Generalized Transmissibilities for Distorted Grids in Reservoir Simulation

Abstract

Abstract Distorted grids or "corner point geometry" have received increased attention as a means of enhancing the modelling flexibility of finite difference type reservoir simulators. Non-rectangular grids permit better alignment with reservoir boundaries and faults and may lead to fewer grid blocks and therefore less computational efforts in simulation of complex reservoirs. This paper shows that caution should be used as regards the transmissibility calculations for distorted grids. Specifically, it is demonstrated by simulation experiments that methods which try to maintain (for 2-D problems) the five-point connectivity of standard finite differences may lead to serious errors. A generalized nine-point scheme is constructed and shown to be more appropriate for distorted grids. For instance, the scheme seems to preserve the accuracy of a square nine-point scheme if the distortion is kept within certain limits. Although based on finite element techniques, the scheme is given a finite difference type form, and can therefore easily be implemented in more general-purpose finite difference type reservoir simulators.