Using an Experiment/Simulation-Integrated Approach To Investigate Fracture-Conductivity Evolution and Non-Darcy Flow in a Proppant-Supported Hydraulic Fracture

Optimizing proppant-pack conductivity in a hydraulic fracture is of critical importance to sustaining effective and economical production of petroleum hydrocarbons. In this study, a hybrid, experiment/simulation-integrated workflow, which combines the discrete element method (DEM) and the lattice Boltzmann (LB) method with laboratory-measured load-embedment correlations, was developed to advance the understanding of fracture-conductivity evolution from partial-monolayer to multilayer concentrations. The influence of compressive stress and proppant-diameter heterogeneity on non-Darcy flow behaviors was also investigated. The DEM method was used to simulate effective-stress increase and the resultant proppant-particle compaction and rearrangement. Proppant-embedment distance was then determined using an empirical correlation obtained by fitting experimental data. The final pore structure of the proppant pack was imported into the LB simulator as interior boundary conditions of fluid-flow modeling in the calculation of time-dependent permeability of the proppant pack. To validate the integrated workflow, proppant-pack conductivity as a function of increasing proppant concentration was simulated and then compared with laboratory data. Good agreement was observed between the workflow-derived and laboratory-measured fracture-conductivity vs. proppant-concentration curves. Furthermore, the role of proppant size, size heterogeneity, and closure pressure on the optimal partial-monolayer proppant concentration was investigated. The optimal partial-monolayer proppant concentration has important engineering implications, because one can achieve a considerable fracture conductivity using a partial-monolayer proppant structure, which has much lower material costs compared with the conventional multilayer proppant structures. To investigate the effect of non-Darcy flow on fracture conductivity, three proppant packs with the same average diameter but different diameter distributions were generated. Specifically, the coefficient of variation (COV) of diameter, defined as the ratio of standard deviation of diameter to mean diameter, was used to characterize the heterogeneity of particle size. The results of this research provide fundamental insights into the multiphysics processes regulating the conductivity evolution of a proppant-supported hydraulic fracture, as well as the role of compressive stress and proppant-size heterogeneity in non-Darcy flows.