Rheology of Fluids Hydraulic Calculations & Drilling Fluid (Mud) Filtration Tests

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DEPARTMENT OF CHEMICAL & PETROLEUM
MSc PETROLEUM ENGINEERING (3616)
EXPERIMENT 2 & 3
Rheology of Fluids & Hydraulic Calculations
&
Drilling Fluid (Mud) Filtration Tests
Team 8
Muhammad Kamal (3325610)
Ghazanfar Khan (3300082)
Adedamola Lawal (3330105)
Submitted To:
Mrs Maria Astrid Centeno
Submission Date:
20/02/2015

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Contents
Experiment No 2 – Rheology of Fluids & Hydraulic Calculations .....................................4
Summary................................................................................................................................4
Introduction.............................................................................................................................4
Objectives...............................................................................................................................5
Flow regimes.......................................................................................................................5
Viscosity..............................................................................................................................6
Shear stress........................................................................................................................6
Share rate ...........................................................................................................................7
Rheological models ............................................................................................................8
Circulating system ............................................................................................................10
Experimental Equipment......................................................................................................10
Procedure & Observation.....................................................................................................11
Experimental procedure ...................................................................................................11
Experimental observations...................................................................................................13
Results & Calculations .........................................................................................................13
Experimental calculations ....................................................................................................17
Calculations of sample Mud A: ............................................................................................17
Calculations of sample Mud B: ............................................................................................18
Calculations of sample Mud A: ............................................................................................20
Calculations of sample Mud B: ............................................................................................22
Mud A - Annulus...................................................................................................................24
Mud B - Annulus..................................................................................................................25
Experiment 3 – Drilling Fluid (Mud) Filtration Tests..........................................................26
Summary..............................................................................................................................26
Introduction...........................................................................................................................26
Experiment Equipment.........................................................................................................27
Background ..........................................................................................................................27
Potential problems from excessive filter-cake thickness .................................................27
Potential problems from excessive filtrate invasion .........................................................28
Filtration theory .................................................................................................................28
Static Filtration ..................................................................................................................28
Factors affecting filtration .................................................................................................28
Fluid-Loss control additives ..............................................................................................28
Polyanionic Cellulose (PAC) ............................................................................................28

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Experiment procedure and observations .........................................................................29
First phase procedure:......................................................................................................29
Second phase procedure: ................................................................................................29
Third phase procedure: ....................................................................................................30
Results & Calculations .........................................................................................................31
Discussion of Results...........................................................................................................33
Conclusions..........................................................................................................................34
References...........................................................................................................................34

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Experiment No 2 – Rheology ofFluids & Hydraulic Calculations
Summary
This experiment was carried out to investigate Rheology of fluids and hydraulic calculations. This
is important to the petroleum engineers in calculating friction loss in pipe or annulus, determination of
the equivalent circulating density of the drilling fluid, determination of the flow regime in the annulus,
determination of the rheological model, estimation of the hole cleaning efficiency and evaluation of the
fluid suspension capacity.
The objective of the experiment is to familiarize with the equipment used in laboratories and oil field to
design and adjust properties of drilling mud, application of rheological values or hydraulic calculations
and measurements of viscosity and rheological behaviour of drilling fluids by the use of viscometer
fann 35.
The key results obtained from the experiment done on two different samples given as mud A and mud
B are respectively, where for mud A PV = 10𝑐𝑝,YP = 67 𝑙𝑏 100𝑓𝑡2⁄ , n = 0.081 and K = 0.5871 and for
mud B PV = 10𝑐𝑝,YP = 67 𝑙𝑏 100𝑓𝑡2⁄ , n = 0.081 and K = 0.5871.
From the experiment we arrived at the conclusion that both mud A and mud B exhibit Herschel-
Bulkley model with shear stress plotted against shear rate and power low model with log-log shear
rate plotted against shear rate. The graphs plotted for apparent viscosity against shear rate for both
muds have very similar L-shape patterns. All this indicates that both muds exhibit similar rheology.
Introduction
Rheology and hydraulics are interrelated studies of fluid behaviour. Fluid rheology and hydraulics are
engineering terms that describe the behaviour of fluids in motion. Rheology is the science of
deformation and flow of matter. Primarily concerned with the relationship between shear stress and
shear rate and the impact they have on fluid flow characteristics inside tabular and annular spaces.
Hydraulic on the other hand deal with the mechanical properties of liquids, describing how fluid flow
creates and apply pressures. In drilling fluids, the flow behaviour of the fluid must be described using
rheological models and equations before the hydraulic equations can be applied. Rheology of fluids
and hydraulics are significant in petroleum industries during drilling operation to ensure the calculation
of frictional loss in pipe or annulus, determining the equivalent circulating density of the drilling fluid,
determining the flow regime in the annulus or pipe, estimating hole cleaning efficiency, evaluating fluid
suspension capacity, provide wellbore stability, provide energy at the bit to maximize Rate of
Penetration (ROP) and remove cuttings from the well.

