Pet E 367
Lab Report #1
 Yield of Bentonite and Attapulgite Clays
 Rheological Characterization of Water-Base Drilling Fluids
Experiment Date: January 31 2007
Prepared by: Jackie Chee (1103396)
Group #7
Beattie L.
Branch T.
Jackie Chee (1103396)
February 13 2007
Lab Report #1
NREF 2-052
Markin/CNRL Natural Resources Engineering Facility
116street 91st ave
February 13, 2007
Barkim Demirdal
PhD Candidate at Petroleum Engineering Department
7-134 Markim CNRL Natural Resources Engineering Facility
Edmonton, Alberta
Canada T6G 2W2
Dear Mr. Demirdal,
Drilling mud is important in the petroleum industry. Drilling mud can be composed of various
types of clay. All the clays have their unique properties and when prepared with water, they will exhibit
different viscosity, gel strength, and most importantly, the rheological characteristic of the drilling mud.
We are required to observe the difference between Bentonite, and Attapulgite clay in both salt water
and fresh water. It was also required to differentiate the few non-Newtonian fluid models, and
determine the model associated with Bentonite, and Xanthan Gum.
It is clear that Bentonite and Attapulgite give different characteristic to the drilling mud.
Bentonite has a low yield of clay and it is highly ineffective in salt water. Attapulgite have a high yield of
clay and it does not shown any significant signs of swelling. Bentonite encountered severe swelling when
mixed with fresh water. Overall, Attapulgite would be a better choice when making drilling mud.
Bentonite with fresh water exhibits Bingham Plastic properties while the Xanthan Gum with
fresh water showed a fluid with a Power Law model.
I hope these observations will be of good use to you.
Thank you for your time
Sincerely,
……………………………..
(Jackie Chee)
Enclosure
Page 2 of 16
Jackie Chee (1103396)
February 13 2007
Lab Report #1
 Objective
This lab is primarily divided into 2 parts. Part 1 of this lab is to determine how bentonite and attapulgite
clay affects viscosity in both water and salt water. Part 2 is to determine the rheological model
describing the relation between shear stress and shear rate in a water based drilling fluid.
 Theory and concept
Properties of water based drilling mud are controlled mainly by the type of clay added to the drilling
fluid to change its properties for better wellbore efficiency. The first part of the lab will produce twelve
samples. There will be bentonite or attapulgite added to either salt water or water. The amount of clay
added will be 3, 6 and 9% of the weight of water. The density and viscosity will be determined. Density
will be determined using the mud balance; and viscosity will be determined using the Fann VG meter
(rotational viscometer). There will also be a marsh funnel used to determine relative viscosity to water.
Water will only be used for this part of the experiment.
Mud Density
Density is the weight per given volume. Measuring the density of the drilling fluid is important to
determine the buoyancy force induced when drilling and the hydrostatic pressure the drilling fluid acts
at the bottom-hole pressure. A higher density will prevent formation fluid from entering the well bore.
In this lab, the density is determined using the mud balance shown in Figure 1. The mud cup takes a
fixed volume of fluid sample and by adjusting the rider until balanced, a reading can be taken. This
apparatus has to be calibrated using fresh water.
Figure 1
Mud Balance
Source: http://www2.mst.dk/udgiv/Publikationer/2001/87-7944-820-8/html/kap01.htm
Page 3 of 16
Jackie Chee (1103396)
February 13 2007
Lab Report #1
Thixotropy
Thixotropy or the Gel strength is measured at a low shear stress after allowing it to thicken/sit for a
given amount of time (10 seconds and 10 minutes by API standards). The strength of the mud cake
formed will help in preventing water from entering the wellbore, as well as the drilling fluid circulating in
the wellbore to leak out into a fracture.
Viscosity
Part 1
Viscosity is the fluid’s resistance to flow. The viscosity of the mud determines the efficiency and even
ability to lift cuttings out of the well bore. Addition of different types of clay will affect the viscosity as
well as the use of salt water as oppose to plain water. Using an API standard Fann VG meter, the
apparent viscosity is defined as:
𝜇𝐴𝑝𝑝 =
[600 𝑟𝑝𝑚 𝑑𝑖𝑎𝑙 𝑟𝑒𝑎𝑑𝑖𝑛𝑔]
2
Part 2
The Fann VG meter also has various rotation speeds, all of
which is useful to determine the drilling fluid rheological
model for shear stress to shear rate. The main components
will be two cylinders; one will be referred as the Rotor, and
the other the Bob. The Rotor is the external cylinder that is
connected to the motor giving it a constant angular velocity.
