Numerical simulation of solid diverting particles transport and plugging in large-scale hydraulic fracture

Diversion technology, also known as temporary plugging technology, has become an integral part of hydraulic fracturing in unconventional reservoirs. The solid diverting particles are a common type of chemical diverting agents used in horizontal well multistage fracturing. The transport and plugging of solid diverting particles within the fractures are crucial physical processes in the far-field diversion technology. In this study, in order to clarify the formation of the plugging layer by solid diverting particles in large-scale hydraulic fracture and to offer insights for the quantitative optimization of far-field diversion technology (FFD), an enhanced simplified two-fluid model within the Euler-Euler framework is employed to simulate the transport and plugging process of solid diverting particles within the fracture. And the numerical schemes of the front settlement region, the plugging layer formation region and the rear settlement region are also optimized. The proposed model is verified through comparison with experimental results from visual fracture test device. Based on the numerical results across various particle, pumping and fracture parameters, our findings indicate that: (1) The duration required to form a complete plugging layer can be reduced to 3%∼20% by increasing injection concentration, injection rate, and fracturing fluid viscosity; (2) Increasing the injection concentration (from 10kg/m³ to 30kg/m³) significantly enhances the length of the plugging layer by about 1∼16 times, compensating for the inability to achieve a complete plugging layer with smaller particle sizes. Merely increasing the injection rate alone (from 0.35m³/min to 0.80m³/min) does not remedy the inability of small particles to form a complete plugging layer under identical plugging conditions. Excessive fracturing fluid viscosity (higher than 6mPa·s) impedes the formation of a complete plugging layer with smaller particles. High fracturing fluid leak-off rate (higher than 2.5×10^-7m/s) markedly reduces the length of the plugging layer by about 37%∼44%; (3) Achieving a high close packing degree of particles within the plugging layer is facilitated by increasing injection concentration, increasing injection rate, and reducing fluid viscosity; (4) The abrupt variation in fracture width or height along the fracture length affects up to about 18% of the length of the plugging layer at the top of fracture. To ensure large length of the plugging layer at the top of fracture and high close packing degree of particles within the plugging layer, we recommend injection concentration above 10kg/m³, fracturing fluid viscosity below 6mPa·s, and injection rate exceeding 0.35m³/min. For particle size less than 1.8mm, we suggest injection concentration above 20kg/m³, and fracturing fluid viscosity not exceeding 3mPa·s.