Pore-scale simulations of gas displacing liquid in a homogeneous pore network using the lattice Boltzmann method

Haihu Liu, Albert J. Valocchi, Qinjun Kang, Charles Werth

Research output: Contribution to journalArticle

62 Citations (Scopus)

Abstract

A lattice Boltzmann high-density-ratio model, which uses diffuse interface theory to describe the interfacial dynamics and was proposed originally by Lee and Liu (J Comput Phys 229:8045–8063, 2010), is extended to simulate immiscible multiphase flows in porous media. A wetting boundary treatment is proposed for concave and convex corners. The capability and accuracy of this model is first validated by simulations of equilibrium contact angle, injection of a non-wetting gas into two parallel capillary tubes, and dynamic capillary intrusion. The model is then used to simulate gas displacement of liquid in a homogenous two-dimensional pore network consisting of uniformly spaced square obstructions. The influence of capillary number (Ca), viscosity ratio ( M M ), surface wettability, and Bond number (Bo) is studied systematically. In the drainage displacement, we have identified three different regimes, namely stable displacement, capillary fingering, and viscous fingering, all of which are strongly dependent upon the capillary number, viscosity ratio, and Bond number. Gas saturation generally increases with an increase in capillary number at breakthrough, whereas a slight decrease occurs when Ca is increased from 8.66×10−4 8.66 × 10 - 4 to 4.33×10−3 4.33 × 10 - 3 , which is associated with the viscous instability at high Ca. Increasing the viscosity ratio can enhance stability during displacement, leading to an increase in gas saturation. In the two-dimensional phase diagram, our results show that the viscous fingering regime occupies a zone markedly different from those obtained in previous numerical and experimental studies. When the surface wettability is taken into account, the residual liquid blob decreases in size with the affinity of the displacing gas to the solid surface. Increasing Bo can increase the gas saturation, and stable displacement is observed for Bo >1 because the applied gravity has a stabilizing influence on the drainage process.
LanguageEnglish
Pages555-580
Number of pages26
JournalTransport in Porous Media
Volume99
Issue number3
DOIs
Publication statusPublished - Sep 2013

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Gases
Liquids
Wetting
Viscosity
Drainage
Capillary tubes
Multiphase flow
Contact angle
Phase diagrams
Porous materials
Gravitation

Keywords

  • pore-scale simulations
  • fingering
  • porous media
  • multiphase flows
  • lattice Boltzmann

Cite this

Liu, Haihu ; Valocchi, Albert J. ; Kang, Qinjun ; Werth, Charles. / Pore-scale simulations of gas displacing liquid in a homogeneous pore network using the lattice Boltzmann method. In: Transport in Porous Media. 2013 ; Vol. 99, No. 3. pp. 555-580.
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Pore-scale simulations of gas displacing liquid in a homogeneous pore network using the lattice Boltzmann method. / Liu, Haihu; Valocchi, Albert J.; Kang, Qinjun; Werth, Charles.

In: Transport in Porous Media, Vol. 99, No. 3, 09.2013, p. 555-580.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Pore-scale simulations of gas displacing liquid in a homogeneous pore network using the lattice Boltzmann method

AU - Liu, Haihu

AU - Valocchi, Albert J.

AU - Kang, Qinjun

AU - Werth, Charles

PY - 2013/9

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N2 - A lattice Boltzmann high-density-ratio model, which uses diffuse interface theory to describe the interfacial dynamics and was proposed originally by Lee and Liu (J Comput Phys 229:8045–8063, 2010), is extended to simulate immiscible multiphase flows in porous media. A wetting boundary treatment is proposed for concave and convex corners. The capability and accuracy of this model is first validated by simulations of equilibrium contact angle, injection of a non-wetting gas into two parallel capillary tubes, and dynamic capillary intrusion. The model is then used to simulate gas displacement of liquid in a homogenous two-dimensional pore network consisting of uniformly spaced square obstructions. The influence of capillary number (Ca), viscosity ratio ( M M ), surface wettability, and Bond number (Bo) is studied systematically. In the drainage displacement, we have identified three different regimes, namely stable displacement, capillary fingering, and viscous fingering, all of which are strongly dependent upon the capillary number, viscosity ratio, and Bond number. Gas saturation generally increases with an increase in capillary number at breakthrough, whereas a slight decrease occurs when Ca is increased from 8.66×10−4 8.66 × 10 - 4 to 4.33×10−3 4.33 × 10 - 3 , which is associated with the viscous instability at high Ca. Increasing the viscosity ratio can enhance stability during displacement, leading to an increase in gas saturation. In the two-dimensional phase diagram, our results show that the viscous fingering regime occupies a zone markedly different from those obtained in previous numerical and experimental studies. When the surface wettability is taken into account, the residual liquid blob decreases in size with the affinity of the displacing gas to the solid surface. Increasing Bo can increase the gas saturation, and stable displacement is observed for Bo >1 because the applied gravity has a stabilizing influence on the drainage process.

AB - A lattice Boltzmann high-density-ratio model, which uses diffuse interface theory to describe the interfacial dynamics and was proposed originally by Lee and Liu (J Comput Phys 229:8045–8063, 2010), is extended to simulate immiscible multiphase flows in porous media. A wetting boundary treatment is proposed for concave and convex corners. The capability and accuracy of this model is first validated by simulations of equilibrium contact angle, injection of a non-wetting gas into two parallel capillary tubes, and dynamic capillary intrusion. The model is then used to simulate gas displacement of liquid in a homogenous two-dimensional pore network consisting of uniformly spaced square obstructions. The influence of capillary number (Ca), viscosity ratio ( M M ), surface wettability, and Bond number (Bo) is studied systematically. In the drainage displacement, we have identified three different regimes, namely stable displacement, capillary fingering, and viscous fingering, all of which are strongly dependent upon the capillary number, viscosity ratio, and Bond number. Gas saturation generally increases with an increase in capillary number at breakthrough, whereas a slight decrease occurs when Ca is increased from 8.66×10−4 8.66 × 10 - 4 to 4.33×10−3 4.33 × 10 - 3 , which is associated with the viscous instability at high Ca. Increasing the viscosity ratio can enhance stability during displacement, leading to an increase in gas saturation. In the two-dimensional phase diagram, our results show that the viscous fingering regime occupies a zone markedly different from those obtained in previous numerical and experimental studies. When the surface wettability is taken into account, the residual liquid blob decreases in size with the affinity of the displacing gas to the solid surface. Increasing Bo can increase the gas saturation, and stable displacement is observed for Bo >1 because the applied gravity has a stabilizing influence on the drainage process.

KW - pore-scale simulations

KW - fingering

KW - porous media

KW - multiphase flows

KW - lattice Boltzmann

U2 - 10.1007/s11242-013-0200-8

DO - 10.1007/s11242-013-0200-8

M3 - Article

VL - 99

SP - 555

EP - 580

JO - Transport in Porous Media

T2 - Transport in Porous Media

JF - Transport in Porous Media

SN - 0169-3913

IS - 3

ER -