MODELING OF DRILLING FLUID FLOW IN DRILLING SIMULATOR
#
Pipih Lestiyadi A.M.#1
Electrical Engineering Department, School of Electrical and Informatics Engineering,
Bandung Institute of Technology
Bandung, West Java, Indonesia
1lestiyadi@yahoo.co.id
Abstract
Drilling Simulator is a system to realize the idea of the workings of oil drilling which can be expected to
approach the reality. Drilling Simulator can be used to explore and strengthen the concept of new technologies
and predict the performance of complex systems to obtain analytic solutions. This study aims to build a model of
the drilling mud flow and to design an implementation of the flow modeling of drilling mud on Drilling
Simulator game. The main purpose of the circulatory system on a drilling operation is to circulate drilling mud
(drilling fluid) to the entire system of the drilling; making drilling mud is able to optimize their function. The
design of the drilling mud flow model is more focused on the modeling of fluid flow in the pipe (drill pipe) and
the annulus with the initial assumptions that paves the way for studying the circulation system in the process of
drilling in the field. That specially to estimating the losses that can be caused by fluid pressure loss due to
friction between the mud and the pipe. For Modeling and simulation in this study, it’s using Simulink (R2010b)
MATLAB ver. 7.11.0.584. Model test results indicate a relationship between changes in pressure, which caused
by friction, with an average velocity of fluid flow, is linear. The graph illustrates that the diameter of pipe and
the diameter of the casing affects the slope of the curve between the parameter changes in pressure and average
velocity of the fluid.
Key words: drilling, fluid systems, flow, mud
I.
PENDAHULUAN
Petroleum as an energy sources, has long been
recognized and further developed till now. People
continue searching oil to increase the production of
fuels, both for its own use or for export to foreign
countries at high prices. The process to do so, starting
from searching the source of crude oil, drilling, then
refining, requires a very high cost.
In the process, the drilling of oil wells is divided
into two groups: well drilling exploration and
exploitation drilling. Exploration drilling aimed to
determine the geological structure of the surface
layer of the earth and to determine the possible
discovery of hydrocarbons (petroleum) on the surface
of the earth. Drilling exploitation wells aims to
increase the production of hydrocarbons (petroleum),
known as Enhanced oil recovery methods (EOR)[1].
A series of special equipment used to drill the
well or to access the wells, called the rig. The main
feature of the rig is there is a tower made of steel
used for raising tubular pipes down the well. Rig
components can be classified into the hoisting
system, rotary system, circulation system and power
system[2].
Drilling Simulator is a system to realize the idea
of the workings of an oil drilling is expected to
approach the reality. Drilling Simulator can be used
to explore and strengthen the concept of new
technologies and predict the performance of complex
systems to obtain analytic solutions.
From the above description, the problem can be
formulated as follows.
1. How to make modeling of the flow of drilling
mud on Drilling Simulator?
2. How the systems work of flow modeling of
drilling mud on Drilling Simulator?
This research aims to build a model of drilling
mud flow and make a design of implementation of
this model on Drilling simulator game.
The constraints in this research are as follows.
1. The drilling mud which used is the water base
mud.
2. The assumptions of the drilling mud in the model
have an ideal fluids characteristic, which are
incompressible, and steady state fluid.
The method used in this research refers to
methodological of building the system in general
term by means of phases as follows.
1
 literature review phase of the drilling circulation
system and issues related to fluid flow;
 phase of data collection,
parameters, variables and
documents;
identification of
other necessary
 the design fluid flow model of the drilling process
phase;
 phase of testing, analysis and evaluation on the
test results;
 report preparation phase.
II. Basic Theory
2.1 Circulation System
The circulation system in a drilling operation
aims to circulate the drilling mud (drilling fluid) to
the entire system of drilling; making the drilling mud
is able to optimize their function. The drilling mud is
a fluid mixture of several components that can be
composed of: water (fresh or salt), oil, clay,
chemicals, gas, air, foam or detergent. The drilling
mud is an important factor and determines the
success, safety and economy of a drilling operation.