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Objectives
 Familiarization with equipment used in laboratories and oilfield to design and adjust properties of
drilling mud.
 Measurements of viscosity and rheological behaviour of drilling fluids by using viscometer Fann
35.
 Application of rheological values in hydraulic calculations.
Flowregimes
The behaviour of a fluid is determined by the flow regime, which has a direct effect on the ability of
that fluid to perform its basic functions. The flow can either be laminar or turbulent, depending on the
velocity, size and shape of the flow channel, fluid density, and viscosity. Between laminar and
turbulent flow, the fluid will pass through a transition region where the flow of fluid has both laminar
and turbulent characteristics.
In laminar flow, the fluid moves parallel to the walls of the flow channel in smooth lines. Flow tends to
be laminar when the fluid is viscous. In laminar flow, the pressure required to move the fluid increases
with velocity and viscosity.
In turbulent flow, the fluid is swirling and eddying as it moves along the flow channel, even though the
bulk of the fluids move forward. These velocity fluctuations arise spontaneously. Wall roughness or
changes in flow direction will increase the amount of turbulence. Flow tends to be turbulent with
higher velocities or when the fluid has low viscosity. In turbulent flow, the pressure required to move
the fluid increases linearly with density and approximately with the square of velocity, meaning more
pump pressure is needed to move a fluid in turbulent flow than in laminar flow.
The transition between laminar and turbulent flow is controlled by the relative importance of viscous
forces in the flow. In laminar flow, the viscous forces dominate, while in turbulent flow the inertial
forces are more important. For Newtonian fluids, viscous forces vary linearly with the flow rate, while
the inertial forces vary as the square of the flow rate.
The ratio of inertial forces to viscous forces is the Reynolds number (Re). If consistent units are
chosen, the ratio will be dimensionless and the Reynolds number (Re) will be:
Re =
DVρ
μ
Where:
D = diameter of the flow channel
V = average flow velocity
ρ = fluid density
μ = viscosity
The flow of any particular liquid in any particular flow channel can either be laminar, transitional, or
turbulent. The transition occurs at a critical velocity, for typical drilling fluids. Its normally occurs over a
range of velocities corresponding to Reynolds number between 2000 and 4000.

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Viscosity
Viscosity is defined as the ratio of shear stress to shear rate. The traditional units of viscosity are
dyne-sec/cm2
, which is termed poise. Since one poise represents a relatively high viscosity for most
fluids, the term centipoise (cp) is normally used. A centipoise equals one-hundredth of poise or one
millipascal-second.
μ=
τ
γ
Where:
μ = viscosity
τ = shear stress
γ = shear rate
Viscosity value is not constant for most drilling fluids. It varies with shear rate. To check for rate
dependent effects, shear stress measurements are made at a number of shear rates. From these
measured data, rheological parameters can be calculated or can be plotted as viscosity versus shear
rate.
The term effective viscosity is used to describe the viscosity either measured or calculated at shear
rate corresponding to existing flow conditions in the wellbore or drill pipe. To be meaningful, a
viscosity measurement must always specify the shear rate.
Shearstress
Shear stress is the force required to sustain a particular rate of fluid flow and is measured as a force
per unit area. Shear stress τ is expressed mathematically as:
τ =
F
A
Where:
F = force
A = surface area subjected to stress
In a pipe, the shear stress at the pipe wall is expressed as:
τw =
F
A
=
DP
4L
In an annulus with inner and outer diameters known, the shear stress is expressed the same manner
as:
τw =
F
A
=
P(D2 − D1)
4L
Where:
D = diameter of pipe
D1= inner diameter of pipe
D2 = outer diameter of pipe
P = pressure on end of liquid column

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A = surface area of the fluid
L = length
Sharerate
Shear rate is a velocity gradient measured across the diameter of a pipe or annulus. It is the rate at
which one layer of fluid slide or move past another layer.
The velocity gradient is the rate of change of velocity (∆V) with distance from the wall (h). Shear rate
is ∆V/h and have a unit of 1/time, the reciprocal of time usually in 1/sec. orsec−1
. It is important to
express the above concept mathematically so that models and calculations can be developed. Shear
rate (γ) is defined as:
γ =
dV
dr
Where:
dV = velocity change between fluid layers
dr = distance between fluid layers
Shear rate γwp at the wall can be expressed as a function of the average velocity (V) and the diameter
of pipe (D).
γwp= f(V, D) =
8VP
D
In which
VP=
Q
A
=
4Q
πD2
Where:
Q = volumetric flow rate
A = surface area of cross section
D = pipe diameter
V = velocity
VP = average velocity in pipe
In an annulus of outside diameter D2 and inside diameterD1, the wall shear rate can be shown as:
γwa= f(V, D1,D2
) =
12Va
D2−D1
In which
Va =
4Q
π(D2
2
−D1
2
)
Where:
γwp = shear rate at annulus wall

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V = velocity
Q = volumetric flow rate
D1 = inner annulus diameter
D2 = outer annulus diameter
Va= average velocity in annulus
Rheological models
The mathematical relationship between shear rate and shear stress is the rheological model of the
fluid. The concept of shear rate and shear stress apply to all fluid flow. Within a circulating system,
shear rate is dependent on the average velocity of the fluid in the geometry in which it flows.
Thus shear rates are higher in small geometries (drill string) and lower in large geometries (casing
and riser annuli). Higher shear rates usually cause a greater resistive force of shear stress. Therefore
shear stresses in drill string exceed those in annulus. The sum of pressure losses throughout the
circulating system (pump pressure) is often associated with shear stress while the pump rate is
associated with shear rate.
Fluids whose viscosity remains constant with change in shear rate are known as Newtonian fluids.
Non-Newtonian fluids are those fluids whose viscosity varies with change in shear rate. Those fluids
in which shear stress is directly proportional to shear rate are called Newtonian. Examples of
Newtonian are water, glycerine, and light oil.
Most drilling fluids are not Newtonian: the shear stress is not proportional to shear rate. Such fluids
are called non-Newtonian. Drilling fluids are shear thinning when they have less viscosity at higher
shear rates than at lower shear rates.
There are non-Newtonian fluids, which have dilatant behaviour. The viscosity of these fluids increases
with increasing shear rate. Dilatant behaviour of drilling fluids rarely, if ever occurs.
The distinction between Newtonian and non-Newtonian fluids is illustrated by using the API standard
concentric cylinder viscometer. If the 600-rpm dial reading is twice the 300-rpm reading, the fluid
exhibits Newtonian flow behaviour. If the 600-rpm reading is less than twice the 300-rpm reading, the
fluid is non-Newtonian and shears thinning.
One fluid type of shear thinning fluid will begin to flow as soon as shearing force or pressure,
regardless of how slight is applied, such fluids are known as pseudo plastic. Another type of shear
thinning fluid will not flow until a given shear stress is applied. This shear stress is called the yield
stress.
Fluids can also exhibit time dependent effects. Under constant shear rate, the viscosity decreases
with time until equilibrium is established. Thixotropic fluids experience a decrease in viscosity with
time while rheopectic fluids experience an increase in viscosity with time.
Most drill fluids are non-Newtonian, pseudo plastic fluids. Rheological models help predict fluid
behaviour across a wide range of shear rates. The most important rheological models that pertain to
drilling fluids are the:
Bingham model: is the most common rheological model used for drilling fluids. This model describes a
fluid in which the shear stress/shear rate ratio is linear once a specific shear stress has been

