Pipeline liquid–solid two-phase flow is a significantly important multiphase flow phenomenon widely encountered in both industrial and natural settings. The flow regime of liquid–solid two-phase flow in pipelines plays a crucial role as it represents the macroscopic manifestation of the suspension diffusion mechanism and the slip deposition law of solid particles. This paper provides an overview of research related to flow regimes and critical deposition velocity (CDV) in liquid–solid two-phase flow in pipelines. After briefly reviewing pioneering theoretical research in this field, the paper focuses on recent research in flow regime identification and prediction using state-of-the-art experimental methods and techniques. The review also rigorously assesses the reliability and validity of the methods, results, and conclusions related to the establishment of the CDV, identifying the deficiencies in the current research. Drawing on dimensional analysis and Pearson correlation analysis, the particle Reynolds number is introduced to establish a highly accurate correlation for predicting the CDV under conditions of wide volume concentration. The new correlation yields a mean absolute percentage error of 9.23% and a root mean square error of 10.29% within the volume concentration range of 0.7%–50.8%. This paper aims to provide clear guidance to researchers and professionals in related industries, enabling them to conduct more in-depth investigations according to their research interest and enhance their understanding of liquid–solid two-phase flow systems within pipelines.

1.
W. L.
Ren
,
Y.
Zhang
,
X. H.
Zhang
et al, “
Investigation of the characteristics and mechanisms of the layer inversion in binary liquid–solid fluidized beds with coarse particles
,”
Phys. Fluids
34
(
10
),
103325
(
2022
).
2.
S.
Lv
,
F.
Jiang
,
G.
Qi
et al, “
Pressure drop of liquid–solid two-phase flow in a down-flow circulating fluidized bed
,”
Powder Technol.
375
,
136
145
(
2020
).
3.
M. A.
Ferrari
,
A.
Lugarini
, and
A. T.
Franco
, “
On the settling of spherical particles in power-law fluid at moderate Reynolds number
,”
Powder Technol.
405
,
117510
(
2022
).
4.
K.
Wang
,
G.
Liu
,
Y.
Li
et al, “
Identification and characterization of solids in sand-water two-phase flows via vibration multi-sensor approaches
,”
Adv. Powder Technol.
30
(
10
),
2240
2250
(
2019
).
5.
S. G.
Sontti
,
M.
Sadeghi
,
K.
Zhou
et al, “
Computational fluid dynamics investigation of bitumen residues in oil sands tailings transport in an industrial horizontal pipe
,”
Phys. Fluids
35
(
1
),
013340
(
2023
).
6.
R.
Zhao
,
Y.
Zhao
,
Q.
Si
et al, “
Effects of different characteristics of the dilute liquid-solid flow on the erosion in a 90° bend
,”
Powder Technol.
398
,
117043
(
2022
).
7.
B.
Abulnaga
,
Slurry Systems Handbook
(
McGraw-Hill Companies, Inc
.,
New York
,
2002
).
8.
L.
Joly
,
C.
Ybert
, and
L.
Bocquet
, “
Probing the nanohydrodynamics at liquid-solid interfaces using thermal motion
,”
Phys. Rev. Lett.
96
(
4
),
046101
(
2006
).
9.
P. D.
Gaudio
,
G.
Ventura
, and
J.
Taddeucci
, “
The effect of particle size on the rheology of liquid-solid mixtures with application to lava flows: Results from analogue experiments
,”
Geochem. Geophys. Geosyst.
14
(
8
),
2661
2669
(
2013
).
10.
V.
Jain
,
L.
Kalo
,
D.
Kumar
et al, “
Experimental and numerical investigation of liquid-solid binary fluidized beds: Radioactive particle tracking technique and dense discrete phase model simulations
,”
Particuology
33
,
112
122
(
2017
).
11.
V.
Stolojanu
and
A.
Prakash
, “
Characterization of slurry systems by ultrasonic techniques
,”
Chem. Eng. J.
84
(
3
),
215
222
(
2001
).
12.
B. C.
Shi
,
J. J.
Wei
,
Y. J.
Qiu
et al, “
PIV test methods and mechanism on liquid turbulence modulation by solid-particles inside a centrifugal pump
(
in Chinese),” Chin. Sci. Bull.
63
,
1050
1061
(
2018
).
13.
W.
Hong
,
B.
Wang
, and
J.
Zheng
, “
Numerical study on the influence of fine particle deposition characteristics on wall roughness
,”
Powder Technol.
360
,
120
128
(
2020
).
14.
T.
Joshi
,
O.
Parkash
, and
G.
Krishan
, “
Slurry flow characteristics through a horizontal pipeline at different Prandtl number
,”
Powder Technol.
413
,
118008
(
2023
).
15.
M.
Parsi
,
K.
Najmi
,
F.
Najafifard
et al, “
A comprehensive review of solid particle erosion modeling for oil and gas wells and pipelines applications
,”
J. Nat. Gas Sci. Eng.
21
,
850
873
(
2014
).
16.
A. S. I.
Ismail
,
I.
Ismail
,
M.
Zoveidavianpoor
et al, “
Review of oil–water through pipes
,”
Flow Meas. Instrum.
45
,
357
374
(
2015
).
17.
S. A.
Miedema
,
Slurry Transport: Fundamentals, A Historical Overview and The Delft Head Loss and Limit Deposit Velocity Framework
(ResearchGate,
2016
), ISBN: 978-94-6186-697-4.
18.
F.
White
,
Fluid Mechanics
(McGraw-Hill Education
,
New York
,
2016
).
19.
P.
Si
,
H.
Shi
, and
X.
Yu
, “
Development of a mathematical model for submarine granular flows
,”
Phys. Fluids
30
,
083302
(
2018
).
20.
Z.
Lin
,
X.
Liu
,
L.
Lao
et al, “
Prediction of two-phase flow patterns in upward inclined pipes via deep learning
,”
Energy
210
,
118541
(
2020
).
21.
S. M.
Peker
,
Solid-Liquid Two Phase Flow
,
1st ed.
