Combining discrete element method with lattice Boltzmann modeling to advance the understanding of the performance of proppant mixtures

In this research, a numerical modeling approach, combining the Discrete Element Method (DEM) with lattice Boltzmann (LB) method, was adopted to investigate the potential effects of mixed proppant sizes on fracture conductivity. DEM was used to simulate effective stress increase and the resultant proppant compaction, rearrangement, and embedment. DEM-simulated pore structure of the compacted proppant pack was extracted and then imported into the LB simulator as internal boundary conditions of fluid flow modeling to measure the time-dependent permeability of the proppant-supported fracture. We first simulated conductivities of proppant packs with mesh size 20, 40, and 20/40 (mixing mass ratio 1:1) under varying proppant areal concentrations (proppant mass per unit area of fracture face). The simulated conductivity curve for the 20/40 mixture agrees well with laboratory data. We then applied the validated model to investigate the propped fracture conductivity for different mass mixing ratios, such as 1:9, 2:8, 3:7, 4:6, and 5:5, with different proppant mesh sizes, effective stresses, and proppant areal concentrations (ranging from partial monolayer to multilayer). At the end, we use the DEM/LB-coupled model to study the influence of proppant mixtures on the maximum attainable reservoir productivity index based on equations derived from the literature.