The inner cylinder, the Bob is connected to a spring that
gives a dial read out. Both cylinders are submerged into the
fluid and there is a small annular space in between the
Rotor and Bob; when the Rotor is rotating, the fluid will
cause a torque on the Bob. Depending on the dimensions,
the Fann VG meter used had this relation to shear stress:
𝜏= 𝜃
τ = shear stress [lbf/100 ft2]
θ =Dial reading
Where:
Figure 2
Schematic diagram of a concentric
cylindrical viscometer
The shear rate is determined by:
𝛾 = 1.7 ∗ 𝑟𝑝𝑚
Where:
Page 4 of 16
γ= shear rate [sec-1]
rpm = revolutions per minute
Jackie Chee (1103396)
February 13 2007
Lab Report #1
Most Drilling fluids are non-Newtonian fluids, either viscosity
changes with shear rate (ie. Power Law Model or HerschelBulkley Model), or a plastic yield must be overcome (ie.
Bingham Plastic Model).
Figure 3
Newtonian Model
A Newtonian model is the simplest. The shear stress is directly
proportional to the shear rate as shown in figure 2. Common
day liquids are Newtonian like water, honey and oil. The
constant proportionality relating the two is called viscosity.
A Bingham Plastic Model is similar to a Newtonian model;
however it requires a plastic yield to be overcome before any
shearing in the fluid will occur. The relation between shear
stress and shear rate is shown in figure 3 and can be expressed
as:
𝜏 = 𝜏𝑦 + 𝜇𝑝 ∗ 𝛾
𝜇𝑝 = 𝜃600 − 𝜃300
Figure 4
Bingham Plastic Model
𝜏𝑦 = 𝜃300 − 𝜇𝑝
Where:
τ = Shear stress [lbf/100 ft2]
τy = yield point [lbf/100 ft2]
𝜇𝑝 = Plastic Viscosity [cp]
𝛾 = Shear Rate [sec-1]
𝜃600 = dial reading at 600rpm
𝜃300 = dial reading at 300rpm
A Power Law Model is similar to a Newtonian model, however
it has no linearity as shown in figure 4. The shear rate and
shear stress are related through an exponential term, ‘n’ which
is the flow behavior index. A power law model can be
expressed as:
𝜏 = 𝐾 ∗ (𝛾)𝑛
𝜃
𝑛 = 3.322 ∗ log(𝜃600 )
Figure 5
Power Law Model
300
𝐾=
Where:
510∗𝜃300
(511)𝑛
τ = Shear stress [lbf/100 ft2]
K= Consistency index [lbf/100 ft2]
𝛾 = Shear Rate [sec-1]
n = flow behavior index
Page 5 of 16
Jackie Chee (1103396)
February 13 2007
Lab Report #1
𝜃𝑥 = dial reading at x rpm
Flow behavior
index ‘n’
Type of fluid
<1
Pseudoplastic, or shear thinning; an increase in shear rate results in a decrease in
viscosity
1
Newtonian; shear rate and shear stress are directly proportional
>1
Dilatants, or shear thickening; an increase in shear rate results in an increase in
viscosity
A Herschel-Bulkley Model is basically a Power Law model with a
Bingham plastic model combined together. A plastic yield is
required to initiate flow, and once the fluid is viscous, the relation
between shear stress and shear rate is similar to one of the Power
Law Model. This can be shown in figure 5. This can be express as:
𝜏 = 𝜏𝑦 + 𝐾 ∗ (𝛾)𝑛
Figure 6
Herschel-Bulkley Model
Where:
τ = Shear stress [lbf/100 ft2]
K= Consistency index [lbf/100 ft2]
𝛾 = Shear Rate [sec-1]
n = flow behavior index
𝜏𝑦 = Yield Stress [lbf/100 ft2]
With four different models in mind, the selection of the appropriate model is done by plotting shear
stress as a function of shear rate will give one of the 4 curves. Linear regression is used to determine the
line of best fit. The two lowest rpm reading, usually 3rpm and 6rpm can be neglected from the plotting.
The low rpm give an inaccurate reading because the fluid is almost at a stand still and gel strengthening
is occurring.
 Experimental Procedure
Part 1
1. Calibrate mud balance using fresh water. (Fresh Water Density at 21 ̊C): 8.3 lb/gal
2. Measure the funnel viscosity of water at room temperature. (Water: 26 seconds)
3. Twelve samples will be prepared in this lab section. Six of these will be mixed using fresh water, and
the other six with salt water. Half of those six samples, three samples, will be mixed using 3%, 6% or
9% of Bentonite or Attapulgite by weight of water.
