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DEPARTMENT OF CHEMICAL & PETROLEUM
MSc PETROLEUM ENGINEERING (3616)
EXPERIMENT 2 & 3Rheology of Fluids & Hydraulic Calculations
&
Drilling Fluid (Mud) Filtration Tests
Team 8Muhammad 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 of Fluids & Hydraulic Calculations
SummaryThis 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 /100 ft2, n = 0.081 and K = 0.5871 and for
mud B PV = 10cp,YP = 67 lb /100 ft2, 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.
IntroductionRheology 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.
Flow regimesThe 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=DVρμ
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.
5 | P a g e
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=τγ
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.
Shear stressShear 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 = FA
Where:
F = force
A = surface area subjected to stress
In a pipe, the shear stress at the pipe wall is expressed as:
τ w=FA
=DP4 L
In an annulus with inner and outer diameters known, the shear stress is expressed the same manner as:
τ w=FA
=P(D ¿¿2−D1)
4 L¿
Where:
D = diameter of pipe
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D1= inner diameter of pipe
D2 = outer diameter of pipe
P = pressure on end of liquid column
A = surface area of the fluid
L = length
Share rateShear 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=dVdr
Where:
dV = velocity change between fluid layers
dr = distance between fluid layers
Shear rate γ℘ at the wall can be expressed as a function of the average velocity (V) and the diameter
of pipe (D).
γ℘= f (V , D )=8V P
D
In which
V P= QA
= 4Q
πD2
Where:
Q = volumetric flow rate
A = surface area of cross section
D = pipe diameter
V = velocity
V P = average velocity in pipe
In an annulus of outside diameter D2and inside diameterD1, the wall shear rate can be shown as:
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γwa= f (V , D1 ,D 2)=12V a
D 2−D1
In which
V a=¿ 4Q
π (D22−D1
2)
Where:
γ℘ = shear rate at annulus wall
V = velocity
Q = volumetric flow rate
D1 = inner annulus diameter
D2 = outer annulus diameter
V a= average velocity in annulus
Rheological modelsThe 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
8 | P a g e
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 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.
9 | P a g e
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.
Circulating systemThe 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.
10 | P a g e
Experimental EquipmentConcentric 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 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.
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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 procedureFor the two different mud given as mud A and mud B respectively, the following procedure was taken:
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.
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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 recorded 200-RPM reading.
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 recorded 6-RPM reading.
Switch changed to the low position with the gear shifted to the centre, waited for a steady value to recorded 3-RPM reading.
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.
Experimental observations
Results & CalculationsTable of results/measurements obtain during laboratory session is as shown below:
13 | P a g e
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
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
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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.
0 200 400 600 800 1000 12000
20
40
60
80
100
120
140
shear stress vs shear rate
shear stress vs shear rate
Shear rate
Shea
r str
ess
Fig3. Shear stress vs shear rate for mud A
15 | P a g e
0.5 1 1.5 2 2.5 3 3.51.7
1.75
1.8
1.85
1.9
1.95
2
2.05
2.1
log-log shear stress vs shear rate
log-log shear stress vs shear rateLinear (log-log shear stress vs shear rate)
Shear rate
Shea
r str
ess
Fig4. Log-log of Shear stress vs shear rate for mud A
0 200 400 600 800 1000 12000
1000
2000
3000
4000
5000
6000
7000
Apparent viscosity vs shear rate
apparent viscosity vs shear rate
Shear rate
appa
rent
visc
osity
Fig5. Apparent viscosity vs shear rate for mud A
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0 200 400 600 800 1000 12000
10
20
30
40
50
60
70
80
90
Shear stress vs shear rate
Shear stress vs shear rate
Shear rate
Shea
r str
ess
Fig6. Shear stress vs shear rate for mud B
0.5 1 1.5 2 2.5 3 3.50
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
log-log of shear stress vs shear rate
log-log of shear stress vs shear rateLinear (log-log of shear stress vs shear rate)Linear (log-log of shear stress vs shear rate)
Shear rate
Shea
r str
ess
Fig7. Log-log of Shear stress vs shear rate for mud B
17 | P a g e
10 20 30 40 50 60 70 80 900
200
400
600
800
1000
1200
1400
Apparent viscosity vs shear rate
Apparent viscosity vs shearrate
Shear rate
Appa
rent
visc
osity
Fig8. Apparent viscosity vs shear rate for mud B
Experimental calculationsExperimental 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.
