A coupled 3D FEM-CZM study of multi-cluster hydraulic fracturing with dynamic perforation erosion and wellbore friction

Multi-cluster hydraulic fracturing is widely used to improve reservoir contact in unconventional formations, but stage treatments commonly evolve toward uneven cluster intake. This study develops a coupled three-dimensional FEM–CZM framework linking poroelastic stress interaction, transient wellbore hydraulics, and time-dependent perforation erosion. The fracture–poroelastic–wellbore variables are solved implicitly in Abaqus/Standard, whereas perforation diameter and discharge coefficient are updated sequentially at increment boundaries through USDFLD. Component-level verification is conducted against PKN, published multi-fracture, and erosion benchmarks. The results indicate that stress shadowing is the primary mechanical selector of cluster dominance, while wellbore and perforation losses amplify the resulting flow redistribution. Perforation erosion is path-dependent rather than universally destabilizing: it amplifies the cluster accumulating the greatest velocity-squared slurry exposure, but can partially compensate a mechanically disadvantaged cluster when that cluster acquires an early hydraulic advantage. Along-well friction introduces a heel-to-toe pressure gradient, so symmetric perforation schemes need not produce symmetric intake. An initial hydraulic restriction contrast, HRC0, is introduced to compare differentiated designs. For the investigated Weiyuan-type cases, the transition toward improved allocation is bracketed between HRC0 = 0.36 and 0.50, subject to erosion and treating-pressure constraints. The framework therefore supports diagnosis-driven, non-symmetric entry design rather than a universal completion rule.