摘要：One of the most important tasks in the numerical simulation of fluid flow problems is the reduction of numerical diffusion contained in the solution. Numerical diffusion is caused by the use of first order interpolation schemes in the approximation of the convective terms in the momentum equations. In petroleum reservoir simulation, a similar problem arises when the mobility is interpolated at the interfaces of the control volumes for the mass fluxes calculation. Depending on the interpolation function used for the mobility, the solution may be contaminated with the so-called grid orientation effect, a similar error as the wellknown numerical diffusion. The grid orientation effect in petroleum reservoir simulation causes different breakthroughs, even when the production wells are symmetrically located with respect to the injection well in a homogeneous media. Usually, the upwind scheme is employed, due to its ability of promoting numerical stability. The price one pays is the introduction of considerable amount of grid orientation effects. In curvilinear grids the problem is even more general, since the grid can be oriented according to the flow lines. In this work it is presented a numerical scheme, using the black-oil model, for the solution of the classical 3-wells and 5-spot problems with the main goal of analyzing the grid orientation effects. A more general interpretation for the grid orientation effect is also given. The UDS and some TVD schemes used for reducing this error are employed and compared.
