Numerical Modeling of Proppant Transport and Placement in Rough Hydraulic Fractures Using a Euler–Euler Two-Fluid Model

Proppant transport and placement in rough fractures strongly influence hydraulic fracture conductivity, while the mechanisms by which fracture-wall heterogeneity affects particle migration and deposition remain insufficiently understood. In this study, a Eulerian–Eulerian two-fluid model coupled with fractal fracture reconstruction is developed to investigate proppant transport and placement in rough fractures. Rough fracture surfaces with different fractal dimensions are generated using the spectral synthesis method, and a modified cosine-weighted transition algorithm is proposed to improve geometric continuity and mesh stability between the inlet and rough fracture regions. The effects of fracture roughness, injection velocity, particle size, particle density, and sand concentration on sand-bank evolution are systematically investigated. The results reveal that fracture roughness has a non-monotonic influence on proppant deposition: moderate roughness enhances near-wall disturbances and particle resuspension, reducing sand-bank accumulation, whereas excessive roughness increases particle interception, collision, and local flow disturbance, resulting in localized deposition. Increasing injection velocity from 0.15 to 0.8 m/s decreases the equilibrium sand-bank height by approximately 44%. Increasing particle diameter from 0.25 to 0.85 mm increases the maximum sand-bank height from 2.23 to 25.64 cm, while increasing sand concentration from 1 to 10 increases the maximum sand-bank height from 3.97 to 15.01 cm. Although rough and smooth fractures have identical average apertures, roughness-induced contraction–expansion channels redistribute particle trajectories and promote deeper fracture placement. This study provides insights into proppant transport mechanisms in heterogeneous fractures.