Fractal Analyses Of The Shape Factor In Kozeny–Carman Equation For Hydraulic Permeability In Hydrate-Bearing Sediments

Hydraulic permeability in hydrate-bearing sediments largely controlling the rate of gas production from hydrate deposits is widely estimated by various modified models based on the Kozeny–Carman equation. However, the effect of hydrate saturation on the shape factor in the Kozeny–Carman equation is not fully understood. In this study, a fractal model of the shape factor is theoretically derived to show physical relations between the shape factor and fractal parameters of fluid occupied pores. Then, verification of the model is performed, and effects of intrinsic porosity, intrinsic pore area and tortuosity fractal dimensions on the hydrate saturation dependent shape factor are analyzed. Finally, how weighted specific surface areas evolve with hydrate saturation is theoretically discussed, and results are further applied to modify the Kozeny–Carman equation. It is shown that the fractal model has a good performance on the shape factor estimation, and value of the shape factor is largely controlled by porosity, pore area and tortuosity fractal dimensions of fluid occupied pores in hydrate-bearing sediments. Multiplying product of the shape factor, the squared specific surface area, and the squared hydraulic tortuosity linearly increases with increasing hydrate saturation in general for the pore-filling hydrate pore habit but linearly decreases due to the presence of grain-coating gas hydrates. This linear relation permits a feasible modification of the Kozeny–Carman equation for hydrate-bearing sediments, and values of the model parameter are suggested for pore-filling and grain-coating hydrate pore habits.