Simulation of proppant transport with gravitational settling and fracture closure in a three-dimensional hydraulic fracturing simulator

We implement proppant transport in a three-dimensional hydraulic fracturing simulator, including proppant settlement due to gravity, tip screen-out, and fracture closure. Constitutive equations are used that account for processes that can cause the flowing fraction of proppant to be different from the volumetric fraction of proppant. The constitutive equations capture the transition from Poiseuille flow to Darcy flow as the slurry transitions from dilute mixture to packed bed. We introduce new constitutive equations that allow the simulator to seamlessly describe the process of fracture closure, including a nonlinear joint closure law expressing fracture compliance and roughness and accounting for the effect of proppant accumulation into a packed layer between the fracture walls. We perform sensitivity analysis simulations to investigate the effect of fluid viscosity, proppant density, proppant size, and formation permeability. The simulations confirm that tip screen-out can limit fracture length, cause proppant banking, and increase injection pressure. Sensitivity analysis indicates that reasonably accurate results can be achieved without excessive mesh refinement. We also perform a simulation of hydraulic fracture propagation through a complex natural fracture network. In this simulation, proppant tends to accumulate at the intersections between natural and hydraulic fractures. Overall, the results suggest that in very low permeability formations, proppant settling is a major problem for proppant placement because proppant tends to gravitationally settle before fracture closure can occur. Because leakoff is so slow, proppant immobilization through bridging is critical for vertical proppant placement. Bridging can occur at aperture approximately three times greater than particle diameter, which will occur much sooner after shut-in than full mechanical closure. Even though larger diameter proppant settles more rapidly, it may lead to better proppant placement because it will bridge sooner, at a larger fracture aperture. These results also suggest that it is critical to optimize injection schedule in order to avoid tip screen-out, which leads to a shorter, wider fracture in which bridging is less likely to occur. Our modeling approach can be used practically for optimization of proppant placement through selection of fluid properties, proppant properties, and injection schedule.