Abstract
This article presents a new theory for flow in porous media of a mixture of nonreacting chemical components. In the examples considered, these components are hydrocarbons and water. The model presented assumes that porosity is constant and uniform, and that the wetting properties of the medium are nearly neutral. The flow equations are obtained by starting with the balance equations (mass, momentum, and energy) at pore level, and averaging them over a large number of pores, using the diffuse interface assumption then the methods of irreversible thermodynamics, thus obtaining, among other things, the collective convective velocity and the component-wise diffusive velocities as functions of the component densities. When the simplification of uniform temperature is introduced, the flow equations are of the Cahn–Hilliard type (with an extra term accounting for gravitation) where the thermodynamic function is the Helmholtz free energy per unit volume of the mixture. There are no relative permeabilities. Also, the set of equations is complete in the sense that no flash calculations are necessary, phase segregation being part of the calculation. The numerical examples considered are: (i) phase segregation in a gravitational field and (ii) coning where the initial state is fully segregated.
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Papatzacos, P. A Model for Multiphase and Multicomponent Flow in Porous Media, Built on the Diffuse-Interface Assumption. Transp Porous Med 82, 443–462 (2010). https://doi.org/10.1007/s11242-009-9405-2
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DOI: https://doi.org/10.1007/s11242-009-9405-2