Phasefield modelling of a liquid/liquid immiscible displacement through a network of capillaries
Abstract
The liquid/liquid displacement through a 2D uniform network of capillaries is numerically modelled with the use of the phasefield approach. The detailed structure of the flow fields within the uniform matrices of different sizes (with the different number of pores) is examined with the aim to reveal the asymptotic behaviour, pertinent for a sufficiently large matrix, that could be used for representation of a porous medium. The integral characteristics of the flow that do not depend on the matrix size can be used for calculation of the parameters of a macroscopic (Darcy) approach. We demonstrate that qualitatively the displacement occurs very similarly in the matrices with the different number of structural elements. In particular, we show that the capillary pressure remains nearly constant during the displacement run until the breakthrough time (with some minor variations related to a particular shape of a matrix). Upon increase of the matrix size the magnitude of the capillary pressure (and all other integral characteristics of the twophase flow) quickly converges to the limiting value (so that the limiting results are already reached for a matrix with 6 × 6 elements), giving the direct procedure for calculation of the capillary pressure in a porous medium.
 Publication:

Journal of Computational Physics
 Pub Date:
 November 2020
 DOI:
 10.1016/j.jcp.2020.109747
 Bibcode:
 2020JCoPh.42109747V
 Keywords:

 Porous medium;
 Capillary pressure;
 Porelevel modelling;
 Phasefield (CahnHilliard) approach;
 GPU calculations