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.

中文翻译：

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“毛细管数、润湿角、无序”坐标中侵袭模式的相图：晶格玻尔兹曼研究


孔隙空间异质性（由无序参数以数值形式描述）是强烈影响多孔介质中位移力学的一个因素。本文系统研究了毛细管数、润湿角和孔隙空间无序对不混相置换侵袭模式的同时影响：粘性和毛细管指状、致密置换和各种交叉状态。结果基于在合成微模型和天然砂岩的天然 X 射线计算机断层扫描模型上执行的晶格玻尔兹曼模拟。本文解决了两个目标。首先是首次以 “毛细管数、润湿角、无序 ”坐标呈现三维相图，准确指示侵袭模式的区域。识别基于许多位移特性，例如扫描效率图、分形维数和领先前运动的动力学。根据相图，定义粘性指状、毛细管指状和紧凑位移状态边界的临界润湿角随着无序的增加而向吸水方向移动。毛细管数的减少使粘性指法和紧密置换模式的临界润湿角向排水方向移动，而毛细管指状模式的临界润湿角向渗吸方向移动。第二个目标是确定孔隙空间无序对扫描效率的最大影响，作为毛细管数和润湿角的函数。已经发现，在高毛细管数下，无序效应与润湿角无关。毛细管数的减少增强了对扫描效率的最大无序效应，并且它变得强烈依赖于润湿角。 随着毛细管力的增加，从深层渗吸和引流状态过渡到具有中性润湿性的模式大大增强了无序的影响。润湿角的极值点（无序影响最大）随着毛细管数的减少而向引流方向移动。