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Three-dimensional control-volume distributed multi-point flux approximation coupled with a lower-dimensional surface fracture model

Raheel Ahmed, Michael G. Edwards, Sadok Lamine, Bastiaan Huisman, Mayur Pal

Journal of Computational Physics, Volume: 303, Pages: 470 - 497

Swansea University Author: Michael G. Edwards

Abstract

A novel cell-centred control-volume distributed multi-point flux approximation (CVD-MPFA) finite-volume formulation is presented for discrete fracture–matrix simulations on unstructured grids in three-dimensions (3D). The grid is aligned with fractures and barriers which are then modelled as lower-d...

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Published in: Journal of Computational Physics
ISSN: 0021-9991
Published: 2015
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URI: https://cronfa.swan.ac.uk/Record/cronfa24695
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first_indexed 2015-11-24T02:01:17Z
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spelling 2021-01-06T12:17:40.0548488 v2 24695 2015-11-23 Three-dimensional control-volume distributed multi-point flux approximation coupled with a lower-dimensional surface fracture model 8903caf3d43fca03602a72ed31d17c59 Michael G. Edwards Michael G. Edwards true false 2015-11-23 FGSEN A novel cell-centred control-volume distributed multi-point flux approximation (CVD-MPFA) finite-volume formulation is presented for discrete fracture–matrix simulations on unstructured grids in three-dimensions (3D). The grid is aligned with fractures and barriers which are then modelled as lower-dimensional surface interfaces located between the matrix cells in the physical domain. The three-dimensional pressure equation is solved in the matrix domain coupled with a two-dimensional (2D) surface pressure equation solved over fracture networks via a novel surface CVD-MPFA formulation. The CVD-MPFA formulation naturally handles fractures with anisotropic permeabilities on unstructured grids. Matrix–fracture fluxes are expressed in terms of matrix and fracture pressures and define the transfer function, which is added to the lower-dimensional flow equation and couples the three-dimensional and surface systems. An additional transmission condition is used between matrix cells adjacent to low permeable fractures to couple the velocity and pressure jump across the fractures. Convergence and accuracy of the lower-dimensional fracture model is assessed for highly anisotropic fractures having a range of apertures and permeability tensors. A transport equation for tracer flow is coupled via the Darcy flux for single and intersecting fractures. The lower-dimensional approximation for intersecting fractures avoids the more restrictive CFL condition corresponding to the equi-dimensional approximation with explicit time discretisation. Lower-dimensional fracture model results are compared with equi-dimensional model results. Fractures and barriers are efficiently modelled by lower-dimensional interfaces which yield comparable results to those of the equi-dimensional model. Pressure continuity is built into the model across highly conductive fractures, leading to reduced local degrees of freedom in the CVD-MPFA approximation. The formulation is applied to geologically complex fracture networks in three-dimensions. The effects of the fracture permeability, aperture and grid resolution are also assessed with respect to convergence and computational cost. Journal Article Journal of Computational Physics 303 470 497 0021-9991 15 12 2015 2015-12-15 10.1016/j.jcp.2015.10.001 COLLEGE NANME Science and Engineering - Faculty COLLEGE CODE FGSEN Swansea University 2021-01-06T12:17:40.0548488 2015-11-23T12:57:20.7382778 College of Engineering Engineering Raheel Ahmed 1 Michael G. Edwards 2 Sadok Lamine 3 Bastiaan Huisman 4 Mayur Pal 5 0024695-11022016172015.pdf AhmedThreeDimensionalControlVolume2015Postprint.pdf 2016-02-11T17:20:15.0700000 Output 6881291 application/pdf Accepted Manuscript true 2016-10-08T00:00:00.0000000 true
title Three-dimensional control-volume distributed multi-point flux approximation coupled with a lower-dimensional surface fracture model
spellingShingle Three-dimensional control-volume distributed multi-point flux approximation coupled with a lower-dimensional surface fracture model
Michael G. Edwards
title_short Three-dimensional control-volume distributed multi-point flux approximation coupled with a lower-dimensional surface fracture model
title_full Three-dimensional control-volume distributed multi-point flux approximation coupled with a lower-dimensional surface fracture model
title_fullStr Three-dimensional control-volume distributed multi-point flux approximation coupled with a lower-dimensional surface fracture model
title_full_unstemmed Three-dimensional control-volume distributed multi-point flux approximation coupled with a lower-dimensional surface fracture model
title_sort Three-dimensional control-volume distributed multi-point flux approximation coupled with a lower-dimensional surface fracture model
author_id_str_mv 8903caf3d43fca03602a72ed31d17c59
author_id_fullname_str_mv 8903caf3d43fca03602a72ed31d17c59_***_Michael G. Edwards
author Michael G. Edwards
author2 Raheel Ahmed
Michael G. Edwards
Sadok Lamine
Bastiaan Huisman
Mayur Pal
format Journal article
container_title Journal of Computational Physics
container_volume 303
container_start_page 470
publishDate 2015
institution Swansea University
issn 0021-9991
doi_str_mv 10.1016/j.jcp.2015.10.001
college_str College of Engineering
hierarchytype
hierarchy_top_id collegeofengineering
hierarchy_top_title College of Engineering
hierarchy_parent_id collegeofengineering
hierarchy_parent_title College of Engineering
department_str Engineering{{{_:::_}}}College of Engineering{{{_:::_}}}Engineering
document_store_str 1
active_str 0
description A novel cell-centred control-volume distributed multi-point flux approximation (CVD-MPFA) finite-volume formulation is presented for discrete fracture–matrix simulations on unstructured grids in three-dimensions (3D). The grid is aligned with fractures and barriers which are then modelled as lower-dimensional surface interfaces located between the matrix cells in the physical domain. The three-dimensional pressure equation is solved in the matrix domain coupled with a two-dimensional (2D) surface pressure equation solved over fracture networks via a novel surface CVD-MPFA formulation. The CVD-MPFA formulation naturally handles fractures with anisotropic permeabilities on unstructured grids. Matrix–fracture fluxes are expressed in terms of matrix and fracture pressures and define the transfer function, which is added to the lower-dimensional flow equation and couples the three-dimensional and surface systems. An additional transmission condition is used between matrix cells adjacent to low permeable fractures to couple the velocity and pressure jump across the fractures. Convergence and accuracy of the lower-dimensional fracture model is assessed for highly anisotropic fractures having a range of apertures and permeability tensors. A transport equation for tracer flow is coupled via the Darcy flux for single and intersecting fractures. The lower-dimensional approximation for intersecting fractures avoids the more restrictive CFL condition corresponding to the equi-dimensional approximation with explicit time discretisation. Lower-dimensional fracture model results are compared with equi-dimensional model results. Fractures and barriers are efficiently modelled by lower-dimensional interfaces which yield comparable results to those of the equi-dimensional model. Pressure continuity is built into the model across highly conductive fractures, leading to reduced local degrees of freedom in the CVD-MPFA approximation. The formulation is applied to geologically complex fracture networks in three-dimensions. The effects of the fracture permeability, aperture and grid resolution are also assessed with respect to convergence and computational cost.
published_date 2015-12-15T03:35:19Z
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