In order to numerically solve the system of nonlinear partial differential equations which describes multiphase flow in porous media, finite volume discretization in space and finite-difference in time are commonly used in reservoir simulation 1 • This requires the calculation of flow at the boundaries between adjacent blocks using the pressure information at a specific point within each block. Consequently, the knowledge of both, block boundaries and grid point locations are required. Therefore, the distribution of grid points in space and the location of block boundaries with respect to grid points influence the accuracy of finite-difference approximations.In this paper, we investigate the accuracy of six different kinds of gridding systems, which are derived from the classical point-dis~ributed and the block-centered methods. Our goal is to obtain maximum accuracy for a given number of blocks. To achieve this goal, two approaches are studied:1. Given a set of grid points, decide where to place the block boundaries.