Artículo
Abstract:
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.
Registro:
| Documento: | Artículo |
| Título: | On some numerical methods for solving 2D radial flow towards an oil well |
| Autor: | Savioli, G.B.; Jacovkis, P.M.; Bidner, M.S. |
| Filiación: | Lab. de Ingenieria de Reservorios, Facultad de Ingenieria, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina Instituto de Cálculo, Departamento de Computación, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina |
| Palabras clave: | Finite differences; Linear system; Oil flow; Taylor series |
| Año: | 1998 |
| Volumen: | 47 |
| Número: | 1 |
| Página de inicio: | 17 |
| Página de fin: | 36 |
| Título revista: | Mathematics and Computers in Simulation |
| Título revista abreviado: | Math Comput Simul |
| ISSN: | 03784754 |
| CODEN: | MCSID |
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03784754_v47_n1_p17_Savioli |
Referencias:
- Aziz, K., Settari, A., (1985) Petroleum Reservoir Simulation, , Elsevier, London
- Craig, Y., Sneyd, A., An alternating-direction implicit scheme for parabolic equations with mixed derivatives (1988) Comput. Math. Appl., 16 (4), pp. 341-350
- Franchi, J.R., Harpole, K.J., Bujnowski, S.W., BOAST - A Three-Dimensional (1982) Three-Phase Black Oil Applied Simulation Tool US Department of Energy Report DOE/BC/10033-3, , two volumes
- Golub, G., Van Loan, C., (1989) Matrix Computations, 2nd Ed., , The Johns Hopkins University Press, Baltimore, MD
- Horne, R., (1990) Modern Well Test Analysis - A Computer Aided Approach, , Petroway, Inc. Palo Alto, CA, USA
- Peaceman, D., (1977) Fundamentals of Numerical Reservoir Simulation, , Elsevier, New York
- Savioli, G.B., (1996) Modelos Matemáticos en Ingeniería de Reservorios, , Ph.D. Thesis, Department of Mathematics, School of Exact Sciences, University of Buenos Aires
- Savioli, G.B., Bidner, M.S., Jacovkis, P.M., The influence of heterogeneities on well test pressure response: A sensitivity analysis (1996) Society of Petroleum Engineers Advanced Technology Series, 4, pp. 67-72
- Savioli, G.B., Goldschmit, M.B., Bidner, M.S., Discusión sobre las soluciones analíticas y numéricas de la ecuación radial de difusividad que representa el flujo en medios porosos (1988) Revista Brasileira de Engenharia, 5 (2), pp. 65-79
- 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 (1997) Comput Math. Appl., 33 (3), pp. 121-135
- Varga, R., (1962) Matrix Iterative Analysis, , Prentice-Hall, Englewood Cliffs, NJ
- Yousif, W., Evans, D., Application of the AGE algorithm to the SLOR and ADI methods (1987) Comput. Math. Appl., 14 (3), pp. 225-228
Citas:
---------- APA ----------
Savioli, G.B., Jacovkis, P.M. & Bidner, M.S. (1998) . On some numerical methods for solving 2D radial flow towards an oil well. Mathematics and Computers in Simulation, 47(1), 17-36.Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03784754_v47_n1_p17_Savioli [ ]
---------- CHICAGO ----------
Savioli, G.B., Jacovkis, P.M., Bidner, M.S. "On some numerical methods for solving 2D radial flow towards an oil well" . Mathematics and Computers in Simulation 47, no. 1 (1998) : 17-36.Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03784754_v47_n1_p17_Savioli [ ]
---------- MLA ----------
Savioli, G.B., Jacovkis, P.M., Bidner, M.S. "On some numerical methods for solving 2D radial flow towards an oil well" . Mathematics and Computers in Simulation, vol. 47, no. 1, 1998, pp. 17-36.Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03784754_v47_n1_p17_Savioli [ ]
---------- VANCOUVER ----------
Savioli, G.B., Jacovkis, P.M., Bidner, M.S. On some numerical methods for solving 2D radial flow towards an oil well. Math Comput Simul. 1998;47(1):17-36.Available from: https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03784754_v47_n1_p17_Savioli [ ]