Equipment in the circulatory system are (1)
mud pumps, (2) flow lines, (3) drill pipe, (4) nozzles,
(5) pit sand mud tanks (settling tanks, mixing tanks,
suction tanks), (6) mud mixing equipment (mud
mixing hopper) and (7) contaminant removal
equipment (shale shaker, desander, desilter,
degasser)[3].
Drilling Mud pump consists of two types of
duplex and triplex pump. The amount of silt and mud
by the amount of pressure so that the mud pumps into
the circulatory system can be controlled by changing
the pump liners and piston to get a good piston
velocity during pumping[3].
.
The functions of drilling mud in a drilling
operation are as follows[4].
1. Lift cutting from the bottom of the bit.
2. Bringing cutting into the surface.
3. Bringing cutting and ballast materials in
suspension when circulation of mud was
suspended.
4. Removing sand and cutting to the surface.
5. To cool down and lubricate the bit and the drill
string.
6. Giving mud cake to the borehole wall.
7. Controlling the formation pressure.
8. Hold the most weight drill pipe and cutting
(buoyancy-effect).
9. Obtain information (mud logs, sample logs).
Determination of drilling mud used in a drilling
operation is based on subsurface conditions of the
formation being penetrated. In the drilling mud type
of water-based mud, some of the material in
suspension, dissolved in water. So, every water-based
mud, consist of an aqueous phase, inert solids,
reactive solid phase and chemical additives.
Water based mud is the most common types of
sludge used as cheap, easy to use is and form a "filter
cake" (mud cake) which is useful for drill holes from
the dangers of the falling of the borehole wall.
2.2 Drilling Hydraulic
Basic knowledge about fluid flow needed along
with many aspects which need being attention in
drilling, such as how the mud flows in the pipe,
through the fitting and annulus. In general term, the
fluid flow can be categorize as laminar flow,
turbulent flow, or the transition flow, between
laminar and turbulent
The Reynolds number can be used to differ the
fluid flow path. Reynolds number determine by
equation (2.2) as follow.
𝑅𝑒 =
𝜌𝑣̅𝑑
𝜇
...(2.1)
𝜌 = fluid density (kg/m3)
𝑑 = pipe diameter (m)
𝑣̅ = average velocity (m/s)
𝜇 = viscosity (Pa.s)
And the characteristic of Reynolds number are[6]:
Re< 1.800 …..............laminar flow
1.800 < Re< 3.000 ....transition flow
Re> 3.000 ….............turbulent flow
All fluids in the drilling process has the
characteristics of the "Newtonian" or "NonNewtonian". Newtonian fluid, such as: water, gas and
oil of high gravity, showing the relationship between
stress and shear strain rate (velocity gradient) in the
form of equation (2.3) following[6].
with:
𝜏 = 𝜇 (−
𝑑𝑣𝑟
𝑑𝑟
)=𝜇𝛾
...(2.2)
𝜏 = shear stress (Pa)
𝛾 = rate of share strain (s-1)
𝜇 = viscosity (Pa.s)
Fluids which the shear stress linearly related to
the rate of shear strain (also often referred to as the
rate of angular deformation) is classified as a
Newtonian fluid. For the fluids which the shear stress
is non-linearly related to the rate of shear strain is
classified as non-Newtonian fluid.
with:
2.3 Fluid Mechanics
Density () of a substance is defined as the ratio
between the mass of the substance (m) and the
volume of substance (V). Mathematically, the mass
of the type defined by equation (2.8) follows.
𝜌=
𝑚
𝑉
...(2.3)
which 𝜌 = density (kg/m3), 𝑚 = mass (kg) dan 𝑉 =
volume (m3).
