Retaining an Upper Bound for the Capillary Retention of Two-Phase Flow in Porous Media

Abstract

At the sub-meter scale, capillary retention occurs when two immiscible phases flow across two heterogeneous media. It happens in the upstream medium, and the phase retained depends on the heterogeneity order and the system wettability. This phenomenon has a major impact on the oil recovery and hence requires comprehension. The analysis of the spatial variation in the phase saturation along the flowing domain is well established. However, the literature lacks the general characteristics of capillary retention caused by such variation at various flowing conditions. The continuum model for the flow of two immiscible phases in porous media at steady-state conditions is examined. The analysis is limited to the medium with a single discontinuity in rock properties. In this examination, the characteristics of the capillary retention upstream of the discontinuity are the primary consideration. Three retention regions related to the flow regime are identified: two plateaus and a transition zone occurring, in general, at intermediate capillary number. The width and location of the transition depend on the fractional flow. The crucial finding is related to the identification of an upper bound for the capillary retention and its dependency on the capillary variable ratio and the form of the Leverett J-curve. Two J-models are investigated, and it is shown that, for a given capillary variable ratio, the upper bound depends on the level of flatness of the J-curve at intermediate saturations. Potential implications of the current analysis to reservoir characterization are also discussed.Article HighlightsThree retention regions related to the ow regime are identified: two plateaus and a transition zone occurring at intermediate capillary numbers. The width and position of the transition depend on the fractional flow.An upper bound for the capillary retention is derived and its dependency on the heterogeneity ratio and the form of the Leverett-J curve is discussed..Potential implication to reservoir characterization: In the case of steeper Leverett-J curves with low to moderate random heterogeneity ratios, the upper bound is minimal regardless of the various lithologies and their congurations. In such conditions, the upper bound can be used to assert the insignicance of the eld-scale capillary retention.