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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
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DOI (Published version): 10.1016/j.jcp.2015.10.001
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...
Published in: | Journal of Computational Physics |
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ISSN: | 0021-9991 |
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2015
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URI: | https://cronfa.swan.ac.uk/Record/cronfa24695 |
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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 Faculty of Science and Engineering School of Engineering and Applied Sciences - Uncategorised 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 |
Faculty of Science and Engineering |
hierarchytype |
|
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facultyofscienceandengineering |
hierarchy_top_title |
Faculty of Science and Engineering |
hierarchy_parent_id |
facultyofscienceandengineering |
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Faculty of Science and Engineering |
department_str |
School of Engineering and Applied Sciences - Uncategorised{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Engineering and Applied Sciences - Uncategorised |
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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 |
2015-12-15T03:29:21Z |
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1763751138676441088 |
score |
11.030209 |