A Generic Fracture Conductivity Model for Partially Propped Fracture Networks with Proppant Embedment and Proppant Pack Deformation

Hydraulic fracturing involving proppant injection is currently the most effective technology to stimulate tight, unconventional reservoirs. The conductivity offered by the created propped and unpropped fracture segments is directly linked to the well deliverability. The accurate modeling of the fracture network conductivity is key to well performance prediction. Unlike most previous studies that have focused on the single-fracture conductivity, a comprehensive fracture network conductivity model was developed by incorporating more complex rock and proppant deformation mechanisms and integrating the conductivity of different propped and unpropped fracture segments through hydraulic–electric analogies. Specifically, for propped fracture segments, the proppant pack permeability was described by simultaneously considering the viscous shear from fracture walls, stress sensitivity, and multiple- or single-proppant-layer placement, while the dynamic width was controlled through proppant pack compaction and proppant embedment. In unpropped fracture segments, as self-supported fracture surface deformation changes the fracture compressibility, the stress-dependent compressibility was utilized to depict the dynamic width. The developed propped and unpropped fracture conductivity models were separately verified against experimental measurement data. Through the hydraulic–electric analogies, a new partially propped fracture network conductivity model was established. For propped fracture segments, an increase in the proppant pack compressibility significantly reduced the fracture conductivity, particularly under high-stress conditions. A larger initial propped fracture aperture offered higher fracture conductivity under identical stress conditions. For single-layer propped fractures, a decrease in the fracture surface elastic modulus from 15 GPa to 10 GPa slightly reduced the fracture conductivity due to greater proppant embedment. For unpropped fractures, a larger compressibility reduction rate (lower fracture compressibility) led to better fracture conductivity maintenance. The fracture network conductivity was dominated by the unpropped fracture segment conductivity when the unpropped length reached 45.5% of the total fracture network length.