Porous media immiscible displacement

The displacement flows can be miscible (brine after polymer solution, C02 after oil, steam after water) or immiscible (water after oil). In the former case, it is the mixing process itself which has to be understood and modeled steam recovery requires the thermal transport problem to be accurately modeled. In the latter case, the two fluid phases coexist within the porous medium their relative proportions are determined not only by flow and mixing processes, but equally by interfacial and surface tensions between the three phases (matrix material included). Local (capillary) variations in pressure between the two fluid phases become important. The overall flow field is determined by large-scale pressure gradients. 

One phase displacing another from a porous medium is termed immiscible displacement. The process is usually inefficient from the standpoint of how much of the original phase can be displaced, which is the reason that large amounts of crude oil remain unrecovered in abandoned reservoirs. 

Mungan, N., 1966b. Interfacial effects in immiscible liquid-liquid displacement in porous medium. SPEJ (September), 247-253. 

More sophisticated one-dimensional models have included deadend pores, ink-bottle pores, pockets or turner structures, and also, periodically constricted tubes. Two-dimensional and three-dimensional network models have also been developed. The first proposal for a two-dimensional network model was given by Fatt (37, 38). Whereas Fatt primarily dealt with immiscible displacement, Simon and Kelsey (39) used a two-dimensional network model for the simulation of miscible displacement. The first three-dimensional network model is due to Irmay (40). Subsequently, the three-dimensional network model or percolation theory for porous medium has received much attention... 

Aqueous immiscible flow, or immiscible displacement, irrvolves the simultaneous flow of two or more immiscible fluids in the porous medium. Since the fluids are immiscible, the interfacial tension between the two fluids is not zero, and a distinct fluid-fluid interface separates the flirids. 

At the end of secondary oil recovery processes, the residual oil is dispersed throughout the reservoir rock in the form of small oil ganglia (nodular blobs) each of which occupies one to, say, fifteen contiguous microchambers of the porous medium. The rest of the porous space is taken by formation water. It is the object of enhanced oil recovery methods to mobilize as much as possible of this residual oil by miscible and/or immiscible displacement. 

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