(
Elsevier, Inc
.,
Amsterdam, The Netherlands
,
2011
).
22.
P.
Doron
and
D.
Barnea
, “
A three-layer model for solid-liquid flow in horizontal pipes
,”
Int. J. Multiphase Flow
19
(
6
),
1029
1043
(
1993
).
23.
F.
Ahmadi
,
M.
Ebrahimian
,
S. R.
Sanders
et al, “
Particle image and tracking velocimetry of solid-liquid turbulence in a horizontal channel flow
,”
Int. J. Multiphase Flow
112
,
83
99
(
2019
).
24.
G.
Liu
,
W.
Zhang
,
L.
Zhang
et al, “
Theoretical prediction method for erosion damage of horizontal pipe by suspended particles in liquid–solid flows
,”
Materials
14
(
15
),
4099
(
2021
).
25.
N.
Behera
,
K. V.
Agarwal
,
G. M.
Jones
et al, “
Modeling and analysis of dilute phase pneumatic conveying of fine particles
,”
Powder Technol.
249
,
196
204
(
2013
).
26.
T.
Mu
,
D.
Ma
,
Y.
Chen
et al, “
Start-migration law of coal powder with different particle sizes under multi-phase flow conditions in coalbed methane wells
,”
Coal Sci. Technol.
48
(
5
),
188
196
(
2020
).
27.
G. V.
Messa
,
Q.
Yang
,
O. E.
Adedeji
et al, “
Computational fluid dynamics modelling of liquid–solid slurry flows in pipelines: State-of-the-art and future perspectives
,”
Processes
9
(
9
),
1566
(
2021
).
28.
R. C.
Silva
, “
Experimental characterization techniques for solid-liquid slurry flows in pipelines: A review
,”
Processes
10
(
3
),
597
(
2022
).
29.
V.
Matoušek
, “
Research developments in pipeline transport of settling slurries
,”
Powder Technol.
156
(
1
),
43
51
(
2005
).
30.
N. I.
Heywood
and
N. J.
Alderman
, “
Developments in slurry pipeline technologies
,”
Chem. Eng. Prog.
99
(
4
),
36
(
2003
).
31.
J. K.
Albion
,
L.
Briens
,
C.
Briens
et al, “
Multiphase flow measurement techniques for slurry transport
,”
Int. J. Chem. Reactor Eng.
9
(
1
),
1542
6580
(
2011
).
32.
R. L.
Powell
, “
Experimental techniques for multiphase flows
,”
Phys. Fluids
20
(
4
),
040605
(
2008
).
33.
K. C.
Wilson
, “
Slip point of beds in solid-liquid pipeline flow
,”
J. Hydraul. Div.
96
(
1
),
1
12
(
1970
).
34.
K. C.
Wilson
,
M.
Streat
, and
R. A.
Bantin
, “
Slip model correlation of dense two phase flow
,” in Proceedings of the
2nd International Conference on Hydraulic Transport of Solids in Pipes
(
BHRA, Cranfield, UK
,
1972
), pp.
1
10
.
35.
K. C.
Wilson
, “
Co-ordinates for the limit of deposition in pipeline flow
,” in
Proceedings of the 3rd International Conference on Hydraulic Transport of Solids in Pipes
, Golden, CO (BHRA Fluid Engineering,
1974
), pp.
1
13
.
36.
K. C.
Wilson
, “
A unified physically-based analysis of solid-liquid pipeline flow
,” in
Proceedings of the 4th International Conference on the Hydraulic Transport of Solids in Pipes
, Banff, AB, Canada (BHRA Fluid Engineering,
1976
), pp.
1
16
.
37.
R. G.
Gillies
,
C. A.
Shook
, and
J.
Xu
, “
Modelling heterogeneous slurry flows at high velocities
,”
Can. J. Chem. Eng.
82
(
5
),
1060
1065
(
2008
).
38.
P.
Doron
,
D.
Granica
, and
D.
Barnea
, “
Slurry flow in horizontal pipes-experimental and modeling
,”
Int. J. Multiphase Flow
13
(
4
),
535
547
(
1987
).
39.
M. R.
Rojas
and
A. E.
Saez
, “
Two-layer model for horizontal pipe flow of Newtonian and non-Newtonian settling dense slurries
,”
Ind. Eng. Chem. Res.
51
(
20
),
7095
7103
(
2012
).
40.
A.
Levy
and
D. J.
Mason
, “
Two-layer model for non-suspension gas–solids flow in pipes
,”
Powder Technol.
112
(
3
),
256
262
(
2000
).
41.
G.
Setia
,
S. S.
Mallick
,
R.
Pan
et al, “
Modeling solids friction factor for fluidized dense-phase pneumatic transport of powders using two layer flow theory
,”
Powder Technol.
294
,
80
92
(
2016
).
42.
A.
Ramadan
,
P.
Skalle
, and
A.
Saasen
, “
Application of a three-layer modeling approach for solids transport in horizontal and inclined channels
,”
Chem. Eng. Sci.
60
(
10
),
2557
2570
(
2005
).
43.
P.
Vlasak
,
Z.
Chara
, and
J.
Konfrst
, “
Flow behaviour and local concentration of coarse particles-water mixture in inclined pipes
,”
J. Hydrol. Hydromech.
65
(
2
),
183
191
(
2017
).
44.
C.
Zhang
,
J.
Tang
,
L.
Wang
et al, “
Flow pattern maps for particle-fluid mixture transport in a horizontal pipe-application of a three-layer model
,”
J. Dispersion Sci. Technol.
39
(
11
),
1664
1674
(
2018
).
45.
R.
Dabirian
,
I.
Gavrielatos
,
R. S.
Mohan
et al, “
Experimental investigation and modeling of moving bed to moving dunes transition
,”
Powder Technol.
357
,
262
268
(
2019
).
46.
S. A.
Miedema
, “
An overview of theories describing head losses in slurry transport: A tribute to some of the early researchers
,” in P
roceedings of the International Conference on Offshore Mechanics and Arctic Engineering
(
American Society of Mechanical Engineers
,
2013
), p.
