Kavli Affiliate: Cheng Peng
| First 5 Authors: Chunhua Zhang, Peiyao Liu, Cheng Peng, Lian-Ping Wang, Zhaoli Guo
| Summary:
In this work, we present a macroscopic model for the flow of two immiscible
and incompressible fluids in inhomogeneous porous medium. At the pore scale,
the flow is governed by the fully Navier-Stokes equations while the evolution
of the phase interface is captured by the Cahn-Hilliard equation. Using the
volume averaging method, the upscaled equations describing the averaged
behavior of two fluids at the Darcy scale are obtained, with unclosed terms
related to spatial deviations. Then, spatial derivations are carefully modeled
up to some undetermined coefficients, which could be evaluated by solving
simplified closure problems in each representative volume element. In
particular, the wetting behavior is incorporated into the averaged chemical
potential. The differences between the proposed equations and the empirical
two-phase Darcy-type models are discussed. Finally, a phase-field-based lattice
Boltzmann model for the averaged equations is presented, and numerical results
demonstrate the abilities of the proposed model.
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