Phase diagram of invasion patterns in «capillary number, wetting angle, disorder» coordinates: A lattice Boltzmann study

Abstract

Pore space heterogeneity, numerically described by the disorder parameter, is a factor that strongly influences the displacement mechanics in porous media. This paper presents a systematic study of the simultaneous effects of capillary number, wetting angle, and pore space disorder on the invasion patterns of immiscible displacement: viscous and capillary fingering, compact displacement, and various crossover regimes. The results are based on lattice Boltzmann simulations performed on synthetic micromodels and natural X-ray computed tomography models of natural sandstones. This paper addresses two objectives. The first is to present for the first time a three-dimensional phase diagram in «capillary number, wetting angle, disorder» coordinates, which accurately indicates the regions of invasion patterns. The identification is based on a number of displacement characteristics, such as sweep efficiency map, fractal dimension, and the dynamics of the leading front movement. Based on the phase diagram, the critical wetting angles, which define the boundary of the viscous fingering, capillary fingering, and compact displacement regimes, shift towards imbibition with increasing disorder. A decrease in capillary number shifts the critical wetting angles for the viscous fingering and compact displacement modes towards drainage, and for the capillary fingering mode towards imbibition. The second goal is to identify the maximum effect of pore space disorder on sweep efficiency as a function of capillary number and wetting angle. It has been found that at high capillary numbers the disorder effect is independent of the wetting angle. A decrease in capillary number enhances the maximum disorder effect on sweep efficiency and it becomes strongly dependent on the wetting angle. With increased capillary forces the transition from deep imbibition and drainage regimes to the mode with neutral wettability greatly enhances the effect of disorder. The extremum point of wetting angle, at which the effect of disorder is maximum, shifts towards drainage with decreasing capillary number.