γ 600 =1.703×600 = 1022s−1
γ 300 =1.703×300 = 510s−1
γ 200 =1.703×200 = 341s−1
γ 100 =1.703×100 = 170s−1
γ 6 =1.703×6 = 10s−1
γ 3 =1.703×3 = 5s−1
Shear stress, τ (lb /100 ft2) = 1.0678×ϴ, where ϴ represent viscometer reading.
τ 600 = 1.0678×107 = 114lb /100 ft2
τ300 = 1.0678×97 = 104 lb /100 ft2
τ 200 = 1.0678×91 = 97 lb /100 ft2
τ100 = 1.0678×83 = 89 lb /100 ft2
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τ 6 = 1.0678×70 = 75 lb /100 ft2
τ3 = 1.0678×63 = 67 lb /100 ft2
Plastic viscosity (PV)
PV = θ600−θ300
PV = 107−97=¿10cp
Yield point (YP)
YP = θ300−¿ PV
YP = 97−10 = 67 lb /100 ft2
Rheological parameter K and n
n =
log0.890.67
log170
5
n = 0.081
K = τ2
γ 2
K = 0.89
(170)0.081 = 0.5871
Apparent viscosity, μa
μa= 300 ϴw
μa= 300× 107600
= 54
μa= 300× 97
300 = 97
μa= 300× 91
200 = 137
μa= 300× 83
100 = 249
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μa= 300× 706
= 3500
μa= 300× 633
= 6300
Calculations of sample Mud B:Shear rate, γ (sec−1) = 1.703×w; where w represent RPM.
γ 600 =1.703×600 = 1022s−1
γ 300 =1.703×300 = 510s−1
γ 200 =1.703×200 = 341s−1
γ 100 =1.703×100 = 170s−1
γ 6 =1.703×6 = 10s−1
γ 3 =1.703×3 = 5s−1
Shear stress, τ (lb /100 ft2) = 1.0678×ϴ, where ϴ represent viscometer reading.
τ 600 = 1.0678×72 = 77lb /100 ft2
τ300 = 1.0678×53 = 57 lb /100 ft2
τ 200 = 1.0678×45 = 48 lb /100 ft2
τ100 = 1.0678×34 = 36 lb /100 ft2
τ 6 = 1.0678×15 = 16 lb /100 ft2
τ3 = 1.0678×13 = 14 lb /100 ft2
Plastic viscosity (PV)
PV = θ600−θ300
PV = 72−53=¿19cp
Yield point (YP)
YP = θ300−¿ PV
YP = 53−19 = 33 lb /100 ft2
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Rheological parameter K and n
n =
log0.360.14
log170
5
n = 0.2678
K = τ2
γ 2
K = 0.36
(170)0.2678 = 0.09098
Apparent viscosity, μa
μa= 300 ϴw
μa= 300× 72
600 = 36
μa= 300× 53
300 = 53
μa= 300× 45
200 = 67.5
μa= 300× 34100
= 102
μa= 300× 156
= 750
μa= 300× 133
= 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 PcL
is given as:
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PcL
=PhLv
+ PaLm
Where,
PhLv
=¿ Hydrostatic pressure gradient
PaLm
= frictional loss pressure gradient
PhLv
= 0.052ρ
Where ρ = density of Mud A:
PhLv
= 0.052ρ = 0.052×9.45 = 0.4914psi/ ft
Hydrostatic pressure gradient = 0.4914psi/ ft
PaLm
= f a×va×ρ
25.51(D2−D1)
Where va= velocity in annulus =? and f a=¿frictional factor in annulus=?
PaLm
= f a×va
2× ρ25.51(D2−D1)
va= 0.408Q
D22−D1
2
Q=¿Flow rate = 210 lb /min=¿0.5619ft3/sec
D2=¿ Pipe outside diameter = 5¿ =0.4167ft
D1= Pipe outside diameter = 3.78¿ = 0.3149ft
va= 0.408×0.5619
0.41672−0.31492 = 3.078ft /sec
f a= 16ℜa
or a
(ℜa)b
Where ℜa is the Reynolds Number.