2
Debit (𝑞) in (m3/s) is the amount (volume) of
fluid flowing per-unit time. Mathematically, the
discharge is formulated with:
𝑞=
𝑉
...(2.4)
𝑡
In an incompressible fluid, amount of debit is
constant.
𝐴1 𝑣1 = 𝐴2 𝑣2
...(2.5)
The equation for continuity can be written as the
equation (2.11) as follows.
−
𝜕𝜌
𝜕𝑡
= ∇ (𝜌𝑣)
...(2.6)
Or in the Cartesian,
−
𝜕𝜌
𝜕𝑡
=
𝜕
𝜕𝑥
(𝜌𝑣𝑥 ) +
𝜕
𝜕𝑦
(𝜌𝑣𝑦 ) +
𝜕
𝜕𝑧
(𝜌𝑣𝑧 )
...(2.7)
The Law of conservation of momentum for fluid
flow with a certain viscosity, or better known as the
Navier-Stokes equation,
𝜕𝑣
𝜕𝑡
+
𝜇∇2 𝑣
𝜌
=−
∇𝑝
𝜌
+𝑔
...(2.8)
In the cylindrical coordinates (the x-axis component)
for steady flow, constant density and constant
viscosity,
0=−
𝜕𝑝
𝜕𝑥
1 𝜕
+𝜇[
𝑟 𝜕𝑟
𝑟 (−
𝜕
𝑣
𝜕𝑟 𝑥
+
𝜕2
𝑣 )
𝜕𝑟 2 𝑥
+
1 𝜕2 𝑣𝑥
𝑟 2 𝜕𝜃 2
] + 𝜌𝑔𝑥
...(2.9)
III. ANALISYS AND DESIGN
3.1 Description of drilling Fluid Drilling
Simulator
Drilling Simulator as the system is a software
that can run on a computer by receiving input from
the user and the system performs a process and
provide feedback on the display screen (visual) and
output parameters. Drilling System Simulator is
divided into three sub-systems, namely petroleum
reservoir simulation, simulation and simulation of bit
rotation
drilling
fluid
(drilling
mud).
The system is built with the following initial
assumptions.
• Reservoir evaluated high economic value and
worth to be exploited.
• Reservoir is located below the land surface (land)
and not the sea (offshore).
• Reservoir is a reservoir used to contain oil and
water, not the gas reservoir, is homogeneous and
isotropic.
• The process of drilling wells that do produce
drilling vertically until it reaches a certain depth
where there are sources of petroleum.
3.2 Modeling of Drilling Fluid
Sub-system that serves in this research is the
simulation of drilling mud. The simulation is a
simulation of the movement which was built in the
drilling mud circulation system during the drilling
process. To analyze the sub-systems and designing
drilling mud, to be able to interact in a scenario of
drilling, then the sub-systems are built based on the
following assumptions.
• Mud drilling is assumed to be water-based mud
(water-based mud), and viewed as a single phase
flow (steady).
• Mud drilling is incompressible (not compressed).
• Mud drilling is isothermal.
• Drill string always right in the center of casing or
drill holes.
• Drill string not spinning with drill bits.
In sub-system simulation of this drilling mud
fluid flow will be simulated. Starting from the mud
pit, mud, mud mixing hopper is passed on, the place
of other materials (material additive) mixed into the
mud, and then sucked up by the mud pump. Of mud
slurry pump is pressurized in accordance with the
recommended pressure, driven to the stand pipe,
rotary hose (flexible hose), through the swivel and
then get into the drill string. In the drill string, mud
flows down to the bit, pushed out through the nozzles
against the base of the hole drilling. Then go up
through the annulus, out through the mud return line
leading to the mud cleaning system is a system that
conditions the mud back to its original state, free
from dust drilling (cutting). Once clean, the mud
back into the mud pit to re-circulate[3].