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exceeded. Two parameters, plastic viscosity and yield point are used to describe this model. Because
these constants are determined between the specified shear rates of 511 and 1022, this model
characterizes a fluid in the higher shear rate range.
Power Law: The power Law is used to describe the flow of shear thinning or pseudo plastic drilling
fluids. This model describes a fluid in which shear stress versus shear rate is a straight line when
plotted on a log-log graph. Since the constants, n and K from this model are determined from data at
any two speeds, it more closely represents an actual fluid over a wide range of shear rates.
Herschel-Buckley (Modified power law) model: The modified Power law is used to describe the flow of
a pseudo plastic drilling fluid, which requires a yield stress to flow. A graph of shear stress minus yield
stress versus shear rate is a stress line on log-log coordinates. This model has the advantages of the
Power Law and more nearly describes the flow of a drilling fluid since it also includes a yield value.
The rheological parameters recorded in an API drilling fluid report are plastic viscosity and yield point
from the Bingham Plastic Model, however for hydraulics calculations in important to have rheological
data shown on linear, semi-log or log-log graphs of shear rate versus shear stress or viscosity.

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Circulatingsystem
The circulating system of a drilling well is made up of a number of components or intervals, each with
a specific pressure drop. The sum of these interval pressure drops is equal to the total system
pressure loss or the measured standpipe pressure.
Experimental Equipment
Concentric cylinder viscometer
The equipment used was concentric cylinder viscometers, these viscometers are rotational
instruments powered by an electric motor or a hand crank. Fluid is contained in the annular space

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between two cylinders. The outer sleeves or rotor sleeve is driven at a constant velocity. The rotation
of the sleeve in the fluid produces a torque on the inner cylinder or bob with a torsion string restraining
the movement. This mechanism is illustrated in the figure below. In most cases, a dial attached to the
bob indicates the displacement of the bob.
When the rotor is rotating at a constant angular velocity w2 and the bob is held motionless (w1 = 0),
the torque applied by torsion spring to the bob must be equal but opposite in direction to the torque
applied to rotor by the motor. The torque is transmitted between the rotor and the bob by the viscous
drag between successive layers of fluid. If there is no slip at the rotor wall, the layer of fluid
immediately adjacent to the rotor also moving at an angular velocity w2. Successive layers of fluid
between r2 and r1 are moving at successively lower velocities. If no slip at the bob wall, the layer of
fluid immediately adjacent to the bob is motionless.
Overview of special features for the concentric cylinder viscometer
“The Fann Model 35 Viscometer is widely known as the “Standard of the Industry” for drilling fluid
viscosity measurements. The Model 35 Viscometer is a versatile instrument for research or production
use.
In the six-speed models, test speeds of 600, 300, 200, 100, 6 and 3 rpm are available via
synchronous motor driving through precision gearing. Any test speed can be selected without
stopping rotation. The shear stress is displayed continuously on the calibrated scale, so that
time-dependent viscosity characteristics can be observed as a function of time. The Model 35A
Viscometer is powered by a 60-Hz motor; Model 35SA Viscometer by a 50-Hz motor.
These instruments are equipped with factory installed R1 Rotor Sleeve, B1 Bob, F1 Torsion Spring,
and a stainless steel sample cup for testing specified by the American Petroleum Institute. Other
rotor-bob combinations and/or torsion springs can be substituted to extend the torque measuring
range or to increase the sensitivity of the torque measurement.
Shear stress is read directly from a calibrated scale. Plastic viscosity and yield point of a fluid can be
determined easily by making two simple subtractions from the observed data when the instrument is
used with the R1-B1 combination and the standard F1 torsion spring.”
Procedure & Observation
Experimental procedure
For the two different mud given as mud A and mud B respectively, the following procedure was taken:

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 Recently agitated sample was place in the cup and the surface of the mud adjusted to scribed line
on the rotor sleeve.
 The motor was started by placing the switch in the high-speed position with the gear shifted all the
way down. Waited for a steady indicator dial value, and recorded the 600-RPM reading. Gear was
changed only when motor was running.
 Switch changed to the low position with the gear shifted down, waited for a steady value and
recorded 300-RPM reading.
Switch changed to the high position with the gear shifted all the way up, waited for a steady value and
Switch changed to the low position with the gear shifted all the way up, waited for a steady value and
recorded 100-RMP reading.
Switch changed to the high position with the gear shifted to the centre, waited for a steady value and
Switch changed to the low position with the gear shifted to the centre, waited for a steady value to
Densities of mud A and Mud B are 9.45lb gal⁄ and 9.8lb gal⁄ respectively as obtained from experiment
Mud A Mud B
RPM Reading (ϴ) RPM Reading (ϴ)
600 107 600 72
300 97 300 53
200 91 200 45
100 83 100 34
6 70 6 15
3 63 3 13
PV PV
YP YP
K K
n n
Table1. Experimental measurements.

