This study analyses the flow of Taylor bubbles through vertical and inclined annular pipes using high-fidelity numerical modeling. A recently developed phase-field lattice Boltzmann method is employed for the investigation. This approach resolves the two-phase flow behavior by coupling the conservative Allen–Cahn equation to the Navier–Stokes hydrodynamics. This paper makes contributions in three fundamental areas relating to the flow of Taylor bubbles. First, the model is used to determine the relationship between the dimensionless parameters (Eötvös and Morton numbers) and the bubble rise velocity (Froude number). There currently exists no surrogate model for the rise of a Taylor bubble in an annular pipe that accounts for fluid properties. Instead, relations generally include the diameter of the outer and inner pipes only. This study covered Eötvös numbers between 10 and 700 and Morton numbers between 10−6 and 100. As such, the proposed correlation is applicable to concentric annular pipes within this range of parameters. An assessment of the correlation to parameters outside of this range was made; however, this was not the primary scope for the investigation. Following this, the effect of pipe inclination was introduced with the impact on rise velocity measured. A correlation between the inclination angle and the rise velocity was proposed and its performance quantified against the limited experimental data available. Finally, the high-fidelity numerical results were analyzed to provide key insights into the physical mechanisms associated with annular Taylor bubbles and the shape they form. To extend this work, future studies on the effect of pipe eccentricity, diameter ratios, and pipe fittings (e.g., elbows and risers) on the flow of Taylor bubbles will be conducted.
REFERENCES
1.
T.
Mandal
, G.
Das
, and P.
Das
, “Prediction of rise velocity of a liquid Taylor bubble in a vertical tube
,” Phys. Fluids
19
(12
), 128109
(2007
).2.
B.
Wu
, M.
Firouzi
, T.
Mitchell
, T.
Rufford
, C.
Leonardi
, and B.
Towler
, “A critical review of flow maps for gas-liquid flows in vertical pipes and annuli
,” Chem. Eng. Sci.
326
, 350
–377
(2017
).3.
X.
Lu
, A.
Watson
, A. V.
Gorin
, and J.
Deans
, “Measurements in a low temperature CO2-driven geysering well, viewed in relation to natural geysers
,” Geothermics
34
(4
), 389
–410
(2005
).4.
G.
Zhou
and A.
Prosperetti
, “Violent expansion of a rising Taylor bubble
,” Phys. Rev. Fluids
4
(7
), 073903
(2019
).5.
E.
Gutiérrez
, N.
Balcázar
, E.
Bartrons
, and J.
Rigola
, “Numerical study of Taylor bubbles rising in a stagnant liquid using a level-set/moving-mesh method
,” Chem. Eng. Sci.
164
, 158
–177
(2017
).6.
V.
Hernandez-Perez
, L.
Abdulkareem
, and B.
Azzopardi
, “Effects of physical properties on the behaviour of Taylor bubbles
,” Comput. Methods Multiphase Flow
63
, 355
–366
(2009
).7.
C. J.
Falconi
, C.
Lehrenfeld
, H.
Marschall
, C.
Meyer
, R.
Abiev
, D.
Bothe
, A.
Reusken
, M.
Schlüter
, and M.
Wörner
, “Numerical and experimental analysis of local flow phenomena in laminar Taylor flow in a square mini-channel
,” Phys. Fluids
28
(1
), 012109
(2016
).8.
E.
Lizarraga-Garcia
, J.
Buongiorno
, and M.
Bucci
, “An analytical film drainage model and breakup criterion for Taylor bubbles in slug flow in inclined round pipes
,” Int. J. Multiphase Flow
84
, 46
–53
(2016
).9.
E.
Lizarraga-Garcia
, J.
Buongiorno
, E.
Al-Safran
, and D.
Lakehal
, “A broadly-applicable unified closure relation for Taylor bubble rise velocity in pipes with stagnant liquid
,” Int. J. Multiphase Flow
89
, 345
–358
(2017
).10.
E.
Massoud
, Q.
Xiao
, and H.
