Underground Infrastructure - February 2023 - 36

CIGMAT Report
TABLE 3: Rheological model parameters for the spacer fl uids with 1% nanoFe2O3 at temperatures of 25°C under magnetic fi eld strengths
of 0 , 0.3 T and 0.6 T.
Model Parameter
NanoFe = 1%
MF = 0 T
NanoFe= 1%
MF = 0.3 T
NanoFe = 1%
MF = 0.6 T
Yield Stress (τ01
(Pa))
Hershel Bulkey Model
n
0.294
0.290
0.300
k
8.14
6.65
8.14
RMSE (Pa)
2.36
2.20
3.01
Yield Stress (τ02
6.63
7.70
7.80
(Pa))
A (Pa.s)-1
1.79
1.92
1.58
Vipulanandan Model
B (Pa)-1
0.017
0.016
0.013
τmax (Pa)
65.5
70.2
84.7
RMSE (Pa)
2.15
2.10
2.01
TABLE 4: Rheological model parameters for the spacer fl uids with diff erent nanoFe2O3
temperature of 25°C.
Model Parameter
NanoFe = 0%
NanoFe= 0.5%
NanoFe = 1%
Yield Stress (τ01
(Pa))
Hershel Bulkey Model
n
0.35
0.33
0.30
k
4.57
6.42
9.36
RMSE (Pa)
1.54
2.83
3.33
content and 0.5 % bentonite contamination at
Yield Stress (τ02
4.18
3.61
5.89
(Pa))
A (Pa.s)-1
3.41
1.96
1.44
Vipulanandan Model
B (Pa)-1
0.019
0.015
0.014
τmax (Pa)
56.8
70.3
77.3
RMSE (Pa)
1.39
1.23
2.16
FIGURE 6: Shear stress-shear strain rate relationship for spacer fluid
with 1% nanoFe2
O3
of 0, 0.3 T and 0.6 T.
Eff ect of Magnetic Field. Shear stress-shear strain rate relationships
were predicted using the Vipulanandan rheological
model and compared with the Herschel Bulkley models, as
shown in FIGURE 6.
Th e root mean square of error (RMSE) for the Herschel
Bulkley model varied between 2.2 to 3.01 Pa. Th e model parameter
k for the spacer fl uid at 25°C varied from 8.15 to 9.97
Pa.sn
as summarized in TABLE 3. Th e model parameter n was
in range of 0.29 to 0.3 and the model predictions are compared
in FIGURE 5.
Increasing the magnetic fi eld strength from 0 T to 0.6 T,
increased the yield stress from 6.64 to 7.8 Pa and τmax
from
63.8 to 84.7 Pa, at room temperature. Th e maximum shear
stress increased by 32.7% with magnetic fi eld increase, from 0
to 0.6 T, as in FIGURE 5. Th e root mean square of error was in
the range of 2 to 2.13 Pa, as summarized in TABLE 3.
36 FEBRUARY 2023 | UndergroundInfrastructure.com
at temperatures of 25°C under magnetic field strengths
FIGURE 7: Shear stress-shear strain rate relationship for spacer fluid
with different nanoFe2
at temperature of 25°C.
O3
content and 0.5 % bentonite contamination
Eff ect of Bentonite Contamination. Th e spacer fl uid
with 0.5% bentonite contamination showed increased rheological
properties with the increase in nanoFe2
O3
content at
25°C temperature, as shown in FIGURE 7.
Th e root mean square of error (RMSE) for the Herschel
Bulkley model varied between 1.54 to 3.33 Pa. Th e model parameter
k for the spacer fl uid at 25°C varied from 4.57 to 9.36
Pa.sn
, as summarized in TABLE 4. Th e model parameter n was
in range of 0.3 to 0.35.
Th e shear thinning behavior of spacer fl uids with diff erent
nanoFe2O3 content and contaminated with 0.5% bentonite was
tested and modeled using the Vipulanandan model (2014), up
to a shear strain rate of 1024 s-1
for the spacer fl uid without nanoFe2
creased with the addition of nanoFe2O3, by 41 %. Th e τmax
the spacer fl uid increased 36%, from 56.8 Pa to 77.3 Pa, with
for
(600 rpm). Average yield stress
O3 was 4.18 Pa, which in
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