A New Mathematical Model for EOR Displacements Honouring Oil Ganglia
Authors: Bedrikovetsky P. 
Published: December 2007

Abstract
During two-phase flow in porous media non-wetting phase is present simultaneously in states of mobile connected continuum and of trapped isolated ganglia. Mass exchange between these two parts of non-wetting phase is going on by dissolution and diffusion of component in the wetting phase, so, compositions of non-wetting phase in both parts are different. Nevertheless, the traditional mathematical model for two-phase multicomponent transport (EOR) in porous media assumes the homogeneous distribution of each component in the overall non-wetting phase. New governing equations honouring ganglia of non-wetting phase are derived. They are successfully verified by a number of laboratory tests. Analytical model is developed for miscible water-alternate-gas (WAG) displacement. The modelling shows that after miscible WAG a significant amount of oil is left in porous media while the traditional model predicts that the miscible displacement results in the total sweep.

Introduction
Basic equations for two-phase multicomponent (EOR) transport in porous media contain phase saturations and concentration of each component in each phase. It means that the model assumes the homogeneity of distribution of components in each phase.
Nevertheless, non-wetting phase is present in porous media as a continuous phase and also as separated ganglia and droplets. If the component is soluble in non-wetting phase and is insoluble in wetting phase, it cannot freely diffuse between the continuous part of non-wetting phase and the ganglia of non-wetting phase. Therefore, concentrations of this component in the continuous part and in the ganglia of the non-wetting phase are different. Therefore, the basic equations for two-phase multicomponent transport in porous media are to be modified.
The separation of non-wetting phase on continuous part and on ganglia was observed during the laboratory displacement under a microscope and by the network micro modelling of two-phase displacements.
The division of the overall phase saturation on the continuous part and on the separated part has been proposed in the literature. Equations for immiscible displacement honouring discontinuity of one phase have been derived, and they coincide with the traditional Rapoport-Leas model.
In the current paper we derive equations for two-phase transport of multicomponent fluids honouring phase discontinuities. The equations derived differ significantly from the traditional model which assume the homogeneous distribution of components in each phase. The model derived has a hysteretic behaviour such that the system of governing equations and formulation of initial and boundary value problems are different for imbibition and for drainage.
The model has been successfully verified by comparison with a number of laboratory experiments.
Analytical solutions for one-dimensional miscible WAG displacement have been obtained. The solutions show that a significant amount of oil is left in porous media after the displacement in ganglia state, while the traditional model gives the total sweep of oil after miscible displacement.

Formulation of the Phenomenon
After displacement of oil by water in water-wet porous media the residual oil forms separated ganglia and droplets (Fig. 1a). Capillary forces equilibrate pressure gradient on isolated ganglia, therefore, ganglia are immobile. The mobile part of non-wetting phase is geometrically connected (Fig. 1b). So non-wetting oleic phase is present in porous media in connected mobile state (active phase) and as separated ganglia (trapped phase). Both parts of non-wetting phase are isolated from each other by water.
Under the strong domination of capillary forces over viscous forces the phases are distributed over the porous space according to wettability.
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