High Resolution Schemes In Curvilinear Grids For Reducing The Grid Orientation Effects

Abstract

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.