Numerical Simulation of Proppant Transport Coupled with Multi-Planar-3D Hydraulic Fracture Propagation for Multi-Cluster Fracturing

A proppant transport simulator coupled with multi-planar 3D (multi-PL3D) fracture propagation has been developed to examine the proppant distribution among multiple hydraulic fractures during multi-cluster fracturing in a horizontal well. The multi-PL3D fracture model considers wellbore friction, multi-fracture stress interaction, fluid leak-off, and multi-scale propagation regimes. The proppant transport is described by the two-phase (slurry/proppant) flow equations that consider proppant settling, jamming and flow regime transition. A high-resolution weighted essentially non-oscillatory (WENO) finite difference (FD) scheme is adopted to solve the nonlinear proppant transport equations. An efficient time-stepping scheme is developed to solve the solid/fluid coupling equations and moving boundaries for the multi-PL3D model. The proppant transport model and multi-PL3D model are both validated against previously published results. Using the model, we examine the proppant distributions under different injection schedules, proppant sizes, proppant density, and fluid viscosity. Results show that proppant distribution among multiple fractures is different as the flow rate and fracture width distribution vary due to multi-fracture stress interaction. The proppant in the middle cluster settles remarkably as the flow rate is lowest among the multiple clusters. The proppant is usually jammed at the pinch point, where the fracture width reduces sharply. Proppant adding schedule has a significant effect on the proppant distribution. A constant-concentration results in a proppant stack at the fracture front. In contrast, an increasing concentration favors the prop of the near-wellbore fracture. The proppant distribution area ratio (defined as the proppant distribution area divided by the fracture area) is only 20% for 20/40 mesh proppant, while the ratio is 45% for 100 mesh proppant. Slick water can increase the fracture area but not favor promoting the proppant distribution area ratio. The results can be helpful for proppant design for multi-cluster fracturing in a horizontal well.