Study on Polydisperse Liquid–Solid Multiphase Flow in a Complex Fracture

The migration dynamics and distances traversed by proppant within the fractures remain ambiguous being considered in the context of fractures induced by hydraulic fracturing and significantly impacting the subsequent production and development efficacy. The migration of proppants in such complex fracture networks is inherent in the polydispersed solid–liquid multiphase flow problems, given the varying size gradations of the proppants used. The solid–solid interactions are not adequately taken into account by traditional monodisperse models, thereby limiting their accuracy in these scenarios. To address these limitations, a solid–liquid multiphase flow approach tailored for polydisperse systems is employed to simulate the migration and settlement of proppant particles in complex fractures. Initially, the conventional monodisperse model is extended to accommodate a polydisperse phase, with the veracity of the numerical model confirmed through experimental validation. Concurrently, a structured grid model for complex fractures is established, ensuring grid independence through verification, which indicates the minimum error margin of 1.5% only. Using the subsequent numerical simulations based on these models, the influence of the varying displacement rates, the fracturing fluid viscosities, and the sand ratios on proppant placement is investigated. Key metrics such as the height of dune, the time required for proppant to penetrate the branch fractures, the proportion of dune, and the unfilled areas proximal to the well are quantified and analyzed. In the final phase, an analysis of the polydispersity of particles within these complex fractures is conducted to further elucidate the migration phenomena.