Simulation of proppant distribution in hydraulically fractured shale network during shut-in periods

Proppant distribution is an important topic, because it is closely related to the success or failure of hydraulic fracturing treatment. Although, many proppant transport models have been published, there is still relatively limited research on proppant distribution between the created fracture network in shale especially during the post-treatment shut-in periods. In this paper, based on the intercoupling of particle hydrodynamics, fluid hydrodynamics, and poro-elastic rock mechanics, a mathematical model regarding the transport of liquid-solid phases has been established to simulate the behavior of the proppant transport and the carrying fluid migration in the fractured shale network during the well shut-in. The coupled model takes main hydraulic fractures, secondary induced fractures and matrix into account, namely a three-dimensional triple-porosity medium. All the important processes in fractured shale network can be explained by the liquid-solid transport simulation with the coupled model, including (1) liquid transport driven by viscous and gravity forces, (2)proppant particle transport driven by the horizontal forces of drag, inertia and collision, and the vertical gravity and buoyancy, and (3) hydraulic-fracture closure, which is considered as a poro-elastic rock deformation during the shut-in periods. Based on the conservation of mass and momentum, the liquid-solid transport coupled with rock deformation, are described by a set of partial differential equations, which are solved by the semi-implicit finite-difference method. The evolution of the proppant concentration and fluid pressure profiles is calculated. The fluxes of the proppant and proppant-carrying fluids between the main fracture and secondary fracture during the post-stimulation well shut-in are also calculated. The influences of proppant properties (concentration, density and size) and proppant-carrying fluid properties (viscosity and density) on the proppant distribution are investigated. The results of this study are expected to provide a better understanding of the proppant and proppant-carrying fluid distribution for different physical properties of proppant and carrying fluids, and explain which is the predominant factor influencing the proppant distribution during the shut-in periods.