Polymer-gel, as a rheological complex fluid, is vulnerable to slip at solid walls. If wall slip occurs, the accuracy of viscosity measurements that are based on the no-slip boundary condition assumption is affected. This paper presents a general numerical procedure based on Tikhonov regularization for correcting Couette viscometry data in the presence of wall slip. This procedure needs only two-measurement viscosity data from two different annular gap sizes. Using the presented procedure, we determined the viscosity and wall slip behavior of a special polymer-gel used for leakage control. The results show that, the polymer-gel ZND-2 does not always exhibit significant wall slip, until the polymer content reaches a critical level of 0.3–0.5% by mass. An empirical correlation was proposed in power law form to describe the relationship between wall slip velocity and wall shear stress. It indicates that there is a minimum wall shear stress that needs to be overcome for a given polymer-gel sample manifesting wall slip phenomenon. The critical minimum wall shear stress and the gel structure strength increase drastically when the polymer content increases beyond a certain value, which is 1.0% by mass for ZND-2. When wall slip occurs, the difference is remarkable between the slip-corrected and apparent rheological parameters for different annular gap sizes. The slip-corrected rheological properties indicate that the polymer-gel ZND-2 used for leakage control behaves as a yield plastic fluid and has good shear thinning capability.

References

References
1.
Boukadi
,
F.
,
Yaghi
,
B.
,
Al-Hadrami
,
H.
,
Bemani
,
A.
,
Babadagli
,
T.
, and
De Mestre
,
P.
,
2004
, “
A Comparative Study of Lost Circulation Materials
,”
Energy Sources
,
26
(
11
), pp.
1043
1051
.
2.
Pilehvari
,
A. A.
, and
Serth
,
R. W.
,
2005
, “
Generalized Hydraulic Calculation Method Using Rational Polynomial Model
,”
ASME J. Energy Resour. Technol.
,
127
(
1
), pp.
15
25
.
3.
Nie
,
X.
,
Luo
,
P.
,
Wang
,
P.
,
Zhang
,
X.
, and
Yang
,
L.
,
2010
, “
Rheology of a New Gel Used for Severe Lost Circulation Control
,”
International Oil and Gas Conference and Exhibition in China
, Beijing, China, June 8–10,
SPE
Paper No. SPE-132136-MS.
4.
Najmi
,
K.
,
McLaury
,
B. S.
,
Shirazi
,
S. A.
, and
Cremaschi
,
S.
,
2016
, “
The Effect of Viscosity on Low Concentration Particle Transport in Single-Phase (Liquid) Horizontal Pipes
,”
ASME J. Energy Resour. Technol.
,
138
(
3
), p.
032902
.
5.
Kutlu
,
B.
,
Takach
,
N.
,
Ozbayoglu
,
E. M.
,
Miska
,
S. Z.
,
Yu
,
M.
, and
Mata
,
C.
,
2017
, “
Drilling Fluid Density and Hydraulic Drag Reduction With Glass Bubble Additives
,”
ASME J. Energy Resour. Technol.
,
139
(
4
), p.
042904
.
6.
Krieger
,
I. M.
,
1968
, “
Shear Rate in the Couette Viscometer
,”
Trans. Soc. Rheol.
,
12
(
1
), pp.
5
11
.
7.
Jin
,
L.
, and
Chenevert
,
M.
,
1994
, “
A Study of Particle Settling in Non-Newtonian Fluids—Part II: Rheological Characterization of Polymer Solutions
,”
ASME J. Energy Resour. Technol.
,
116
(1), pp.
16
21
.
8.
Pilehvari
,
A.
, and
Clark
,
P.
,
1985
, “
Rheology of Hydraulic Fracturing Fluids: Wall Slip During Viscosity Measurement
,”
J. Pet. Technol.
,
37
(
10
), pp.
1840
1846
.
9.
Barnes
,
H. A.
,
1995
, “
A Review of the Slip (Wall Depletion) of Polymer Solutions, Emulsions and Particle Suspensions in Viscometers: Its Cause, Character, and Cure
,”
J. Non-Newtonian Fluid Mech.
,
56
(
3
), pp.
221
251
.
10.
Brunn
,
P.
,
Müller
,
M.
, and
Bschorer
,
S.
,
1996
, “
Slip of Complex Fluids in Viscometry
,”
Rheol. Acta
,
35
(
3
), pp.
242
251
.
11.
Mooney
,
M.
,
1931
, “
Explicit Formulas for Slip and Fluidity
,”
J. Rheol. (1929–1932)
,
2
(
2
), pp.
210
222
.
12.
Yoshimura
,
A.
, and
Prud'homme
,
R. K.
,
1988
, “
Wall Slip Corrections for Couette and Parallel Disk Viscometers
,”
J. Rheol.
,
32
(
1
), pp.
53
67
.
13.
Yoshimura
,
A. S.
, and
Prud'homme
,
R. K.
,
1988
, “
Viscosity Measurements in the Presence of Wall Slip in Capillary, Couette, and Parallel-Disk Geometries
,”
SPE Reservoir Eng.
,
3
(
2
), pp.
735
742
.
14.
Kiljański
,
T.
,
1989
, “
A Method for Correction of the Wall-Slip Effect in a Couette Rheometer
,”
Rheol. Acta
,
28
(
1
), pp.
61
64
.
15.
Yeow
,
Y. L.
,
Choon
,
B.
,
Karniawan
,
L.
, and
Santoso
,
L.
,
2004
, “
Obtaining the Shear Rate Function and the Slip Velocity Function From Couette Viscometry Data
,”
J. Non-Newtonian Fluid Mech.
,
124
(
1
), pp.
43
49
.
16.
Andreas
,
K.
,
1996
, “
An Introduction to the Mathematical Theory of Inverse Problems
,”
Applied Mathematical Sciences
,
Springer
,
New York
, p.
120
.
17.
Yeow
,
Y. L.
,
Ko
,
W. C.
, and
Tang
,
P. P.
,
2000
, “
Solving the Inverse Problem of Couette Viscometry by Tikhonov Regularization
,”
J. Rheol.
,
44
(
6
), pp.
1335
1351
.
18.
Leong
,
Y.
, and
Yeow
,
Y.
,
2003
, “
Obtaining the Shear Stress Shear Rate Relationship and Yield Stress of Liquid Foods From Couette Viscometry Data
,”
Rheol. Acta
,
42
(
4
), pp.
365
371
.
19.
De Hoog
,
F.
, and
Anderssen
,
R.
,
2006
, “
Regularization of First Kind Integral Equations With Application to Couette Viscometry
,”
J. Integr. Equations Appl.
,
18
(
2
), pp.
249
265
.
20.
Weese
,
J.
,
1993
, “
A Regularization Method for Nonlinear Ill-Posed Problems
,”
Comput. Phys. Commun.
,
77
(
3
), pp.
429
440
.
21.
Mourniac
,
P.
,
Agassant
,
J.
, and
Vergnes
,
B.
,
1992
, “
Determination of the Wall Slip Velocity in the Flow of a SBR Compound
,”
Rheol. Acta
,
31
(
6
), pp.
565
574
.
22.
Wein
,
O.
, and
Tovchigrechko
,
V.
,
1992
, “
Rotational Viscometry Under Presence of Apparent Wall Slip
,”
J. Rheol.
,
36
(
5
), pp.
821
844
.
You do not currently have access to this content.