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Three-dimensional unstructured gridding for complex wells and geological features in subsurface reservoirs, with CVD-MPFA discretization performance

Shahid Manzoor, Michael G. Edwards, Ali H. Dogru

Computer Methods in Applied Mechanics and Engineering, Volume: 373

Swansea University Author: Michael G. Edwards

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Abstract

Grid generation for reservoir simulation, must honour classical key geological features and multilateral wells. The features to be honoured are classified into two groups; (1) involving layers, faults, pinchouts and fractures, and (2) involving well distributions. In the former, control-volume bound...

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Published in: Computer Methods in Applied Mechanics and Engineering
ISSN: 0045-7825
Published: Elsevier BV 2021
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URI: https://cronfa.swan.ac.uk/Record/cronfa55003
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In the former, control-volume boundary aligned grids (BAGs) are required, while in the latter, control-point (defined as the centroid of the control-volume) well aligned grids (WAGs) are required. Depending on discretization method type and formulation, a choice of control-point and control-volume type is made, i.e. for a cell-centered method the primal grid cells act as control-volumes, otherwise for a vertex-centered method the dual-grid cells act as control-volumes. Novel three-dimensional unstructured grid generation methods are proposed that automate control-volume boundary alignment to geological features and control point alignment to complex wells, yielding essentially perpendicular bisector (PEBI) meshes either with respect to primal or dual-cells depending on grid type. Both grid types use tetrahedra, pyramids, prisms and hexahedra as grid elements. Primal-cell feature aligned grids are generated using special boundary surface protection techniques together with constrained cell-centered well trajectory alignment. Dual-cell feature aligned grids are generated from underlying primal-meshes, whereby features are protected such that dual-cell control-volume faces are aligned with interior feature boundaries, together with protected vertex-centered (control point) well trajectory alignment. The novel methods of grid generation presented enable practical application of both method types in 3-D for the first time. The primal and dual grids generated here demonstrate the gridding methods, and enable the first comparative performance study of cell-vertex versus cell-centered control-volume distributed multi-point flux approximation (CVD-MPFA) finite-volume formulations using equivalent mesh resolution on challenging problems in 3-D. Pressure fields computed by the cell-centered and vertex-centered CVD-MPFA schemes are compared and contrasted relative to the respective degrees of freedom employed, and demonstrate the relative benefits of each approximation type. Stability limits of the methods are also explored. For a given mesh the cell-vertex method uses approximately a fifth of the unknowns used by a cell-centered method and proves to be the most beneficial with respect to accuracy and efficiency. 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spelling 2020-10-08T09:12:05.5004031 v2 55003 2020-08-18 Three-dimensional unstructured gridding for complex wells and geological features in subsurface reservoirs, with CVD-MPFA discretization performance 8903caf3d43fca03602a72ed31d17c59 Michael G. Edwards Michael G. Edwards true false 2020-08-18 FGSEN Grid generation for reservoir simulation, must honour classical key geological features and multilateral wells. The features to be honoured are classified into two groups; (1) involving layers, faults, pinchouts and fractures, and (2) involving well distributions. In the former, control-volume boundary aligned grids (BAGs) are required, while in the latter, control-point (defined as the centroid of the control-volume) well aligned grids (WAGs) are required. Depending on discretization method type and formulation, a choice of control-point and control-volume type is made, i.e. for a cell-centered method the primal grid cells act as control-volumes, otherwise for a vertex-centered method the dual-grid cells act as control-volumes. Novel three-dimensional unstructured grid generation methods are proposed that automate control-volume boundary alignment to geological features and control point alignment to complex wells, yielding essentially perpendicular bisector (PEBI) meshes either with respect to primal or dual-cells depending on grid type. Both grid types use tetrahedra, pyramids, prisms and hexahedra as grid elements. Primal-cell feature aligned grids are generated using special boundary surface protection techniques together with constrained cell-centered well trajectory alignment. Dual-cell feature aligned grids are generated from underlying primal-meshes, whereby features are protected such that dual-cell control-volume faces are aligned with interior feature boundaries, together with protected vertex-centered (control point) well trajectory alignment. The novel methods of grid generation presented enable practical application of both method types in 3-D for the first time. The primal and dual grids generated here demonstrate the gridding methods, and enable the first comparative performance study of cell-vertex versus cell-centered control-volume distributed multi-point flux approximation (CVD-MPFA) finite-volume formulations using equivalent mesh resolution on challenging problems in 3-D. Pressure fields computed by the cell-centered and vertex-centered CVD-MPFA schemes are compared and contrasted relative to the respective