Abstract

The aggregation behavior and the subsequent deposition behavior of wax crystals own undesirable effects on the production and transportation of waxy crude oil. The understanding and prediction of these behaviors are essential to ensure economic and uninterrupted flow of waxy crude oil when the oil temperature decreases below the wax appearance temperature (WAT). In this paper, a novel method of fractal dimensional analysis was introduced to elucidate the aggregation behavior of wax crystals in different shear flow fields. The fractal methodology for characterizing wax crystal aggregation was then developed, and a blanket algorithm was introduced to compute the fractal dimension of the aggregated wax crystals. Considering the flow characteristics of waxy crude oil in a pipeline can be correlated with the shearing stress work, a modified wax deposition model focusing on shearing energy analysis was established. The results indicate that a quantitative interpretation of the wax crystal aggregation behavior can be realized using the fractal methodology. The aggregation behavior of the wax crystals is closely related to the temperature and shearing experienced by the waxy crude oil. The aggregation behavior will be intensified with decreasing temperature and shearing effect, and a wider fractal dimension distribution appears at lower temperatures when the same shear rate range is used. Furthermore, the improved model provides a method for discussing the effects of the operating conditions on wax deposition. The average relative deviation between the improved model prediction results and experimental results from the literature is 3.01–5.32%.

References

1.
Mendes
,
R.
,
Vinay
,
G.
,
Ovarlez
,
G.
, and
Coussot
,
P.
,
2015
, “
Modeling the Rheological Behavior of Waxy Crude Oils as a Function of Flow and Temperature History
,”
J. Rheol.
,
59
(
3
), pp.
703
732
. 10.1122/1.4916531
2.
Wang
,
Z.
,
Bai
,
Y.
,
Zhang
,
H.
, and
Liu
,
Y.
,
2019
, “
Investigation on Gelation Nucleation Kinetics of Waxy Crude Oil Emulsions by Their Thermal Behavior
,”
J. Pet. Sci. Eng.
,
181
(
99
), p.
106230
. 10.1016/j.petrol.2019.106230
3.
Aiyejina
,
A.
,
Chakrabarti
,
D. P.
,
Pilgrim
,
A.
, and
Sastry
,
M. K. S.
,
2011
, “
Wax Formation in Oil Pipelines: A Critical Review
,”
Int. J. Multiphase Flow
,
37
(
7
), pp.
671
694
. 10.1016/j.ijmultiphaseflow.2011.02.007
4.
Liu
,
Y.
,
Wang
,
Z.
,
Cheng
,
Q.
, and
Li
,
Y.
,
2012
, “
The Study of Pipeline Wax Deposition Law and Pigging Period for Daqing Waxy Crude Oil
,”
Acta Pet. Sin.
,
33
(
5
), pp.
892
897
(in Chinese).
5.
Sun
,
G.
,
Zhang
,
J.
,
Ma
,
C.
, and
Wang
,
X.
,
2016
, “
Start-up Flow Behavior of Pipelines Transporting Waxy Crude Oil Emulsion
,”
J. Pet. Sci. Eng.
,
147
, pp.
746
755
. 10.1016/j.petrol.2016.10.007
6.
Hoffmann
,
R.
,
Amundsen
,
L.
,
Huang
,
Z.
,
Zheng
,
S.
, and
Scott Fogler
,
H.
,
2012
, “
Wax Deposition in Stratified Oil/Water Flow
,”
Energy Fuels
,
26
(
6
), pp.
3416
3423
. 10.1021/ef2018989
7.
Sun
,
W.
,
Cheng
,
Q.
,
Zheng
,
A.
,
Zhang
,
T.
, and
Liu
,
Y.
,
2018
, “
Heat Flow Coupling Characteristics Analysis and Heating Effect Evaluation Study of Crude Oil in the Storage Tank Different Structure Coil Heating Processes
,”
Int. J. Heat Mass Transfer
,
127
, pp.
89
101
. 10.1016/j.ijheatmasstransfer.2018.08.035
8.
