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In this paper, numerical simulations of fractured vertical well in low-permeable oil reservoir are carried out and two issues: threshold pressure gradient (TPG) in reservoir matrix and proppant distribution in hydraulic fractures are focused on. A physical definition of effective fracture length (EFL) is presented to evaluate the fracture effectiveness due to uneven proppant distribution. In terms of numerical processing for TPG, based on the subsurface Darcy's flow module in COMSOL Multiphysics, an effective numerical simulation method is adopted by substituting the gravitational acceleration vector in Darcy's law (Liu et al., 2019b). The simulation results show that, proppant distribution has great influence on fracture effectiveness. Unappealing proppant distribution can reduce effective fracture length by 49.6%, which is negative for low-permeable oil reservoir development. TPG in reservoir matrix mainly affects the moving boundary and pressure-disturbed area in reservoir. When TPG in matrix reduces from 0.02 MPa/m to 0 MPa/m, the distance of moving boundary at 300 days could increase for almost double and pressure-disturbed area enlarged drastically for around 74%. Furthermore, a heterogenous low-permeable oil with secondary fracture networks is designed to study the joint effect of TPG and proppant distribution. If we neglect these two factors, cumulative oil rate will be greatly overestimated by 38.6% at 1000 days. At the same time, the existence of natural fractures could also affect the streamline distribution in low-permeable oil reservoir and contribute to fluid flow in reservoir.

Proppants are used to resist fracture closure during hydraulic fracking treatments. Understand the proppant transport and distribution characteristics in fracture and fracture network become a meaningful topic for its effects on the conductivities of fractures. Since experiments are expensive, and it is also difficult to consider various conditions and detect the movement of particles during experiments, numerical simulation methods are often applied. In this work, the coupled Computational Fluid Dynamics-Discrete Element Method (CFD-DEM) was implemented to investigate the factors affecting proppant distribution in fracture and fracture networks. First, the CFD-DEM model was built for proppant flow and settlement. We validated the model by comparing with the published numerical simulation result. After that, we designed a series of cases to investigate the effects of fracture closure, injection velocity and no-uniform opening of the inlet on proppant distribution in a single fracture. Then, the effects of proppant diameter, density and perforation height differences on proppant sorting were studied. Next, we computed the proppant transport in fracture networks considering the aperture difference, the orientation of branch fractures and leak-off in fracture tips. The simulation results in this paper can help engineers to understand the transport and distribution of proppants visually in the fracture and fracture networks in unconventional reservoirs.