Numerical simulation of the migration and deposition of fine particles in a proppant-supported fracture

Many hydrocarbon-bearing geologic formations, especially shales, contain high clay contents. During hydrocarbon production, pore pressure reduces and the effective stress of the rock matrix increases, which may lead to formation failure and consequently fine particles production within the formation fluids. Invasion of fine particles into proppant assemblies in a hydraulic fracture can clog the pore spaces between proppant particles and consequently lead to loss of fracture permeability and conductivity. Although fine particle migration and clogging in a proppant-supported hydraulic fracture is critical to effective production of hydrocarbons, the role of effective stress, proppant particle size, and proppant size distribution is still unclear. In this study, a discrete element method-lattice Boltzmann (DEM-LB) numerical framework was developed to study the mechanisms that regulate the migration and deposition of fine particles in a proppant-supported fracture, which is subjected to a closure pressure. Specifically, DEM was used to generate proppant assemblies and to simulate effective stress increase and the resultant proppant particle compaction. The DEM-simulated pore structure of the compacted proppant assembly was then extracted and imported into the LB simulator as internal boundary conditions of fluid flow modeling. Fine particle transport in the pore spaces was numerically simulated based on the LB-simulated pore flow field, and three transport mechanisms that regulate fine particle migration, including interception collection, Brownian motion, and gravitational settling, were accounted for. The numerical results of pore-scale particle tracking and deposition were fitted using a continuum-scale fine particle deposition model to determine the macroscopic deposition coefficient, as well as how fine particle size, proppant size heterogeneity, and effective stress influence the macroscopic deposition coefficient. Good agreement between numerically-simulated and correlation-predicted deposition coefficients was observed. The simulation results confirmed the non-monotonic change of fine particle deposition coefficient as a function of fine particle size. This study indicates that proppant assemblies having the same mean proppant diameter but a more heterogeneous proppant diameter distribution (i.e., a wider distribution of proppant diameter) favors fine particle migration through the pore space under low to moderate closure stresses. The developed simulation framework can be used to effectively model the migration and deposition of fine particles having varying sizes at the pore scale.