A Regime-Adaptive Imbibition Model for Fracturing-Fluid Species Transport in Ultra-Low-Permeability Gas Reservoirs

Hydraulic fracturing creates long-lasting contact between aqueous fracturing fluids and gas-bearing ultra-low permeability matrix rock, making fluid retention and dissolved-species penetration important for interpreting matrix–fracture mass exchange and post-fracturing flowback behavior. These processes are controlled by the coupled effects of capillary imbibition, fracture–matrix pressure assistance, and species diffusion, but their relative importance is difficult to distinguish through a concentration profile. This study develops a regime-adaptive pressure-assisted imbibition and species-transport framework for interpreting fracturing-fluid species movement from a hydraulic fracture into a gas-bearing porous matrix. The framework couples a pressure-assisted imbibition (PAI) model with a one-dimensional advection–diffusion equation (ADE), where the PAI-derived velocity provides the transient advective input for species transport. The same formulation continuously represents capillary-dominated, mixed pressure–capillary, and pressure-dominated behavior without switching governing equations. Three diagnostic limiting cases, Capillary-driven Advection, Pressure-driven Advection, and Diffusion-only, are introduced to compare reduced mechanism-specific responses with the Full PAI-ADE response without interpreting them as additive components of the full solution. At 100 days, the Full PAI-ADE concentration front in the Ultra-Low Matrix reached 31.9 cm at C = 0.10, compared with 18.0 cm for Capillary-driven Advection, 9.2 cm for Pressure-driven Advection, and 21.7 cm for Diffusion-only, indicating a mixed diffusion–capillary response. For the High-Perm Matrix at 0.20 day, the Full PAI-ADE and Pressure-driven Advection fronts reached 211.6 and 210.9 cm, respectively, with a normalized profile error of 0.003, identifying a pressure-advection-dominated limiting behavior. A dimensionless mechanism-weight analysis based on the pressure–capillary ratio (Πpc) and front-scale Péclet number (Pe) further summarizes these behaviors. The results demonstrate that the proposed framework provides a compact diagnostic tool for linking pressure–capillary driving, advective–diffusive tendency, and observable species-transport profiles in ultra-low permeability gas-reservoir applications.