Patterns of vertical fracture propagation in heterogeneous shale reservoirs and optimized parameter design

Shale reservoirs often exhibit interbedded lithologies that enhance vertical mechanical heterogeneity, inhibiting hydraulic fracture propagation and reducing vertical reservoir utilization. To address this, appropriate fracturing techniques are needed to improve vertical fracture growth. This study employs an extended finite element method combined with a cohesive zone model to simulate hydraulic fracture propagation in vertically heterogeneous shale. The model investigates the effects of cluster number, cluster spacing, vertical stress difference, clay content, fluid viscosity, and injection rate on fracture height and width. Response surface methodology (RSM) is used to evaluate parameter sensitivity and coupling effects, identifying optimal combinations. Results show that fewer clusters, smaller spacing, higher stress contrast, and lower clay content promote vertical fracture penetration. In contrast, more clusters, larger spacing, higher injection rate, and increased viscosity enhance fracture width. Cluster number and spacing are the most influential parameters; reducing both simultaneously significantly improves fracture height and width. Fluid viscosity and clay content have weaker effects. The optimal cluster number is 3–4 with spacing of 6–11.77 m. Fluid viscosity should be maintained within the range of 24.56–mPa s. The injection rate should be dynamically optimized between 9.09 and 21.19 m3/min. These findings offer theoretical guidance for fracturing design in heterogeneous shale reservoirs.