Giving the physics a chance: how to reduce the impact of numerical errors

Numerical errors are generally a bother, but in the case of adverse mobility ratio flows, such as those encountered when injecting water or gas (CO2) in oil reservoirs, they can be a real nuisance. In this talk we discuss the well-known grid orientation effect, which causes solutions to be very different depending on the orientation of the grid with respect to the general flow direction. It is not possible to completely remove this effect without introducing unacceptable levels of numerical damping. However, careful analysis of numerical errors in some popular discretization methods for the governing transport equations gave us two ideas to reduce their impact. The first is a correction of the solution in the critical near-well region, which can be applied to any discretization and gridding method. The second idea amounts to augmentation of existing schemes to render the numerical error that causes most problems isotropic.