Porous media miscible 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. 

When a solution containing a particular chemical species is displaced from a porous medium with the same solution but without the particular chemical species, this miscible displacement produces a chemical species distribution that is dependent on (1) microscope velocities, (2) chemical species diffusion rates, (3) physicochemical reactions of the chemical species with the porous medium, (e.g., soil), and (4) volume of water not readily displaced at saturation (this not-readily displaced water increases as desaturation increases (Nielsen and Biggar, 1961). 

If interfacial tension between two phases becomes zero, then the two phases become miscible. This result is the ultimate aim of many types of FOR to make oil-water interfacial tension equal to 0, so that a displacing fiuid can miscibly displace oil trapped in the porous medium. In practice, it is difficult to make interfacial tension approach 0 for liquids of such different characteristics as oil and water. 

The third problem is known as the Saffinan-Taylor instability of a fluid interface for motion of a pair of fluids with different viscosities in a porous medium. It is this instability that leads to the well-known and important phenomenon of viscous fingering. In this case, we first discuss Darcy s law for motion of a single-phase fluid in a porous medium, and then we discuss the instability that occurs because of the displacement of one fluid by another when there is a discontinuity in the viscosity and permeability across an interface. The analysis presented ignores surface-tension effects and is thus valid strictly for miscible displacement. ... 

Bues, M.A., and M. Aachib. 1991. Influence of the heterogeneity of the solutions on the parameters of miscible displacement in saturated porous medium. I. Stable displacement with density and viscosity contrasts. Exp. Fluids 11 25-32. 

Moissis, D.E., and M.F. Wheeler. 1990. Effect of the structure of the porous medium on unstable miscible displacement, p. 243-271. In J.H. Cushman (ed.) Dynamics of fluids in hierarchical porous media. Acad. Press, San Diego, CA. 

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... 

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. 

Finally, it is worth noting that, before application, the defoamer consists of a hydrophobic porous medium containing a hydrophobic fluid trapped in the smaller pores with the remainder of the pore space occupied by air. Before exposure to blood flow, it is usual to prime the defoamer with a suitable fluid to remove air. However, we should remember that use of a fluid to displace another fluid (air in this case) with which it is not miscible in a porous medium is not usually complete as those familiar with crude oil production will attest. Perhaps the best approach to this problem is to first flush out the defoamer with CO2 followed by an aqueous priming fluid. 

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