Relationship between normalized permeability and resistivity index in hydrate-bearing sediments: fractal model and numerical simulation

Permeability is a critical factor in evaluating the fluid flow capacity and production performance of natural gas hydrate reservoirs. The similarity of electrical conduction and hydraulic flow makes it possible to predict reservoir permeability using electrical data. Clarifying the relationship between the permeability and resistivity of sediments with different hydrate growth habits contributes to the efficient exploration and development of natural gas hydrate resources. In this work, normalized permeability and the resistivity index models for grain-coating (GC) and pore-filling (PF) hydrates are developed based on the fractal geometry theory, forming a new relationship between normalized permeability and resistivity index. The empirical exponent is determined by fractal dimension. Meanwhile, we selected five sets of 3-D computed tomography (CT) images of quartz sand with different particle sizes, GC and PF hydrate digital rocks are constructed using random simulation methods. The numerical simulation of permeability and resistivity index is carried out, based on the pore microstructure images, the box counting method was used to calculate the fractal dimension and analyse the relationship between pore space and transport paths. Furthermore, the pore radius, throat radius and pore connection number are extracted through the pore network method to study the evolution of pore space. The results show that the tortuosity fractal dimension is a critical parameter in the relationship between normalized permeability and resistivity index. The proposed analytical expressions are validated by laboratory and well log data, and the exponent ranges cover existing hydrate permeability-resistivity index data. The models provide the possibility to predict the normalized permeability of hydrate reservoirs based on electrical data alone.