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Multi-dimensional higher resolution methods for flow in porous media. / Mohamed Sadok Lamine

Swansea University Author: Mohamed Sadok Lamine

Abstract

Currently standard first order single-point upstream weighting methods are employed in reservoir simulation for integrating the essentially hyperbolic system components. These methods introduce both coordinate-line numerical diffusion (even in 1-D) and cross-wind diffusion into the solution that is...

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Published: 2009
Institution: Swansea University
Degree level: Doctoral
Degree name: Ph.D
URI: https://cronfa.swan.ac.uk/Record/cronfa42721
first_indexed 2018-08-02T18:55:23Z
last_indexed 2018-08-03T10:10:55Z
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recordtype RisThesis
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spelling 2018-08-02T16:24:30.2270047 v2 42721 2018-08-02 Multi-dimensional higher resolution methods for flow in porous media. 03a3ab30cc708935b5e6fce7dbbde513 NULL Mohamed Sadok Lamine Mohamed Sadok Lamine true true 2018-08-02 Currently standard first order single-point upstream weighting methods are employed in reservoir simulation for integrating the essentially hyperbolic system components. These methods introduce both coordinate-line numerical diffusion (even in 1-D) and cross-wind diffusion into the solution that is grid and geometry dependent. These effects are particularly important when steep fronts and shocks are present and for cases where flow is across grid coordinate lines. In this thesis, families of novel edge-based and cell-based truly multidimensional upwind formulations that upwind in the direction of the wave paths in order to minimise crosswind diffusion are presented for hyperbolic conservation laws on structured and unstructured triangular and quadrilateral grids in two dimensions. Higher resolution as well as higher order multidimensional formulations are also developed for general structured and unstructured grids. The schemes are coupled with existing consistent and efficient continuous CVD (MPFA) Darcy flux approximations. They are formulated using an IMPES (Implicit in Pressure Explicit in Saturation) strategy for solving the coupled elliptic (pressure) and hyperbolic (saturation) system of equations governing the multi-phase multi-component flow in porous media. The new methods are compared with single point upstream weighting for two-phase and three-component two-phase flow problems. The tests arc conducted on both structured and unstructured grids and involve full-tensor coefficient velocity fields in homogeneous and heterogeneous domains. The comparisons demonstrate the benefits of multidimensional and higher order multidimensional schemes in terms of improved front resolution together with significant reduction in cross-wind diffusion. E-Thesis Petroleum engineering.;Computer engineering. 31 12 2009 2009-12-31 COLLEGE NANME Engineering COLLEGE CODE Swansea University Doctoral Ph.D 2018-08-02T16:24:30.2270047 2018-08-02T16:24:30.2270047 Faculty of Science and Engineering School of Engineering and Applied Sciences - Uncategorised Mohamed Sadok Lamine NULL 1 0042721-02082018162516.pdf 10807490.pdf 2018-08-02T16:25:16.7930000 Output 17396595 application/pdf E-Thesis true 2018-08-02T16:25:16.7930000 false
title Multi-dimensional higher resolution methods for flow in porous media.
spellingShingle Multi-dimensional higher resolution methods for flow in porous media.
Mohamed Sadok Lamine
title_short Multi-dimensional higher resolution methods for flow in porous media.
title_full Multi-dimensional higher resolution methods for flow in porous media.
title_fullStr Multi-dimensional higher resolution methods for flow in porous media.
title_full_unstemmed Multi-dimensional higher resolution methods for flow in porous media.
title_sort Multi-dimensional higher resolution methods for flow in porous media.
author_id_str_mv 03a3ab30cc708935b5e6fce7dbbde513
author_id_fullname_str_mv 03a3ab30cc708935b5e6fce7dbbde513_***_Mohamed Sadok Lamine
author Mohamed Sadok Lamine
author2 Mohamed Sadok Lamine
format E-Thesis
publishDate 2009
institution Swansea University
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 Currently standard first order single-point upstream weighting methods are employed in reservoir simulation for integrating the essentially hyperbolic system components. These methods introduce both coordinate-line numerical diffusion (even in 1-D) and cross-wind diffusion into the solution that is grid and geometry dependent. These effects are particularly important when steep fronts and shocks are present and for cases where flow is across grid coordinate lines. In this thesis, families of novel edge-based and cell-based truly multidimensional upwind formulations that upwind in the direction of the wave paths in order to minimise crosswind diffusion are presented for hyperbolic conservation laws on structured and unstructured triangular and quadrilateral grids in two dimensions. Higher resolution as well as higher order multidimensional formulations are also developed for general structured and unstructured grids. The schemes are coupled with existing consistent and efficient continuous CVD (MPFA) Darcy flux approximations. They are formulated using an IMPES (Implicit in Pressure Explicit in Saturation) strategy for solving the coupled elliptic (pressure) and hyperbolic (saturation) system of equations governing the multi-phase multi-component flow in porous media. The new methods are compared with single point upstream weighting for two-phase and three-component two-phase flow problems. The tests arc conducted on both structured and unstructured grids and involve full-tensor coefficient velocity fields in homogeneous and heterogeneous domains. The comparisons demonstrate the benefits of multidimensional and higher order multidimensional schemes in terms of improved front resolution together with significant reduction in cross-wind diffusion.
published_date 2009-12-31T15:07:16Z
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score 11.08899

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