Unsteady state capillary retention in porous media

Compared to the standard Buckley–Leverett viscous flow, the capillary force causes phase retention in a medium characterized by discontinuous heterogeneity in the direction of displacement. A cross-bedded sandstone is a good example of such heterogeneity. Recent reviews have shown that during unsteady state displacement of oil by water, oil retention occurs and leads to an underestimation of oil recovery when compared to the standard Buckley–Leverett theory. To the best of current knowledge, The mechanism by which capillary effects give rise to this observation is not well explained. The current work aims to describe this mechanism in depth using the two phase steady and unsteady state theory.

The analysis is applied to the steady state governing flow equations for a semi-infinite and water-wet flow domain composed of a finite heterogeneous followed by infinitely homogeneous medium. Near the capillary limit, it shows that the retention in the heterogeneity region depends primarily on the capillary variable at the homogeneous part. At this regime, water or oil retention is possible. In the capillary-viscous regime, however, oil retention occurs and it is independent of the fractional flow injected. The concept of (stationary zone) in the capillary pressure-saturation profile helps explain why oil is retained in water-wet medium. These steady state results are demonstrated numerically to hold for unsteady state displacement. The oil recovery of the viscous flow is overestimated, and the difference becomes larger for larger end-point mobility ratios. The retention theory are discussed in conjunction with drainage experiment using a porous medium composed of packs of glass beads of different diameters to establish permeability variation. The retained phase is in agreement with analytical results on capillary retention.