Fresh Water
Salt Water (20,000 ppm NaCl)
Bentonite
Attapulgite
Bentonite
Attapulgite
Each sample will be mixed with 3%, 6% or 9% of clay by weight of water.
Page 6 of 16
Jackie Chee (1103396)
February 13 2007
Lab Report #1
4. Obtain 350cc of either fresh or salt water in the mixing cup and start blender.
5. Obtain right amount of clay from bulk container.
6. Using a spatula, slowly and carefully, add reasonable amounts of clay into the mixing cup while
blender is on. Be careful with spatula hitting the mixer and clay dust puffing into the air. Avoid
inhaling clay dust.
7. Mix sample for a minimum of 10 minutes or when sample is well mixed.
8. Place sample into Fann VG viscometer and measure apparent viscosity of sample at 600 rpm.
Apparent viscosity can be calculated using formula from theory.
9. Measure density of sample using mud balance.
10. Dispose of sample properly, clean equipment and repeat with the other samples until done.
Part 2
1. Calibrate mud balance using fresh water. (Fresh Water Density at 21 ̊C): 8.3 lb/gal
2. Measure the funnel viscosity of water at room temperature. (Water: 26 seconds)
3. Two samples will be prepared in this lab section. Both will use fresh water. One sample will have 35
grams of bentonite, and the either will have 4 grams of Xanthan Gum.
4. Obtain 350cc of either fresh or salt water in the mixing cup and start blender.
5. Obtain right amount of clay from bulk container.
6. Using a spatula, slowly and carefully, add reasonable amounts of clay into the mixing cup while
blender is on. Be careful with spatula hitting the mixer and clay dust puffing into the air. Avoid
inhaling clay dust.
7. Mix sample for a minimum of 10 minutes or when sample is well mixed.
8. Record mud temperature using digital thermometer. Place thermometer well in the center of the
mud, avoiding contact with the mixing cup.
9. Measure density of sample using mud balance.
10. Place sample into Fann VG viscometer and record dial readings at 600, 300, 200, 100, 6 and 3 rpms.
11. Determine 10 sec and 10 minute gel strength.
12. Dispose of sample properly, clean equipment and repeat with the other samples until done.
 Results and Calculations
Recorded Data
Part 1
Water Properties
Density:
Funnel Viscosity:
8.3 ppg
28.54 sec/qt
Page 7 of 16
Jackie Chee (1103396)
February 13 2007
Lab Report #1
Mud Apparent Viscosity, µApp
Fresh Water
Salt Water
Clay Content Bentonite Attapulgite Bentonite Attapulgite
3%
6.5 cp
4.5 cp
3.5 cp
5.5 cp
6%
16.6 cp
33.9 cp
3.4 cp
30.2 cp
9%
37.0 cp
51.0 cp
6.0 cp
79.0 cp
Mud Density, ρmud
Clay Content
3%
6%
9%
Fresh Water
Bentonite
8.82 lbs/gal 1.06 g/cc
8.62 lbs/gal 1.03 g/cc
8.60 lbs/gal 1.03 g/cc
Attapulgite
8.58 lbs/gal 1.03 g/cc
8.58 lbs/gal 1.03 g/cc
8.60 lbs/gal 1.03 g/cc
Clay Content
3%
6%
9%
Salt Water
Bentonite
8.72 lbs/gal
1.04 g/cc
8.72 lbs/gal
1.04 g/cc
8.78 lbs/gal
1.05 g/cc
Attapulgite
8.64 lbs/gal
1.04 g/cc
8.51 lbs/gal
1.02 g/cc
8.70 lbs/gal
1.04 g/cc
Part 2
Bentonite
Added:
Density:
Temperature:
Xanthan Gum
Added:
Density:
Temperature:
35.02g
8.7lbs/gal
28.4 ̊C
Viscometer
rpm
dial reading
600
114.9
300
98.8
200
92.1
100
84.4
6
68.1
3
68.5
Gel Strength
10 sec (average) 57.5 cp
Run 1
58.0 cp
Run 2
58.4 cp
Run 3
56.2 cp
10 min:
63.0 cp
4.01g
7.5lbs/gal
35.2 ̊C
Viscometer
rpm
dial reading
104.5
600
90
300
81.5
200
70
100
43.5
6
38.5
3
Gel Strength
10 sec (average) 37.1 cp
Run 1
37.1 cp
Run 2
37.0 cp
10 min:
43.5 cp
Page 8 of 16
Jackie Chee (1103396)
February 13 2007
Lab Report #1
Data Analysis and Discussion
Part 1
Bentonite Fresh Water
Attapulgite Fresh Water
Bentonite Salt Water
Attapulgite Salt Water
90.0
Apparent Viscosity for all 12 Mud Samples
80.0
Apparent Viscosity (cp)
70.0
60.0
50.0
40.0
30.0
20.0
10.0
0.0
1%
2%
3%
4%
5%
6%
7%
8%
9%
10%
Clay Content (% Weight)
Figure 7
Apparent Viscosity vs. Clay Content for 4 different Mud Compositions
All samples had the same viscosity with 3% clay content added. The samples with Attapulgite present
gave a high yield of clay compared to Bentonite. With an addition of 3% more, the viscosity of
Attapulgite Fresh water and saltwater gave similar results. However, when more attapulgite was added,
the salt water mixture continued to become more viscous than the fresh water. The bentonite clay does
not build up viscosity in salt water. It will just absorb the water and not change the viscosity at all. The
bentonite in fresh water has some affects but it does not increase the viscosity as much as the
attapulgite.
