Crossover from diffusive to convective regimes during miscible displacements in 2D porous media

Miscible displacements are involved in many applications, including enhanced oil recovery and groundwater remediation. When a less viscous and miscible fluid displaces another more viscous one, an unstable front occurs, and its evolution is controlled by the interplay between diffusion and convection. Much of the research has focused on the instability of the mixing zone front, but the crossover of flow regimes during miscible flooding remains unclear. Here, we conduct unstable miscible displacement experiments in rectangular 2D microfluidic models with controlled pore-scale disorder under various flow rates. By quantifying the features of mixing zone and sweep efficiency, we observe and characterize the crossover from diffusive regime to convective regime during flooding. We further study the effects of the flow rate and pore-scale disorder on the crossover time. We show that the increase in flow rate results in an earlier crossover by promoting the convection in the horizontal direction. Moreover, the increasing pore-scale disorder also results in an earlier crossover by inducing a more unstable mixing zone front. We then perform scaling analysis of the crossover time by introducing the coefficient of variation that represents the heterogeneity of the flow geometry. We establish a unified relationship between the scaled crossover time and the Péclet number, which provides a useful approach to predict the crossover time under various conditions. Our work reveals the crossover between flow regimes and improves our understanding of the front evolution during unstable miscible displacement.