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Experimental observations
Results & Calculations
Table of results/measurements obtain during laboratory session is as shown below:
Mud A Mud B
RPM Reading (ϴ) RPM Reading (ϴ)
600 107 600 72
300 97 300 53
200 91 200 45
100 83 100 34
6 70 6 15
3 63 3 13
PV PV
YP YP
K K
n n
Table2. Results/experimental measurements.
Table of all calculated results obtained during laboratory session is as shown below, with yield point
(YP) and shear stress (γ) measured in pounds per 100 square feet (lb/100ft2
):
Mud A Mud B
RPM Reading
(ϴ)
Shear
rate, γ
Shear
Stress,τ
Apparent
Viscosity
RPM Reading
(ϴ)
Shear
rate, γ
Shear
Stress,τ
Apparent
Viscosity
600 107 1022 114.3 54 600 72 1022 76.9 36
300 97 511 103.5 97 300 53 511 56.6 53
200 91 341 97.2 137 200 45 341 48.1 68

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100 83 170 88.6 249 100 34 170 36.3 102
6 70 10.0 74.7 3500 6 15 10.0 16.0 750
3 63 5.0 67.3 6300 3 13 5.0 13.9 1300
PV 10 PV 19
YP 67 YP 33
K 0.5923 K 0.0887
n 0.0784 n 0.2743
Table3. Calculated experimental results.
Fig3. Shear stress vs shear rate for mud A
0
20
40
60
80
100
120
140
-500 0 500 1000 1500
Shearstress
Shear rate
shear stress vs shear rate
shear stress vs shear
rate

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Fig4. Log-log of Shear stress vs shear rate for mud A
Fig5. Apparent viscosity vs shear rate for mud A
0
0.5
1
1.5
2
2.5
0 2 4 6
Shearstress
Shear rate
log-log shear stress vs shear rate
log-log shear stress vs
shear rate
Linear (log-log shear
stress vs shear rate)
-1000
0
1000
2000
3000
4000
5000
6000
7000
-500 0 500 1000 1500
apparentviscosity
Shear rate
Apparent viscosity vs shear rate
apparent viscosity vs
shear rate

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Fig6. Shear stress vs shear rate for mud B
Fig7. Log-log of Shear stress vs shear rate for mud B
0
10
20
30
40
50
60
70
80
90
-500 0 500 1000 1500
Shearstress
Shear rate
Shear stress vs shear rate
Shear stress vs shear
rate
0
0.5
1
1.5
2
2.5
3
0 2 4 6
Shearstress
Shear rate
log-log of shear stress vs shear rate
log-log of shear stress
vs shear rate
Linear (log-log of shear
stress vs shear rate)

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Fig8. Apparent viscosity vs shear rate for mud B
Experimental calculations
Experimental sample calculations for each type of calculated results shown above in table 1 are
illustrated for mud A and mud B respectively below:
Calculations of sample Mud A:
Shear rate, γ (sec−1
) = 1.703× w; where w represent RPM.
γ600 =1.703×600 = 1022s−1
γ300 =1.703×300 = 510s−1
γ200 =1.703×200 = 341s−1
γ100 =1.703×100 = 170s−1
γ6 =1.703×6 = 10s−1
γ3 =1.703×3 = 5s−1
Shear stress, τ (lb 100ft2⁄ ) = 1.0678×ϴ, where ϴ represent viscometer reading.
τ600 = 1.0678×107 = 114 lb 100ft2⁄
τ300 = 1.0678×97 = 104 lb 100ft2⁄
τ200 = 1.0678×91 = 97 lb 100ft2⁄
τ100 = 1.0678×83 = 89 lb 100ft2⁄
τ6 = 1.0678×70 = 75 lb 100ft2⁄
τ3 = 1.0678×63 = 67 lb 100ft2⁄
0
200
400
600
800
1000
1200
1400
0 20 40 60 80 100
Apparentviscosity
Shear rate
Apparent viscosity vs shear rate
Apparent viscosity vs
shearrate

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Plastic viscosity (PV)
PV = θ600 − θ300
PV = 107 − 97 = 10cp
Yield point (YP)
YP = θ300 − PV
YP = 97 − 10 = 67 lb 100ft2⁄
Rheological parameter K and n
n =
log
0.89
0.67
log
170
5
n = 0.081
K =
τ2
γ2
K =
0.89
(170)0.081
= 0.5871
Apparent viscosity, μa
μa= 300
ϴ
w
μa= 300×
107
600
= 54
μa= 300×
97
300
= 97
μa= 300×
91
200
= 137
μa= 300×
83
100
= 249
μa= 300×
70
6
= 3500
μa= 300×
63
3
= 6300
Calculations of sample Mud B:
Shear rate, γ (sec−1
) = 1.703× w; where w represent RPM.
γ600
=1.703×600 = 1022s−1
γ300
=1.703×300 = 510s−1
γ200
=1.703×200 = 341s−1

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γ100
=1.703×100 = 170s−1
γ6
=1.703×6 = 10s−1
γ3
=1.703×3 = 5s−1
Shear stress, τ (lb 100ft2⁄ ) = 1.0678×ϴ, where ϴ represent viscometer reading.
τ600 = 1.0678×72 = 77 lb 100ft2⁄
τ300 = 1.0678×53 = 57 lb 100ft2⁄
τ200 = 1.0678×45 = 48 lb 100ft2⁄
τ100 = 1.0678×34 = 36 lb 100ft2⁄
τ6 = 1.0678×15 = 16 lb 100ft2⁄
τ3 = 1.0678×13 = 14 lb 100ft2⁄
Plastic viscosity (PV)
PV = θ600 − θ300
PV = 72 − 53 = 19cp
Yield point (YP)
YP = θ300 − PV
YP = 53 − 19 = 33 lb 100ft2⁄
Rheological parameter K and n
n =
log
0.36
0.14
log
170
5
n = 0.2678
K =
τ2
γ2
K =
0.36
(170)0.2678 = 0.09098
Apparent viscosity, μa
μa= 300
ϴ
w
μa= 300×
72
600
= 36