Attapulgite is clay that provides a high yield in salt water and reasonable yield in fresh water. Attapulgite
in salt water does not provide filtration control though. Bentonite should not be used in salt water at all
because has no affects on the viscosity and use in fresh water is recommended, however the amount of
bentonite clay required to increase the apparent viscosity will be a large amount compared to
Attapulgite. Similar to Figure 2 in the lab manual, Bentonite in Salt water increases viscosity so slightly
Page 9 of 16
Jackie Chee (1103396)
February 13 2007
Lab Report #1
showing a low yield drilling clay. All the other three samples seem to resemble a premium drilling clay.
The biggest difference is the affect on viscosity with the amount of clay added.
If salt water is being used in a drilling operation, the use of bentonite clay will have no affect on the
drilling fluid. However, the use of attapulgite is suitable for all both salt water and fresh water.
Bentonite maybe suitable in fresh water if the viscosity increase desired is low, otherwise to get a high
viscosity for the drilling fluid may require a lot of Bentonite to be added which is not cost effective.
Bentonite Fresh Water
Attapulgite Fresh Water
Bentonite Salt Water
Attapulgite Salt Water
Density for all 12 Mud Samples
1.06
1.06
1.05
Density (g/cc)
1.05
1.04
1.04
1.03
1.03
1.02
1.02
1%
2%
3%
4%
5%
6%
7%
8%
9%
10%
Clay Content (% Weight)
Figure 8
Density vs. Clay Content for 4 different Mud Compositions
The Bentonite and Fresh Water sample had the highest density at the beginning, but as more clay was
added, the density was similar with the other Fresh Water sample of Attapulgite. This is due to the fact
that bentonite is swelling. Rather, the Bentonite and Salt water sample hardly changed in density. The
Attapulgite in Fresh Water shows a small density increase as more clay is added. The Attapulgite in Salt
Water shows a dip at 6% clay content. This may just be bad data since the density shows a concavity in
the curve. It should be expected the Attapulgite in Salt Water to have a higher density when compared
with Attapulgite in Fresh Water because of the salt crystals present in the water. The density of Salt
Water with 20,000 ppm NaCl is 20,250 mg/L, equivalent to 0.02025 g/cc. The difference between
Attapulgite in Salt Water and Fresh Water, as seen in Figure 8, is about 0.02 g/cc difference. It can be
concluded that the Attapulgite does not swell disproportionally in Salt Water nor Fresh Water.
Page 10 of 16
Jackie Chee (1103396)
February 13 2007
Lab Report #1
Yield of Bentonite Fresh Water: 85 bbl per ton
Clay Content % of Bentonite Fresh Water at 15 cp =5.5%
Yield of Attapulgite Fresh Water: 130 bbl per ton
Clay Content % of Attapulgite Fresh Water at 15 cp =4.0%
Part 2
Bentonite
Density = 8.70 lbs/gal
𝜇𝑝 = Plastic Viscosity = 16.1 cp
τy = yield point = 82.7 lbf/100 ft2
𝜏 = 𝜏𝑦 + 𝜇𝑝 ∗ 𝛾
𝜏 = 82.7 + 16.1 ∗ 𝛾
Viscometer
Shear Rate Shear Stress
τ [lbf/100 ft2]
rpm dial reading
γ [sec-1]
1020.0
114.9
600
114.9
510.0
98.8
300
98.8
340.0
92.1
200
92.1
170.0
84.4
100
84.4
10.2
68.1
6
68.1
5.1
68.5
3
68.5
*reading at 6 and 3 rpm excluded from graph.
