Fractal characteristics of unsaturated sands - implications to relative permeability in hydrate-bearing sediments

Precise estimation of gas production from hydrate deposits heavily relies on an accurate description of relative permeability to water and gas in hydrate-bearing sediments. Relative permeability innately depicts the competing flow of gas and water phases for the pore spaces in sediments, and thus, is affected by pore characteristics and pore-scale morphology of water and gas. Characterization and quantification of water and gas distribution in pores at various water and hydrate saturation are not always offered. This study aims to establish a fractal theory based relative permeability model considering pore characteristics and the physics of pore-scale water and gas distribution. X-ray computed tomography (CT) images show that the distribution of water and gas phases in quartzitic sands are fractal. The area and tortuosity fractal dimensions, that quantitatively describe the water and gas distribution in the pores, can be computed from the CT images using the box-counting method. These fractal dimensions are further used to establish a fractal theory based relative permeability model. The proposed model implies that relative gas permeability is expected to increase and relative water permeability slightly decreases even the effective water saturation is unchanged during gas production from hydrate deposits, as hydrate dissociation increases the overall pore diameter and lowers capillarity that allows gas to migrate with less effort.