An analytical equivalent permeability model for characterizing fluid flow through a bounded empty-porous system

Natural fractures are critical for hydrocarbon extraction in unconventional reservoirs, but they are often cemented by minerals. Hydraulic fracturing can open these cemented fractures, creating a bounded empty-porous system with an empty region and a cement pack. However, no studies have yet characterized fluid flow in this scenario, leading to inaccurate predictions of the delivery capacity of opening cemented natural fractures (OCNFs). This study presents a novel analytical model to evaluate the equivalent permeability of OCNFs, incorporating viscous shear from fracture walls and the coupled empty-porous system. Unlike traditional Darcy's law, fluid flow in the cement pack is described using the Brinkman equation to account for effects from the porous medium, fracture walls, and viscous drag at the empty-porous interface. The model is validated through commercial software (e.g., COMSOL Multiphysics). The equivalent permeability and flow velocity profiles of OCNFs are analyzed with various impact factors. Results show that fracture wall and empty-porous interface effects become more significant as cement pack permeability increases, while their influence on fluid flow decreases with greater cement pack width. If the fracture width is large enough, these effects become negligible. Integrating the permeability predicted by both models into reservoir simulations reveals that neglecting fracture wall and interface effects leads to significant errors in well performance evaluation.