55362,
Paper No. V04AT04A038.
47.
S. A.
Miedema
, “
An analytical approach to explain the Fuehrboeter equation
,”
Proc. Inst. Civ. Eng.: Maritime Engineering
167
(
2
),
68
81
(
2014
).
48.
S. A.
Miedema
, “
A head loss model for homogeneous slurry transport for medium sized particles
,”
J. Hydrol. Hydromech.
63
(
1
),
1
12
(
2015
).
49.
S. A.
Miedema
and
R. C.
Ramsdell
, “
The limit deposit velocity model, a new approach
,”
J. Hydrol. Hydromech.
63
(
4
),
273
286
(
2015
).
50.
S. A.
Miedema
and
R. C.
Ramsdell
, “
The delft head loss and limit deposit velocity framework
,”
J. Dredging Eng.
15
(
2
),
28
(
2015
).
51.
S. A.
Miedema
, “
A head loss model for slurry transport in the heterogeneous regime
,”
Ocean Eng.
106
,
360
370
(
2015
).
52.
S. A.
Miedema
, “
The heterogeneous to homogeneous transition for slurry flow in pipes
,”
Ocean Eng.
123
,
422
431
(
2016
).
53.
S. A.
Miedema
and
R. C.
Ramsdell
, “
A head loss and limit deposit velocity framework
,”
J. Mar. Environ. Eng.
10
(
1
),
45
69
(
2017
).
54.
E.
Riet
,
V.
Matousek
, and
S. A.
Miedema
, “
A reconstruction of and sensitivity analysis on the Wilson model for hydraulic particle transport
,” in
Proceedings of the 8th International Conference on Transport and Sedimentation of Solid Particles
, Prague, Czech Republic (Institute of Hydrodynamics CAS,
1995
), pp.
24
26
.
55.
E. J.
Riet
,
V.
Matousek
, and
S. A.
Miedema
, “
A theoretical description and numerical sensitivity analysis on Wilson's model for hydraulic particle transport in pipelines
,”
J. Hydrol. Hydromech.
44
(
4
),
1
17
(
1996
).
56.
V.
Matoušek
and
P.
Vlasák
, “
Research advances in settling slurry flows
,” in
Proceedings of the 8th International Conference for Conveying and Handling of Particulate Solids
(
2015
).
57.
T. N.
Ofei
and
A. Y.
Ismail
, “
Eulerian-Eulerian simulation of particle-liquid slurry flow in horizontal pipe
,”
J. Pet. Eng.
2016
,
1
10
.
58.
X.
Ting
,
S. A.
Miedema
, and
C.
Xiuhan
, “
Comparative analysis between CFD model and DHLLDV model in fully-suspended slurry flow
,”
Ocean Eng.
181
,
29
42
(
2019
).
59.
Z. M.
Li
,
Y. P.
He
,
Y. D.
Liu
et al, “
Development of calculation and analysis software for CSD slurry transportation system
,”
Res. Explor. Lab.
36
(
11
),
126
129
(
2017
).
60.
S. A.
Miedema
and
X.
Chen
, “
Criterion for the transition from heterogeneous flow to fully stratified flow in slurry transportation
,” in
Proceedings of the 1st International Water Environment Ecological Construction Development Conference
(
2018
).
61.
R.
Durand
and
E.
Condolios
, “
Experimental investigation of the transport of solids in pipes
,”
Deuxieme Journée de lhydraulique
(
Societé Hydrotechnique de France
,
1952
), pp.
29
55
.
62.
H.
Matsubara
and
K.
Naito
, “
Effect of liquid viscosity on flow patterns of gas–liquid two-phase flow in a horizontal pipe
,”
Int. J. Multiphase Flow
37
(
10
),
1277
1281
(
2011
).
63.
G. F.
Hewitt
and
D. N.
Roberts
, “
Studies of two-phase flow patterns by simultaneous x-ray and flash photography
,”
Report No. AERE-M-2159
(
Atomic Energy Research Establishment
,
Harwell, England, UK
,
1969
).
64.
G. F.
Hewitt
, “
Measurement of two phase flow parameters
,”
Nasa Sti/recon Tech. Rep. A
79
,
47262
(
1978
).
65.
G. W.
Govier
and
K.
Aziz
,
The Flow of Complex Mixtures in Pipes
(
Van Nostrand Reinhold Company
,
New York
,
1972
).
66.
R. J.
Durand
, “
Basic relationships of the transportation of solids in pipes-experimental research
,” in
Proceedings of the IAHR 5th Congress
, Minneapolis (International Association for Hydraulic Research,
1953
), pp.
89
103
.
67.
E.
Condolios
and
E. E.
Chapus
, “
Designing solids handling pipelines
,”
Chem. Eng.
70
(
14
),
131
138
(
1963
).
68.
R. P.
King
,
Introduction to Practical Fluid Flow
(
Elsevier, Butterworth-Heinemann
,
Burlington, MA
,
2002
).
69.
D. M.
Newitt
, “
Hydraulic conveying of solids in horizontal pipes
,”
Trans. Inst. Chem. Eng.
33
,
93
113
(
1955
).
70.
H. S.
Ellis
and
G. F.
Round
, “
Laboratory studies on the flow of nickel–water suspensions
,”
Can. Min. Metall. Bull.
56
,
773
781
(
1963
).
71.
D. G.
Thomas
, “
Transport characteristics of suspensions. IX. Representation of periodic phenomena on a flow regime diagram for dilute suspension transport
,”
AIChE J.
10
(
3
),
303
308
(
1964
).
72.
M.
Wicks
, “
Transport of solids at low concentration in horizontal pipes
,”
Advances in Solid–Liquid Flow in Pipes and its Application
(
Pergamon
,
1971
), pp.
101
124
.
73.
