Pore-Scale Study of Miscible Displacements in Porous Media Using Lattice Boltzmann Method

Abstract

In the past few years, the miscible displacements in porous media were usually simulated by some semiempirical models based on the volume averaging at the representative elementary volume scale. To better understand the microscopic mechanism of the viscous fingering phenomenon in porous media for miscible fluids, in this paper the miscible displacements processes in porous media are studied using the lattice Boltzmann method (LBM) at the pore scale. First, the code of LBM is tested by simulating the displacement process of two miscible fluids with the same viscosity between two parallel plates which is the well-known Taylor–Aris dispersion problem, and comparing the results with the theoretical predictions. Then, the effects of the Peclet number Pe, the viscosity ratio M and the structure of the porous media on the displacement phenomenon are investigated, and the location and velocity of the finger tip, the displacement efficiency are also studied. In this paper, the displacement efficiency is calculated by $$1-m$$ , here the quantity m is defined as $$m=V_M/V_T$$ , where $$V_M$$ is the volume of more viscous fluids (the displaced fluid) left behind the finger tip, $$V_T$$ is the total pore volume behind the finger tip. It can be found that the “interface” of two fluids will become clearer with the increasing of the Peclet number. As Pe and M are large enough, the viscous fingering phenomenon will occur, and in the front of the finger, “mushroom-like” pattern can be observed. Besides, with the increasing of Pe or M the quantity m will be increased too, i.e., the displacement efficiency will be decreased. While Pe (or M) is greater than a certain value, the growth rate of the quantity m will slow down. The same trend was observed for the miscible displacement in capillary tubes or Hele–Shaw cells. Besides, changing the structure of the porous media makes the finger pattern different. The present simulation results provide a good understanding of the microscopic mechanism of the miscible displacement process in porous media, and also show that the LBM can be a useful tool for investigation miscible fluids behavior in porous media.