition under consideration. SPP is pre-

dicted using the frictional pressure drop relations de-

veloped for the four rheological models considered.

This phenomenon is well explained in the literature

[9–13].

5. Results and Discussion

The rheological constants obtained and the pre-

dicted SPP by the four models are presented in Table 5

and 6 respectively in the Appendix. It can be seen that

the Newtonian model produces the worst estimate for

each of the three ﬂow rates. It is quite logical, since

drilling muds are Non-Newtonian ﬂuids. Among the

other three models, the Bingham plastic model pro-

duces the best estimate for each ﬂow rate with a maxi-

mum absolute error of less than one bar. For the Power

law model, the highest absolute error found is approx-

imately 16 bars at 3270 liter/min while it is approxi-

mately 13 bars for the Herschel-Bulkley model at the

same ﬂow rate. The predictions made by the Power

law model and the Herschel-Bulkley model are con-

siderably close to each other with a maximum discrep-

ancy of 2.9 bars. The absolute error in predicted SPP

by the Bingham plastic model, the Power law model

and the Herschel-Bulkley model is shown in Figure 3.

The ﬁgure shows the large amount of error in predicted

SPP by the Power law model and the Herschel-Bulkley

model at the two higher ﬂow rates.

One interesting observation is made. As indicated

by Figure 4, the best rheogram is produced by the

Herschel-Bulkley model with an R2value of 0.999.

However, the Bingham model with an R2value of

0.945 produces the best SPP estimates for all the ﬂow

rates considered. The R2value for the Power law

model is 0.996. In this ﬁgure, ‘Fann’ indicates the ac-

tual rheological measurements obtained by the Fann

viscometer.

There are two major limitations of this work. First,

the results obtained are limited to the single water

based mud used during the circulation test and the

drilling scenario considered. Second, the frictional

10 Chemical Engineering Research Bulletin 13(2009) 7-11 /Chowdhury et al.

Figure 3: Absolute error in predicted SPP by the three Non-

Newtonian models

Figure 4: Rheogram for the non-Newtonian models

pressure drop relations used are based on a number of

simplifying assumptions, such as concentric annular

and circular sections, non-rotating drillstring, isother-

mal conditions in the bore hole and steady state ax-

ial ﬂow. These simplifying assumptions are not com-

pletely valid in real life [4]. The eﬀect of pipe ec-

centricity, pipe rotation, and temperature and pressure

variations can have signiﬁcant eﬀect on frictional pres-

sure drop in the annulus. The computational complex-

ity in determining the eﬀects of these parameters on

SPP may not be justiﬁed sometime for simple verti-

cal wells drilled onshore. However, their eﬀects are

signiﬁcant while drilling deviated holes in complex

formations where the mud window is narrow. They

also need to be taken into consideration for High Pres-

sure High Temperature (HPHT) wells where high tem-

perature conditions cause the ﬂuid in the wellbore

to expand and high pressure conditions cause ﬂuid

compression [14]. These limitations of the conven-

tional approach have led to the development of alter-

native methods for SPP prediction. One such method

known as instance-based reasoning, a machine learn-

ing method, is discussed by Chowdhury [15].

6. Conclusion and Recommendations

Four rheological models are tested to ﬁnd out their

ability of predicting SPP with suﬃcient accuracy using

the conventional one dimensional frictional pressure

drop relations. The Bingham plastic model is found to

produce SPP estimates considerably close to the mea-

sured values for the drilling data considered. However,

it should be kept in mind that the conventional ap-

proach of SPP prediction is based on a number of sim-

plifying assumptions which are not completely valid

in real life.

There is scope for further work. The conventional

approach of SPP prediction can be tested with Fann

viscometer data collected using diﬀerent types of mud

samples, borehole geometries and surface equipment

dimensions.