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μa= 300×
53
300
= 53
μa= 300×
45
200
= 67.5
μa= 300×
34
100
= 102
μa= 300×
15
6
= 750
μa= 300×
13
3
= 1300
The Calculations below are for the circulating pressure gradient, equivalent circulating density and
standpipe pressure for Mud A and Mud B respectively.
Calculations of sample Mud A:
Circulating pressure gradient
Pc
L
is given as:
Pc
L
=
Ph
Lv
+
Pa
Lm
Where,
Ph
Lv
= Hydrostatic pressure gradient
Pa
Lm
= frictional loss pressure gradient
Ph
Lv
= 0.052ρ
Where ρ = density of Mud A:
Ph
Lv
= 0.052ρ = 0.052×9.45 = 0.4914psi ft⁄
Hydrostatic pressure gradient = 0.4914𝐩𝐬𝐢 𝐟𝐭⁄
Pa
Lm
=
fa ×va × ρ
25.51(D2−D1 )
Where va = velocity in annulus =? and fa = frictional factor in annulus=?
Pa
Lm
=
fa ×va
2
× ρ
25.51(D2−D1 )
va =
0.408Q
D2
2
− D1
2
Q = Flow rate = 210 lb min⁄ = 0.5619ft3
sec⁄

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D2 = Pipe outside diameter = 5in =0.4167ft
D1 = Pipe outside diameter = 3.78 in = 0.3149ft
va =
0.408×0.5619
0.41672 − 0.31492
= 3.078ft sec⁄
fa =
16
Rea
or
a
(Rea)b
Where 𝐑𝐞 𝐚 is the Reynolds Number.
Rea =
928va (D2 − D1 )ρ
μea
Where μea = effective viscosity in an annulus:
μea = 100Ka (
144 Va
D2−D1
)
(na − 1)
(
2na +1
3na
)
na
μea = 100×0.5871(
144×3.078
0.4167 −0.3149
)
(0.081 − 1)
(
2×0.081+1
3×0.081
)
0.081
μea = 0.03017cp
Then;
Rea =
928va (D2 − D1 )ρ
μea
Rea =
928 × 3.078(0.4167 − 0.3149)58.86
0.03017
Density of mud A = 9.45 lb gal⁄ = 58.86lb ft3⁄
Rea = 567295.47
Since the Reynolds Number Rea > 2100, friction factor fa =
a
(Rea )b
Where a = (log na + 3.93)/50 = (log 0.081 + 3.93)/50 = 0.0568
b = (1.75 − log na
)/7 = (1.75 − log0.081)/7 = 0.4059
fa =
a
(Rea)b =
0.0568
(567295.47)0.4059 = 2.623×10−4
From the above values obtained the frictional loss pressure gradient,
Pa
Lm
is obtained
Pa
Lm
=
fa ×va
2
× ρ
25.51(D2−D1 )
Pa
Lm
=
2.623 ×10−4
×3.0782
× 58.86
25.51(0.4167−0.3149)
= 0.05632 psi ft⁄
Circulating pressure gradient,
𝐏𝐜
𝐋

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From calculations above
Ph
Lv
was calculated in lb gal⁄ , so:
Ph
Lv
= 0.4914psi ft⁄
Pc
L
=
Ph
Lv
+
Pa
Lm
= 0.4914+0.05632= 0.5477psi ft⁄
Equivalent circulating density, 𝛒 𝐜
ρc=
19.625Pc
Lv
ρc = 19.625×0.5477 = 10.75lb gal⁄
Calculations of sample Mud B:
Circulating pressure gradient
Pc
L
is given as:
𝑃𝑐
𝐿
=
𝑃ℎ
𝐿 𝑣
+
𝑃 𝑎
𝐿 𝑚
Where,
𝑃ℎ
𝐿 𝑣
= Hydrostatic pressure gradient
𝑃 𝑎
𝐿 𝑚
= frictional loss pressure gradient
𝑃ℎ
𝐿 𝑣
= 0.052ρ
Where ρ = density of Mud B:
𝑃ℎ
𝐿 𝑣
= 0.052ρ = 0.052×9.80 = 0.5096𝑝𝑠𝑖 𝑓𝑡⁄
Hydrostatic pressure gradient = 0.5096 𝑝𝑠𝑖 𝑓𝑡⁄
𝑃 𝑎
𝐿 𝑚
=
𝑓𝑎 ×𝑣 𝑎 × 𝜌
25.51(𝐷2 −𝐷1 )
Where 𝑣𝑎 = velocity in annulus =? and 𝑓𝑎 = frictional factor in annulus=?
𝑃 𝑎
𝐿 𝑚
=
𝑓𝑎 ×𝑣 𝑎
2
× 𝜌
25.51(𝐷2 −𝐷1 )
𝑣𝑎 =
0.408𝑄
𝐷2
2
− 𝐷1
2
𝑄 = Flow rate = 210 𝑙𝑏 𝑚𝑖𝑛⁄ = 0.5619𝑓𝑡3
𝑠𝑒𝑐⁄
𝐷2 = Pipe outside diameter = 5𝑖𝑛 = 0.4167𝑓𝑡
𝐷1 = Pipe outside diameter = 3.78 𝑖𝑛 = 0.3149𝑓𝑡