J. J.
Vocadlo
and
M. E.
Charles
, “
Prediction of pressure gradient for the horizontal turbulent flow of slurries
,” in
Proceedings of the 2nd
International Conference on the Hydraulic Transport of Solids in Pipes
(BHRA Fluid Engineering,
1972
), Vol.
2
, pp.
1
14
.
74.
W.
Parzonka
,
J. M.
Kenchington
, and
M. E.
Charles
, “
Hydrotransport of solids in horizontal pipes: Effects of solids concentration and particle size on the deposit velocity
,”
Can. J. Chem. Eng.
59
(
3
),
291
296
(
1981
).
75.
P. A.
Shamlou
, “
Hydraulic transport of particulate solids
,”
Chem. Eng. Commun.
62
(
1–6
),
233
249
(
1987
).
76.
R. M.
Turian
and
T. F.
Yuan
, “
Flow of slurries in pipelines
,”
AIChE J.
23
(
3
),
232
243
(
1977
).
77.
I.
Zandi
and
G.
Govatos
, “
Heterogeneous flow of solids in pipelines
,”
J. Hydraul. Div.
93
(
3
),
145
159
(
1967
).
78.
J. H.
Lazarus
, “
Mixed-regime slurries in pipelines. I. Mechanistic model
,”
J. Hydraul. Eng.
115
(
11
),
1496
1509
(
1989
).
79.
K. C.
Wilson
, “
Pipeline design for settling slurries
,”
Slurry Handling Design for Solid-Liquid Systems
, edited by
N. P.
Brown
and
N. I.
Heywood
(
Elsevier
,
London
,
1991
).
80.
K. C.
Wilson
,
G. R.
Addie
,
A.
Sellgren
et al,
Slurry Transport Using Centrifugal Pumps
(
Springer Science and Business Media
,
2006
).
81.
P.
Doron
and
D.
Barnea
, “
Flow pattern maps for solid-liquid flow in pipes
,”
Int. J. Multiphase Flow
22
(
2
),
273
283
(
1996
).
82.
T.
Maruyama
,
K.
Kojima
, and
T.
Mizushina
, “
The flow structure of slurries in horizontal pipes
,”
J. Chem. Eng. Jpn.
12
(
3
),
177
182
(
1979
).
83.
B.
Bbosa
,
E.
Dellecase
,
M.
Volk
et al, “
A comprehensive deposition velocity model for slurry transport in horizontal pipelines
,”
J. Pet. Explor. Prod. Technol.
7
(
1
),
303
310
(
2017
).
84.
K.
Li
,
High-Precision Extraction of Electrical Impedance Tomography Objects and Three-Dimensional Visualisation of Two-Phase Flow
(
North University of China
,
Taiyuan, Shanxi
,
2019
).
85.
K.
Li
,
M.
Wang
, and
Y.
Han
, “
Visualization of horizontal settling slurry flow using electrical resistance tomography
,” in
Proceedings of the International Conference on Sensing and Imaging
(
Springer International Publishing
,
Liuzhou, China
,
2019
), pp.
65
75
.
86.
K.
Ekambara
,
R. S.
Sanders
,
K.
Nandakumar
et al, “
Hydrodynamic simulation of horizontal slurry pipeline flow using ANSYS-CFX
,”
Ind. Eng. Chem. Res.
48
(
17
),
8159
8171
(
2009
).
87.
V. C.
Kelessidis
,
G. E.
Bandelis
, and
J.
Li
, “
Flow of dilute solid-liquid mixtures in horizontal concentric and eccentric annuli
,”
J. Can. Pet. Technol.
46
(
5
),
56
61
(
2007
).
88.
Y. H.
Song
,
J. G.
Joo
,
J. H.
Lee
et al, “
Numerical assessment of shear boundary layer formation in sewer systems with fluid-sediment phases
,”
Water
12
(
5
),
1332
(
2020
).
89.
G. V.
Messa
and
S.
Malavasi
, “
Improvements in the numerical prediction of fully-suspended slurry flow in horizontal pipes
,”
Powder Technol.
270
,
358
367
(
2015
).
90.
D.
Eskin
, “
A simple model of particle diffusivity in horizontal hydrotransport pipelines
,”
Chem. Eng. Sci.
82
,
84
94
(
2012
).
91.
S. A.
Hashemi
,
A.
Sadighian
,
S. I. A.
Shah
et al, “
Solid velocity and concentration fluctuations in highly concentrated liquid–solid (slurry) pipe flows
,”
Int. J. Multiphase Flow
66
,
46
61
(
2014
).
92.
Y.
Yang
,
H.
Peng
, and
C.
Wen
, “
Sand transport and deposition behaviour in subsea pipelines for flow assurance
,”
Energies
12
(
21
),
4070
(
2019
).
93.
R.
Giguère
,
L.
Fradette
,
D.
Mignon
et al, “
Analysis of slurry flow regimes downstream of a pipe bend
,”
Chem. Eng. Res. Des.
87
(
7
),
943
950
(
2009
).
94.
R. C.
Chen
, “
Analysis of homogeneous slurry pipe flow
,”
J. Mar. Sci. Technol.
2
(
1
),
37
54
(
1994
).
95.
G. V.
Messa
and
V.
Matoušek
, “
Analysis and discussion of two fluid modelling of pipe flow of fully suspended slurry
,”
Powder Technol.
360
,
747
768
(
2020
).
96.
X.
Ting
,
Z.
Xinzhuo
,
S. A.
Miedema
et al, “
Study of the characteristics of the flow regimes and dynamics of coarse particles in pipeline transportation
,”
Powder Technol.
347
,
148
158
(
2019
).
97.
H.
Zhang
,
F.
Dong
, and
C.
Tan
, “
Liquid–solid two-phase flow rate measurement by electrical and ultrasound Doppler sensors
,”
IEEE Trans. Instrum. Meas.
71
,
1
9
(
2022
).
98.
J.
Capecelatro
and
O.
Desjardins
, “
Eulerian–Lagrangian modeling of turbulent liquid–solid slurries in horizontal pipes
,”
Int. J. Multiphase Flow
55
,
64
79
(
2013
).
