Multi-component fractal representation of multi-scale structure of natural gas hydrate-bearing sediments

Fractal is a set owning an infinitely fine structure in a self-similar or self-affine way covering all scales, and is widely used to model the structure of porous media. Hydrate-bearing sediments belong to porous media, so this paper attempts to construct a structure model of hydrate-bearing sediments with the three-component fractal extended from the two-component fractal. The three-component fractal is capable to display structural details at arbitrarily small scale. Additionally, in the three-component fractal, any parameter defined as the ratio (such as porosity and hydrate saturation) of two different volumes approaches a determined value when considering the infinitesimal scale. The interface between hydrate elements and pore elements is suggested to be a potential way to classify the hydrate-bearing sediments. Using the proposed three-component fractal model to calculate the interface between one arbitrary hydrate particle and surrounding pores, we obtain the theoretical solutions of the amount of substance, the dissociation rate and maximal dissociation time of one arbitrary hydrate element in sediments. It is found that the effective reacting surface of one hydrate element in sediments could be equal to even greater than that of the pure hydrate element in the late period of hydrate dissociation, during which the amount of substance of one hydrate element in sediments is still greater though. Finally, we further extend the three-component fractal to any-component fractal, and show how to model more complex porous media by using a suitable generator.