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Abstract

A model is formulated in order to study the transient behavior of oil ganglion populations during immiscible displacement in oil recovery processes. The model is composed of three components: a suitable model for granular porous media; a stochastic simulation method capable of predicting the expected fate (mobilization, breakup, stranding) of solitary oil ganglia moving through granular porous media; and two coupled ganglion population balance equations, one applying to moving ganglia and the other to stranded ones. The porous medium model consists of a regular network of randomly sized unit cells of the constricted tube type. Based on this model and a mobilization-breakup criterion, computer aided simulations provide probabilistic information concerning the fate of solitary oil ganglia. Such information is required in the ganglion population balance equations, the solution of which delineates the conditions under which oil bank formation suceeds or fails. Successful oil bank formation depends on the outcome of the competition between the process of oil ganglion deterioration through breakup and stranding on one hand and the process of oil ganglion collision and coalescence on the other. The parameters entering the system of population balances are initial ganglion number concentration, average ganglion velocity, ganglion dispersion coefficients, ganglion stranding coefficient, ganglion breakup coefficient and probability of coalescence given a collision. These parameters are, in turn, functions of the porous medium geometry, capillary number, ganglion size distribution, flood velocity, oil saturation and flood composition.