References

[1] Okafor M and Evers J, Experimental Comparison of Rheology

Models for Drilling Fluids,in SPE Western Regional Meeting,

1992

[2] Maglione R and Robotti G, Field Rheological Parameters Im-

prove Stand Pipe Pressure Prediction While Drilling,in SPE

Latin America/Caribbean Petroleum Engineering Conference,

1996

[3] De Sa C, Martins A and Amaral M, A Computer Programme

for Drilling Hydraulics Optimisation Considering Realistic

Rheological Models,in European Petroleum Computer Con-

ference, 1994

[4] Bourgoyne Jr A, Millheim K, Chenevert M and Young Jr F,

Applied Drilling Engineering, SPE Textbook Series Vol. 2,

SPE, Richardson, TX, 2003

[5] Rabia H, Oilwell drilling engineering: principles and prac-

tice, Graham & Trotman, London, 1985

[6] Aadnøy B and Ravnøy J, Improved pressure drop/ﬂow rate

equation for non-Newtonian ﬂuids in laminar ﬂow, Journal of

petroleum science & engineering, 1994. 11(3):pp. 261–266

[7] Islam A, Drilling Fluid Rheology Note, Lecture Note, IPT,

NTNU, Trondheim, 2008

[8] Chowdhury D, Hydraulic Pressure Losses in Drilling Fluid,

MSc Project Report (for the course TPG 4520), IPT, NTNU,

Trondheim, 2008

[9] Skalle P, Compendium: Drilling Fluids and Borehole Hy-

draulics, Tapir Akademisk Forlag, Trondheim, 2005

[10] Graves W and Collins R, A New Rheological Model for Non-

Newtonian Fluids, Paper SPE, 1978. 7654

[11] Whittaker A, Theory and application of drilling ﬂuid hy-

draulics, Reidel, Boston, 1985

[12] Modi PN and Seth SM, Hydraulics and Fluid Mechanics

Including Hydraulic Machines, Standard Book House, New

Delhi, 14th edition, 2002

[13] Chilingarian GV and Vorabutr P, Drilling and Drilling Fluids,

Elsevier, Amsterdam, updated text book edition, 1983

[14] Harris O and Osisanya S, Evaluation of Equivalent Circulat-

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perature Conditions,in SPE Annual Technical Conference and

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Time Data, MSc Thesis Report (for the course TPG 4920),

IPT, NTNU, Trondheim, 2009

Chemical Engineering Research Bulletin 13(2009) 7-11 /Chowdhury et al. 11

Appendix

Table 1: Casing and hole dimension

Casing Size Depth Open Hole

(in) (m) (in)

OD ID From To

20 19 0 598

598 798 171/2

Table2: Mud rheology measurements at

standard conditions

Rotor Speed Fann Dial Reading

(rpm) (degree)

600 38

300 26

200 22

100 15

6 5

3 4.5

Table 3: Drillstring dimension

Type Length OD ID

(m) (in) (in)

Stand Pipe 20 - 4

Rotary Hose 20 - 3.5

Swivel 3.5 - 3.5

Kelly 12 - 3.5

Drill Pipe 513.6 5 4.28

Heavy Wate 137 5 3

Drill Collar 70 9 3

Drill Collar 77 11 1/43

Bit 0.4 Nozzles :

3×15/32"+

1×14/32"

Table 4: Measured SPP for

diﬀerent ﬂow rates

Pump Rate SPP

(liter/min) (bar)

1640 46.6

2460 103.3

3270 176.3

Table 5: Rheological constants

Newton Bingham plastic Power law Herschel-Bulkley

µ=0.022 Pas τy=3.57 Pa k =0.671 τy=1.15 Pa

µp=0.0167 Pas m =0.482 k =0.362

m=0.565

Table 6: Predicted SPP

Flow rate (liter/min) Measured SPP (bar) Predicted SPP (bar)

Newton Bingham plastic Power law Herschel-Bulkley

1640 46.6 493.24 47.14 45.32 45.95

2460 103.3 1027.99 102.34 94.92 96.49

3270 176.3 1721.75 176.6 160.25 163.15