Abstract 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.

中文翻译：

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含天然气水合物沉积物多尺度结构的多分量分形表示

摘要 分形是具有无限精细结构的覆盖所有尺度的自相似或自仿射方式的集合，广泛用于模拟多孔介质的结构。含水合物沉积物属于多孔介质，因此本文试图构建一个由二组分分形扩展的三组分分形的含水合物沉积物结构模型。三分量分形能够在任意小尺度上显示结构细节。此外，在三分量分形中，任何定义为两个不同体积的比率（例如孔隙度和水合物饱和度）的参数在考虑无穷小尺度时都接近确定值。水合物元素和孔隙元素之间的界面被认为是一种潜在的水合物沉积物分类方法。利用提出的三组分分形模型计算任意一种水合物颗粒与周围孔隙的界面，我们得到沉积物中任意一种水合物元素的物质量、解离速率和最大解离时间的理论解。研究发现，在水合物分解后期，沉积物中一种水合物元素的有效反应面甚至可能大于纯水合物元素的有效反应面，在此期间沉积物中一种水合物元素的物质含量更大。尽管。最后，我们进一步将三分量分形扩展到任意分量分形，并展示如何使用合适的发生器模拟更复杂的多孔介质。