Miscible Displacement of Oil in Heterogenous Porous Media

Miscible displacement in porous media is encountered often in the chemical and petroleum industries. This Demonstration illustrates a model of one-dimensional miscible oil displacement in heterogenous porous media. The media are composed of connected pores that permit fluid flow and pores that have no outlet and contain stagnant oil; the stagnant oil is replaced by the solvent via diffusion.

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The following coupled partial and ordinary differential equations describe the mechanism governing the displacement of oil from a porous medium:
,
,
with the following initial and boundary conditions:
,
,
, and
where:
diffusion coefficient
interstitial solvent velocity
fraction of stagnant pore space
mass transfer coefficient
concentration of solvent in the flowing pore space
concentration of solvent in the stagnant pore space
length
time
inlet solvent concentration
initial solvent concentration in the stagnant pore space
initial solvent concentration in the stagnant pore space.
Solutions of these equations exhibit the following characteristics:
1. The effluent solvent concentration profile exhibits the more realistic asymmetry observed in laboratory experiments compared to the symmetric results obtained by solutions of the advection convection equation; the asymmetric tail is the result of stagnant oil being recovered by molecular diffusion.
2. Increasing the solvent velocity increases the rate of solvent and thus the rate of oil removal.
3. For sufficiently high mass transfer coefficient or low fraction of stagnant pore space, the modified equations reduce to the advection convection equation.
Reference
[1] M. Bai and D. Elsworth "On the Modeling of Miscible Flow in Multi-component Porous Media," Transport in Porous Media, 21(1), 1995 pp. 19–46. doi:10.1007/BF00615333.
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