Numerical simulation and multi-factor optimization of hydraulic fracturing in deep naturally fractured sandstones based on response surface method

•Investigation of mesoscopic 3D HF and SRV evolution using a coupled FSD model.•Contributions of multi-factors on HF geometry and SRV are investigated.•A novel SRV optimization method is proposed based on Box-Behnken design and RSM. Hydraulic fracturing is an effective stimulation technology for enhancing recovery in deep reservoirs. Multi-factor analysis and fracturing design optimization are essential for the efficient development of deep naturally fractured sandstones. A three-dimensional flow-stress-damage (FSD) coupled model was presented to simulate the hydraulic fracture (HF) propagation and stimulated reservoir volume (SRV). The numerical model was validated with experimental results of the HF-natural fracture (NF) intersection. The sensitivity analysis is conducted to screen the significant factors affecting HF geometry and SRV. The response surface method was employed to investigate the coupling effects of multiple geomechanical and hydraulic factors on SRV by integrating Box-Behnken design and numerical modeling. Subsequently, the SRV was optimized by identifying the optimum combinations of uncertain parameters based on the established response surface model (RSM). The results indicated that the injection rate, NF density, fluid viscosity, and horizontal stress difference are the key factors controlling SRV. It is more difficult to improve SRV by increasing injection rate at higher horizontal stress difference than at lower horizontal stress difference. The proposed method is effective for enhancing the artificial ability to optimize the HF geometry and SRV. The results can provide insight into the fracture geometry control mechanism in deep naturally fractured sandstones, and offer a guideline for treatment design and optimization of well performance.