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Control-volume distributed multi-point flux approximation coupled with a lower-dimensional fracture model

R. Ahmed, Michael G. Edwards, S. Lamine, B.A.H. Huisman, M. Pal

Journal of Computational Physics, Volume: 284, Pages: 462 - 489

Swansea University Author: Michael G. Edwards

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DOI (Published version): 10.1016/j.jcp.2014.12.047

Abstract

A novel cell-centered control-volume distributed multi-point flux approximation (CVD-MPFA) finite-volume formulation is presented for discrete fracture-(rock)matrix flow simulations. The grid is aligned with the fractures and barriers which are then modeled by lower-dimensional interfaces located be...

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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/cronfa21407
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fullrecord <?xml version="1.0"?><rfc1807><datestamp>2022-11-15T16:28:05.4184665</datestamp><bib-version>v2</bib-version><id>21407</id><entry>2015-05-14</entry><title>Control-volume distributed multi-point flux approximation coupled with a lower-dimensional fracture model</title><swanseaauthors><author><sid>8903caf3d43fca03602a72ed31d17c59</sid><firstname>Michael G.</firstname><surname>Edwards</surname><name>Michael G. Edwards</name><active>true</active><ethesisStudent>false</ethesisStudent></author></swanseaauthors><date>2015-05-14</date><deptcode>FGSEN</deptcode><abstract>A novel cell-centered control-volume distributed multi-point flux approximation (CVD-MPFA) finite-volume formulation is presented for discrete fracture-(rock)matrix flow simulations. The grid is aligned with the fractures and barriers which are then modeled by lower-dimensional interfaces located between rock matrix cells in the physical domain. The n D (n-dimension) pressure equation in the rock matrix is coupled with the (n&#x2212;1)D pressure equation in the fractures, leading to the first reduced dimensional flux-continuous CVD-MPFA formulation. This formulation naturally handles fractures efficiently on unstructured grids. Matrix-fracture fluxes are expressed in terms of matrix and fracture pressures, resulting in a transfer function, which is added to the lower-dimensional flow equation. An additional transmission condition is used between matrix cells separated by low permeable fractures to couple the velocity and pressure jump across the fractures. Numerical tests serve to assess the convergence and accuracy of the lower-dimensional fracture model for lower anisotropic fractures having a range of apertures and permeability tensors. A tracer flow transport equation is solved for problems with single and intersecting fractures. A lower-dimensional mass balance for intersecting fracture cells circumvents the more restrictive CFL condition corresponding to standard equi-dimensional approximation with explicit time discretization. Lower-dimensional fracture model results are compared with hybrid-grid and equi-dimensional model results. Fractures and barriers are efficiently modeled by lower-dimensional interfaces which yield comparable results to those of the equi-dimensional model. Highly conductive fractures are modeled as lower-dimensional entities without the use of locally refined grids that are required by the equi-dimensional model, while pressure continuity across fractures is built into the model, without depending on the extra degrees of freedom which must be added locally by the hybrid-grid method. The lower-dimensional fracture model also yields improved results when compared to those of the hybrid-grid model for fractures with low-permeability in the normal direction to the fracture where pressure is discontinuous. In addition, transient pressure simulation involving geologically representative complex fracture networks is presented.</abstract><type>Journal Article</type><journal>Journal of Computational Physics</journal><volume>284</volume><journalNumber/><paginationStart>462</paginationStart><paginationEnd>489</paginationEnd><publisher/><placeOfPublication/><isbnPrint/><isbnElectronic/><issnPrint>0021-9991</issnPrint><issnElectronic/><keywords/><publishedDay>1</publishedDay><publishedMonth>3</publishedMonth><publishedYear>2015</publishedYear><publishedDate>2015-03-01</publishedDate><doi>10.1016/j.jcp.2014.12.047</doi><url/><notes/><college>COLLEGE NANME</college><department>Science and Engineering - Faculty</department><CollegeCode>COLLEGE CODE</CollegeCode><DepartmentCode>FGSEN</DepartmentCode><institution>Swansea University</institution><apcterm/><funders/><projectreference/><lastEdited>2022-11-15T16:28:05.4184665</lastEdited><Created>2015-05-14T13:05:03.3987543</Created><path><level id="1">Faculty of Science and Engineering</level><level id="2">School of Engineering and Applied Sciences - Uncategorised</level></path><authors><author><firstname>R.