Modeling of early- and late-time countercurrent spontaneous imbibition in porous media: A semi-analytical approach

Abstract

Countercurrent spontaneous imbibition (SI) is an important flow mechanism to recover oil in water-wet porous media through capillarity. Experimental imbibition tests conducted in core samples show that oil recovery as a function of time occurs in a characteristic S-shaped curve, which describes the infinite-acting and the boundary-dominated regime. Although several dimensionless time groups have been proposed to model countercurrent SI in porous media, they fail to properly scale the results, causing inaccurate estimates of oil recovery. In this work, we present a new approach, using a hybrid solution, to model countercurrent SI for oil-water systems dominated by capillary forces. The infinite-acting regime is modeled by an early-time solution using a new dimensionless time group, which enables the correct scaling of imbibition results onto a universal single curve. To model the boundary-dominated regime, we introduce a late-time solution derived as a function of a characteristic distribution of saturation to estimate the flow behavior after the imbibing fluid reaches the no-flow boundary. The novelty of the model is that it enables the accurate estimation of fluid imbibition under the boundary-dominated regime, a flow condition critical to evaluate the true potential of countercurrent SI driven by capillarity for oil recovery in porous media. We verified the model against numerical simulations under a wide range of flow conditions relevant in water-oil systems, and used experimental data reported in the literature to validate our model. The solution presented provides an accurate approach to model countercurrent SI, which could be extended for dynamic conditions and the modeling of the flow of fluids in fractured media.