23 | P a g e
𝑣𝑎 =
0.408×0.5619
0.41672 − 0.31492
= 3.078𝑓𝑡 𝑠𝑒𝑐⁄
𝑓𝑎 =
16
𝑅𝑒 𝑎
or
𝑎
(𝑅𝑒 𝑎) 𝑏
Where 𝑅𝑒 𝑎 is the Reynolds Number.
𝑅𝑒 𝑎 =
928𝑣𝑎 (𝐷2 − 𝐷1 )𝜌
𝜇 𝑒𝑎
Where 𝜇 𝑒𝑎 = effective viscosity in an annulus:
𝜇 𝑒𝑎 = 100𝐾𝑎 (
144𝑉𝑎
𝐷2 −𝐷1
)
( 𝑛 𝑎 − 1)
(
2𝑛 𝑎 +1
3𝑛 𝑎
)
𝑛 𝑎
𝜇 𝑒𝑎 = 100×0.091(
144×3.078
0.4167−0.3149
)
(0.2678 − 1)
(
2×0.2678+1
3×0.2678
)
0.2678
𝜇 𝑒𝑎 = 0.02344cp
Then;
𝑅𝑒 𝑎 =
928𝑣𝑎 (𝐷2 − 𝐷1 )𝜌
𝜇 𝑒𝑎
𝑅𝑒 𝑎 =
928 × 3.078(0.4167 − 0.3149)61.04
0.02344
Density of mud B = 9.80𝑙𝑏 𝑔𝑎𝑙⁄ = 61.04𝑙𝑏 𝑓𝑡3⁄
𝑅𝑒 𝑎 = 17749.20
Since the Reynolds Number 𝑅𝑒 𝑎 > 2100, friction factor 𝑓𝑎 =
𝑎
Where a = (log 𝑛 𝑎 + 3.93)/50 = (log 0.091 + 3.93)/50 = 0.0578
b = (1.75 − log 𝑛 𝑎
)/7 = (1.75 − log0.091)/7 = 0.3987
𝑓𝑎 =
𝑎
=
0 .0578
(567295.47)0.3987
= 2.937×10−4
From the above values obtained the frictional loss pressure gradient,
𝑃 𝑎
𝐿 𝑚
is obtained
𝑃 𝑎
𝐿 𝑚
=
𝑓𝑎 ×𝑣 𝑎
2
× 𝜌
25.51(𝐷2 −𝐷1 )
𝑃 𝑎
𝐿 𝑚
=
2.937×10−4
×3.0782
× 61.04
25.51(0.4167−0.3149)
= 0.06540𝑝𝑠𝑖 𝑓𝑡⁄
Circulating pressure gradient,
𝑃𝑐
𝐿
From calculations above
𝑃ℎ
𝐿 𝑣
was calculated in 𝑙𝑏 𝑔𝑎𝑙⁄ , so:

24 | P a g e
𝑃ℎ
𝐿 𝑣
= 0.5096𝑝𝑠𝑖 𝑓𝑡⁄
𝑃𝑐
𝐿
=
𝑃ℎ
𝐿 𝑣
+
𝑃 𝑎
𝐿 𝑚
= 0.5096+0.06540 = 0.5750𝑝𝑠𝑖 𝑓𝑡⁄
Equivalent circulating density, 𝜌𝑐
𝜌𝑐 =
19.625𝑃𝑐
𝐿 𝑣
𝜌𝑐 = 19.625× 0.5750 = 11.28𝑙𝑏 𝑔𝑎𝑙⁄
The total friction loss pressure gradient in the pipe:
Drill pipe:
𝑃 𝑎
𝐿 𝑚
×10,500= 0.05632 ×10,500=591.87𝑝𝑠𝑖
Drill collar:
𝑃 𝑎
𝐿 𝑚
×400= 0.05632×400=22.528 𝑝𝑠𝑖
Drill pipe + Drill collar = 591.87 + 22.528 = 614.398 𝑝𝑠𝑖
Mud A - Annulus
Drill pipe:
For 10500ft:
𝑃 𝑎
𝐿 𝑚
× 10500= 0.05326×10500=559.23 𝑝𝑠𝑖
Drill collar:
For 400ft:
𝑃 𝑎
𝐿 𝑚
×400=0.05632 ×400=22.528 𝑝𝑠𝑖
Drill pipe (Annulus) + Drill collar (Annulus) = 559.23 +22.528 = 581.758 𝑝𝑠𝑖
Calculation of the Friction Loss in Bit Nozzles
𝑃𝑛= 156 × 𝜌 × 𝑄2 [(𝐷𝑛1 2+ 𝐷𝑛2 2+⋯) 2]
Therefore: 𝑃𝑛= 156 × 9.45 × 2102(11 2+ 11 2+ 12 2)2=443.261 𝑝𝑠𝑖
Calculation of the Standpipe Pressure for mud A
𝑃𝑠𝑝= ∑((𝑃𝑝𝑖/𝐿𝑝𝑖) × 𝐿𝑝𝑖)+ ∑((𝑃𝑎𝑗/𝐿𝑎𝑗) × 𝐿𝑎𝑗) + 𝑃𝑛
Therefore: 𝑃𝑠𝑝= 581.758+ 614.398+443.261 =1639.417 𝑝𝑠𝑖

25 | P a g e
Mud B - Annulus
Drill pipe:
𝑃 𝑎
𝐿 𝑚
×10,500= 0.06540×10,500=686.7𝑝𝑠𝑖
Drill collar:
𝑃 𝑎
𝐿 𝑚
×400= 0.06540×400=26.16 𝑝𝑠𝑖
Drill pipe + Drill collar = 686.7 + 26.16 = 712.86 𝑝𝑠𝑖
Drill pipe (Annulus) + Drill collar (Annulus) = 559.23 +22.528 = 581.758 𝑝𝑠𝑖
Calculation of the Friction Loss in Bit Nozzles
𝑃𝑛= 156 × 𝜌 × 𝑄2 [(𝐷𝑛1 2+ 𝐷𝑛2 2+⋯) 2]
Therefore: 𝑃𝑛= 156 × 9.8 × 2102(11 2+ 11 2+ 12 2)2= 𝑝𝑠𝑖
Calculation of the Standpipe Pressure for mud A
𝑃𝑠𝑝= ∑((𝑃𝑝𝑖/𝐿𝑝𝑖) × 𝐿𝑝𝑖)+ ∑((𝑃𝑎𝑗/𝐿𝑎𝑗) × 𝐿𝑎𝑗) + 𝑃𝑛
Therefore: 𝑃𝑠𝑝= 712.86+ 614.398+443.261 = 1770.52 𝑝𝑠𝑖

