MODELING OF CAPILLARY PRESSURE HYSTERESIS AND OF HYSTERESIS 
OF RELATIVE PHASE PERMEABILITIES IN POROUS MATERIALS
ON THE BASIS OF THE PORE ENSEMBLE CONCEPT

O. Yu. Dinariev and D. N. Mikhailov

UDC 532.546

We propose a class of models of porous media based on the 
pore ensemble concept with a certain distribution of the main geometric 
parameters (e.g., pore size). The case of the saturation of the pore 
space with a two-phase liquid mixture has been considered. The transfer 
laws are deduced from the free energy dissipation condition. The hydrodynamic 
connection of pores is described by two kinds of kernels: one kernel 
describes the connection of pores in the space, and the other kernel 
describes the connection of pores in an elementary macrovolume. A 
simple model of capillary pressure hysteresis associated with the 
monotonicity of the function of the area-to-volume ratio of the pore 
is proposed. The results of numerical calculations of the capillary 
pressure hysteresis and relative phase permeabilities are presented.

O. Yu. Schmidt Joint Institute of Physics of the Earth, Russian Academy 
of Sciences, 10 B. Gruzinskaya Str., Moscow, 123810, Russia; 
email: dinariev@mail.ru. Translated from Inzhenerno-Fizicheskii 
Zhurnal, Vol. 81, No. 6, pp. 1086-1093, November-December, 
2008. Original article submitted June 15, 2007.