</firstname><surname>Ahmed</surname><order>1</order></author><author><firstname>Michael G.</firstname><surname>Edwards</surname><order>2</order></author><author><firstname>S.</firstname><surname>Lamine</surname><order>3</order></author><author><firstname>B.A.H.</firstname><surname>Huisman</surname><order>4</order></author><author><firstname>M.</firstname><surname>Pal</surname><order>5</order></author></authors><documents><document><filename>21407__2660__d2aad2c6657b486e939b64bf4466e1c0.pdf</filename><originalFilename>FracMPFA_2D_jcp.pdf</originalFilename><uploaded>2016-03-31T15:28:44.4700000</uploaded><type>Output</type><contentLength>3571745</contentLength><contentType>application/pdf</contentType><version>Accepted Manuscript</version><cronfaStatus>true</cronfaStatus><embargoDate>2016-03-31T00:00:00.0000000</embargoDate><documentNotes>This manuscript is available on cronfa as per University open access policy. copyright ISS-Research@swansea.ac.uk.</documentNotes><copyrightCorrect>true</copyrightCorrect></document></documents><OutputDurs/></rfc1807>
spelling 2022-11-15T16:28:05.4184665 v2 21407 2015-05-14 Control-volume distributed multi-point flux approximation coupled with a lower-dimensional fracture model 8903caf3d43fca03602a72ed31d17c59 Michael G. Edwards Michael G. Edwards true false 2015-05-14 FGSEN A novel cell-centered control-volume distributed multi-point flux approximation (CVD-MPFA) finite-volume formulation is presented for discrete fracture-(rock)matrix flow simulations. The grid is aligned with the fractures and barriers which are then modeled by lower-dimensional interfaces located between rock matrix cells in the physical domain. The n D (n-dimension) pressure equation in the rock matrix is coupled with the (n−1)D pressure equation in the fractures, leading to the first reduced dimensional flux-continuous CVD-MPFA formulation. This formulation naturally handles fractures efficiently on unstructured grids. Matrix-fracture fluxes are expressed in terms of matrix and fracture pressures, resulting in a transfer function, which is added to the lower-dimensional flow equation. An additional transmission condition is used between matrix cells separated by low permeable fractures to couple the velocity and pressure jump across the fractures. Numerical tests serve to assess the convergence and accuracy of the lower-dimensional fracture model for lower anisotropic fractures having a range of apertures and permeability tensors. A tracer flow transport equation is solved for problems with single and intersecting fractures. A lower-dimensional mass balance for intersecting fracture cells circumvents the more restrictive CFL condition corresponding to standard equi-dimensional approximation with explicit time discretization. Lower-dimensional fracture model results are compared with hybrid-grid and equi-dimensional model results. Fractures and barriers are efficiently modeled by lower-dimensional interfaces which yield comparable results to those of the equi-dimensional model. Highly conductive fractures are modeled as lower-dimensional entities without the use of locally refined grids that are required by the equi-dimensional model, while pressure continuity across fractures is built into the model, without depending on the extra degrees of freedom which must be added locally by the hybrid-grid method. The lower-dimensional fracture model also yields improved results when compared to those of the hybrid-grid model for fractures with low-permeability in the normal direction to the fracture where pressure is discontinuous. In addition, transient pressure simulation involving geologically representative complex fracture networks is presented. Journal Article Journal of Computational Physics 284 462 489 0021-9991 1 3 2015 2015-03-01 10.1016/j.jcp.2014.12.047 COLLEGE NANME Science and Engineering - Faculty COLLEGE CODE FGSEN Swansea University 2022-11-15T16:28:05.4184665 2015-05-14T13:05:03.3987543 Faculty of Science and Engineering School of Engineering and Applied Sciences - Uncategorised R. Ahmed 1 Michael G. Edwards 2 S. Lamine 3 B.A.H. Huisman 4 M. Pal 5 21407__2660__d2aad2c6657b486e939b64bf4466e1c0.pdf FracMPFA_2D_jcp.pdf 2016-03-31T15:28:44.4700000 Output 3571745 application/pdf Accepted Manuscript true 2016-03-31T00:00:00.0000000 This manuscript is available on cronfa as per University open access policy. copyright ISS-Research@swansea.ac.uk. true