3.3 Modeling of Mud Flow in Pipe
and Annulus
Modeling Flow in Pipe
For ease in modeling the flow of drilling mud, it
is assumed that the fluid used is incompressible,
Newtonian fluid with steady flow in pipes in the xaxis component. Thus,
𝜕𝜌
𝜕𝑥
=0
...(3.1)
𝑣𝑥 = 𝑣, 𝑣𝑦 = 𝑣𝑧 = 0,
𝜕𝑣
𝜕𝑥
=0
...(3.2)
And the momentum,
𝜕𝑝
𝜕𝑥
= 𝜇[
1 𝜕
𝑟 𝜕𝑟
(−𝑟
𝜕𝑣
𝜕𝑟
)+
𝜕2 𝑣
𝜕𝑥 2
] + 𝜌𝑔𝑥
...(3.3)
For the x-axis component and the substitution of
equation (3.2) into equation (3.3) yield equation
(3.4).
𝜕𝑝
𝜕𝑥
=−
1 𝜕
𝑟 𝜕𝑟
(𝑟. 𝜇
𝜕𝑣
𝜕𝑟
)
...(3.4)
With these equations, the modeling of the mud flow
in the pipe can be modeled by the following
equation.
𝑑𝑝
𝑑𝑥
=
32 𝜇 𝑣̅
𝑑2
...(3.5)
3
By equation (3.5), then the pressure drop per meter
𝑑𝑝
length of pipe ( ) in (Pa/m) is affected by the
𝑑𝑥
coefficient of viscosity (𝜇 in Pa.s), pipe diameter (d
in m) and linear on the average flow velocity mud (𝑣̅
in m/s).
Flow model in annulus
To explain the model of Newtonian fluid, namely the
reading of 300 rpm [6], obtained the value of the
𝜏
49,75
viscosity of the fluid used is 𝜇 = 300 =
=
𝛾300
511
0,09736 𝑃𝑎. 𝑠 = 97,36 𝑐𝑃
The size of the pipe’s diameter (drill pipe) and the
casing as the following Table 4.2[7].
Table 4.2 Drill Pipe and Casing in Annulus
Casing size
(in)
1
4
Nominal Size of Drill Pipe (in)
2
2
2
5
5
1
Figure 3.2 Annulus cross-section
6
Modeling the flow of mud in the annulus can be
modeled by the following equation.
7
𝑑𝑝
𝑑𝑥
with
=
32𝜇𝑣̅
...(3.6)
𝑑𝐿 2
𝑑𝐿 2 = [(𝑑𝑜 2 + 𝑑𝑖 2 ) −
(𝑑𝑜 2 −𝑑𝑖 2 )
]
𝑑
ln 𝑜⁄𝑑
𝑖
By equation (3.6), the pressure drop per meter length
𝑑𝑝
of the annulus ( ) is affected by the viscosity
𝑑𝑥
coefficient (𝜇), the inner pipe diameter (𝑑𝑖 ), the outer
pipe diameter (𝑑𝑜 ) and the rate of the linear velocity
of the mud flow (𝑣̅ ).
IV. IMPLEMENTATION AND
TESTING
4.1 Implementation
Implementation of Hardware and
Software
The hardware that used to support the testing of
drilling mud flow model in an optimal Drilling
Simulator is a computer requires the following
minimum specifications.
Table 4.1 The hardware requirements for testing models of
fluid
Operating System
Computer Processor
System Memory
Hard Disk Space
Video Card
Sound Card
Display
Minimum
Windows XP
800 MHz
256 MB atau lebih
500 MB
64 MB Video Card
AC 97 Compatible
CRT, 1024x768 resoluiton
2
2
5
2
8
2
3
8
3
2
8
3
2
8
3
2
8
3
2
8
7
8
7
8
7
8
7
8
3
3
1
2
1
2
4
Tests for Mud Flow Model in Pipe
Mud's flow model in the pipe and the annulus is
a model that describes pressure changes per length of
the pipe caused by friction of the mud flow with the
pipe and with an average speed of the mud flow in
the pipe.
