On some numerical methods for solving 2D radial flow towards an oil well

In this paper we study a family of finite difference schemes in two dimensions to model the single phase flow of oil through heterogeneous porous media. That family depends on one parameter θ, O ≤ θ ≤ 1. Using a suitable order of equations and unknowns, a linear system of equations, with a particula...

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Detalles Bibliográficos
Autores principales:	Savioli, G.B., Jacovkis, P.M., Bidner, M.S.
Formato:	JOUR
Materias:	Finite differences Linear system Oil flow Taylor series
Acceso en línea:	http://hdl.handle.net/20.500.12110/paper_03784754_v47_n1_p17_Savioli
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

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spelling	todo:paper_03784754_v47_n1_p17_Savioli2023-10-03T15:33:06Z On some numerical methods for solving 2D radial flow towards an oil well Savioli, G.B. Jacovkis, P.M. Bidner, M.S. Finite differences Linear system Oil flow Taylor series In this paper we study a family of finite difference schemes in two dimensions to model the single phase flow of oil through heterogeneous porous media. That family depends on one parameter θ, O ≤ θ ≤ 1. Using a suitable order of equations and unknowns, a linear system of equations, with a particular structure, is obtained. The corresponding matrix, excluding the first row and column, has up to five elements in each row, arranged in five diagonals. The system of linear equations is solved by a method based on Taylor series of matrix functions (TSMF). The convergence conditions for this technique are established and the most convenient θ is selected to increase the time step Δt Besides, TSMF is compared with two iterative methods, ADI and block-SOR, usually applied to solve multidimensional equations. Both methods, ADI and block-SOR, are adapted to this particular problem. We conclude that TSMF is the fastest technique using adequate values of θ and Δt, but the time increment Δt must remain small because of the convergence condition. On the other hand, block-SOR converges using large values of Δt, but it uses a large amount of CPU time. ADI is discarded for not presenting advantages over the other two techniques. Therefore, TSMF is recommended when a short period of time must be simulated, and block-SOR is suitable for long simulations and applying a variable time increment. © 1998 IMACS/Elsevier Science B.V. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_03784754_v47_n1_p17_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 Linear system Oil flow Taylor series
spellingShingle	Finite differences Linear system Oil flow Taylor series Savioli, G.B. Jacovkis, P.M. Bidner, M.S. On some numerical methods for solving 2D radial flow towards an oil well
topic_facet	Finite differences Linear system Oil flow Taylor series
description	In this paper we study a family of finite difference schemes in two dimensions to model the single phase flow of oil through heterogeneous porous media. That family depends on one parameter θ, O ≤ θ ≤ 1. Using a suitable order of equations and unknowns, a linear system of equations, with a particular structure, is obtained. The corresponding matrix, excluding the first row and column, has up to five elements in each row, arranged in five diagonals. The system of linear equations is solved by a method based on Taylor series of matrix functions (TSMF). The convergence conditions for this technique are established and the most convenient θ is selected to increase the time step Δt Besides, TSMF is compared with two iterative methods, ADI and block-SOR, usually applied to solve multidimensional equations. Both methods, ADI and block-SOR, are adapted to this particular problem. We conclude that TSMF is the fastest technique using adequate values of θ and Δt, but the time increment Δt must remain small because of the convergence condition. On the other hand, block-SOR converges using large values of Δt, but it uses a large amount of CPU time. ADI is discarded for not presenting advantages over the other two techniques. Therefore, TSMF is recommended when a short period of time must be simulated, and block-SOR is suitable for long simulations and applying a variable time increment. © 1998 IMACS/Elsevier Science B.V.
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	On some numerical methods for solving 2D radial flow towards an oil well
title_short	On some numerical methods for solving 2D radial flow towards an oil well
title_full	On some numerical methods for solving 2D radial flow towards an oil well
title_fullStr	On some numerical methods for solving 2D radial flow towards an oil well
title_full_unstemmed	On some numerical methods for solving 2D radial flow towards an oil well
title_sort	on some numerical methods for solving 2d radial flow towards an oil well
url	http://hdl.handle.net/20.500.12110/paper_03784754_v47_n1_p17_Savioli
work_keys_str_mv	AT savioligb onsomenumericalmethodsforsolving2dradialflowtowardsanoilwell AT jacovkispm onsomenumericalmethodsforsolving2dradialflowtowardsanoilwell AT bidnerms onsomenumericalmethodsforsolving2dradialflowtowardsanoilwell
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On some numerical methods for solving 2D radial flow towards an oil well

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