Shear Rate vs. Shear Stress for Bentonite
120
Shear Stress [lbf/100 ft2]
115
110
R² = 0.980
Power
105
100
R² = 0.992
Linear
95
90
85
80
150.0
250.0
350.0
bentonite
450.0
550.0
650.0
Shear Rate [sec-1]
Linear (bentonite)
750.0
850.0
Power (bentonite)
Page 11 of 16
Figure 9
Shear Rate vs. Shear Stress for Bentonite Mud
950.0
1050.0
Jackie Chee (1103396)
February 13 2007
Lab Report #1
According to the R2 values, the best fit line for Bentonite is a linear line. It can be concluded that this
bentonite mud is not of the Power Law Model but of the Bingham Plastic Model.
Xanthan Gum
Density = 7.50 lbs/gal
n = flow behavior index = 0.21551
K= Consistency index = 11970.68 lbf/100 ft2
𝜏 = 11970.68 ∗ (𝛾)0.21551
Viscometer
Shear Rate Shear Stress
τ [lbf/100 ft2]
rpm dial reading
γ [sec-1]
1020.0
104.5
600
104.5
510.0
90
300
90.0
340.0
81.5
200
81.5
170.0
70
100
70.0
10.2
43.5
6
43.5
5.1
38.5
3
38.5
*reading at 6 and 3 rpm excluded from graph.
Shear Rate vs. Shear Stress for Xanthan Gum
105
Shear Stress [lbf/100 ft2]
100
R² = 0.999
Power
95
90
R² = 0.954
Linear
85
80
75
70
65
150.0
250.0
350.0
Xanthan Gum
450.0
550.0
650.0
Shear Rate
[sec-1]
Linear (Xanthan Gum)
750.0
950.0
Power (Xanthan Gum)
Figure 10
Shear Rate vs. Shear Stress for Xanthan Gum Mud
Page 12 of 16
850.0
1050.0
Jackie Chee (1103396)
February 13 2007
Lab Report #1
According to the R2 values, the best fit line for Xanthan Gum is a power line. It can be concluded that this
Xanthan Gum mud is not of the Bingham Plastic Model but of the Power Law Model.
 Sample Calculations
Part 1
Apparent Viscosity:
𝜇𝐴𝑝𝑝 =
𝜇𝐴𝑝𝑝
[600 𝑟𝑝𝑚 𝑑𝑖𝑎𝑙 𝑟𝑒𝑎𝑑𝑖𝑛𝑔]
2
[600rpm dial reading] for 3% Bentonite Fresh Water = 13
13
=
= 6.5 𝑐𝑝
2
Unit Conversion:
1 lbs/gal = 0.119826427 g/cc
Density for 3% Bentonite Fresh Water = 8.82 lbs/gal
Density for 3% Bentonite Fresh Water = 8.82 * 0.119826427
Density for 3% Bentonite Fresh Water = 1.06 g/cc
Part 2
Bentonite:
𝜇𝑝 = 𝜃600 − 𝜃300
𝜇𝑝 = 114.9 − 98.8 = 16.1𝑐𝑝
𝜏𝑦 = 𝜃300 − 𝜇𝑝
𝜏𝑦 = 98.8 − 16.1 = 82.7 lbf/100 ft2
Xanthan Gum:
𝜃
𝑛 = 3.322 ∗ log(𝜃600 )
300
104.5
𝑛 = 3.322 ∗ log ( 90.0 ) = 0.21551
𝐾=
510 ∗ 𝜃300
(511)𝑛
510∗90.0
𝐾 = (511)0.21551 = 11970.68 lbf/100 ft2
Shear Rate:
Page 13 of 16
Jackie Chee (1103396)
February 13 2007
Lab Report #1
𝛾 = 1.7 ∗ 𝑟𝑝𝑚
Where: γ= shear rate [sec-1]
rpm = revolutions per minute
rpm of 600
𝛾 = 1.7 ∗ 600
𝛾 = 1020 sec-1
Sources of Errors:
The use of Bentonite was not pure. When preparing the mud, dark lines appeared on Bentonite mud
showing impurities in Bentonite clay. These impurities may not be homogenous throughout the entire
Bentonite bulk container. If research is done on drilling fluid, pure Bentonite should be use, however to
stimulate real field mixing, it is not significant.