26 | P a g e
Experiment 3 – Drilling Fluid (Mud) Filtration Tests
Summary
Experiment 3 is based upon drilling fluid filtration tests, which is quite significant to drilling
engineering. The objectives of this experiment have been listed as follows:
 Understanding the mud filtration process and its applications in Drilling Engineering.
 Evaluation of mud-cake building characteristics and effects of temperature and
pressure on mud filtrate behaviour.
 Evaluation of the effects of polymer additive for fluid loss control properties.
 Effects of mud filtrate in formation damage.
To carry out this experiment we used API Filter press and cell assembly equipment. This
experiment was carried out in three phases. First phase was based upon evaluating the
effects of differential pressure on mud filtrate and mud cake building characteristics and the
results are shown in the results and calculations section below. We observed loss of liquid
with respect to time under two different pressures respectively (100 psi and 400 psi). First
phase took an hour, 30 minutes for each pressure conditions.
The second phase was based upon the evaluation of effects of temperature on mud filtrate
and mud cake characteristics. This phase took 30 minutes and the readings were noted down
with respect to time and increasing temperature.
The third phase was based upon investigation on the effects of polymer additive to control
filtration. This phase had further two parts, which were based upon quantities of additive
added to the drilling fluid. 1g and 2g respectively were added in the drilling fluid and readings
noted down. Due to lack of time we carried out this experiment with 1g of additive and we
were instructed to obtain the reading of 2g additive part from another group and share our
readings with them. This phase was completed in 30 minutes and the readings were taken
with respect to time of the volume of fluid loss. At the end of each phase mud cakes were
observed and their thickness and diameters were measure with the digital Vernier calliper.
In this experiment we learned about the effects of temperature and pressure on drilling fluid
with and without additive respectively with respect to fluid loss and evaluation of their
respective mud cakes.
Introduction
The main function of the drilling fluid is to control the fluid loss, so measurements of the fluid
loss and mud cake evaluation is of utmost importance.
The objectives of this experiment have been listed as follows:
 Understanding the mud filtration process and its applications in Drilling Engineering.
 Evaluation of mud-cake building characteristics and effects of temperature and
pressure on mud filtrate behaviour.
 Evaluation of the effects of polymer additive for fluid loss control properties.
 Effects of mud filtrate in formation damage.

27 | P a g e
Experiment Equipment
Background
Experiment 3 was basically conducted to show the importance of drilling mud and its
significance in Drilling Engineering. In general drilling fluid is used to seal permeable
formations and also to control the fluid loss that is filtration. After careful calculation and study
the mud is prepared which depends on the formations under interest. These tests are
performed on both low temperature and pressure & high temperature and pressure (HPHT).
There are numbers of potential problems associated with thick filter cake and excessive
filtration which includes tight holes, enlarged torque and drag values, drilling pipe trapped, lost
circulations, deprived log quality and formation damage.
Potential problemsfromexcessivefilter-cakethickness
High cake permeability's results in thick filter cakes, which reduce the effective torque when
rotating the pipe, excessive drag when pulling it. Thick cakes may cause the drill pipe to stick

28 | P a g e
by a mechanism known as deferential sticking. There are two types of filtration involved in
drilling an oil well which are static filtration and dynamic filtration.
Potential problemsfromexcessivefiltrateinvasion
Excessive filtration invasion includes formation damage due to filtrate and solids invasion and
invalid formation fluid sampling test.
Filtrationtheory
For filtration to occur, the following three conditions are required:
A liquid or a liquid/solid slurry fluid must be present.
A permeable medium must be present.
The fluid must be at a higher pressure than the permeable medium.
Static Filtration
Static filtration is related to the fact when mud is not circulating. There are many factors
controlling under this condition but the main one to consider is the Darcy's law which is
related to flow of fluids through a permeable materials/formations (sandstone, sand or mud
filtrate).
Q = (k A ΔP) / μh
Factorsaffectingfiltration
Factors affecting filtration includes:
Time
Pressure differential filter cake compressibility
Filter cake permeability
Viscosity
Fluid-Losscontrol additives
There are several types of filtration control additives that are in practice, which depend upon
the mud system and its chemistry for example:
Clays
Polymers
PolyanionicCellulose(PAC)

