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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 over all the six Fann viscometer readings obtained for the water based mud used. 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.
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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 dierent 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 sucient accuracy for selecting proper jet
bit nozzle size, determining optimum flow rate to en-
sure ecient 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. Dierent 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-Sti, 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-Stimodel.
They also observed that Robertson-Stiand Power
Law model predicted frictional pressure loss with no
significant dierence 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 dierent 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 obot-
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
[913].
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 eect of pipe ec-
centricity, pipe rotation, and temperature and pressure
variations can have significant eect on frictional pres-
sure drop in the annulus. The computational complex-
ity in determining the eects of these parameters on
SPP may not be justified sometime for simple verti-
cal wells drilled onshore. However, their eects 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 sucient 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 dierent 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-
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[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
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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-
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Including Hydraulic Machines, Standard Book House, New
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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
dierent 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
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The equation of the rheological model of Herschel & Bulkley and the relevant expressions of pressure drops, valid both for circular and annular sections, are applied to determine the three characteristic parameters of a drilling fluid, having yield pseudoplastic behaviour, and flowing in the drilling hydraulic circuit, starting from circulation tests. A typical standard drilling hydraulic circuit consists of the surface circuit (stand pipe, rotary hose, swivel and kelly), the circular section (inside the drill string with variable diameters), the bit and the annular section (the gap between the wall borehole or casing and the drill string). In this circuit the drilling mud enters the drill pipe, comes out from the bit, flows up to the annulus up to the surface, where it after a short time for cleaning is put back in the circuit. The parameters to be solved are the yield point, the consistency index k and the flow behaviour index n. By means at least three flow tests at a certain drilling depth, with the bit off bottom, the pump rates and the relative stand pipe pressures are recorded. The obtained N couple of values of stand pipe pressure and pump rate, the geometry of the hydraulic circuit and the fluid density are the input data for a numerical procedure to determine the three parameters of the considered drilling fluid. In this way, using this numerical process, a non linear system of N equations (with N 3) with three unknowns (the three parameters of the fluid: n, k and) is solved determining the Herschel & Bulkley rheological parameters. This procedure takes into account the more probable solution for each tentative value of the flow behaviour index np, considering the infinite couples of and k satisfying the input value of stand pipe pressure, and the mean square deviation is calculated for each tentative value of, np: the minimum value of the MSD gives the solution tern of the non linear system of N equations. In this paper a brief description of the mathematical model and the numerical process used will he reported and a calculation using field data from circulation test carried out in a surface section of an ultradeep well located in the Po valley, will be done. The results will be compared with the obtained results using the readings on the same drilling mud performed on Fann VG 35 viscometer and it can be seen that not always the rheological tern determined from the viscometer data coincides with the equivalent rheological tern found considering the drilling well as viscometer. Besides the stand pipe pressure relative to an 17 1/2" run (from 2900 m to 3060 m) will be monitored using this procedure: calculated SPP data using the equivalent rheological tern and the rheological parameters from viscometer readings, using different rheological models such as Bingham, Ostwald & de Waele and Herschel & Bulkley, will be compared to field stand pipe pressure data. It can be seen that the overall average error between measured and calculated SPP (using the Herschel & Bulkley equivalent tern) has been drastically reduced to very low error while the calculated SPP using viscometer readings with the most rheological models today used in practice could lead to large errors misleading an accurate evaluation of the SPP on the rig floor. This method could be useful not only to calculate and predict exactly the SPP, but also to evaluate with accuracy the annular pressure drop and the corresponding ECD in order to have the maximum allowable pump rates without fracturing the crossed formation, besides could be used to monitor the SPP behaviour for potential occurring problem in the hydraulic circuit such as wash out, plugged nozzles and in the case of gas kicks in the well. Also this method, if applied to different drilling depths, could give information on the influence of pressure and temperature, existing in the well, on the rheology of the drilling mud. Introduction During drilling operations it is very important to know exactly the pressure drop along the hydraulic circuit for many reasons. The most important are the following: P. 271
Article
Drilling fluids while circulating in oilwells are submitted to a wide range of shear rates, varying from very low values (in the mud tank or in riser/drill pipe annular region) to very high ones (through the bit nozzles). It is common sense among rheologists involved in the area, that the conventional rheological models (Bingham and Ostwald de Waele) do not represent adequately the behaviour of drilling fluids in such a wide range of shear rates. Other rheological models have been proposed to characterize drilling fluids. However, their current use in the design and supervision of drilling operations is not overspread yet. Since most drilling rigs today have computational facilities, there is no longer necessity to use inaccurate models for engineering calculations. Adequate rheological characterization is an essential starting point for several calculations, such as hydraulics, cutting transport, kick control, etc. This paper presents a procedure for drilling hydraulics calculation based on dial readings at the six available rotation speeds of the conventional oilfield viscometer, calculation of five rheological models and use of specific friction loss correlations for each model. An user friendly computer program was developed for optimum flow rate calculations based on this procedure and validated with data obtained from a real scale well. The program was developed based on the requirements of several drilling activities such as offshore operations, compressible fluids, high angle wells, etc.
Article
The shear stresses and frictional pressure losses that exist in a circulating system could be predicted through rheology models. This paper presents the experimental comparison of a relatively new rheology model called the Robertson-Stiff [1] model to widely used Ostwald-de Walle (Power Law) [2] and Bingham Plastic [3] models. The models were used to predict shear stresses and frictional pressure losses in laboratory experiments using clay-water drilling fluids for flows through pipes and annuli. Two types of clay-water drilling fluids were used; one with a low yield stress and the other with a high yield stress. The result of the research showed that the Robertson-Stiff [1] model predicted the best fit of the rheologic data for the two types of drilling fluids used. However, for fluid velocities greater than 2 ft/sce (0.61 m/sec) the frictional pressure losses predicted by the Robertson-Stiff [1] model differ from that of the Power Law [2] model by less than three percent.
Book
This book is a treatise on the drilling of wells and the part played by drilling fluids. The main body of the book deals with the many aspects of the subject while the extensive appendices have been expanded and brought up-to-date to cover the latest developments in drilling and drilling fluids technology.