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

doi:10.1002/fld.4275

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

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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 language	English
Pages (from-to)	431–445
Number of pages	23
Journal	International Journal for Numerical Methods in Fluids
Volume	83
Issue number	5
Early online date	4 Aug 2016
DOIs	https://doi.org/10.1002/fld.4275
Publication status	Published - 20 Feb 2017

Keywords

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

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10.1002/fld.4275Licence: CC BY

A Force-Balanced Control Volume Finite Element Method for Multi-Phase Porous media flow modelling
© 2016 The Authors International Journal for Numerical Methods in Fluids Published by John Wiley & Sons Ltd The copyright line for this article was changed on 16 September 2016 after original online publication. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. https://creativecommons.org/licenses/by/4.0/
Final published version, 923 KBLicence: CC BY

Jefferson Gomes
- Centre for Energy Transition
- Engineering, Engineering - Lecturer
Person: Academic

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@article{10a3faa654b5418ba85df98d93d5f2e6,

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

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. ",

keywords = "CVFEM mixed formulation, discontinuous Galerkin, ﬂux-limiting, high-order method, multi-phase ﬂows, porous media ﬂows",

author = "J.L.M.A. Gomes and D Pavlidis and P Salinas and Z Xie and Percival, {J. R.} and Y. Melnikova and Pain, {C. C.} and Jackson, {M. D.}",

note = "Dr D. Pavlidis would like to acknowledge the support from the following research grants: Innovate UK {\textquoteleft}Octopus{\textquoteright}, EPSRC {\textquoteleft}Reactor Core-Structure Re-location Modelling for Severe Nuclear Accidents{\textquoteright}) and Horizon 2020 {\textquoteleft}In-Vessel Melt Retention{\textquoteright}. Funding for Dr P. Salinas from ExxonMobil is gratefully acknowledged. Dr Z. Xie is supported by EPSRC {\textquoteleft}Multi-Scale Exploration of Multi-phase Physics in Flows{\textquoteright}. Part funding for Prof Jackson under the TOTAL Chairs programme at Imperial College is also acknowledged. The authors would also like to acknowledge Mr Y. Debbabi for supplying analytic solutions. ",

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AU - Gomes, J.L.M.A.

AU - Pavlidis, D

AU - Salinas, P

AU - Xie, Z

AU - Percival, J. R.

AU - Melnikova, Y.

AU - Pain, C. C.

AU - Jackson, M. D.

N1 - Dr D. Pavlidis would like to acknowledge the support from the following research grants: Innovate UK ‘Octopus’, EPSRC ‘Reactor Core-Structure Re-location Modelling for Severe Nuclear Accidents’) and Horizon 2020 ‘In-Vessel Melt Retention’. Funding for Dr P. Salinas from ExxonMobil is gratefully acknowledged. Dr Z. Xie is supported by EPSRC ‘Multi-Scale Exploration of Multi-phase Physics in Flows’. Part funding for Prof Jackson under the TOTAL Chairs programme at Imperial College is also acknowledged. The authors would also like to acknowledge Mr Y. Debbabi for supplying analytic solutions.

PY - 2017/2/20

Y1 - 2017/2/20

N2 - 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.

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.

KW - CVFEM mixed formulation

KW - discontinuous Galerkin

KW - ﬂux-limiting

KW - high-order method

KW - multi-phase ﬂows

KW - porous media ﬂows

U2 - 10.1002/fld.4275

DO - 10.1002/fld.4275

M3 - Article

VL - 83

SP - 431

EP - 445

JO - International Journal for Numerical Methods in Fluids

JF - International Journal for Numerical Methods in Fluids

SN - 0271-2091

IS - 5

ER -

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

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Jefferson Gomes

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