Using Adaptive Mesh Refinement strategies to investigate immiscible fluid flow in fractures

In this paper, we consider two Adaptive Mesh Refinement (AMR) methods to simulate flow through fractures using a novel multiphase model. The approach represents the fluid using a two-dimensional parallel-plate model that employs techniques adapted from lattice-Boltzmann simulations to track the fluid interface. We discuss different mesh refinement strategies for the model and compare their performance to that of a uniform grid. Results from the simulations show excellent agreement between the model and analytical solutions for both unrefined and refined meshes. We also present results from the study that illustrate the behavior of the AMR front-tracking method. The AMR model is able to accurately track the interfacial properties in cases where uniform fine meshes would significantly increase the simulation cost. The ability of the model to dynamically refine the domain is demonstrated by presenting the results from an example with evolving interfaces. Using the AMR model, we compute the relative permeability of immiscible two-phase flow in fractures. The results are successfully validated against the laboratory measurements. From this study, we introduce the interface specific surface area as a parameter to quantify the effect of flow pattern on the relative permeability. It is shown that by decreasing this parameter the fluids intervention decreases and the relative permeability curves approach the linear model. •Adaptive Mesh Refinement is implemented in a Novel Immiscible Fracture Flow Model.•Cell-based and patch-based refinement strategies are presented.•Excellent agreement is obtained between the model and analytical solutions.•With AMR the model successfully simulates sub-grid sized droplets.