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Abstract:

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.

Registro:

Documento: Artículo
Título:Stability analysis and numerical simulation of 1-D and 2-D radial flow towards an oil well
Autor:Savioli, G.B.; Jacovkis, P.M.; Bidner, M.S.
Filiación:Lab. de Ing. de Reservorios, Facultad de Ingeniería, Ciudad Universitaria, 1428 Buenos Aires, Argentina
Institute de Cálculo, Departamento de Computation, Ciudad Universitaria, 1428 Buenos Aires, Argentina
Palabras clave: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
Año:1997
Volumen:33
Número:3
Página de inicio:121
Página de fin:135
DOI: http://dx.doi.org/10.1016/S0898-1221(96)00242-8
Título revista:Computers and Mathematics with Applications
Título revista abreviado:Comput Math Appl
ISSN:08981221
CODEN:CMAPD
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_08981221_v33_n3_p121_Savioli

Referencias:

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  • Savioli, G., Bidner, M.S., Jacovkis, P., The influence of heterogeneities on well test pressure response - A sensitivity analysis (1996) Society of Petroleum Engineers Advanced Technology Series, 4 (1), pp. 67-72
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Citas:

---------- APA ----------
Savioli, G.B., Jacovkis, P.M. & Bidner, M.S. (1997) . Stability analysis and numerical simulation of 1-D and 2-D radial flow towards an oil well. Computers and Mathematics with Applications, 33(3), 121-135.
http://dx.doi.org/10.1016/S0898-1221(96)00242-8
---------- CHICAGO ----------
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" . Computers and Mathematics with Applications 33, no. 3 (1997) : 121-135.
http://dx.doi.org/10.1016/S0898-1221(96)00242-8
---------- MLA ----------
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" . Computers and Mathematics with Applications, vol. 33, no. 3, 1997, pp. 121-135.
http://dx.doi.org/10.1016/S0898-1221(96)00242-8
---------- VANCOUVER ----------
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. Comput Math Appl. 1997;33(3):121-135.
http://dx.doi.org/10.1016/S0898-1221(96)00242-8