ABSTRACT
The grid orientation effect is a long-standing problem plaguing reservoir simulators that employ finite difference schemes for solution. The nine-point finite difference scheme is a well known way of reducing this effect. The schemes available in the literature are applicable only to point distributed grid systems. However, most simulators used in practice employ block centered grid systems. In this report we present a derivation of a new nine-point scheme for the block centered grid systems. The derivation is based on physical consideration and hence is free from any problems such as asymmetry or negativity of interblock transmissibilities that arise in some published schemes. The scheme is applicable to nonuniform rectangular grids and to reservoirs with inhomogeneous permeability distributions; both isotropic and anisotropic cases are treated. The expressions resulting from the new scheme reduce to those published in the literature when a square uniform grid and homogeneous isotropic permeability are considered. The reduction in the grid orientation effect due to the new scheme is illustrated by a study of the steam-flood process in a five-spot pattern.