title Control-volume distributed multi-point flux approximation coupled with a lower-dimensional fracture model
spellingShingle Control-volume distributed multi-point flux approximation coupled with a lower-dimensional fracture model
Michael G. Edwards
title_short Control-volume distributed multi-point flux approximation coupled with a lower-dimensional fracture model
title_full Control-volume distributed multi-point flux approximation coupled with a lower-dimensional fracture model
title_fullStr Control-volume distributed multi-point flux approximation coupled with a lower-dimensional fracture model
title_full_unstemmed Control-volume distributed multi-point flux approximation coupled with a lower-dimensional fracture model
title_sort Control-volume distributed multi-point flux approximation coupled with a lower-dimensional fracture model
author_id_str_mv 8903caf3d43fca03602a72ed31d17c59
author_id_fullname_str_mv 8903caf3d43fca03602a72ed31d17c59_***_Michael G. Edwards
author Michael G. Edwards
author2 R. Ahmed
Michael G. Edwards
S. Lamine
B.A.H. Huisman
M. Pal
format Journal article
container_title Journal of Computational Physics
container_volume 284
container_start_page 462
publishDate 2015
institution Swansea University
issn 0021-9991
doi_str_mv 10.1016/j.jcp.2014.12.047
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title 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
document_store_str 1
active_str 0
description A novel cell-centered control-volume distributed multi-point flux approximation (CVD-MPFA) finite-volume formulation is presented for discrete fracture-(rock)matrix flow simulations. The grid is aligned with the fractures and barriers which are then modeled by lower-dimensional interfaces located between rock matrix cells in the physical domain. The n D (n-dimension) pressure equation in the rock matrix is coupled with the (n−1)D pressure equation in the fractures, leading to the first reduced dimensional flux-continuous CVD-MPFA formulation. This formulation naturally handles fractures efficiently on unstructured grids. Matrix-fracture fluxes are expressed in terms of matrix and fracture pressures, resulting in a transfer function, which is added to the lower-dimensional flow equation. An additional transmission condition is used between matrix cells separated by low permeable fractures to couple the velocity and pressure jump across the fractures. Numerical tests serve to assess the convergence and accuracy of the lower-dimensional fracture model for lower anisotropic fractures having a range of apertures and permeability tensors. A tracer flow transport equation is solved for problems with single and intersecting fractures. A lower-dimensional mass balance for intersecting fracture cells circumvents the more restrictive CFL condition corresponding to standard equi-dimensional approximation with explicit time discretization. Lower-dimensional fracture model results are compared with hybrid-grid and equi-dimensional model results. Fractures and barriers are efficiently modeled by lower-dimensional interfaces which yield comparable results to those of the equi-dimensional model. Highly conductive fractures are modeled as lower-dimensional entities without the use of locally refined grids that are required by the equi-dimensional model, while pressure continuity across fractures is built into the model, without depending on the extra degrees of freedom which must be added locally by the hybrid-grid method. The lower-dimensional fracture model also yields improved results when compared to those of the hybrid-grid model for fractures with low-permeability in the normal direction to the fracture where pressure is discontinuous. In addition, transient pressure simulation involving geologically representative complex fracture networks is presented.
published_date 2015-03-01T03:25:23Z
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