When using the mixer in preparing the mud, there was a lot of powder from the clay that was not mixed
in the mixing cup and even some that blew away onto the table. The actual amount of clay added may
be less than prepared. An alternative way of adding the exact amount of clay is by having the clay in
tabulate forms or pill forms so that the clay cannot be blown away.
 Conclusions
Bentonite works well in Fresh Water; however it does swell a few times its own size. Bentonite should
not be used with Salt Water as has a low yield of clay.. Attapulgite on the other hand has a high yield of
clay in both Fresh Water and Salt Water, and it does not swell too much.
Drilling mud is a non-Newtonian fluid. To determine which type of model the fluid follows cannot be
approximated using eye judgment. A graph must be constructed and linear regression or power law
regression must be performed to determine the rheological character of the drilling mud. Bentonite
mixed with fresh water will give a Bingham Plastic fluid and Xanthan Gum gives a Power Law fluid.
References:
http://www.glossary.oilfield.slb.com/Display.cfm?Term=gel%20strength, February 10 2007
http://en.wikipedia.org/wiki/Newtonian_fluid, February 10 2007
http://www.glossary.oilfield.slb.com/DisplayImage.cfm?ID=373, February 10 2007
Page 14 of 16
Jackie Chee (1103396)
February 13 2007
Lab Report #1
Assignment
Apparent Viscosity using Power Law Laminar Flow Equations
Approach 1
𝜇𝐴𝑝𝑝
1
2+𝑛
𝐾 ∗ (𝐷ℎ − 𝐷𝑝 )1−𝑛
=
∗(
)𝑛
144 ∗ 𝑣𝑎 1−𝑛
0.0208
𝜇𝐴𝑝𝑝 = apparent mud viscosity, cp
𝑣𝑎 = average annular mud velocity, ft/sec
𝐷ℎ = hole diameter, inch
𝐷𝑝 = pipe outer diameter, inch
𝐾= consistency index, equivalent cp
Where:
Pipe Rheological Parameters
𝜃600
𝑛𝑝 = 3.322 ∗ log(
)
𝜃300
100
𝑛𝑝 = 3.322 ∗ log ( 65 ) = 0.62150
𝐾𝑝 =
510 ∗ 𝜃300
(511)𝑛𝑝
𝐾𝑝 =
510 ∗ 65
= 687.376
(511).62150
For 𝑣𝑎 = 150 ft/min
𝜇𝐴𝑝𝑝
1
687.376 ∗ (8.5 − 4.5)1−.62150 2 + . 62150 .62150
=
∗(
)
144 ∗ 2.51−.62150
0.0208
𝜇𝐴𝑝𝑝 = 140.551 𝑐𝑝
Annular rheological Parameters
𝜃100
𝑛𝐴𝑛𝑛 = 0.657 ∗ log(
)
𝜃3
32
𝑛𝐴𝑛𝑛 = .657 ∗ log (3.0) = 0.67541
𝐾𝐴𝑛𝑛 =
511 ∗ 𝜃3
(5.11)𝑛𝐴𝑛𝑛
Page 15 of 16
Jackie Chee (1103396)
February 13 2007
Lab Report #1
𝐾𝐴𝑛𝑛 =
511 ∗ 3.0
= 509.406
(5.11).67541
For 𝑣𝑎 = 150 ft/min
𝜇𝐴𝑝𝑝
1
509.406 ∗ (8.5 − 4.5)1−.67541 2 + . 67541 .67541
=
∗(
)
144 ∗ 2.51−.67541
0.0208
𝜇𝐴𝑝𝑝 = 130.857 𝑐𝑝
ft/min
ft/sec
Pipe Rheological
Annular Rheological
% error of u
U (cp)
n
k
U (cp)
n
k
6.357202
180
3 131.1794 0.621502 687.377 123.3385 0.675415 509.4061
7.407796
150
2.5 140.5516 0.621502 687.377 130.8579 0.675415 509.4061
8.707753
120
2 152.9382 0.621502 687.377 140.6875 0.675415 509.4061
10.40693
90
1.5 170.5316 0.621502 687.377 154.4574 0.675415 509.4061
The pipe rheological viscosity is higher than the annular rheological viscosity. The % error of
viscosity is small when the annular velocity is highest. As the velocity decrease, the error increases.
va
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