Rui
,
Z.
,
Peng
,
F.
,
Ling
,
K.
,
Chang
,
H.
,
Chen
,
G.
, and
Zhou
,
X.
,
2017
, “
Investigation Into the Performance of Oil and Gas Projects
,”
J. Nat. Gas Sci. Eng.
,
38
, pp.
12
20
. 10.1016/j.jngse.2016.11.049
9.
Wu
,
X.
,
Pu
,
H.
,
Zhu
,
K.
, and
Lu
,
S.
,
2017
, “
Formation Damage Mechanisms and Protection Technology for Nanpu Nearshore Tight Gas Reservoir
,”
J. Pet. Sci. Eng.
,
158
, pp.
509
515
. 10.1016/j.petrol.2017.07.033
10.
Phan
,
D. H. B.
,
Tran
,
V. T.
, and
Nguyen
,
D. T.
,
2018
, “
Crude Oil Price Uncertainty and Corporate Investment: New Global Evidence
,”
Energy Econ.
,
77
, pp.
54
65
. 10.1016/j.eneco.2018.08.016
11.
Liu
,
Y.
,
Chen
,
S.
,
Guan
,
B.
, and
Xu
,
P.
, “
Layout Optimization of Large-Scale Oil-Gas Gathering System Based on Combined Optimization Strategy
,”
Neurocomputing
,
332
, pp.
159
183
. 10.1016/j.neucom.2018.12.021
12.
Piroozian
,
A.
,
Hemmati
,
M.
,
Ismail
,
I.
,
Manan
,
M. A.
,
Bayat
,
A. E.
, and
Mohsin
,
R.
,
2016
, “
Effect of Emulsified Water on the Wax Appearance Temperature of Water-in-Waxy-Crude-Oil Emulsions
,”
Thermochim. Acta
,
637
, pp.
132
142
. 10.1016/j.tca.2016.05.014
13.
Zhu
,
J.
,
Zhu
,
H.
,
Zhang
,
J.
, and
Zhang
,
H.-Q.
,
2019
, “
A Numerical Study on Flow Patterns Inside an Electrical Submersible Pump (ESP) and Comparison With Visualization Experiments
,”
J. Pet. Sci. Eng.
,
173
, pp.
339
350
. 10.1016/j.petrol.2018.10.038
14.
Karami
,
H. R.
, and
Mowla
,
D.
,
2012
, “
Investigation of the Effects of Various Parameters on Pressure Drop Reduction in Crude Oil Pipelines by Drag Reducing Agents
,”
J. Non-Newtonian Fluid Mech.
,
177–178
, pp.
37
45
. 10.1016/j.jnnfm.2012.04.001
15.
Wang
,
Z.
,
Li
,
J.
,
Zhang
,
H. Q.
,
Liu
,
Y.
, and
Li
,
W.
,
2017a
, “
Treatment on Oil/Water Gel Deposition Behavior in Non-Heating Gathering and Transporting Process With Polymer Flooding Wells
,”
Environ. Earth Sci.
,
76
(
8
), p.
326
. 10.1007/s12665-017-6646-1
16.
Huang
,
Q.
,
Wang
,
J.
, and
Zhang
,
J.
,
2009
, “
Physical Properties of Wax Deposits on the Walls of Crude Pipelines
,”
Pet. Sci.
,
6
(
1
), pp.
64
68
. 10.1007/s12182-009-0011-2
17.
Gong
,
J.
,
Zhang
,
Y.
,
Liao
,
L.
,
Duan
,
J.
,
Wang
,
P.
, and
Zhou
,
J.
,
2011
, “
Wax Deposition in the Oil/Gas Two-Phase Flow for a Horizontal Pipe
,”
Energy Fuels
,
25
(
4
), pp.
1624
1632
. 10.1021/ef101682u
18.
Zheng
,
S.
,
Saidoun
,
M.
,
Palermo
,
T.
,
Mateen
,
K.