99.
S. K.
Arolla
and
O.
Desjardins
, “
Transport modeling of sedimenting particles in a turbulent pipe flow using Euler-Lagrange large eddy simulation
,”
Int. J. Multiphase Flow
75
,
1
11
(
2015
).
100.
P. V.
Skudarnov
,
C. X.
Lin
, and
M. A.
Ebadian
, “
Double-species slurry flow in a horizontal pipeline
,”
J. Fluids Eng.
126
(
1
),
125
132
(
2004
).
101.
C. S.
Campbell
,
F.
Avila-Segura
, and
Z.
Liu
, “
Preliminary observations of a particle lift force in horizontal slurry flow
,”
Int. J. Multiphase Flow
30
(
2
),
199
216
(
2004
).
102.
A. P.
Poloski
,
M. L.
Bonebrake
,
A. M.
Casella
et al, “
Deposition velocities of non-Newtonian slurries in pipelines: Complex simulant testing
,” Report No. PNNL-18316 (
Pacific Northwest National Laboratory (PNNL)
,
Richland, WA
,
2009
).
103.
A. P.
Poloski
,
H. E.
Adkins
,
J.
Abrefah
et al, “
Deposition velocities of Newtonian and non-Newtonian slurries in pipelines
,” Report No. PNNL-17639 (
Pacific Northwest National Laboratory (PNNL)
,
Richland, WA
,
2009
).
104.
S. T.
Yokuda
,
A. P.
Poloski
,
H. E.
Adkins
et al, “
A qualitative investigation of deposition velocities of a non-Newtonian slurry in complex pipeline geometries
,” Report No. PNNL-17973 (
Pacific Northwest National Laboratory (PNNL)
,
Richland, WA
,
2009
).
105.
W.
Peng
,
X.
Cao
,
L.
Ma
et al, “
Sand erosion prediction models for two-phase flow pipe bends and their application in gas-liquid-solid multiphase flow erosion
,”
Powder Technol.
421
,
118421
(
2023
).
106.
Y.
Zhang
,
X.
Lu
, and
X.
Zhang
, “
Numerical simulation on transportation behavior of dense coarse particles in vertical pipe with an optimized Eulerian–Lagrangian method
,”
Phys. Fluids
34
(
3
),
033305
(
2022
).
107.
J.
Xu
,
Y.
Wu
,
Z.
Zheng
et al, “
Measurement of solid slurry flow via correlation of electromagnetic flow meter, electrical resistance tomography and mechanistic modelling
,”
J. Hydrodyn., Ser. B
21
(
4
),
557
563
(
2009
).
108.
R.
Shams
,
A.
Tavakoli
, and
S.
Shad
, “
Experimental investigation of two phase flow in horizontal wells: Flow regime assessment and pressure drop analysis
,”
Exp. Therm. Fluid Sci.
88
,
55
64
(
2017
).
109.
K.
Albion
,
L.
Briens
,
C.
Briens
et al, “
Flow regime determination in horizontal hydrotransport using non‐intrusive acoustic probes
,”
Can. J. Chem. Eng.
86
(
6
),
989
1000
(
2008
).
110.
L.
Wang
,
S.
Li
,
Y.
Yuan
et al, “
Measurement of flow rate in solid-liquid two-phase flow in pipes at low volume concentration with venturimeter
,”
Measurement
138
,
409
415
(
2019
).
111.
F.
Ravelet
,
F.
Bakir
,
S.
Khelladi
et al, “
Experimental study of hydraulic transport of large particles in horizontal pipes
,”
Exp. Therm. Fluid Sci.
45
,
187
197
(
2013
).
112.
K.
Albion
,
L.
Briens
,
C.
Briens
et al, “
Modelling of oversized material flow through a horizontal hydrotransport slurry pipe to optimize its acoustic detection
,”
Powder Technol.
194
(
1–2
),
18
32
(
2009
).
113.
P.
Zhang
,
Y.
Yang
,
J.
Sun
et al, “
Acoustic analysis of particle dispersion state and prediction of solid concentration in horizontal hydraulic conveying
,”
Chem. Eng. Sci.
245
,
116973
(
2021
).
114.
P.
Zhang
,
S.
Tian
,
Y.
Yang
et al, “
Flow regime identification in horizontal pneumatic conveying by nonintrusive acoustic emission detection
,”
AIChE J.
65
(
5
),
e16552
(
2019
).
115.
V.
Matousek
, “
Pressure drops and flow patterns in sand-mixture pipes
,”
Exp. Therm. Fluid Sci.
26
(
6–7
),
693
702
(
2002
).
116.
V.
Matousek
, “
Concentration profiles and solids transport above stationary deposit in enclosed conduit
,”
J. Hydraul. Eng.
135
(
12
),
1101
1106
(
2009
).
117.
R.
Giguere
,
L.
Fradette
,
D.
Mignon
et al, “
Characterization of slurry flow regime transitions by ERT
,”
Chem. Eng. Res. Des.
86
(
9
),
989
996
(
2008
).
118.
Y.
Faraj
,
M.
Wang
, and
J.
Jia
, “
Automated horizontal slurry flow regime recognition using statistical analysis of the ERT signal
,”
Proc. Eng.
102
,
821
830
(
2015
).
119.
R.
Kotzé
,
A.
Adler
,
A.
Sutherland
et al, “
Evaluation of electrical resistance tomography imaging algorithms to monitor settling slurry pipe flow
,”
Flow Meas. Instrum.
68
,
101572
(
2019
).
120.
R.
Silva
,
C.
Cotas
,
F. A. P.
Garcia
et al, “
Particle distribution studies in highly concentrated solid-liquid flows in pipe using the mixture model
,”
Proc. Eng.
102
,
1016
1025
(
2015
).
121.
A.
Bordet
,
S.
Poncet
,
M.
Poirier
et al, “
Flow visualizations and pressure drop measurements of isothermal ice slurry pipe flows
,”
Exp. Therm. Fluid Sci.
