A Force-Balanced Control Volume Finite Element Method for Multi-Phase Porous Media Flow Modelling

J.L.M.A. Gomes, D Pavlidis, P Salinas, Z Xie, J. R. Percival, Y. Melnikova, C. C. Pain, M. D. Jackson

Research output: Contribution to journalArticle

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Abstract

A novel method for simulating multi-phase flow in porous media is presented. The approach is based on a control volume finite element mixed formulation and new force-balanced finite element pairs. The novelty of the method lies in: (a) permitting both continuous and discontinuous description of pressure and saturation between elements; (b) the use of arbitrarily high-order polynomial representation for pressure and velocity and (c) the use of high-order flux-limited methods in space and time to avoid introducing non-physical oscillations while achieving high-order accuracy where and when possible. The model is initially validated for two-phase flow. Results are in good agreement with analytically obtained solutions and experimental results. The potential of this method is demonstrated by simulating flow in a realistic geometry composed of highly permeable meandering channels.
Original languageEnglish
Pages (from-to)431–445
Number of pages23
JournalInternational Journal for Numerical Methods in Fluids
Volume83
Issue number5
Early online date4 Aug 2016
DOIs
Publication statusPublished - 20 Feb 2017

Fingerprint

Porous Media Flow
Multiphase Flow
Control Volume
Force control
Porous materials
Finite Element Method
Finite element method
Multiphase flow
Modeling
Two phase flow
Polynomials
Higher Order
Finite Element
Fluxes
High Order Accuracy
Mixed Formulation
Flow in Porous Media
Geometry
Two-phase Flow
Saturation

Keywords

  • CVFEM mixed formulation
  • discontinuous Galerkin
  • flux-limiting
  • high-order method
  • multi-phase flows
  • porous media flows

Cite this

A Force-Balanced Control Volume Finite Element Method for Multi-Phase Porous Media Flow Modelling. / Gomes, J.L.M.A.; Pavlidis, D; Salinas, P; Xie, Z; Percival, J. R.; Melnikova, Y.; Pain, C. C.; Jackson, M. D.

In: International Journal for Numerical Methods in Fluids, Vol. 83, No. 5, 20.02.2017, p. 431–445 .

Research output: Contribution to journalArticle

Gomes, JLMA, Pavlidis, D, Salinas, P, Xie, Z, Percival, JR, Melnikova, Y, Pain, CC & Jackson, MD 2017, 'A Force-Balanced Control Volume Finite Element Method for Multi-Phase Porous Media Flow Modelling', International Journal for Numerical Methods in Fluids, vol. 83, no. 5, pp. 431–445 . https://doi.org/10.1002/fld.4275
Gomes, J.L.M.A. ; Pavlidis, D ; Salinas, P ; Xie, Z ; Percival, J. R. ; Melnikova, Y. ; Pain, C. C. ; Jackson, M. D. / A Force-Balanced Control Volume Finite Element Method for Multi-Phase Porous Media Flow Modelling. In: International Journal for Numerical Methods in Fluids. 2017 ; Vol. 83, No. 5. pp. 431–445 .
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AB - A novel method for simulating multi-phase flow in porous media is presented. The approach is based on a control volume finite element mixed formulation and new force-balanced finite element pairs. The novelty of the method lies in: (a) permitting both continuous and discontinuous description of pressure and saturation between elements; (b) the use of arbitrarily high-order polynomial representation for pressure and velocity and (c) the use of high-order flux-limited methods in space and time to avoid introducing non-physical oscillations while achieving high-order accuracy where and when possible. The model is initially validated for two-phase flow. Results are in good agreement with analytically obtained solutions and experimental results. The potential of this method is demonstrated by simulating flow in a realistic geometry composed of highly permeable meandering channels.

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