Summary
Grid orientation artifacts and smeared fluid fronts can often be seen in the predictions generated by numerical simulations of EOR processes, or even in the simulations of adverse mobility waterfloods. Nine-point techniques exist that can attack these problems but various complications result when these methods are extended to non-square blocks and reservoirs with permeability contrasts.
A new method that avoids these complications is presented and discussed in this paper. The method calculates interblock fluid flows on a staggered grid using an interpolation between pressures taken at the usual finite difference nodes. The computation takes strong reservoir permeability contrasts into account, including those induced by differing fluid saturations at a sharp front. A stream tube decomposition is used to track the actual fluid movements in the reservoir.
Also, a new higher order modification for the calculation of (Darcy) velocities is described. This technique calculates the average effect on mobility of the saturation distribution created during the invasion of a shock into a grid cell and adjusts the velocity accordingly.
The combination of stream tubes and careful convective differencing provides the strong geometric component and accuracy required for accurate modelling.