29 | P a g e
Polyaninic Cellulose which is non-ionic cellulose has high properties of purity, high DS, high
to low ranges of viscosity. It helps flow any solids present in the system and improves wall
mud cake characteristics. PAC is also very useful as it lowers the chance for stuck pipe.
Experimentprocedureandobservations
First of all we wore our PPE (Personal Protective Equipment) keeping in mind the H&S
procedures. After that we were given an initial demonstration by the technician and the
procedure is listed below. This experiment was carried out in three phases respectively and
same procedure was used to carry out three phases except the experimental conditions.
First phaseprocedure:
 Loose the T-screw at the top until the filter cell can be detached.
 Remove the filter cell and dissemble it, taking precautions.
 Make sure all parts of the filter cell are clean & dry.
 Check that the filtrate tube in the base cap is free of obstruction.
 Place the filter paper on top of the screen.
 Place the second rubber on top of the filter paper.
 Replace the cell body.
 Rotate the cell body according to the arrow head given until it’s fully fastened itself into the J-
Slot.
 Now fill the filter cell with the mud sample and make sure to leave some space/gap in the cell
as the fluid expands under pressure & temperature.
 Place the mud filled cell body into the equipment.
 Make sure to correctly tighten the T-screw.
 Place a graduated cylinder under the filtrate tube.
 Rotate the pressure relief valve & the regulator valve until you get the desired pressure value
in, first of all 100 psi and then 400psi.
 Let each experiment of the first phase test run for 30 minutes & take the required reading for
the experiment after every 5 minutes.(Stop watch used)
 Now open the cell body according to the opening instructions on the equipment.
 Also open the pressure relief valve by moving it in the vertical direction.
 Wait for some time so that the pressure is fully released.
 Remove the cell by loosening the T-screw.
 Open the top cap & take the mud out and also remove the bottom cap.
 To take out the filter paper by moving the bottom cap in the upside down direction.
 Inspect the filter paper for the physical properties and measurement of the thickness and
diameter of the mud cake with the help of Vernier calliper.
 Clean & dry all parts of the equipment.
Secondphaseprocedure:

30 | P a g e
Slot.
 Increasing temperature at 400 psi, water loss form the drilling mud was observed.
Thirdphaseprocedure:
Slot.
 An additive was added the drilling mud, firstly 1g and then 2g. Water loss was observed in
both cases. We carried out the 1g additive sample and 2g sample values were shared from
another group.

31 | P a g e
Results & Calculations
The effects of pressure on mud filtrate behaviour and mud cake building characteristics of
drilling fluids were taken into consideration. In this part we evaluate the effect of the
differential pressure on the fluid loss and mud cake thickness of a water based drilling fluid.
For this we prepared a drilling fluid by mixing 120 grs of bentonite in 2 litres of water. The
value for initial pressure was 400 psi and then reduced slightly to 350 psi.
100 PSI (Room Temp) 400 PSI (Room Temp)
Time (min) Volume (ml) Time (min)
Volume
(ml)
Initial (spurt lost)
5 5.5 5 8
10 8.5 10 12
15 10.5 15 15
20 12.2 20 17.4
25 13.86 25 21
30 15.25 30 22
Mud Cake Thickness (mm)
2.31
Mud Cake Thickness
(mm) 2.45
Mud Cake Diameter (mm) 77.36 Mud Cake Diameter (mm) 59.52
Table 1
0
5
10
15
20
0 1 2 3 4 5 6
Volume(ml)
time (sec)
100 psi

32 | P a g e
Bentonite + Water 19° C (From Exp-1
400psi) Bentonite + Water 60° C
Time (min) Volume (ml) Time (min) Volume (ml)
5 5.5 5 6.9
10 8.5 10 9.1
15 10.5 15 10.9
20 12.2 20 12.45
25 13.8 25 14.6
30 15.25 30 15
Table 2
0
5
10
15
20
25
0 1 2 3 4 5 6
Volume(ml)
time (sec)
400 psi
0
5
10
15
20
0 2 4 6
Volume(ml)
time (sec)
400psi)
Bentonite + Water 19°
C (From Exp-1 400psi)

33 | P a g e
Effect of the temperature on mud filtrate and mud cake characteristics of a drilling fluid
formation.
400psi) Bentonite + Water 60° C
Time (min) Volume (ml)
Time
(min)
Volume
(ml)
Temperature
°C
Pressure
(psi)
5 5.5 5 6.9 44.2°C 400
10 8.5 10 9.1 45.8°C 400
15 10.5 15 10.9 46.8°C 400
20 12.2 20 12.45 47.2°C 400
25 13.8 25 14.6 47.6°C 400
30 15.25 30 15 47.8°C 400
Table 3
Discussion of Results
The results show that with increase in pressure, more water loss has been seen (Table 1).
There was no much in water loss when the temperature was increased from 19C to 60C
(Table 2).
At an increasing temperature, at 400 psi, there was no much change noticed in terms of water
loss as shown in Table 3.
0
2
4
6
8
10
12
14
16
0 2 4 6
Volume(ml)
time (sec)
Bentonite + Water 60° C
Bentonite + Water 60°
C

34 | P a g e
Conclusions
Experiment 2 and 3 carried out in the lab proved to be very helpful, as it provided us an opportunity to
experience the practical aspects of the theory.
From the experiment 2 we arrived at the conclusion that both mud A and mud B exhibit Herschel-
Bulkley model with shear stress plotted against shear rate and power low model with log-log shear
rate plotted against shear rate. The graphs plotted for apparent viscosity against shear rate for both
muds have very similar L-shape patterns. All this indicates that both muds exhibit similar rheology.
In experiment 3, we learned about the water loss from the drilling mud at various pressures and
temperatures as shown above through graphs and tables (readings noted down from experiments).
References
A.T Bourgoyne Jr, K.K. Millheim, M.E. Chenevert & F.S. Young Jr. (1986) “Applied Drilling
Engineering”, SPE Textbook Series Vol. 2, Chapter 2.
Fann (1995) Series 300 API Filter Press Instruction manual, (1995)
ISO 10414:2001 (Modified) (2003), “Recommended Practice for Field Testing Water-based Drilling
Fluids. API Recommended Practice 13 B-1 Third Edition.
Model 35 Viscometer. Instruction Manual . 2015. . [ONLINE] Available
at:http://www.fann.com/public1/pubsdata/Manuals/Model%2035%20Viscometer.pdf. [Accessed 17
February 2015].
OFITE (2009) HTHP Filter Press Instruction Manual, Ver. 2.0, 5/28/2009

Rheology of Fluids Hydraulic Calculations & Drilling Fluid (Mud) Filtration Tests

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