Since long time it has been recognized that the typical pore size is a fundamental scale in understanding of transport phenomena and determination of global transport properties of porous media. In a similar way like the Navier-Stokes equations may be used at certain limit to derive the Darcy law and define single phase transport properties, the modified Navier-Stokes model might be used to determine medium two-phase flow properties. Instead of using a regularization technique to capture the interface (cf. VOF or level-set functions approach), which may affect the modelling results in a non-trivial way, the diffuse interface method offers a thermodynamic treatment of phase “mixing” zone. As a result, it is a good choice for a numerical technique, handling the morphological changes of the interface which is of great importance for modelling of such a kind. Like zero-order approximation which is at the same time the classical theory assumptions case, the two-phase flow properties (e.g. phase relative permeabilities) are simply two ultimate single phase flow configurations, one per each phase. In both cases only volumes occupied by one fluid are considered so that wetting and capillary properties becomes very important, probably along with the process history as they all are responsible for particular fluid distribution in pore space. Taking advantage of recent advancements in X-ray computed micro-tomography (μCT), the reconstructed real porous medium samples (Bentheimer sandstone) are used for direct numerical simulations (DNS) of single and two-phase transport problems. Main model parameters - capillary, Reynolds, Cahn and Peclet numbers - are defined for each flow case. Emphasis is made on characterization of different steps and features of methodology based on μCT measurements, geometrical reconstruction, grid generation and computational models. The contribution of DNS to understanding of transport phenomena in real media becomes increasingly important factor of porous medium description efforts.


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