, and
Fogler
,
H. S.
,
2017
, “
Wax Deposition Modeling With Considerations of Non-Newtonian Characteristics: Application on Field-Scale Pipeline
,”
Energy Fuels
,
31
(
5
), pp.
5011
5023
. 10.1021/acs.energyfuels.7b00504
19.
Liu
,
Y.
,
Pan
,
C.
,
Cheng
,
Q.
,
Wang
,
B.
,
Wang
,
X.
, and
Gan
,
Y.
,
2018
, “
Wax Deposition Rate Model for Heat and Mass Coupling of Piped Waxy Crude Oil Based on Non-Equilibrium Thermodynamics
,”
J. Dispersion Sci. Technol.
,
39
(
2
), pp.
259
269
. 10.1080/01932691.2017.1312432
20.
Shuang
,
K.
,
Liang
,
H.
, and
Zhang
,
J.
,
2002
, “
Quantitative Characterization of Wax Crystal Morphology in Waxy Crudes
,”
J. Univ. Pet.
,
26
(
5
), pp.
100
103
(in Chinese).
21.
Yi
,
S.
, and
Gao
,
P.
,
2013
, “
Study of Mechanism of Shear Process Quantitatively Affects the Morphology and Structure of Wax Crystals in Waxy Crudes
,”
J. Wuhan Univ. Technol. (Transp. Sci. Eng.)
,
37
(
3
), pp.
598
602
(in Chinese).
22.
Peleg
,
M.
, and
Normand
,
M. D.
,
1993
, “
Determination of the Fractal Dimension of the Irregular, Compressive Stress-Strain Relationships of Brittle, Crumbly Particulates
,”
Part. Part. Syst. Charact.
,
10
(
6
), pp.
301
307
. 10.1002/ppsc.19930100603
23.
Lasota
,
A.
,
2006
, “
A Variational Principle for Fractal Dimensions
,”
Nonlinear Anal.: Theory Methods Appl.
,
64
(
3
), pp.
618
628
. 10.1016/j.na.2005.06.026
24.
Zhu
,
H.
,
Zhu
,
J.
,
Rutter
,
R.
, and
Zhang
,
H.
,
2019
, “
A Numerical Study on Erosion Model Selection and Effect of Pump Type and Sand Characters in Electrical Submersible Pumps (ESPs) by Sandy Flow
,”
ASME J. Energy Resour. Technol.
,
141
(
12
), p.
122004
. 10.1115/1.4044941
25.
Cutler
,
C. D.
, and
Olsen
,
L.
,
1994
, “
A Variational Principle for the Hausdorff Dimension of Fractal Sets
,”
Math. Scand.
,
74
(
1
), pp.
64
72
. 10.7146/math.scand.a-12480
26.
Zhao
,
X.
, and
Wang
,
X.
,
2017
, “
An Approach to Compute Fractal Dimension of Color Images
,”
Fractals
,
25
(
1
), p.
1750007
. 10.1142/S0218348X17500074
27.
Foroutan-pour
,
K.
,
Dutilleul
,
P.
, and
Smith
,
D. L.
,
1999
, “
Advances in the Implementation of the Box-Counting Method of Fractal Dimension Estimation
,”
Appl. Math. Comput.
,
105
(
2–3
), pp.
195
210
. 10.1016/S0096-3003(98)10096-6
28.
Fernández-Martínez
,
M.
, and
Sánchez-Granero
,
M. A.
,
2014
, “
Fractal Dimension for Fractal Structures: A Hausdorff Approach Revisited
,”
J. Math. Anal. Appl.
,
409
(
1
), pp.
321
330
. 10.1016/j.jmaa.2013.07.011
29.
Chamorro-Posada
,
P.
,
2016
, “
A Simple Method for Estimating the Fractal Dimension From Digital Images: The Compression Dimension
,”
Chaos Solitons Fractals
,
91
, pp.
562
572
. 10.1016/j.chaos.2016.08.002
30.
Couto
,
G. H.
,
Chen
,
H.
,
Dellecase
,
E.
,
Sarica
,
C.
