Numerical analysis of multiphase flows in porous media on non-rectangular geometry

dc.contributor.advisorArbogast, Todd James, 1957-
dc.contributor.committeeMemberWheeler, Mary F
dc.contributor.committeeMemberGhattas, Omar
dc.contributor.committeeMemberDemkowicz, Leszek F
dc.contributor.committeeMemberHesse, Marc A
dc.creatorTao, Zhen
dc.creator.orcid0000-0001-5063-5889
dc.date.accessioned2018-08-28T17:12:27Z
dc.date.available2018-08-28T17:12:27Z
dc.date.created2017-12
dc.date.issued2017-12-06
dc.date.submittedDecember 2017
dc.date.updated2018-08-28T17:12:27Z
dc.description.abstractFluid flow through porous media is a subject of common interest in many branches of engineering as well as applied natural science. In this work, we investigate the behavior and numerical treatment of multiphase flow in porous media. To be more specific, we take the sequestration of CO₂ in geological media as an example. Mathematical modeling and numerical study of carbon sequestration helps to predict both short and long-term behavior of CO₂ storage in geological media, which can be a benefit in many ways. This work aims at developing accurate and efficient numerical treatment for problems in porous media on non-rectangular geometries. Numerical treatment of Darcy flow and transport have been developed for many years on rectangular and simplical meshes. However, extra effort is required to extend them to general non-rectangular meshes. In this dissertation work, for flow simulation, we develop new H(div)- conforming mixed finite elements (AT and AT [superscript red] ) which are accurate on cuboidal hexahedra. We also develop the new direct serendipity finite element (DS [subscript r] ), which is H¹ -conforming and accurate on quadrilaterals and a special family of hexahedra called truncated cubes. The use of the direct serendipity finite element reduces the number of degrees of freedom significantly and therefore accelerates numerical simulations. For transport, we use the newly developed direct serendipity elements in an enriched Galerkin method (EG), which is locally conservative. The entropy viscosity stabilization is applied to eliminate spurious oscillations. We test the EG-DS [subscript r] method on problems with diffusion, transport, and coupled flow and transport. Finally, we study two-phase flow in heterogeneous porous media with capillary pressure. We work on a new formulation of the problem and force the continuity of the capillary flux with a modification to conquer the degeneracy. The numerical simulation of two-phase flow is conducted on non-rectangular grids and uses the new elements.
dc.description.departmentComputational Science, Engineering, and Mathematics
dc.format.mimetypeapplication/pdf
dc.identifierdoi:10.15781/T2VH5D31P
dc.identifier.urihttp://hdl.handle.net/2152/68171
dc.language.isoen
dc.subjectMultiphase flow
dc.subjectPorous media
dc.subjectMixed finite element
dc.subjectH(div)-approximation
dc.subjectArbogast-Tao element
dc.subjectArbogast-Correa element
dc.subjectDirect serendipity element
dc.subjectSerendipity element
dc.subjectEnriched Galerkin method
dc.subjectEntropy viscosity stabilization
dc.subjectCapillary flux reconstruction
dc.subjectHeterogeneous capillary pressure
dc.subjectTwo-phase flow
dc.titleNumerical analysis of multiphase flows in porous media on non-rectangular geometry
dc.typeThesis
dc.type.materialtext
thesis.degree.departmentComputational Science, Engineering, and Mathematics
thesis.degree.disciplineComputational Science, Engineering, and Mathematics
thesis.degree.grantorThe University of Texas at Austin
thesis.degree.levelDoctoral
thesis.degree.nameDoctor of Philosophy

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