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Description
Macroscopic modeling of two phase flow in porous media requires a so-called capillary pressure relationship that has been motivating active research during the past 40 years. So far, existing models remain however empirical at some level of their derivation Hassanizadeh and Gray (1990, 1993).
In this work, a macroscopic dynamic capillary pressure equation is derived assuming the existence of a representative (periodic) unit cell to locally describe momentum transport. This is carried out with an adjoint method and a Green's formulation, requiring no other simplifying assumption. The macroscopic dynamic capillary pressure is shown to be controlled by the pressure gradient (and body forces) in each phase, and interfacial effects (Lasseux and Valdés-Parada, 2023). The effective coefficients involved in this equation are all obtained from the solution of the adjoint (or closure) problem on a periodic unit cell. Predictions of this model are validated through excellent comparisons with direct numerical simulations on a model porous structure.
References
Hassanizadeh, S.M. and Gray, W.G. 1990 Mechanics and thermodynamics of multiphase flow in porous media including interphase boundaries. Adv. Water Resour. 13 (4), 169–186.
Hassanizadeh, S.M. and Gray, W.G. 1993 Thermodynamic basis of capillary pressure in porous media. Water Resour. Res. 29 (10), 3389–3405.
Lasseux, D. and Valdés-Parada, F.J., 2023, Upscaled dynamic capillary pressure for two-phase flow in porous media, J. Fluid Mech., 959, R2.
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