degrees of freedom employed, and demonstrate the relative benefits of each approximation type. Stability limits of the methods are also explored. For a given mesh the cell-vertex method uses approximately a fifth of the unknowns used by a cell-centered method and proves to be the most beneficial with respect to accuracy and efficiency. Numerical results show that vertex-centered CVD-MPFA methods outperform cell-centered CVD-MPFA method. Journal Article Computer Methods in Applied Mechanics and Engineering 373 Elsevier BV 0045-7825 Boundary aligned unstructured hybrid gridding, Three dimensional Delaunay mesh generation, Control volume distributed multipoint flux approximation (CVD-MPFA), Cell-centered versus vertex-centered methods 1 1 2021 2021-01-01 10.1016/j.cma.2020.113389 http://dx.doi.org/10.1016/j.cma.2020.113389 COLLEGE NANME Science and Engineering - Faculty COLLEGE CODE FGSEN Swansea University 2020-10-08T09:12:05.5004031 2020-08-18T11:03:35.5330686 College of Engineering Engineering Shahid Manzoor 1 Michael G. Edwards 2 Ali H. Dogru 3 55003__17994__26e09cf319a641a386a5ae18eb53fd79.pdf 55003.pdf 2020-08-19T16:56:23.8069076 Output 19610566 application/pdf Accepted Manuscript true 2021-10-07T00:00:00.0000000 Released under the terms of a Creative Commons Attribution Non-Commercial No Derivatives License (CC-BY-NC-ND). true English
title Three-dimensional unstructured gridding for complex wells and geological features in subsurface reservoirs, with CVD-MPFA discretization performance
spellingShingle Three-dimensional unstructured gridding for complex wells and geological features in subsurface reservoirs, with CVD-MPFA discretization performance
Michael G. Edwards
title_short Three-dimensional unstructured gridding for complex wells and geological features in subsurface reservoirs, with CVD-MPFA discretization performance
title_full Three-dimensional unstructured gridding for complex wells and geological features in subsurface reservoirs, with CVD-MPFA discretization performance
title_fullStr Three-dimensional unstructured gridding for complex wells and geological features in subsurface reservoirs, with CVD-MPFA discretization performance
title_full_unstemmed Three-dimensional unstructured gridding for complex wells and geological features in subsurface reservoirs, with CVD-MPFA discretization performance
title_sort Three-dimensional unstructured gridding for complex wells and geological features in subsurface reservoirs, with CVD-MPFA discretization performance
author_id_str_mv 8903caf3d43fca03602a72ed31d17c59
author_id_fullname_str_mv 8903caf3d43fca03602a72ed31d17c59_***_Michael G. Edwards
author Michael G. Edwards
author2 Shahid Manzoor
Michael G. Edwards
Ali H. Dogru
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institution Swansea University
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doi_str_mv 10.1016/j.cma.2020.113389
publisher Elsevier BV
college_str College of Engineering
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url http://dx.doi.org/10.1016/j.cma.2020.113389
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description Grid generation for reservoir simulation, must honour classical key geological features and multilateral wells. The features to be honoured are classified into two groups; (1) involving layers, faults, pinchouts and fractures, and (2) involving well distributions. In the former, control-volume boundary aligned grids (BAGs) are required, while in the latter, control-point (defined as the centroid of the control-volume) well aligned grids (WAGs) are required. Depending on discretization method type and formulation, a choice of control-point and control-volume type is made, i.e. for a cell-centered method the primal grid cells act as control-volumes, otherwise for a vertex-centered method the dual-grid cells act as control-volumes. Novel three-dimensional unstructured grid generation methods are proposed that automate control-volume boundary alignment to geological features and control point alignment to complex wells, yielding essentially perpendicular bisector (PEBI) meshes either with respect to primal or dual-cells depending on grid type. Both grid types use tetrahedra, pyramids, prisms and hexahedra as grid elements. Primal-cell feature aligned grids are generated using special boundary surface protection techniques together with constrained cell-centered well trajectory alignment. Dual-cell feature aligned grids are generated from underlying primal-meshes, whereby features are protected such that dual-cell control-volume faces are aligned with interior feature boundaries, together with protected vertex-centered (control point) well trajectory alignment. The novel methods of grid generation presented enable practical application of both method types in 3-D for the first time. The primal and dual grids generated here demonstrate the gridding methods, and enable the first comparative performance study of cell-vertex versus cell-centered control-volume distributed multi-point flux approximation (CVD-MPFA) finite-volume formulations using equivalent mesh resolution on challenging problems in 3-D. Pressure fields computed by the cell-centered and vertex-centered CVD-MPFA schemes are compared and contrasted relative to the respective degrees of freedom employed, and demonstrate the relative benefits of each approximation type. Stability limits of the methods are also explored. For a given mesh the cell-vertex method uses approximately a fifth of the unknowns used by a cell-centered method and proves to be the most beneficial with respect to accuracy and efficiency. Numerical results show that vertex-centered CVD-MPFA methods outperform cell-centered CVD-MPFA method.
published_date 2021-01-01T04:09:53Z
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