In this work, we simulate natural miscible process and miscible fluids displacement in pore space by using lattice-Boltzmann method. In the natural miscible case, the results including concentration profile and thickness of miscible zone agree well with analytical solutions, which verifies the model’s reliability and veracity. The viscosity ratio is also taken into account to study its influence on the miscible process. Furthermore, we apply pressure boundary at inlet and outlet of the channel to study the displacement of miscible fluids. The whole process, in general, is divided into three phases: fluid flow rate increasing driven by pressure gradient, transitional period, and relatively stable stage. And we carefully give each phase explanations of physical mechanisms. The numerical results provide a good understanding of the mechanisms of miscible fluids displacement and confirm that the LBM can be a promising tool for investigating miscible fluids behavior.

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