A new adaptive modeling of flow and transport in porous media using an enhanced velocity scheme

dc.contributor.advisorWheeler, Mary F. (Mary Fanett)
dc.contributor.committeeMemberArbogast, Todd
dc.contributor.committeeMemberBalhoff, Matthew
dc.contributor.committeeMemberTsai, Yen-Hsi Richard
dc.contributor.committeeMemberWildey, Tim
dc.creatorAmanbek, Yerlan
dc.creator.orcid0000-0002-3958-8871
dc.date.accessioned2018-10-17T16:25:45Z
dc.date.available2018-10-17T16:25:45Z
dc.date.created2018-08
dc.date.issued2018-10-09
dc.date.submittedAugust 2018
dc.date.updated2018-10-17T16:25:45Z
dc.description.abstractMultiscale modeling of subsurface flow and transport is a major area of interest in several applications including petroleum recovery evaluations, nuclear waste disposal systems, CO₂ sequestration, groundwater remediation and contaminant plume migration in heterogeneous porous media. During these processes the direct numerical simulation is computationally intensive due to detailed fine scale characterization of the subsurface formations. The main objective of this work is to develop an efficient multiscale framework to reduce usage of fine scale properties associated with advection and diffusion/dispersion, while maintaining accuracy of quantities of interest including mass balance, pressure, velocity, concentration. Another purpose of this work is to investigate the adaptivity criteria in transport and flow problems numerically and/or theoretically based on error estimates. We propose a new adaptive numerical homogenization method using numerical homogenization and Enhanced Velocity Mixed Finite Element Method (EVMFEM). We focus on upscaling the permeability and porosity fields for slightly (nonlinear) compressible single phase Darcy flow and transport problems in heterogeneous porous media. The fine grids are used in the transient regions where spatial changes in transported species concentrations are large while a coarse scale problem is solved in the remaining subdomains. Away from transient region, effective macroscopic properties are obtained using local numerical homogenization. An Enhanced Velocity Mixed Finite Element Method (EVMFEM) as a domain decomposition scheme is used to couple these coarse and fine subdomains [85]. Specifically, homogenization is employed here only when coarse and fine scale problems can be decoupled to extract temporal invariants in the form of effective parameters. In this dissertation, a number of numerical tests are presented for demonstrating the capabilities of this adaptive numerical homogenization approach in upscaling flow and transport in heterogeneous porous medium. We have also derived a priori error estimate for a parabolic problem using Backward Euler and Crank-Nicolson method in time and EVMFEM in space. Next, we have established a posteriori error estimate in EVMFEM setting for incompressible flow problems. We first propose the flux reconstruction for error estimates and prove the upper and lower bound theorems. Next, the explicit residual-based estimates and the recovery-based error estimates with the post-processed pressure are derived theoretically. Numerical experiments are conducted to show that the proposed estimators are effective indicators of local error for incompressible flow problems.
dc.description.departmentComputational Science, Engineering, and Mathematics
dc.format.mimetypeapplication/pdf
dc.identifierdoi:10.15781/T26M33P3X
dc.identifier.urihttp://hdl.handle.net/2152/68968
dc.language.isoen
dc.subjectEnhanced velocity
dc.subjectNumerical homogenization
dc.subjectAdaptive mesh refinement
dc.subjectMultiscale methods
dc.subjectError estimates
dc.subjectA posteriori error
dc.subjectA priori error
dc.subjectSPE10 dataset
dc.titleA new adaptive modeling of flow and transport in porous media using an enhanced velocity scheme
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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