El-Gamal
, “Numerical study of an individual Taylor bubble drifting through stagnant liquid in an inclined pipe
,” Ocean Eng.
195
, 106648
(2020
).11.
L.
Rohilla
and A.
Das
, “On transformation of a Taylor bubble to an asymmetric sectorial wrap in an annuli
,” Ind. Eng. Chem. Res.
56
, 14384
–14395
(2017
).12.
L.
Rohilla
and A.
Das
, “Experimental study on the interfacial evolution of Taylor bubble at inception of an annulus
,” Ind. Eng. Chem. Res.
58
, 2356
–2369
(2019
).13.
B.
Towler
, M.
Firouzi
, J.
Underschultz
, W.
Rifkin
, A.
Garnett
, H.
Schultz
, J.
Esterle
, S.
Tyson
, and K.
Witt
, “An overview of the coal seam gas developments in Queensland
,” J. Nat. Gas Sci. Eng.
31
, 249
–271
(2016
).14.
M.
Carrizales
, J.
Jaramillo
, and D.
Fuentes
, “Prediction of multiphase flow in pipelines: Literature review
,” Ing. Cienc.
11
, 213
–233
(2015
).15.
V.
Pugliese
, E.
Panacharoensawad
, and A.
Ettehadtavakkol
, “Numerical study of the motion of a single elongated bubble in high viscosity stagnant liquids along pipelines
,” J. Pet. Sci. Eng.
190
, 107088
(2020
).16.
F.
Viana
, R.
Pardo
, R.
Yánez
, J.
Trallero
, and D.
Joseph
, “Universal correlation for the rise velocity of long gas bubbles in round pipes
,” J. Fluid Mech.
494
, 379
–398
(2003
).17.
J.
Moreiras
, E.
Pereyra
, C.
Sarica
, and C.
Torres
, “Unified drift velocity closure relationship for large bubbles rising in stagnant viscous fluids in pipes
,” J. Pet. Sci. Eng.
124
, 359
–366
(2014
).18.
M.
Firouzi
, B.
Towler
, and T.
Rufford
, “Developing new mechanistic models for predicting pressure gradient in coal bed methane wells
,” J. Nat. Gas Sci. Eng.
33
, 961
–972
(2016
).19.
X.
Lu
and A.
Prosperetti
, “A numerical study of Taylor bubbles
,” Ind. Eng. Chem. Res.
48
, 242
–252
(2009
).20.
Z.
Mao
and A.
Dukler
, “The motion of Taylor bubbles in vertical tubes. I. A numerical simulation for the shape and rise velocity of Taylor bubbles in stagnant and flowing liquid
,” J. Comput. Phys.
91
, 132
–160
(1990
).21.
C.
Hirt
and B.
Nichols
, “Volume of fluid (VOF) method for the dynamics of free boundaries
,” J. Comput. Phys.
39
(1
), 201
–225
(1981
).22.
S.
Osher
and J.
Sethian
, “Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations
,” J. Comput. Phys.
79
(1
), 12
–49
(1988
).23.
J.
Bugg
, K.
Mack
, and K.
Rezkallah
, “A numerical model of Taylor bubbles rising through stagnant liquids in vertical tubes
,” Int. J. Multiphase Flow
24
(2
), 271
–281
(1998
).24.
T.
Taha
and Z.
Cui
, “CFD modelling of slug flow inside square capillaries
,” Chem. Eng. Sci.
61
, 665
–675
(2006
).25.
E.
Massoud
, Q.
Xiao
, H.
El-Gamal
, and M.
Teamah
, “Numerical study of an individual Taylor bubble rising through stagnant liquids under laminar flow regime
,” Ocean Eng.
162
, 117
–137
(2018
).26.
T.
Mitchell
, C.
Leonardi
, M.
Firouzi
, and B.
Towler
, “Towards closure relations for the rise velocity of Taylor bubbles in annular piping using phase-field lattice Boltzmann techniques
,” in Proceedings of the 21st Australasian Fluid Mechanics Conference, AFMC 2018
(Australasian Fluid Mechanics Society
, 2018
), p. 591
.27.
