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CVD-MPFA full pressure support, coupled unstructured discrete fracture–matrix Darcy-flux approximations

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

Journal of Computational Physics, Volume: 349, Pages: 265 - 299

Swansea University Author: Michael G. Edwards

Abstract

Two novel control-volume methods are presented for flow in fractured porous media, involving coupling the control-volume distributed multi-point flux approximation (CVD-MPFA (c.f. Edwards et al.)) constructed with full pressure support (FPS), to two types of discrete fracture-matrix approximation fo...

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Published in: Journal of Computational Physics
ISSN: 0021-9991
Published: 2017
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URI: https://cronfa.swan.ac.uk/Record/cronfa34815
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spelling 2020-07-14T15:27:08.6595975 v2 34815 2017-07-28 CVD-MPFA full pressure support, coupled unstructured discrete fracture–matrix Darcy-flux approximations 8903caf3d43fca03602a72ed31d17c59 Michael G. Edwards Michael G. Edwards true false 2017-07-28 FGSEN Two novel control-volume methods are presented for flow in fractured porous media, involving coupling the control-volume distributed multi-point flux approximation (CVD-MPFA (c.f. Edwards et al.)) constructed with full pressure support (FPS), to two types of discrete fracture-matrix approximation for flow simulation on unstructured grids; (i) involving hybrid grids and (ii) a lower dimensional fracture model. Flow is governed by Darcy's law together with mass conservation both in the rock matrix and in fractures, where large discontinuous permeability tensors can occur. Finite-volume FPS schemes are more robust than the earlier CVD-MPFA triangular pressure support (TPS) schemes for problems involving strongly anisotropic homogeneous and heterogeneous full-tensor permeability fields. We use a cell-centred hybrid-grid method, where fractures are represented by lower-dimensional interfaces between matrix grid cells in the physical mesh, and expanded to equi-dimensional cells in the computational domain. We present a simple procedure to form a consistent hybrid-grid locally for a dual-cell. We also propose a novel hybrid-grid for intersecting fractures, for the FPS method, which improves the condition number of the global linear system and permits larger time steps for tracer transport. The tracer flow transport equation is coupled with the pressure equation and the results provide flow parameter assessment of the fracture models. Transport results obtained via TPS and FPS hybrid-grid formulations are compared with corresponding results of fine-scale explicit equi-dimensional formulations. The results show that the hybrid-grid FPS method applies to general full-tensor fields and provides improved robust approximations compared to the hybrid-grid TPS method for fractured domains, for both weakly anisotropic permeability fields and in particular for very strong anisotropic full-tensor permeability fields where the TPS scheme exhibits spurious oscillations. The hybrid-grid FPS formulation is extended to compressible flow and the results demonstrate the method is also robust for transient flow. Furthermore, FPS is coupled with a lower-dimensional fracture model, where fractures are strictly lower-dimensional in the physical mesh. Comparisons of the hybrid-grid FPS method and the FPS lower-dimensional fracture model are presented for several cases of isotropic and strongly anisotropic fractured media which illustrate the benefits of the respective methods. Journal Article Journal of Computational Physics 349 265 299 0021-9991 CVD-MPFA; Full pressure support (FPS); Discrete-fracture; Hybrid-grid; Anisotropy 31 12 2017 2017-12-31 10.1016/j.jcp.2017.07.041 COLLEGE NANME Science and Engineering - Faculty COLLEGE CODE FGSEN Swansea University 2020-07-14T15:27:08.6595975 2017-07-28T09:58:38.9788642 College of Engineering Engineering Raheel Ahmed 1 Michael G. Edwards 2 Sadok Lamine 3 Bastiaan A.H. Huisman 4 Mayur Pal 5 0034815-28072017100146.pdf ahmed2017.pdf 2017-07-28T10:01:46.2130000 Output 11539924 application/pdf Accepted Manuscript true 2018-07-28T00:00:00.0000000 false eng
title CVD-MPFA full pressure support, coupled unstructured discrete fracture–matrix Darcy-flux approximations
spellingShingle CVD-MPFA full pressure support, coupled unstructured discrete fracture–matrix Darcy-flux approximations
Michael G. Edwards
title_short CVD-MPFA full pressure support, coupled unstructured discrete fracture–matrix Darcy-flux approximations
title_full CVD-MPFA full pressure support, coupled unstructured discrete fracture–matrix Darcy-flux approximations
title_fullStr CVD-MPFA full pressure support, coupled unstructured discrete fracture–matrix Darcy-flux approximations
title_full_unstemmed CVD-MPFA full pressure support, coupled unstructured discrete fracture–matrix Darcy-flux approximations
title_sort CVD-MPFA full pressure support, coupled unstructured discrete fracture–matrix Darcy-flux approximations
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 A.H. Huisman
Mayur Pal
format Journal article
container_title Journal of Computational Physics
container_volume 349
container_start_page 265
publishDate 2017
institution Swansea University
issn 0021-9991
doi_str_mv 10.1016/j.jcp.2017.07.041
college_str College of Engineering
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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
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description Two novel control-volume methods are presented for flow in fractured porous media, involving coupling the control-volume distributed multi-point flux approximation (CVD-MPFA (c.f. Edwards et al.)) constructed with full pressure support (FPS), to two types of discrete fracture-matrix approximation for flow simulation on unstructured grids; (i) involving hybrid grids and (ii) a lower dimensional fracture model. Flow is governed by Darcy's law together with mass conservation both in the rock matrix and in fractures, where large discontinuous permeability tensors can occur. Finite-volume FPS schemes are more robust than the earlier CVD-MPFA triangular pressure support (TPS) schemes for problems involving strongly anisotropic homogeneous and heterogeneous full-tensor permeability fields. We use a cell-centred hybrid-grid method, where fractures are represented by lower-dimensional interfaces between matrix grid cells in the physical mesh, and expanded to equi-dimensional cells in the computational domain. We present a simple procedure to form a consistent hybrid-grid locally for a dual-cell. We also propose a novel hybrid-grid for intersecting fractures, for the FPS method, which improves the condition number of the global linear system and permits larger time steps for tracer transport. The tracer flow transport equation is coupled with the pressure equation and the results provide flow parameter assessment of the fracture models. Transport results obtained via TPS and FPS hybrid-grid formulations are compared with corresponding results of fine-scale explicit equi-dimensional formulations. The results show that the hybrid-grid FPS method applies to general full-tensor fields and provides improved robust approximations compared to the hybrid-grid TPS method for fractured domains, for both weakly anisotropic permeability fields and in particular for very strong anisotropic full-tensor permeability fields where the TPS scheme exhibits spurious oscillations. The hybrid-grid FPS formulation is extended to compressible flow and the results demonstrate the method is also robust for transient flow. Furthermore, FPS is coupled with a lower-dimensional fracture model, where fractures are strictly lower-dimensional in the physical mesh. Comparisons of the hybrid-grid FPS method and the FPS lower-dimensional fracture model are presented for several cases of isotropic and strongly anisotropic fractured media which illustrate the benefits of the respective methods.
published_date 2017-12-31T03:47:29Z
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