99
,
595
604
(
2018
).
122.
H.
Takahashi
,
T.
Masuyama
, and
K.
Noda
, “
Unstable flow of a solid-liquid mixture in a horizontal pipe
,”
Int. J. Multiphase Flow
15
(
5
),
831
(
1989
).
123.
Y.
Cao
,
J.
Wang
, and
Y.
Yang
, “
Multi-scale analysis of acoustic emissions and measurement of particle mass flowrate in pipeline
,”
J. Chem. Ind. Eng. (China)
58
(
6
),
1404
1410
(
2007
).
124.
C.
Ren
,
X.
Jiang
,
J.
Wang
et al, “
Determination of critical speed for complete solid suspension using acoustic emission method based on multiscale analysis in stirred tank
,”
Ind. Eng. Chem. Res.
47
(
15
),
5323
5327
(
2008
).
125.
C.
Ren
,
J.
Wang
,
X.
Zhang
et al, “
Measurement of slurry suspension height in stirred tank by multi-scale analysis of acoustic emission technology
,”
J. Chem. Ind. Eng. (China)
59
(
6
),
1383
1389
(
2008
).
126.
C.
Huang
,
X.
Cai
, and
M.
Su
, “
Acoustic emission for particle size distribution measurement based on Hertz-Zener theory
,”
J. Chem. Ind. Eng. (China)
64
(
4
),
1191
1197
(
2013
).
127.
R.
Hou
,
A.
Hunt
, and
R. A.
Williams
, “
Acoustic monitoring of pipeline flows: Particulate slurries
,”
Powder Technol.
106
(
1–2
),
30
36
(
1999
).
128.
M.
Mahmud
,
Y.
Faraj
, and
M.
Wang
, “
Visualisation and metering of two phase counter-gravity slurry flow using ERT
,”
Proc. Eng.
102
,
930
935
(
2015
).
129.
S.
Lotfiman
,
S.
Bhattacharya
, and
R.
Parthasarathy
, “
A novel approach for measuring particle settling and settled bed build-up velocities in concentrated slurries using electrical resistance tomography
,”
Powder Technol.
411
,
117938
(
2022
).
130.
J.
Krupicka
and
V.
Matousek
, “
Gamma-ray-based measurement of concentration distribution in pipe flow of settling slurry: Vertical profiles and tomographic maps
,”
J. Hydrol. Hydromech.
62
(
2
),
126
(
2014
).
131.
M.
Elkarii
,
R.
Boukharfane
,
S.
Benjelloun
et al, “
Global sensitivity analysis for phosphate slurry flow in pipelines using generalized polynomial chaos
,”
Phys. Fluids
35
(
6
),
063323
(
2023
).
132.
J.
Ling
,
P. V.
Skudarnov
,
C. X.
Lin
et al, “
Numerical investigations of liquid–solid slurry flows in a fully developed turbulent flow region
,”
Int. J. Heat Fluid Flow
24
(
3
),
389
398
(
2003
).
133.
D. R.
Kaushal
,
T.
Thinglas
,
Y.
Tomita
et al, “
CFD modeling for pipeline flow of fine particles at high concentration
,”
Int. J. Multiphase Flow
43
,
85
100
(
2012
).
134.
M. K.
Gopaliya
and
D. R.
Kaushal
, “
Analysis of effect of grain size on various parameters of slurry flow through pipeline using CFD
,”
Part. Sci. Technol.
33
(
4
),
369
384
(
2015
).
135.
D. R.
Kaushal
,
A.
Kumar
,
Y.
Tomita
et al, “
Flow of bi-modal slurry through horizontal bend
,”
KONA Powder Part. J.
34
,
258
274
(
2017
).
136.
R.
Ohlan
,
M. K.
Gopaliya
, and
D. R.
Kaushal
, “
Simulation of sand-water slurry flows through pipeline
,”
Multiphase Sci. Technol.
30
(
4
),
293
(
2018
).
137.
G. V.
Messa
,
M.
Malin
, and
S.
Malavasi
, “
Numerical prediction of fully-suspended slurry flow in horizontal pipes
,”
Powder Technol.
256
,
61
70
(
2014
).
138.
W.
Liu
,
Y.
He
,
M.
Li
et al, “
Effect of specularity coefficient on hydrodynamic behaviors of slurry flows in horizontal pipes
,”
Ocean Eng.
246
,
110617
(
2022
).
139.
W.
Liu
,
Y.
He
,
M.
Li
et al, “
Effect of drag models on hydrodynamic behaviors of slurry flows in horizontal pipes
,”
Phys. Fluids
34
(
10
),
103311
(
2022
).
140.
O.
Visuri
,
M.
Liiri
, and
V.
Alopaeus
, “
Comparison and validation of CFD models in liquid–solid suspensions
,”
Can. J. Chem. Eng.
89
(
4
),
696
706
(
2011
).
141.
T.
Joshi
,
O.
Parkash
, and
G.
Krishan
, “
Estimation of energy consumption and transportation characteristics for slurry flow through a horizontal straight pipe using computational fluid dynamics
,”
Phys. Fluids
35
(
5
),
053303
(
2023
).
142.
D. O.
Njobuenwu
and
M.
Fairweather
, “
Simulation of deterministic energy-balance particle agglomeration in turbulent liquid-solid flows
,”
Phys. Fluids
29
(
8
),
083301
(
2017
).
143.
M.
Zhou
,
S.
Kuang
,
K.
Luo
et al, “
Modeling and analysis of flow regimes in hydraulic conveying of coarse particles
,”
Powder Technol.
373
,
543
554
(
2020
).
144.
A.
Uzi
and
A.
Levy
, “
Flow characteristics of coarse particles in horizontal hydraulic conveying
,”
Powder Technol.
326
,
302
321
(
2018
).
145.
C.
Wan
,
S.
Xiao
,
D.
Zhou
et al, “
Numerical simulation on transport behavior of gradated coarse particles in deep-sea vertical pipe transportation
,”
Phys. Fluids
35
(
4
),
043328
(
2023
).