Testing of the model aims to determine the truth
of a model with the real reality on the field. Testing
is done by inserting the input parameters obtained
from the literature or in the field and then compare it
with the relevant empirical data.
The data that used in the testing can be seen in
Table 4.3 below.
Table 4.3 Data for simulating the mud flow in pipe
No
1.
Symbol
µ
2.
d1
3.
d2
Information
Viscosity of
Newtonian Fluid
Pipe diameter
first data
Pipe diameter
second data
Value
0,09376 Pa
0,060325 m
0,101600 m
The used equation is
𝑑𝑝
𝑑𝑥
=
32 𝜇 𝑣̅
𝑑2
(4.1)
𝑑𝑝
Tests using Simulink R2010b considering
as
𝑑𝑥
output and 𝑣̅ as input. The first step is to create a
circuit in accordance with equation (4.1) as follows.
The main software used for testing process of
fluid flow model in the pipe and the annulus is
Simulink R2010b Matlab Ver. 7.11.0.584.
4.2 Tests of Mud Flow Model
Testing the model aims to ensure the true model
of the fluid. Testing is done by entering the model
input parameters obtained from field and literature
and then compare with the relevant empirical data.
Figure 4.1 Block Diagram of the simulation In Pipe
Figure 4.1 is a circuit of the simulations
according to equation (4.1). Input parameter in 𝑣̅ is
the average flow velocity of mud in the pipe (m / s).
4
𝑑𝑝
And the output parameter
is the pressure change
𝑑𝑥
along the length of the pipe. Signal's form from the
input and output is displayed in graphical two
dimensional x-y as shown below.
Table 4.4 Data on the annular mud flow simulation
No
1.
Symbol
µ
2a.
di1
2b.
do1
3a.
di2
3b.
do2
Information
Viscosity for Newtonian
Fluid
Pipe diameter
first data
Casing diameter
first data
Pipe diameter
second data
Casing diameter
second data
Value
0,09376 Pa
0,060325 m
0,114300 m
0,060325 m
0,127000 m
The equation used is as follows.
𝑑𝑝
𝑑𝑥
Figure 4.2 Charts of the influence of the average
velocity toward the changes in pressure on the first
pipe
In Figure 4.2, the X axis is the average velocity of the
mud flow in pipe 𝑣̅ (m / s), and the Y axis is the
𝑑𝑝
change in pressure per unit length of pipe
(Pa/m).
𝑑𝑥
The graph above shows that the greater of the
velocity of mud's flow, the greater the pressure
change per unit length of the pipe. With the input
signal coming from increasing value of 𝑣̅ , which is
between 0 to 0.5 m/s, was found that the value of
changes in pressure per length of pipe between 0 and
above 400 Pa/m.
If the parameters of the diameter of the pipe using the
second data, then the resulting graph as follows.
=
32𝜇𝑣̅
𝑑𝐿 2 = [(𝑑𝑜 2 + 𝑑𝑖 2 ) −
which
...(4.2)
𝑑𝐿 2
(𝑑𝑜 2 −𝑑𝑖 2 )
]
𝑑
ln 𝑜⁄𝑑
𝑖
...(4.3)
The equation 𝑑𝐿 2 can be solved by the usual
empirical methods, so the values of 𝑑𝐿 2 for each pair
of data and the casing pipe diameter as shown in
Table 4.5 below.
Table 4.5 Value of 𝑑𝐿 2
Data
𝑑𝑖
𝑑𝑖
𝑑𝐿 2
1.
0,060325 m
0,114300 m
0,001955 m
2.
0,060325 m
0,127000 m
0,002991 m
The equation to simulate the flow of mud in the
annulus is similar to the equation for simulating the
flow of mud on the pipe. Circuit block in accordance
with equation (4.2) is shown in Figure 4.4.
Figure 4.4 Block diagram of the simulation In Pipe
Figure 4.3 Charts of the influence of the average
velocity toward the changes in pressure on the
second pipe
By using the first data, the graph of simulation of
mud's flow in annulus, is obtained as shown below.