, and
Volk
,
M.
,
2008
, “
An Investigation of Two-Phase Oil/Water Paraffin Deposition
,”
SPE Prod. Oper.
,
23
(
1
), pp.
49
55
.
31.
Hoffmann
,
R.
, and
Amundsen
,
L.
,
2010
, “
Single-phase Wax Deposition Experiments
,”
Energy Fuels
,
24
(
2
), pp.
1069
1080
. 10.1021/ef900920x
32.
Hernandez
,
O. C.
,
Hensley
,
H.
,
Sarica
,
C.
,
Brill
,
J. P.
,
Volk
,
M.
, and
Delle-Case
,
E.
,
2004
, “
Improvements in Single-phase Paraffin Deposition Modeling
,”
SPE Prod. Facil.
,
19
(
4
), pp.
237
244
. 10.2118/84502-PA
33.
Wang
,
Z.
,
Liu
,
Y.
,
Li
,
J.
,
Zhuge
,
X.
, and
Zhang
,
L.
,
2016
, “
Study on Two-phase Oil−Water Gelling Deposition Behavior in Low-Temperature Transportation
,”
Energy Fuels
,
30
(
6
), pp.
4570
4582
. 10.1021/acs.energyfuels.6b00294
34.
Opawale
,
A.
,
Osisanya
,
S.
,
Dulu
,
A.
, and
Otakoro
,
S.
,
2011
, “
An Integrated Approach to Selecting and Optimizing Demulsifier Chemical Injection Points Using Shearing Energy Analysis: A Justification for Downhole Injection in High Pressured Well
,”
Offshore Technology Conference
,
Houston, TX
,
May 2–5
, OTC-21151-MS.
35.
Wang
,
Z.
,
Lin
,
X.
,
Rui
,
Z.
,
Xu
,
M.
, and
Zhan
,
S.
,
2017b
, “
The Role of Shearing Energy and Interfacial Gibbs Free Energy in the Emulsification Mechanism of Waxy Crude Oil
,”
Energies
,
10
(
5
), p.
721
. 10.3390/en10050721
36.
Sun
,
G.
,
Zhang
,
J.
, and
Li
,
H.
,
2014
, “
Structural Behaviors of Waxy Crude Oil Emulsion Gels
,”
Energy Fuels
,
28
(
6
), pp.
3718
3729
. 10.1021/ef500534r
37.
Peleg
,
S.
,
Naor
,
J.
,
Hartley
,
R.
, and
Avnir
,
D.
,
1984
, “
Multiple Resolution Texture Analysis and Classification
,”
IEEE Trans. Pattern Anal. Mach. Intell.
,
6
(
4
), pp.
518
523
. 10.1109/TPAMI.1984.4767557
38.
Hayduk
,
W.
, and
Minhas
,
B.
,
1982
, “
Correlations for Prediction of Molecular Diffusivities in Liquids
,”
Can. J. Chem. Eng.
,
60
(
2
), pp.
295
299
. 10.1002/cjce.5450600213
39.
Singh
,
P.
,
Gler
,
H. S.
, and
Garajan
,
N.
,
1999
, “
Prediction of the Wax Content of the Incipient Wax-oil Gel in a Pipeline: An Application of the Controlled-Stress Rhometer
,”
J. Rheol.
,
43
(
6
), pp.
176
189
. 10.1122/1.551054
40.
Hoteit
,
H.
,
Banki
,
R.
, and
Firoozabadi
,
A.
,
2008
, “
Wax Deposition and Aging in Flowlines From Irreversible Thermodynamics
,”
Energy Fuels
,
22
(
4
), pp.
2693
2706
. 10.1021/ef800129t
41.
Chen
,
X. T.
,
Butler
,
T.
,
Volk
,
M.
, and
Brill
,
J. P.
,
1997
, “
Techniques for Measuring Wax Thickness During Single and Multiphase Flow
,”
SPE Annual Technical Conference and Exhibition
,
San Antonio, TX
,
Oct. 5–8
.
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