Naslov
Generalized nonequilibrium capillary relations for two-phase flow through heterogeneous media

Autori
Amaziane, Brahim ; Milišić, Josipa Pina ; Panfilov, Mikhail ; Pankratov, Leonid

Izvornik
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics (1539-3755) 85 (2012), 1; 6304-1

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
immiscible; incompressible; two-phase flow; heterogeneous porous media; non-equilibrium; capillary pressure

Sažetak
For two-phase flow in porous medium, the natural medium heterogeneity necessarily gives rise to capillary non-equilibrium effects. The relaxation to the equilibrium is a slow process which should be introduced in the macroscopic flow models. Many non-equilibrium models are based on the phenomenological approach. At the same time there exists a rigorous mathematical way to develop the non-equilibrium equations. Its formalism, developed in Bourgeat and Panfilov , is based on the homogenization of the micro-scale flow equations over medium heterogeneities. In contrast with the mentioned paper in which the case of a sufficiently fast relaxation was analyzed, we consider the case of long relaxation, which leads to the appearance of the long memory at the macroscale. Due to the coupling between the non-linearity and the non-locality in time, the macroscopic model remains however incompletely homogenized in general case. At the same time, frequently only the relationship for the non-equilibrium capillary pressure is of interest for applications. In the present paper, we obtained such an exact relation in two different independent forms, for the case of long memory. This relation is more general than that obtained in . In addition we proved the comparison theorem which determines the upper and lower bounds for the macroscopic model. These bounds represent linear flow models, which are completely homogenized. The results obtained are illustrated by numerical simulations.

Izvorni jezik
Engleski

Znanstvena područja
Matematika, Fizika

POVEZANOST RADA