Hydraulic fracture conductivity as a function of proppant concentration under various effective stresses: From partial monolayer to multilayer proppants

Understanding of proppant transport and deposition patterns in a hydraulic fracture is vital for effective and economical production of petroleum hydrocarbons. In this research, a numerical modeling approach, combining Particle Flow Code (PFC) with lattice Boltzmann (LB) simulation, was adopted to advance the understanding of the hydraulic fracture conductivity as a function of proppant concentration under various effective stresses from partial monolayer to multilayer proppant concentrations. PFC was used to simulate effective stress increase and the resultant proppant particle movement and rearrangement during the process of reservoir depletion due to hydrocarbon production. The pore structure of the proppant pack was extracted and used as boundary conditions of the LB simulation to calculate the time-dependent permeability of the proppant pack. We first validated the PFC-LB numerical workflow, and the simulated proppant pack permeabilities as functions of effective stress were in good agreement with laboratory measurements. Furthermore, several proppant packs were generated with various proppant concentrations, ranging from partial monolayer proppant packs to multilayer ones. The fracture conductivities for proppant packs from partial monolayers to multilayers were simulated. A partial monolayer proppant pack with large-diameter proppants may be an alternative to increase the fracture conductivity. Then, three proppant packs with the same average diameter but different diameter distributions were generated. Specifically, we used the coefficient of variation (COV) of diameter, defined as the ratio of standard deviation of diameter to mean diameter, to characterize the heterogeneity of particle size. We obtained proppant pack porosity, permeability, and fracture width reduction (compressed distance) as functions of effective stress. Under the same effective stress, a proppant pack with a higher diameter COV had lower porosity and permeability and larger fracture width reduction. This was because the high diameter COV gave rise to a wider diameter distribution of proppant particles; smaller particles were compressed into the pore space between larger particles with the increasing stress, leading to larger compressed distance and lower porosity and permeability. The transition time distributions for proppant packs with diameter COV5% and COV19% were determined and hydrocarbons transported more difficultly within the COV19% proppant geometry. With identical stress increase, the proppant assembly having a more heterogeneous particle diameter distribution experienced more dramatic changes with respect to pore structure and connectivity, which directly led to a reduced hydrocarbon transport in the hydraulic fracture.