Finite volume approximation of the three-dimensional flow equation in axisymmetric, heterogeneous porous media based on local analytical solution

Handle URI:
http://hdl.handle.net/10754/562936
Title:
Finite volume approximation of the three-dimensional flow equation in axisymmetric, heterogeneous porous media based on local analytical solution
Authors:
Salama, Amgad ( 0000-0002-4463-1010 ) ; Li, Wang; Sun, Shuyu ( 0000-0002-3078-864X )
Abstract:
In this work the problem of flow in three-dimensional, axisymmetric, heterogeneous porous medium domain is investigated numerically. For this system, it is natural to use cylindrical coordinate system, which is useful in describing phenomena that have some rotational symmetry about the longitudinal axis. This can happen in porous media, for example, in the vicinity of production/injection wells. The basic feature of this system is the fact that the flux component (volume flow rate per unit area) in the radial direction is changing because of the continuous change of the area. In this case, variables change rapidly closer to the axis of symmetry and this requires the mesh to be denser. In this work, we generalize a methodology that allows coarser mesh to be used and yet yields accurate results. This method is based on constructing local analytical solution in each cell in the radial direction and moves the derivatives in the other directions to the source term. A new expression for the harmonic mean of the hydraulic conductivity in the radial direction is developed. Apparently, this approach conforms to the analytical solution for uni-directional flows in radial direction in homogeneous porous media. For the case when the porous medium is heterogeneous or the boundary conditions is more complex, comparing with the mesh-independent solution, this approach requires only coarser mesh to arrive at this solution while the traditional methods require more denser mesh. Comparisons for different hydraulic conductivity scenarios and boundary conditions have also been introduced. © 2013 Elsevier B.V.
KAUST Department:
Physical Sciences and Engineering (PSE) Division; Environmental Science and Engineering Program; Computational Transport Phenomena Lab; Earth Science and Engineering Program
Publisher:
Elsevier BV
Journal:
Journal of Hydrology
Issue Date:
Sep-2013
DOI:
10.1016/j.jhydrol.2013.07.036
Type:
Article
ISSN:
00221694
Appears in Collections:
Articles; Environmental Science and Engineering Program; Physical Sciences and Engineering (PSE) Division; Earth Science and Engineering Program; Computational Transport Phenomena Lab

Full metadata record

DC FieldValue Language
dc.contributor.authorSalama, Amgaden
dc.contributor.authorLi, Wangen
dc.contributor.authorSun, Shuyuen
dc.date.accessioned2015-08-03T11:16:12Zen
dc.date.available2015-08-03T11:16:12Zen
dc.date.issued2013-09en
dc.identifier.issn00221694en
dc.identifier.doi10.1016/j.jhydrol.2013.07.036en
dc.identifier.urihttp://hdl.handle.net/10754/562936en
dc.description.abstractIn this work the problem of flow in three-dimensional, axisymmetric, heterogeneous porous medium domain is investigated numerically. For this system, it is natural to use cylindrical coordinate system, which is useful in describing phenomena that have some rotational symmetry about the longitudinal axis. This can happen in porous media, for example, in the vicinity of production/injection wells. The basic feature of this system is the fact that the flux component (volume flow rate per unit area) in the radial direction is changing because of the continuous change of the area. In this case, variables change rapidly closer to the axis of symmetry and this requires the mesh to be denser. In this work, we generalize a methodology that allows coarser mesh to be used and yet yields accurate results. This method is based on constructing local analytical solution in each cell in the radial direction and moves the derivatives in the other directions to the source term. A new expression for the harmonic mean of the hydraulic conductivity in the radial direction is developed. Apparently, this approach conforms to the analytical solution for uni-directional flows in radial direction in homogeneous porous media. For the case when the porous medium is heterogeneous or the boundary conditions is more complex, comparing with the mesh-independent solution, this approach requires only coarser mesh to arrive at this solution while the traditional methods require more denser mesh. Comparisons for different hydraulic conductivity scenarios and boundary conditions have also been introduced. © 2013 Elsevier B.V.en
dc.publisherElsevier BVen
dc.subjectAnalytical methodsen
dc.subjectCylindrical coordinate systemen
dc.subjectFinite volume methoden
dc.subjectFlow in porous mediaen
dc.titleFinite volume approximation of the three-dimensional flow equation in axisymmetric, heterogeneous porous media based on local analytical solutionen
dc.typeArticleen
dc.contributor.departmentPhysical Sciences and Engineering (PSE) Divisionen
dc.contributor.departmentEnvironmental Science and Engineering Programen
dc.contributor.departmentComputational Transport Phenomena Laben
dc.contributor.departmentEarth Science and Engineering Programen
dc.identifier.journalJournal of Hydrologyen
dc.contributor.institutionBeijing Key Laboratory of Urban Oil and Gas Distribution Technology, China University of Petroleum, Beijing 102249, Chinaen
kaust.authorSalama, Amgaden
kaust.authorSun, Shuyuen
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