Theoretical analysis of shape factor of gas hydrate sediments under stress dependence

The Kozeny-Carman (KC) equation is used extensively to characterize the effective permeability of gas hydrate sediments. However, most existing modeling approaches ignore the changes in the effective stress, hydrate saturation, and pore structures of porous media, which significantly affect the extraction and exploration of gas hydrates. In addition, theoretical models that can accurately describe shape factors during the imbibition process and predict the effective permeability of gas hydrate sediments are rarely reported. This paper proposes a theoretical stress-dependent shape factor model to study the physical relations between the shape factor and relevant parameters (e.g., effective stress, hydrate saturation, effective porosity, and pore fractal dimension). Then, the derived model is extended to study the shape factor during the imbibition process. The two main novel features of the proposed model are: (1) it takes the effective stress, hydrate saturation, and pore structures into account; and (2) it can be used to study the evolution of shape factors during the imbibition process in gas hydrate sediments. The predictions from the developed model provide a good agreement with experimental results, which validates the model. In addition, based on the derived model, the effects of relevant parameters on shape factors are studied theoretically. From a practical standpoint, the model can not only estimate the effective permeability of gas hydrate sediments under stress dependence but also provide insight into the evolution of shape factor, pore structures (e.g., capillary total number, pore fractal dimension, tortuosity fractal dimension, and effective porosity) and hydrate pore habits during the extraction of hydrates.