146.
Q.
Chen
,
T.
Xiong
,
X.
Zhang
et al, “
Study of the hydraulic transport of non-spherical particles in a pipeline based on the CFD-DEM
,”
Eng. Appl. Comput. Fluid Mech.
14
(
1
),
53
69
(
2020
).
147.
J. R.
Januário
and
C.
Maia
, “
CFD-DEM simulation to predict the critical velocity of slurry flows
,”
J. Appl. Fluid Mech.
13
(
1
),
161
168
(
2020
).
148.
F.
Tian
,
E.
Zhang
,
C.
Yang
et al, “
Research on the characteristics of the solid–liquid two-phase flow field of a submersible mixer based on CFD-DEM
,”
Energies
15
(
16
),
6096
(
2022
).
149.
L.
Yao
,
Y.
Liu
,
J.
Liu
et al, “
An optimized CFD-DEM method for particle collision and retention analysis of two-phase flow in a reduced-diameter pipe
,”
Powder Technol.
405
,
117547
(
2022
).
150.
L. B.
Lucy
, “
A numerical approach to the testing of the fission hypothesis
,”
Astron. J.
82
,
1013
1024
(
1977
).
151.
R. A.
Gingold
and
J. J.
Monaghan
, “
Smoothed particle hydrodynamics: Theory and application to non-spherical stars
,”
Mon. Not. R. Astron. Soc.
181
(
3
),
375
389
(
1977
).
152.
Z. B.
Wang
,
R.
Chen
,
H.
Wang
et al, “
An overview of smoothed particle hydrodynamics for simulating multiphase flow
,”
Appl. Math. Modell.
40
(
23–24
),
9625
9655
(
2016
).
153.
I.
Hammani
,
S.
Marrone
,
A.
Colagrossi
et al, “
Detailed study on the extension of the δ-SPH model to multi-phase flow
,”
Comput. Methods Appl. Mech. Eng.
368
,
113189
(
2020
).
154.
F.
Chen
,
H.
Li
,
Y.
Gao
et al, “
Two-particle method for liquid–solid two-phase mixed flow
,”
Phys. Fluids
35
(
3
),
033317
(
2023
).
155.
X.
Lian
,
C.
Savari
,
K.
Li
et al, “
Coupled smoothed particle hydrodynamics and discrete element method for simulating coarse food particles in a non-Newtonian conveying fluid
,”
Phys. Fluids
35
(
4
),
043325
(
2023
).
156.
A. V.
Potapov
,
M. L.
Hunt
, and
C. S.
Campbell
, “
Liquid–solid flows using smoothed particle hydrodynamics and the discrete element method
,”
Powder Technol.
116
(
2–3
),
204
213
(
2001
).
157.
M.
Robinson
,
M.
Ramaioli
, and
S.
Luding
, “
Fluid–particle flow simulations using two-way-coupled mesoscale SPH–DEM and validation
,”
Int. J. Multiphase Flow
59
,
121
134
(
2014
).
158.
T.
Douillet-Grellier
,
F.
De Vuyst
,
H.
Calandra
et al, “
Simulations of intermittent two-phase flows in pipes using smoothed particle hydrodynamics
,”
Comput. Fluids
177
,
101
122
(
2018
).
159.
R.
Vacondio
,
C.
Altomare
,
M.
De Leffe
et al, “
Grand challenges for smoothed particle hydrodynamics numerical schemes
,”
Comput. Part. Mech.
8
,
575
588
(
2021
).
160.
S. K.
Lahiri
and
K. C.
Ghanta
, “
A support vector classification method for regime identification of slurry transport in pipelines
,”
Hydrocarbon Process.
88
(
8
),
71
84
(
2009
).
161.
S. K.
Lahiri
and
K. C.
Ghanta
, “
Development of a hybrid support vector machine and genetic algorithm model for regime identification of slurry transport in pipelines
,”
Asia‐Pac. J. Chem. Eng.
5
(
6
),
847
861
(
2010
).
162.
S. K.
Lahiri
and
K. C.
Ghanta
, “
Regime identification of slurry transport in pipelines: A novel modelling approach using ANN and differential evolution
,”
Chem. Ind. Chem. Eng. Q.
16
(
4
),
329
343
(
2010
).
163.
S. K.
Lahiri
and
K. C.
Ghanta
, “
Artificial neural network model with parameter tuning assisted by genetic algorithm technique: Study of critical velocity of slurry flow in pipeline
,”
Asia-Pac. J. Chem. Eng.
5
(
5
),
763
777
(
2009
).
164.
X.
Ma
,
Y.
Duan
,
M.
Liu
et al, “
Prediction of pressure drop of coke water slurry flowing in pipeline by PSO-BP neural network
,”
Proc. CSEE
32
(
5
),
54
60
(
2012
).
165.
K. C.
Ghanta
and
S.
Das
, “
Neural networks based modeling of viscosity for facilitating transportation of magnetite ore-water slurry
,”
J. Assoc. Eng. India
83
(
2
),
43
54
(
2013
).
166.
W.
Zhong
,
A.
Yu
,
X.
Liu
et al, “
DEM/CFD-DEM modelling of non-spherical particulate systems: Theoretical developments and applications
,”
Powder Technol.
302
,
108
152
(
2016
).
167.
S.
Ji
,
S.
Wang
, and
Z.
Zhou
, “
Influence of particle shape on mixing rate in rotating drums based on super-quadric DEM simulations
,”
Adv. Powder Technol.
31
(
8
),
3540
3550
(
2020
).
168.
D. G.
Thomas
, “
Transport characteristics of suspensions. VI. Minimum transport velocity for large particle size suspensions in round horizontal pipes
,”
AIChE J.
8
(
3
),
373
378
(
1962
).
169.
R.
Durand
, “
The hydraulic transportation of coal and solid materials in pipes
,” in
Proceedings of the Colloquium on Hydraulic Transportation
, France (National Coal Board,
1952
), pp.
