The formation of viscous limited saturation zones behind rapid drainage fronts in porous media

Abstract

Drainage characteristics of porous media are shaped by an interplay between gravitational, capillary and viscous forces that result in complex phase invasion patterns and dynamics. We propose a mechanistic model for viscous separation of temporary phase detention behind rapidly moving drainage fronts. The viscous-limited region forming behind the front tip (tip of furthest penetrated air finger) drains at a slower rate with a characteristic time scale τ dictated by hydraulic decoupling expressed by the hydraulic properties of the medium. The region where saturation becomes viscously detained (temporarily entrapped) is determined by a critical water content θcrit that defines a viscous length LV behind the front tip. Theory developed to predict the critical water content θcrit and the characteristic secondary timescale τ was in good agreement with measured drainage characteristics using neutron radiography and direct imaging. The observed critical water content θcrit increased with higher drainage rates as predicted by theory with consideration of a percolation threshold. The observed slow drainage timescale τ as a function of mean drainage rate depended on the critical water content θcrit and the resulting counteracting effects of increased detained liquid volume and increased conductivity of the viscous limited region. The concept of drainage zonation illustrates how increasing flow rates enhances the extent of viscous limitations behind the main drainage front. The new insights could be useful for management of immiscible fluid displacement, quantification of averaging effects in experimental measurements (dynamic effects on pc-S relationship), and explain some of the underpinnings of the field capacity phenomenon.