The effect of capillary forces on immiscible two-phase flow in heterogeneous porous media

A selection of these reports is available in PostScript form at the Faculty's anonymous ftp-Abstract We consider the one-dimensional two-phase ow including capillary eeects through a heterogeneous porous medium. The heterogeneity is due to the spatial variation of the absolute permeability and the poros-ity. Both these quantities are assumed to be piecewise constant. At interfaces where the rock properties are discontinuous, we derive, by a regularisation technique, conditions to match the values of the saturation on both sides. There are two conditions: a ux condition and an extended pressure condition. Applying these conditions we show that trapping of the wetting phase may occur near heterogeneities. To illustrate the behaviour of the saturation we consider a time-dependent diiusion problem without convection, a stationary convection-diiusion problem, and the full time-dependent convection-diiusion problem (numerically). In particular the last two problems explicitly show the trapping behaviour.