39
52
.
170.
W. H.
Graf
, “
The critical deposit velocity for solid-liquid mixtures
,” in
Proceedings of the First International Conference on the Hydraulic Transport of Solids in Pipes
(
BHRA Fluid Engineering
,
Cranfield, UK
,
1970
).
171.
I.
Larsen
and
D. I. H.
Barr
, “
Discussion of “heterogeneous flow of solids in pipelines
,”
J. Hydraul. Div.
94
(
1
),
332
336
(
1968
).
172.
C. A.
Shook
, “
Pipelining solids: The design of short-distance pipelines
,” in
Proceedings of the Symposium on Pipeline Transport of Solids
(
1969
).
173.
A. G.
Bain
and
S. T.
Bonnington
,
The Hydraulic Transport of Solids by Pipelines
(
Pergamon Press Ltd.
,
New York
,
1970
).
174.
H. A.
Babcock
, “
Heterogeneous flow of heterogeneous solids
,”
Advances in Solid Liquid Flow in Pipes and its Applications
(Elsevier,
1971
), pp.
125
148
.
175.
K. C.
Wilson
and
G.
Judge
, “
New techniques for the scale-up of pilot plant results to coal slurry pipelines
,” in
Proceedings of the International Symposium on Freight Pipelines
, Washington D.C. (
University of Pennsylvania
,
Philadelphia
,
1976
).
176.
M.
Gogus
,
M. A.
Kokpinar
,
M.
Gogus
et al, “
Determination of critical flow velocity in slurry transporting pipeline systems
,” in
Proceedings of the 12th International Conference on Slurry Handling and Pipeline Transport
(
British Hydraulic Research Group
,
Bedfordshire, UK
,
1993
), pp.
743
757
.
177.
M. A.
Kökpinar
and
M.
Gögüs
, “
Critical flow velocity in slurry transporting horizontal pipelines
,”
J. Hydraul. Eng.
127
(
9
),
763
771
(
2001
).
178.
F. M.
Hepy
,
Z.
Ahmad
, and
M. L.
Kansal
, “
Critical velocity for slurry transport through pipeline
,”
Dam Eng.
19
(
3
),
169
184
(
2008
).
179.
M. P.
Robinson
and
W. H.
Graf
, “
Pipelining of low-concentration sand-water mixtures
,”
J. Hydraul. Div.
98
(
7
),
1221
1241
(
1972
).
180.
E. J.
Wasp
,
J. P.
Kenny
, and
R. L.
Gandhi
,
Solid-Liquid Flow Slurry Pipeline Transportation
(
Trans Tech Publications
,
San Francisco
,
1977
).
181.
R. M.
Turian
,
F. L.
Hsu
, and
T. W.
Ma
, “
Estimation of the critical velocity in pipeline flow of slurries
,”
Powder Technol.
51
(
1
),
35
47
(
1987
).
182.
W.
Wiendenroth
, “
Researches on the conveying of solid-liquid mixtures through pipelines and centrifugal pumps
,” Ph.D. dissertation (
Technische Hochschule Honnover
,
1967
).
183.
A. D.
Thomas
, “
Predicting the deposit velocity for horizontal turbulent pipe flow of slurries
,”
Int. J. Multiphase Flow
5
(
2
),
113
129
(
1979
).
184.
A. R.
Oroskar
and
R. M.
Turian
, “
The critical velocity in pipeline flow of slurries
,”
AIChE J.
26
(
4
),
550
558
(
1980
).
185.
H. M.
Azamathulla
and
Z.
Ahmad
, “
Estimation of critical velocity for slurry transport through pipeline using adaptive neuro-fuzzy interference system and gene-expression programming
,”
J. Pipeline Syst. Eng. Pract.
4
(
2
),
131
137
(
2013
).
186.
S.
Sayari
,
A.
Mahdavi-Meymand
, and
M.
Zounemat-Kermani
, “
Prediction of critical velocity in pipeline flow of slurries using TLBO algorithm: A comprehensive study
,”
J. Pipeline Syst. Eng. Pract.
11
(
2
),
04019057
(
2020
).
187.
X.
Zhang
and
K.
He
, “
Prediction of critical velocity of long distance slurry pipeline based on SSA-CNN
,”
J. Saf. Environ.
22
(
05
),
2524
2531
(
2022
).
188.
J.
Fei
,
Hydraulics of Slurry and Granular Material Transportation
(
Tsinghua University Press
,
1994
).
189.
N.
Yotsukura
, “
Some effects of bentonite suspensions on sand transport in a smooth 4-inch pipe
,” Ph.D. dissertation (
Colorado State University, Fort Collins, CO
,
1961
).
190.
W. H.
Graf
, “
Critical velocity for solid-liquid mixtures: The Lehigh experiments
,” Ph.D. dissertation (
Lehigh University
,
Bethlehem, PA
,
1970
).
191.
I.
Avci
, “
Experimentally determination of critical flow velocity in sediment carrying pipeline systems
,” Ph.D. dissertation (
Istanbul Technical University
,
Istanbul, Turkey
,
1981
).
192.
S.
Zhang
, “
Research on numerical calculation method for deposit velocity in slurry pipeline
,”
Hydraul. Coal Min. Pipeline Transport
4
(
04
),
6
9
(
2011
).
193.
P. P.
Brown
and
D. F.
Lawler
, “
Sphere drag and settling velocity revisited
,”
J. Environ. Eng.
129
(
3
),
222
231
(
2003
).
194.
Y.
Mu
,
X.
Liu
, and
L.
Wang
, “
A Pearson's correlation coefficient based decision tree and its parallel implementation
,”
Inf. Sci.
435
,
40
58
(
2018
).
195.
B.
Everitt
and
T.
Hothorn
,
An Introduction to Applied Multivariate Analysis with R
(
Springer Science and Business Media
,
2011
).
196.
R. S.
Witte
and
J. S.
Witte
,
Statistics
(
John Wiley and Sons
,
2017
).
You do not currently have access to this content.