Content uploaded by Mahbubur Rahman
Author content
All content in this area was uploaded by Mahbubur Rahman on Apr 20, 2023
Content may be subject to copyright.
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-
ing Density of Drilling Fluids Under High Pressure/High Tem-
perature Conditions,in SPE Annual Technical Conference and
Exhibition, 2005
[15] Chowdhury D, Prediction of Standpipe Pressure Using Real
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