22 | P a g e
ℜa=928va(D 2−D1) ρ
μea
Where μea = effective viscosity in an annulus:
μea = 100Ka( 144V a
D2−D1)
(na−1)
( 2na+13na )
na
μea = 100×0.5871( 144×3.0780.4167−0.3149 )
( 0.081−1 )
( 2×0.081+13×0.081 )
0.081
μea = 0.03017cp
Then;
ℜa=928va(D2−D1) ρ
μea
ℜa=928×3.078 (0.4167−0.3149 ) 58.86
0.03017
Density of mud A = 9.45 lb /gal= 58.86lb / ft3
ℜa=¿ 567295.47
Since the Reynolds Numberℜa>2100, friction factor f a=a
(ℜa)b
Where a = ( logna+3.93 )/50 = ( log 0.081+3.93 ) /50 = 0.0568
b = (1.75−log na ) /7 = (1.75−log 0.081 )/7 = 0.4059
f a=a
(ℜa)b=
0.0568
(567295.47)0.4059 = 2.623×10−4
From the above values obtained the frictional loss pressure gradient, PaLm
is obtained
PaLm
= f a×va
2× ρ25.51(D2−D1)
PaLm
= 2.623×10−4×3.0782×58.86
25.51(0.4167−0.3149)= 0.05632 psi/ ft
23 | P a g e
Circulating pressure gradient, PcL
From calculations above PhLv
was calculated inlb /gal , so:
PhLv
= 0.4914psi/ ft
PcL
=PhLv
+ PaLm
= 0.4914+0.05632= 0.5477psi/ ft
Equivalent circulating density,ρc
ρc= 19.625Pc
Lv
ρc = 19.625×0.5477 = 10.75lb /gal
Calculations of sample Mud B:
Circulating pressure gradient PcL
is given as:
PcL
=PhLv
+ PaLm
Where,
PhLv
=¿ Hydrostatic pressure gradient
PaLm
= frictional loss pressure gradient
PhLv
= 0.052ρ
Where ρ = density of Mud B:
PhLv
= 0.052ρ = 0.052×9.80 = 0.5096psi/ ft
Hydrostatic pressure gradient = 0.5096psi/ ft
24 | P a g e
PaLm
= f a×va×ρ
25.51(D2−D1)
Where va= velocity in annulus =? and f a=¿frictional factor in annulus=?
PaLm
= f a×va
2× ρ25.51(D2−D1)
va= 0.408Q
D22−D1
2
Q=¿Flow rate = 210 lb /min=¿0.5619ft3/sec
D2=¿ Pipe outside diameter = 5¿ = 0.4167ft
D1= Pipe outside diameter = 3.78¿ = 0.3149ft
va= 0.408×0.5619
0.41672−0.31492 = 3.078ft /sec
f a= 16ℜa
or a
(ℜa)b
Where ℜa is the Reynolds Number.
ℜa=928va(D 2−D1) ρ
μea
Where μea = effective viscosity in an annulus:
μea = 100Ka( 144V a
D2−D1)
(na−1)
( 2na+13na )
na
μea = 100×0.091( 144×3.0780.4167−0.3149 )
( 0.2678−1 )
( 2×0.2678+13×0.2678 )
0.2678
μea = 0.02344cp
Then;
ℜa=928va(D2−D1) ρ
μea
ℜa=928×3.078 (0.4167−0.3149 ) 61.04
0.02344
Density of mud B = 9.80l b/ gal= 61.04lb / ft3
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ℜa=¿ 17749.20
Since the Reynolds Numberℜa>2100, friction factor f a=a
(ℜa)b
Where a = ( logna+3.93 )/50 = ( log 0.091+3.93 ) /50 = 0.0578
b = (1.75−log na ) /7 = (1.75−log 0.091 )/7 = 0.3987
f a=a
(ℜa)b=
0.0578
(567295.47)0.3987 = 2.937×10−4
From the above values obtained the frictional loss pressure gradient, PaLm
is obtained
PaLm
= f a×va
2× ρ25.51(D2−D1)
PaLm
= 2.937×10−4×3.0782×61.04
25.51(0.4167−0.3149)= 0.06540psi/ ft
Circulating pressure gradient, PcL
From calculations above PhLv
was calculated inlb /gal , so:
PhLv
= 0.5096psi/ ft
PcL
=PhLv
+ PaLm
= 0.5096+0.06540 = 0.5750psi/ ft
Equivalent circulating density,ρc
ρc= 19.625Pc
Lv
ρc = 19.625× 0.5750 = 11.28lb /gal
The total friction loss pressure gradient in the pipe:
Drill pipe:
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PaLm
×10,500= 0.05632 ×10,500=591.87psi
Drill collar: PaLm
×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:PaLm
× 10500= 0.05326×10500=559.23psi
Drill collar:
For 400ft: PaLm
×400=0.05632 ×400=22.528psi
Drill pipe (Annulus) + Drill collar (Annulus) = 559.23 +22.528 = 581.758psi
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=443.261psi
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
Mud B - Annulus
Drill pipe:
PaLm
×10,500= 0.06540×10,500=686.7psi
Drill collar:
PaLm
×400= 0.06540×400=26.16 psi
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Drill pipe + Drill collar = 686.7 + 26.16 = 712.86 psi
Drill pipe (Annulus) + Drill collar (Annulus) = 559.23 +22.528 = 581.758psi
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
Experiment 3 – Drilling Fluid (Mud) Filtration Tests
