Numerical simulation of proppant transport in dynamic fracture networks using Eulerian-Eulerian method

The effectiveness of hydraulic fracturing is largely determined by the fracture propagation and proppant transport, while the numerical simulation of proppant transport in dynamic hydraulic fracture (HF) is a critical yet challenging computational problem. Based on the displacement discontinuity method (DDM) and finite volume method (FVM), an integrated hydraulic fracturing simulator is established by coupling a non-planer three-dimensional fracture propagation model with a Eulerian-Eulerian proppant transport model. The embedded discrete fracture model (EDFM) is adopted to describe the fluid flow between fracture and matrix. The fluid–solid coupling equations for fracture deformation and fluid flow are derived, and the one-way coupling strategy is employed to model the proppant transport in dynamic fracture networks. To avoid the problem of numerical oscillations, the high-order spatial and temporal discretization schemes are introduced. The fracture propagation and proppant transport models are validated by analytical solutions and published numerical results. Compared with the low-order discretization strategy, a more precise prediction of proppant distribution in dynamic HF can be obtained with high-order discretization schemes. Based on the established model, the parametric sensitivity analysis is conducted to investigate the intricate interaction between proppant transport and complex fracture propagation. The results show that the accumulation and bridging of proppant can promote the full opening of natural fracture (NF) during hydraulic fracturing. Increasing the proppant particle size and decreasing the injection rate, despite being detrimental to proppant transport efficiency, are instrumental in the formation of a stable temporary plugging zone. Moreover, the characteristics of fluid pressure reflect the formation process of temporary plugging zones and the propagation patterns of HF. A higher fracture propagation pressure signifies the successful establishment of the temporary plugging zone, which facilitates the creation of complex fracture networks during hydraulic fracturing.