In naturally fractured reservoirs, multi-cluster hydraulic fracturing poses significant challenges due to the strong coupling between fracture propagation and proppant transport. These challenges include hydraulic-natural fracture interactions, non-uniform proppant transport in curved fractures, and the resulting nonlinearities and numerical instabilities. To address these challenges, this paper proposes a bidirectionally coupled fracturing numerical method suitable for complex naturally fractured systems. The method integrates multi-fracture propagation and proppant transport driven by low-viscosity fluids. Compared with conventional models, the proposed method captures both hydraulic-natural fracture interactions and proppant transport in curved fractures, while explicitly accounting for the feedback of proppant concentration on fracture propagation. A high-order Weighted Essentially Non-Oscillatory scheme (WENO) is employed to solve the proppant transport equation, improving numerical stability. The model incorporates the Constant Displacement Discontinuity Method (CDDM) and introduces a weakening function to mitigate convergence issues caused by strong stress interactions. Verification involves theoretical–experimental comparisons in fracture propagation, hydraulic-natural fracture interaction, and proppant transport. The overall error in proppant transport compared with experiments is 9.64%, meeting engineering accuracy requirements. Based on this, a series of sensitivity analyses were conducted. Results show a strong bidirectional coupling between fracture propagation and proppant transport, with proppant concentration significantly influencing fracture aperture. Fracturing fluid viscosity governs fracture morphology and proppant-carrying capacity: lower viscosity favors fracture extension, while higher viscosity improves proppant transport but limits fracture growth. A larger intersection angle between hydraulic and natural fractures reduces fracture conductivity. In complex fracture networks, stress interference and fracture curvature limit proppant placement, with only about one-third of hydraulic fractures effectively filled. These findings provide theoretical support and modeling guidance for hydraulic fracturing in unconventional reservoirs.
Huang et al. (Tue,) studied this question.