T.
Mitchell
, B.
Hill
, M.
Firouzi
, and C.
Leonardi
, “Development and evaluation of multiphase closure models used in the simulation of unconventional wellbore dynamics
,” in Unconventional Resources Technology Conference
(Society of Petroleum Engineers
, 2019
), p. 198239
.28.
T.
Mitchell
and C.
Leonardi
, “On the rise characteristics of Taylor bubbles in annular piping
,” Int. J. Multiphase Flow
(published online 2020
).29.
G.
Das
, P.
Das
, N.
Purohit
, and A.
Mitra
, “Rise velocity of a Taylor bubble through concentric annulus
,” Chem. Eng. J.
53
(5
), 977
–993
(1998
).30.
H.
Gouidmi
, R.
Benderradji
, A.
Beghidja
, and T.
Tayebi
, “Numerical study of upward vertical two-phase flow through an annulus concentric pipe
,” J. Adv. Res. Fluid Mech. Therm. Sci.
58
(2
), 187
–206
(2019
).31.
C.
Friedemann
, M.
Mortensen
, and J.
Nossen
, “Gas-liquid slug flow in a horizontal concentric annulus, a comparison of numerical simulations and experimental data
,” Int. J. Heat Fluid Flow
78
, 108437
(2019
).32.
C.
Friedemann
, M.
Mortensen
, and J.
Nossen
, “Two-phase flow simulations at 0−4° inclination in an eccentric annulus
,” Int. J. Heat Fluid Flow
83
, 108586
(2020
).33.
E.
Caetano
, O.
Shoham
, and J.
Brill
, “Upward vertical two-phase flow through an annulus. Part II: Modeling bubble, slug, and annular flow
,” J. Energy Res. Technol.
114
, 14
–30
(1991
).34.
T.
Mitchell
, C.
Leonardi
, and A.
Fakhari
, “Development of a three-dimensional phase-field lattice Boltzmann method for the study of immiscible fluids at high density ratios
,” Int. J. Multiphase Flow
107
, 1
–15
(2018
).35.
A.
Fakhari
, T.
Mitchell
, C.
Leonardi
, and D.
Bolster
, “Improved locality of the phase-field lattice-Boltzmann model for immiscible fluids at high density ratios
,” Phys. Rev. E
96
(5
), 053301
(2017
).36.
S.
Mirjalili
, S.
Jain
, and M.
Dodd
, “Interface-capturing methods for two-phase flows: An overview and recent developments
,” in Annual Research Briefs
(Center for Turbulence Research
, 2017
), pp. 117
–135
.37.
E.
Dinesh Kumar
, S. A.
Sannasiraj
, and V.
Sundar
, “Phase field lattice Boltzmann model for air-water two phase flows
,” Phys. Fluids
31
(7
), 072103
(2019
).38.
M.
Geier
, A.
Fakhari
, and T.
Lee
, “Conservative phase-field lattice Boltzmann model for interface tracking equation
,” Phys. Rev. E
91
, 063309
(2015
).39.
Y.
Sun
and C.
Beckermann
, “Sharp interface tracking using the phase-field equation
,” J. Comput. Phys.
220
(2
), 626
–653
(2007
).40.
P.
Chiu
and Y.
Lin
, “A conservative phase field method for solving incompressible two-phase flows
,” J. Comput. Phys.
230
, 185
–204
(2011
).41.
D.
D’Humières
, I.
Ginzburg
, M.
Krafczyk
, P.
Lallemand
, and L.-S.
Luo
, “Multiple–relaxation–time lattice Boltzmann models in three dimensions
,” Philos. Trans. R. Soc., A
360
(1792
), 437
–451
(2002
).42.
P. J.
Dellar
, “Incompressible limits of lattice Boltzmann equations using multiple relaxation times
,” J. Comput. Phys.
190
(2
), 351
–370
(2003
).43.
A.
Fakhari
and M.
