Lawrence Berkeley National Laboratory

Using an asymptotic technique, valid for a medium with smoothly varying heterogeneity, I derive an expression for the velocity of a propagating, coupled saturation and pressure front. The asymptotic approach produces an explicit expression for the slowness, the inverse of the velocity, of a propagating two-phase front. Because of the nonlinearity of the governing equations, the velocity of the propagating front depends upon the magnitude of the saturation and pressure changes across the front in addition to the properties of the medium. Thus, the expression must be evaluated in conjunction with numerical reservoir simulation. The slowness is governed by the background saturation distribution, the saturation-dependent component of the fluid mobility, the porosity, the permeability, the capillary pressure function, the medium compressibility, and the ratio of the slopes of the relative permeability curves. Numerical simulation of water injection into a porous layer saturated with a nonaqueous phase liquid indicates that two modes of propagation are important. The fastest mode of propagation is a disturbance that is dominated by the change in fluid pressure. This is followed, much later, by a coupled mode associated with a much larger saturation change. These two modes are also observed in a numerical simulation using a heterogeneous porous layer. A comparison between the propagation times estimated from the results of the numerical simulation and predictions from the asymptotic expression indicates overall agreement.