Unstable fronts in a porous medium (Q1086098)

A stochastic numerical scheme is used to follow the motion of a fluid interface through a porous medium. Fluid velocities are computed by Darcy's law, but the interface is advanced at a single point chosen with probability proportional to the pressure gradient. Although the expected result of each time step is proportional to that predicted by a continuum calculation, the discreteness of the scheme excites the (physical) instability which occurs when the fluid initially saturating the porous medium is displaced by a fluid of lower viscosity. The example of a five-spot oil reservoir is studied; predicted sweep efficiencies are slightly higher than experimental results, but the form of the fingering is in good qualitative agreement with experiments, even at high viscosity ratios. Grid orientation effects are low, and the effect of grid size can be reduced if care is taken to preserve trapped islands of fluid.