Rahimian
, “Phase-field modeling by the method of lattice Boltzmann equations
,” Phys. Rev. E
81
, 036707
(2010
).44.
S.
Kim
and H.
Pitsch
, “On the lattice Boltzmann method for multiphase flows
,” in Annual Research Briefs
(Center for Turbulence Research
, 2009
).45.
D.
Jacqmin
, “Contact-line dynamics of a diffuse fluid interface
,” J. Fluid Mech.
402
, 57
–88
(2000
).46.
A.
Hasan
and C.
Kabir
, “Two-phase flow in vertical and inclined annuli
,” Int. J. Multiphase Flow
18
(2
), 279
–293
(1992
).47.
B.
Wu
, A.
Ribeiro
, M.
Firouzi
, T.
Rufford
, and B.
Towler
, “Use of pressure signal analysis to characterise counter-current two-phase flow regimes in annuli
,” Chem. Eng. Res. Des.
153
, 547
–561
(2020
).48.
V.
Kelessidis
and A.
Dukler
, “Motion of large gas bubbles through liquids in vertical concentric and eccentric annuli
,” Int. J. Multiphase Flow
16
(3
), 375
–390
(1990
).49.
P.
Griffith
, “The prediction of low-quality boiling voids
,” J. Heat Transfer
86
, 327
–333
(1964
).50.
M.
Sadatomi
, Y.
Sato
, and S.
Saruwatari
, “Two-phase flow in vertical noncircular channels
,” Int. J. Multiphase Flow
8
(6
), 641
–655
(1982
).51.
D.
Rader
, A.
Bourgoyne
, and R.
Ward
, “Factors affecting bubble-rise velocity of gas kicks
,” J. Pet. Technol.
27
(5
), SPE–4647–PA
(1975
).52.
A.
Hasan
and C.
Kabir
, “Predicting multiphase flow behavior in a deviated well
,” SPE Prod. Eng.
3
, SPE–15449–PA
(1988
).53.
K.
Bendiksen
, “An experimental investigation of the motion of long bubbles in inclined tubes
,” Int. J. Multiphase Flow
10
(4
), 467
–483
(1984
).54.
R.
Ibarra
and J.
Nossen
, “Bubble velocity in horizontal and low-inclination upward slug flow in concentric and fully eccentric annuli
,” Chem. Eng. Sci.
192
, 774
–787
(2018
).55.
R.
Ibarra
, J.
Nossen
, and M.
Tutkun
, “Holdup and frequency characteristics of slug flow in concentric and fully eccentric annuli pipes
,” J. Pet. Sci. Eng.
182
, 106256
(2019
).56.
R.
Ibarra
, J.
Nossen
, and M.
Tutkun
, “Two-phase gas-liquid flow in concentric and fully eccentric annuli. Part I: Flow patterns, holdup, slip ratio and pressure gradient
,” Chem. Eng. Sci.
203
, 489
–500
(2019
).57.
T.
Funada
, D.
Joseph
, T.
Maehara
, and S.
Yamashita
, “Ellipsoidal model of the rise of a Taylor bubble in a round tube
,” Int. J. Multiphase Flow
31
(4
), 473
–491
(2005
).58.
R.
Davies
and G.
Taylor
, “The mechanics of large bubbles rising through extended liquids and through liquids in tubes
,” Proc. R. Soc. London, Ser. A
200
(1062
), 375
–390
(1950
).59.
D.
Joseph
, “Rise velocity of a spherical cap bubble
,” J. Fluid Mech.
488
, 213
–223
(2003
).60.
61.
J.
Grace
and D.
Harrison
, “The influence of bubble shape on the rising velocities of large bubbles
,” Chem. Eng. Sci.
22
, 1337
–1347
(1967
).62.
V.
Agarwal
, A. K.
Jana
, G.
Das
, and P.
Das
, “Taylor bubbles in liquid filled annuli: Some new observations
,” Phys. Fluids
19
(10
), 108105
(2007
).© 2020 Author(s).
2020
Author(s)
You do not currently have access to this content.
