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Jacovkis, P.M.; Savioli, G.B.; Bidner, M.S. "Mathematical modelling of flow towards an oil well" (1999) Proceedings of the 1998 4th World Congress on Computational Mechanics (IV WCCM). 46(9):1521-1540
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Abstract:

We describe the numerical approximations and applications of a mathematical model that governs the flow of oil towards a well. The flow of a single-phase fluid in a porous medium is governed by a parabolic equation obtained by combining the Darcy's and the continuity equations. In order to account for the spatial variations of porosity and permeability, and for permeability anisotropy, a two-dimensional model is put forward. A mixed initial-boundary value problem is numerically solved by a finite-difference family of numerical schemes, which depends on a parameter θ. The stability - conditional or unconditional, depending on θ - and the convergence of the schemes have been proved. The linear system originated at each time step is solved by the iterative ADI and block-SOR methods, and by a Taylor series of matrix functions (TSMF). These methods are compared and their relative efficiencies are carefully assessed. TSMF is the fastest technique given that adequate values of θ and time step Δt are used - but Δt must remain small. A combination of TSMF and block-SOR with variable At seems to be the best policy. Our numerical simulator is tested by reproducing the existing analytical solutions for limiting cases, and then applied in well test analysis. The contributions of this work are: (1) we introduce the TSMF technique to reservoir simulation and (2) vertical permeability and permeability spatial variations are included in a well test simulator for further developments. Copyright © 1999 John Wiley & Sons, Ltd.

Registro:

Documento: Artículo
Título:Mathematical modelling of flow towards an oil well
Autor:Jacovkis, P.M.; Savioli, G.B.; Bidner, M.S.
Ciudad:Buenos Aires
Filiación:Instituto de Cálcula, Departamento de Computación, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina
Laboratario de Ing. de Reservorios, Universidad de Buenos Aires, Ciudad Universitaria, 1428 Buenos Aires, Argentina
Charcas 3497, 1425 Buenos Aires, Argentina
Palabras clave:Finite differences; Oil flow; Simulation; Stability; Computer simulation; Convergence of numerical methods; Equations of motion; Finite difference method; Initial value problems; Iterative methods; Linear systems; Mathematical models; Matrix algebra; Alternating direction method; Block successive over relaxation method; Darcy law; Oil wells; finite difference technique; mathematical modeling; oil hydraulics; porous medium
Año:1999
Volumen:46
Número:9
Página de inicio:1521
Página de fin:1540
DOI: http://dx.doi.org/10.1002/(SICI)1097-0207(19991130)46:9<1521::AID-NME710>3.0.CO;2-2
Título revista:Proceedings of the 1998 4th World Congress on Computational Mechanics (IV WCCM)
Título revista abreviado:Int J Numer Methods Eng
ISSN:00295981
CODEN:IJNMB
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00295981_v46_n9_p1521_Jacovkis

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Citas:

---------- APA ----------
Jacovkis, P.M., Savioli, G.B. & Bidner, M.S. (1999) . Mathematical modelling of flow towards an oil well. Proceedings of the 1998 4th World Congress on Computational Mechanics (IV WCCM), 46(9), 1521-1540.
http://dx.doi.org/10.1002/(SICI)1097-0207(19991130)46:9<1521::AID-NME710>3.0.CO;2-2
---------- CHICAGO ----------
Jacovkis, P.M., Savioli, G.B., Bidner, M.S. "Mathematical modelling of flow towards an oil well" . Proceedings of the 1998 4th World Congress on Computational Mechanics (IV WCCM) 46, no. 9 (1999) : 1521-1540.
http://dx.doi.org/10.1002/(SICI)1097-0207(19991130)46:9<1521::AID-NME710>3.0.CO;2-2
---------- MLA ----------
Jacovkis, P.M., Savioli, G.B., Bidner, M.S. "Mathematical modelling of flow towards an oil well" . Proceedings of the 1998 4th World Congress on Computational Mechanics (IV WCCM), vol. 46, no. 9, 1999, pp. 1521-1540.
http://dx.doi.org/10.1002/(SICI)1097-0207(19991130)46:9<1521::AID-NME710>3.0.CO;2-2
---------- VANCOUVER ----------
Jacovkis, P.M., Savioli, G.B., Bidner, M.S. Mathematical modelling of flow towards an oil well. Int J Numer Methods Eng. 1999;46(9):1521-1540.
http://dx.doi.org/10.1002/(SICI)1097-0207(19991130)46:9<1521::AID-NME710>3.0.CO;2-2