An Integral Model for Gas Transport and Sorption in Tight Dual-Porosity Systems

Abstract To optimize recovery during shale gas operations and enable efficient CO 2 storage in depleted shale formations, it is crucial to accurately model all relevant transport and storage mechanisms. Despite significant progress in the technical literature, comprehensive modeling of diffusion and sorption in shale remains a major challenge due to the inherent complexity and scale of the system. This study introduces a volume-averaged dual-porosity model for gas diffusion and sorption in shale. We focus on the matrix segments of the shale system where larger natural or induced fractures dictate the boundary conditions. The new model, represented by coupled ordinary differential equations (ODEs), accommodates gases with a wide range of sorption affinities and extends the application of Vermeulen’s approximation to a broad range of the characteristic times for diffusion and sorption. Calculation results are validated against fully discretized finite-difference numerical solutions to the governing partial differential equations (PDEs) for both inert gases (e.g., helium - He) and highly adsorptive gases (e.g., CO 2 ). The new model accurately captures gas transport and sorption in dual-porosity systems without requiring a full domain discretization. Additionally, we discuss its application in characterizing transport and storage mechanisms in shale cores using tandem experiments with He and CO 2 . In summary, this study introduces and validates a novel integral model for gas transport and sorption in dual-porosity systems. The model can serve as an efficient tool for the interpretation of core-scale experiments and provide a pathway for upscaling transport and sorption processes by translating relevant characteristic times.