From Figure 4.3 above, the input signal from value
of v, increased from 0 to 0.5 m/s was found that
changes in pressure per length of pipe is also
increased from 0 to at below 150 Pa/m.
That means the larger of the diameter of the pipe
used, the smaller of the pressure changes in the flow
of mud along the length of the pipe.
Tests of Mud Flow Model in the
annulus
The data used in testing can be seen in Table 4.4
below.
Figure 4.5 Charts the influence of average velocity
toward the changes in pressure in the annulus, the
first data
With the input parameters of the second data, the
graph obtained as follows.
5
accompanied by other tool that support the
circulatory system such as mud pumps and so on.
REFERENCES
Figure 4.6 Charts the influence of average velocity
toward the changes in pressure in the annulus, the
second data
From figure 4.5 and figure 4.6, the chart of the
influence of average velocity toward the changes in
pressure inform that the bigger size of casing causes
the smaller of the changes in pressure along the
length of pipe.
From the first data, using the casing diameter 4
1/2 inch or 0.114300 meter and the pipe diameter to 2
3/8 inch or 0.060325 m, with a change of variable
speed from 0 to 0.5 m / s obtained the change of
pressure along the length of pipe from 0 to less than
about 800 Pa / m.
From the second data that uses a diameter of 5
inches or 0.127000 meter for casing and pipe's
diameter equal to the first data, which is 2 3/8 inch or
0.060325 m, with a change of variable speed from 0
to 0.5 m/s obtained change of pressure along the
length of the pipe from 0 to nearly 500 Pa/m.
V. Conclusions and Suggestions
Conclusions
The conclusions to be drawn from this study are
as follows.
[1] Darley,H.C.H, Gray,George R, Composition and
Properties of Drilling and Completion Fluids,
Fifth Edition, Gulf Publishing Company,
Houston, 1988.
[2] Bourgoyne Jr, Adam T, Millheim, Keith K,
Chenevert, Martin E., dan Young Jr, F.S.,
Applied Drilling Engineering, SPE, Richardson,
TX, 1991.
[3] Prassl, Wolfgang F., Drilling Engineering,
Departement of Petroleum Engineering, Curtin
University of Technology.
[4] Baker Hughes INTEQ, Drilling Engineering
Workbook, Houston, TX, United States of
America, 1995.
[5] Munson,Bruce R., Young,Donald F., Okiishi,
Theodore H., Mekanika Fluida, alih bahasa,
Harinaldi, Budiarso, Erlangga, Jakarta, 2005.
[6] Pal Skalle, Drilling Fluid Engineering, Skalle &
Ventus Publishing, 2010.
[7] Gabolde, G, Nguyen J.P, Drilling Data
Handbook, Institut francais du Petrole
Publications, Paris, 1999.
[8] Barret, Bob et al., Drilling Fluids Processing
Handbook, Elsevier Inc, Oxford UK, 2005
[9] William Lyons, Standard Handbook of Petroleum
and Natural Gas Engineering, Gulf Publishing
Company, Houston, Texas, 1996.
 A mathematical model for calculation of pressure
loss due to friction effects can be more accurate
to estimate the losses that will be encountered
during drilling compared with experiment.
 The use of larger diameter pipe can reduce the
disadvantages of pressure loss in the mud flow
caused by mud's friction with the pipe, either on
the pipe (drill pipe) and the annulus.
 System circulating mud flow is crucial in the
process of drilling. Many parameters involved in
the process of the drilling circulation. A
mathematical model will be more accurate if
more parameters were included in the modeling
calculations.
Suggestions
 Model the flow of drilling mud can be further
refined by the research of the characteristics of
fluid flow outside the Newtonian fluid, laminar
flow, or taking into account the factor of
temperature on the fluid.
 Further Development in Drilling Simulator game,
can implement the fluid flow model is
6