Effective proppant placement within fractures is crucial for establishing high-conductivity fracture channels. Most theoretical studies focus on single-size proppant injection during proppant transport and placement, with limited attention to mixed-size proppant injection strategies. Therefore, to accurately characterize proppant transport in the field applications, in this work, we proposed an efficient numerical method for describing proppant transport and placement. A Eulerian–Lagrangian numerical framework was first developed to reasonably characterize proppant transport in complex fractures, and we then established a laboratory-scale analog of field-scale fracture configurations based on geometric similarity principles and Reynolds number scaling criteria. After that, the influence of proppant diameter, injection ratio, and injection sequence on proppant transport was fully analyzed. The results demonstrate that particle diameter governs the placement behavior of proppants by affecting their settling angle, with smaller particles being more likely to penetrate deeper into the fracture. When the size of 0.2 and 0.4 mm is mixed injected with the ratio of 6:4, it will obtain the proppant distribution and filling efficiency. Moreover, the simulation results reveal nonlinear fluid–solid coupling phenomena during the proppant transport. These findings offer valuable insights into proppant transport behavior in complex fractures and provide guidance for optimizing operational parameters in the fracturing design.
Liu et al. (Tue,) studied this question.