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 di mensions to model the single phase flow of oil through heterogeneous p orous media. That family depends on one parameter theta, 0 less than o r equal to theta less than or equal to 1. Using a suitable order of eq uations 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 condition s for this technique are established and the most convenient theta is selected to increase the time step Delta t. Besides, TSMF is compared with two iterative methods, ADI and block-SOP, usually applied to solv e multidimensional equations. Both methods, ADI and block-SOR, are ada pted to this particular problem. We conclude that TSMF is the fastest technique using adequate Values of theta and Delta t, but the time inc rement Delta t must remain small because of the convergence condition. On the other hand, block-SOP converges using large values of Delta t, but it uses a large amount of CPU time. ADI is discarded for not pres enting advantages over the other two techniques. Therefore, TSMF is re commended when a shea period of time must be simulated, and block-SOP is suitable for long simulations and applying' a variable time increme nt. (C) 1998 IMACS/Elsevier Science B.V.