Phase-field modelling of a liquid/liquid immiscible displacement through a network of capillaries
Phase-field modelling of a liquid/liquid immiscible displacement through a network of capillaries
The liquid/liquid displacement through a 2D uniform network of capillaries is numerically modelled with the use of the phase-field approach. The detailed structure of the flow fields within the uniform matrices of different sizes (with the different number of pores) is examined with the aim to reveal the asymptotic behaviour, pertinent for a sufficiently large matrix, that could be used for representation of a porous medium. The integral characteristics of the flow that do not depend on the matrix size can be used for calculation of the parameters of a macroscopic (Darcy) approach. We demonstrate that qualitatively the displacement occurs very similarly in the matrices with the different number of structural elements. In particular, we show that the capillary pressure remains nearly constant during the displacement run until the break-through time (with some minor variations related to a particular shape of a matrix). Upon increase of the matrix size the magnitude of the capillary pressure (and all other integral characteristics of the two-phase flow) quickly converges to the limiting value (so that the limiting results are already reached for a matrix with 6×6 elements), giving the direct procedure for calculation of the capillary pressure in a porous medium.
GPU calculations, capillary pressure, phase-field (Cahn-Hilliard) approach, pore-level modelling, porous medium
Vorobev, Anatoliy
911a4e1e-0c34-4297-b52e-c22a2b9dec01
Prokopev, Sergei
ac7f4544-8463-4ff7-8c11-42d003c543e9
Lyubimova, Tatiana
ea977036-7fca-4d61-abf5-1da0a94c9b35
15 November 2020
Vorobev, Anatoliy
911a4e1e-0c34-4297-b52e-c22a2b9dec01
Prokopev, Sergei
ac7f4544-8463-4ff7-8c11-42d003c543e9
Lyubimova, Tatiana
ea977036-7fca-4d61-abf5-1da0a94c9b35
Vorobev, Anatoliy, Prokopev, Sergei and Lyubimova, Tatiana
(2020)
Phase-field modelling of a liquid/liquid immiscible displacement through a network of capillaries.
Journal of Computational Physics, 421, [109747].
(doi:10.1016/j.jcp.2020.109747).
Abstract
The liquid/liquid displacement through a 2D uniform network of capillaries is numerically modelled with the use of the phase-field approach. The detailed structure of the flow fields within the uniform matrices of different sizes (with the different number of pores) is examined with the aim to reveal the asymptotic behaviour, pertinent for a sufficiently large matrix, that could be used for representation of a porous medium. The integral characteristics of the flow that do not depend on the matrix size can be used for calculation of the parameters of a macroscopic (Darcy) approach. We demonstrate that qualitatively the displacement occurs very similarly in the matrices with the different number of structural elements. In particular, we show that the capillary pressure remains nearly constant during the displacement run until the break-through time (with some minor variations related to a particular shape of a matrix). Upon increase of the matrix size the magnitude of the capillary pressure (and all other integral characteristics of the two-phase flow) quickly converges to the limiting value (so that the limiting results are already reached for a matrix with 6×6 elements), giving the direct procedure for calculation of the capillary pressure in a porous medium.
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More information
Accepted/In Press date: 28 July 2020
e-pub ahead of print date: 4 August 2020
Published date: 15 November 2020
Additional Information:
Funding Information:
This research work is partially financially supported by the Russian Foundation for Basic Research (grant 18-01-00782 ). The authors acknowledge the use of the IRIDIS High Performance Computing Facility, and associated support services at the University of Southampton, in the completion of this work.
Publisher Copyright:
© 2020 Elsevier Inc.
Keywords:
GPU calculations, capillary pressure, phase-field (Cahn-Hilliard) approach, pore-level modelling, porous medium
Identifiers
Local EPrints ID: 443009
URI: http://eprints.soton.ac.uk/id/eprint/443009
ISSN: 0021-9991
PURE UUID: 70efdaa6-ebf1-4721-adaf-07fd71d9417b
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Date deposited: 05 Aug 2020 16:35
Last modified: 17 Mar 2024 05:47
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Author:
Sergei Prokopev
Author:
Tatiana Lyubimova
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