Upscaling of Transport Properties in Complex Hydraulic Fracture Systems

Fluid flow in complex fracture systems near wellbore is influenced by heterogeneous fluid pathway structure, proppant distribution, and stress-induced fracture aperture change. The current physical experiments and pore -scale simulations only study the multiphase flow properties of hydraulic fracture (HF) with no proppant while the multiphase flow properties of induced fracture network (IFN) and HF with proppant are not available. It is well known that the simplified "straightline" relative permeability model does not apply to multi-phase flow in IFN and HF with proppant. Consequently, there is no upscaled relative permeability model that works. In this study, we develop the physics-driven level set lattice Boltzmann method (LS- LBM)-coupled model to study multiphase flow properties in complex fractures during injected water flowback and propose the upscaled relative permeability models of IFN and HF with proppant. The im-aged HF is applied to generate HFs with different aperture and proppant distributions using morphology operation and discrete element method (DEM). The imaged IFN is further applied to generate IFN with different aperture distributions by image dilation. The oil/water interface at different drainage pressures is tracked by LS, and the resultant fluid distributions are applied to calculate each phase's effective permeability by LBM. We found that the aperture variation coefficient difference leads to various fluid expansion patterns in IFN and HF. The oil/water interface moving pattern exhibits "face expansion" in IFN and HF while the oil/water interface moving pattern resembles "finger expansion" in HF with embedded proppant with notably larger aperture variation coefficient. The upscaled relative permeability model is further established considering channel tortuosity variation and pore structure difference based on LS- LBM simulation results.