A novel apparent permeability model for shale considering the influence of multiple transport mechanisms

Changes in pore pressure during the extraction of shale gas lead to dynamic alterations in the pore structure and permeability, making it challenging to gain a comprehensive understanding of the flow behaviors of shale gas. The pore structure of shale is complex, with a variety of storage modes and gas transport processes constrained by a number of factors. For instance, when gas flows through a transport channel with a finite length, it is imperative to take into account the flow loss caused by the bending of inlet and outlet streamlines, prior models typically neglect the impact of end effects, resulting in an exaggerated estimation of the shale permeability. Furthermore, a decrease in pore pressure corresponds to an increase in the Knudsen number, resulting in the breakdown of the continuity assumption of the Navier–Stokes equation, this signifies the gradual shift of the transport regimes from continuum flow to other transport regimes. The gas flow process is nonlinear due to the alternating impact of multicomponent transport mechanisms and various microscale effects. In this paper, we presented a novel apparent permeability model for shale that incorporates the impact of real gas effect, end effects, transport regimes, adsorption, and effective stress. First, we assumed the channel for shale gas transport to be circular pore and calculated the viscosity under the influence of a real gas effect as well as the corresponding Knudsen number. Subsequently, building upon the foundation of the slip model, we introduce the influence of the end effects to establish a bulk phase permeability for shale, further considering the impact of surface diffusion. Then, the pore radius was quantified under the influences of adsorption and effective stress. Using the intrinsic correlation between permeability and pore radius as a bridge, a shale apparent permeability model was further derived. The model encompasses various transport regimes and microscale effects, replicating the gas flow behaviors in shale. The new model was verified through comparison with published experimental data and other theoretical models, while analyzing the evolution of apparent permeability. Additionally, this paper discusses the influence of various factors, including end effects, pore radius, internal swelling coefficient, sorption-induced strain, and model-related parameters on the shale apparent permeability.