SummaryExperiment 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.
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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.
29 | P a g e
Experiment Equipment
BackgroundExperiment 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 problems from excessive filter-cake thicknessHigh 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
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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 problems from excessive filtrate invasionExcessive filtration invasion includes formation damage due to filtrate and solids invasion and invalid formation fluid sampling test.
Filtration theoryFor 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 FiltrationStatic 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
Factors affecting filtration
Factors affecting filtration includes:
Time
Pressure differential filter cake compressibility
Filter cake permeability
Viscosity
Fluid-Loss control 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
Polyanionic Cellulose (PAC)
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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.
Experiment procedure and observations
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 phase procedure:
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.
Second phase procedure:
Loose the T-screw at the top until the filter cell can be detached. Remove the filter cell and dissemble it, taking precautions.
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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. Increasing temperature at 400 psi, water loss form the drilling mud was observed. 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.
Third phase procedure:
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. 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.
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.
33 | P a g e
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.
Results & CalculationsThe 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 5 810 8.5 10 1215 10.5 15 1520 12.2 20 17.425 13.86 25 2130 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) 59.52Table 1
2 2.5 3 3.5 4 4.5 5 5.5 602468
1012141618
100 psi
time (sec)
Volu
me
(ml)
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2 2.5 3 3.5 4 4.5 5 5.5 60
5
10
15
20
25
400 psi
time (sec)
Volu
me
(ml)
Bentonite + Water 19° C (From Exp-1 400psi) Bentonite + Water 60° CTime (min) Volume (ml) Time (min) Volume (ml)
Initial (spurt lost)
5 5.5 5 6.910 8.5 10 9.115 10.5 15 10.920 12.2 20 12.4525 13.8 25 14.630 15.25 30 15
Table 2
2 2.5 3 3.5 4 4.5 5 5.5 602468
1012141618
Bentonite + Water 19° C (From Exp-1 400psi)
Bentonite + Water 19° C (From Exp-1 400psi)
time (sec)
Volu
me
(ml)
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2 2.5 3 3.5 4 4.5 5 5.5 602468
10121416
Bentonite + Water 60° C
Bentonite + Water 60° C
time (sec)
Volu
me
(ml)
Effect of the temperature on mud filtrate and mud cake characteristics of a drilling fluid formation.
Bentonite + Water 19° C (From Exp-1 400psi) Bentonite + Water 60° C
Time (min) Volume (ml)Time (min)
Volume (ml)
Temperature °C
Pressure (psi)
Initial (spurt lost)
5 5.5 5 6.9 44.2°C 40010 8.5 10 9.1 45.8°C 40015 10.5 15 10.9 46.8°C 40020 12.2 20 12.45 47.2°C 40025 13.8 25 14.6 47.6°C 40030 15.25 30 15 47.8°C 400
Table 3
Discussion of ResultsThe 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.
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ConclusionsExperiment 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).
ReferencesA.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
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