Stability analysis and numerical simulation of 1-D and 2-D radial flow towards an oil well

The radial flow of oil towards a well in one and two dimensions is modeled by a family of finite difference schemes. This family depends on one parameter θ, 0 ≤ θ ≤ 1. The stability of the proposed schemes is analyzed applying the matrix method, which takes into account boundary conditions. Particul...

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Autores principales: Savioli, G.B., Jacovkis, P.M., Bidner, M.S.
Formato: JOUR
Materias:
Finite differences
Oil flow
Simulation
Stability analysis
Boundary conditions
Computer simulation
Eigenvalues and eigenfunctions
Finite difference method
Mathematical transformations
Matrix algebra
Oil wells
Block successive over relaxation (BSOR) method
Radial flow
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_08981221_v33_n3_p121_Savioli
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id todo:paper_08981221_v33_n3_p121_Savioli
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spelling todo:paper_08981221_v33_n3_p121_Savioli2023-10-03T15:43:58Z Stability analysis and numerical simulation of 1-D and 2-D radial flow towards an oil well Savioli, G.B. Jacovkis, P.M. Bidner, M.S. Finite differences Oil flow Simulation Stability analysis Boundary conditions Computer simulation Eigenvalues and eigenfunctions Finite difference method Mathematical transformations Matrix algebra Oil wells Block successive over relaxation (BSOR) method Radial flow The radial flow of oil towards a well in one and two dimensions is modeled by a family of finite difference schemes. This family depends on one parameter θ, 0 ≤ θ ≤ 1. The stability of the proposed schemes is analyzed applying the matrix method, which takes into account boundary conditions. Particularly, in the 2-D case, an "almost pentadiagonal" matrix is obtained choosing an appropriate order of equations and unknowns. We prove that this matrix may be symmetrized by a similarity transformation. Therefore, studying bounds for the corresponding eigenvalues, unconditional stability is found for θ ≥ 1/2 and stability restrictions are established for θ < 1/2. Numerical simulations are presented using the BSOR (Block Successive Over Relaxation) method to solve the resulting system of linear equations. The finite difference solution has perfectly reproduced the analytical solution of a simplified 1-D model. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_08981221_v33_n3_p121_Savioli
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Finite differences
Oil flow
Simulation
Stability analysis
Boundary conditions
Computer simulation
Eigenvalues and eigenfunctions
Finite difference method
Mathematical transformations
Matrix algebra
Oil wells
Block successive over relaxation (BSOR) method
Radial flow
spellingShingle Finite differences
Oil flow
Simulation
Stability analysis
Boundary conditions
Computer simulation
Eigenvalues and eigenfunctions
Finite difference method
Mathematical transformations
Matrix algebra
Oil wells
Block successive over relaxation (BSOR) method
Radial flow
Savioli, G.B.
Jacovkis, P.M.
Bidner, M.S.
Stability analysis and numerical simulation of 1-D and 2-D radial flow towards an oil well
topic_facet Finite differences
Oil flow
Simulation
Stability analysis
Boundary conditions
Computer simulation
Eigenvalues and eigenfunctions
Finite difference method
Mathematical transformations
Matrix algebra
Oil wells
Block successive over relaxation (BSOR) method
Radial flow
description The radial flow of oil towards a well in one and two dimensions is modeled by a family of finite difference schemes. This family depends on one parameter θ, 0 ≤ θ ≤ 1. The stability of the proposed schemes is analyzed applying the matrix method, which takes into account boundary conditions. Particularly, in the 2-D case, an "almost pentadiagonal" matrix is obtained choosing an appropriate order of equations and unknowns. We prove that this matrix may be symmetrized by a similarity transformation. Therefore, studying bounds for the corresponding eigenvalues, unconditional stability is found for θ ≥ 1/2 and stability restrictions are established for θ < 1/2. Numerical simulations are presented using the BSOR (Block Successive Over Relaxation) method to solve the resulting system of linear equations. The finite difference solution has perfectly reproduced the analytical solution of a simplified 1-D model.
format JOUR
author Savioli, G.B.
Jacovkis, P.M.
Bidner, M.S.
author_facet Savioli, G.B.
Jacovkis, P.M.
Bidner, M.S.
author_sort Savioli, G.B.
title Stability analysis and numerical simulation of 1-D and 2-D radial flow towards an oil well
title_short Stability analysis and numerical simulation of 1-D and 2-D radial flow towards an oil well
title_full Stability analysis and numerical simulation of 1-D and 2-D radial flow towards an oil well
title_fullStr Stability analysis and numerical simulation of 1-D and 2-D radial flow towards an oil well
title_full_unstemmed Stability analysis and numerical simulation of 1-D and 2-D radial flow towards an oil well
title_sort stability analysis and numerical simulation of 1-d and 2-d radial flow towards an oil well
url http://hdl.handle.net/20.500.12110/paper_08981221_v33_n3_p121_Savioli
work_keys_str_mv AT savioligb stabilityanalysisandnumericalsimulationof1dand2dradialflowtowardsanoilwell
AT jacovkispm stabilityanalysisandnumericalsimulationof1dand2dradialflowtowardsanoilwell
AT bidnerms stabilityanalysisandnumericalsimulationof1dand2dradialflowtowardsanoilwell
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