A pseudo function approach in reservoir simulation

Abstract. In this paper we develop a pseudo function approach to obtain relative permeabilities for the numerical simulation of three-dimensional petroleum reservoirs. This approach follows the idea of an experimental approach and combines an analytical solution technique for two-phase flow with a numerical simulation technique for cross-sectional models of these three-dimensional reservoirs. The advantages of this pseudo function approach are that the heterogeneity of these reservoirs in the vertical direction and various forces such as capillary and gravitational forces can be taken into account in the derivation of the relative permeabilities. Moreover, this approach considers more physical and fluid factors and is more robust and accurate than the experimental approach. To reservoir engineers, the study of pseudo functions for the crosssectional models of different types itself is the study of numerical simulation sensitivity of displacement processes in reservoirs. From this study they can understand the reservoir production mechanism and development indices. Key Words. Reservoir simulation, pseudo function, mechanics of porous medium flow, cross-sectional model, non-dimensional cumulative production, relative permeability. 1

Block compressed storage and computation in the large-scale reservoir simulation

The block compressed storage and solving methods in reservoir simulation are explored to resolve large sparse linear equations emerging in three-phase black oil model. In this paper, the active nodes are compressed firstly, and then the block main diagonal elements, nonzero block elements in lower triangular and upper triangular are separately stored into three real arrays. Owing to the coefficient matrix arising in the reservoir simulation being symmetrical, the addresses of block elements in lower triangular are deposited in three integer arrays. This block compressed storage method can save lots of memory and reduce the search frequencies of non-zero elements. On the basis of such compression storage, the block incomplete LU preconditioned generalized minimal residual method (GMRES) is adopted to solve the equations, showing that it is an effective method possessing fast convergence and good stability. Testing of black oil model example reveals that the block compressed storage and solving methods are effective in solving the large-scale reservoir simulation. Key words: reservoir simulation, black oil model, active nodes compression, block compressed storage, block ILU factorization, block generalized minimal residual metho