Fractal analyses on saturation exponent in Archie's law for electrical properties of hydrate-bearing porous media

Abstract

Hydrate saturation estimation in the field is mainly controlled by proper interpretations of downhole electrical logging data based on Archie's law. However, saturation exponent value in Archie's law is site dependent, and its proper selection for hydrate-bearing sediments is still a challenge. In this study, a fractal model of saturation exponent is derived to show physical connections between saturation exponent and pore structure parameters. Hydrate saturation dependent pore-area and tortuosity fractal dimensions of effective pores to electrical conductivity are extracted from X-ray computed tomography (CT) images of xenon-hydrate-bearing alumina ball packings, and these values of pore structure parameters are applied to validate the model. Effects of hydrate saturation, intrinsic/primary pore structure parameters, and salt-removing effect due to hydrate formation on values of saturation exponent in Archie's law are discussed. Results and discussions show that model predicted and experimental values of formation factor in hydrate-free porous media are consistent; Pore-area fractal dimension of effective pores to electrical conductivity decreases while tortuosity fractal dimension increases with increasing hydrate saturation; The discrepancy in saturation exponent values is largely due to the different enhancement degrees of tortuosity due to hydrate formation; A larger intrinsic volume porosity, lower pore-area and tortuosity fractal dimensions, and the salt-removing effect due to hydrate formation all lead to a lower saturation exponent in Archie's law. This study has a great potential to facilitate interpretations of downhole electrical logging data in gas hydrate sites.