Narrow Results

The pore space of a porous medium is typically considered to consist of a collection of curved capillaries with rough walls. A model describing roughness is established by applying fractal theory. As a result, a modified permeability model is derived theoretically, which is closely related to roughness. To validate this model, a new form of Kozeny–Carman (KC) equation is also developed for estimating permeability on a set of benchmark rock samples, and a good agreement was achieved in terms of small relative error between measured and predicted permeabilities. Therefore, we can conclude that pore roughness should not be ignored in predicting permeability. Although the improved KC equation can predict permeability effectively too, it is not practical as the KC constant is difficult to determine.

Studying the rough structure characteristics of rock fracture surfaces under microwave irradiation is of a great significance for understanding the rock-breaking mechanism. Therefore, this work takes fracture surface as the research object under three failure modes: microwave irradiation, uniaxial loading and microwave-uniaxial loading. The undulation and roughness are used to describe the morphological characteristics of the fractured surface. Research shows that the fracture surface under microwave irradiation is the smoothest, which exhibits undulation and rough fractal dimension in the range of 1–7mm and 2.0005–2.0657, respectively. The fractal anisotropy of the fracture surface is the most obvious under microwave irradiation. The roughness along the fracture surface is about 1.02 times that is perpendicular to the fracture direction. In the perspective of size effect characteristics, the roughness of the fracture surface under microwave irradiation shows a positive correlation with the selected size. The results provide a certain basis for interpreting the mechanism of microwave rock breaking.

Gas permeability is an important parameter for gas transport in microporous and nanoporous media. A probability model of gas permeability of fractal porous media with rough surfaces is proposed and numerically simulated by the Monte Carlo technique. This model consists of two gas flow mechanisms: the Poiseuille flow and the Knudsen flow, and can be expressed by structural parameters, such as the pore fractal dimension, the tortuosity fractal dimension, the relative roughness and porosity. The validity of the proposed model is investigated through the available experimental data, and a good agreement is obtained. The predicted results indicate that gas permeability of microporous and nanoporous media with rough surfaces decreases with the increase of the relative roughness and the tortuosity fractal dimension, and increases with the increase of porosity and the pore fractal dimension. Our gas permeability model could reveal the physical mechanisms of gas transport in porous media with rough surfaces.

Although the hydraulic features of the tree-like branching network have been widely investigated, the seepage characteristics of the networks have not been studied sufficiently. In this study, the seepage characteristics of porous media embedded with a tree-like branching network with the effects of roughness are studied based on fractal theory. Then, the Kozeny–Carman (KC) constant of the composite network is derived. The KC constant of porous media embedded with a tree-like branching network with roughened surfaces is in good agreement with the experimental data in the literature. The effects of structural parameters on seepage characteristics are also discussed. Notably, the results show that the KC constant of the composite network increases with an increasing volume porosity, and decreases with an increase in the relative roughness. Besides, the model established in this paper contains no empirical constants to ensure that each parameter has its physical significance. Thus, the proposed model can facilitate a better understanding of the seepage characteristics of fluid transport through a tree-like branching network embedded in porous media.

The morphological characteristics of core disking can reflect the in-situ stress field characteristics to a certain extent, but a quantitative description method for disking-induced fracture surfaces is needed. The fractal geometry was introduced to refine the three-dimensional characteristics of the core disking fracture surfaces, and the disking mechanism was explored through morphological characteristics. The innovative concentric-different scale method was proposed to divide the circular surfaces into square surfaces of different sizes. Furthermore, the applicability of four cubic covering methods for single fractal calculation was studied. Finally, the relative differential cubic covering method and multifractal method were used to calculate the three-dimensional data of core disking fracture surfaces in the Jinping area. The results showed that the concentric-different scale method fits the fractal dimension changing law in the exploration of different surface sizes. Using the differential cubic covering method and the relative differential cubic covering method can obtain good results for smoother surfaces. The disking was caused by tensile stress due to high crustal stress unloading, and the cracks originated from the inside of the core. Fractal theory is conducive to analyzing the morphology of rock fracture surfaces and provides guidance for exploring the failure mechanism and influencing factors.

The influence of surface roughness on X-ray microanalysis results of cerium hexaboride crystals obtained by floating zone and flux methods is investigated. It is shown that the surface of crystals grown by the floating zone method is much rougher than the one of crystals obtained by the flux method. The correction one should apply to the experimental EDX results, depending on the standard arithmetic mean roughness amplitude R_a and the inclination angle α of the studied surface area to the horizontal, i.e. the parameters determining the surface roughness, are calculated. The Ce/B ratio EDX data error due to surface roughness for a sample grown by the floating zone method is within the limits of ~2% and is less than for samples grown by the flux method. The obtained results have been used to determine the B/Ce ratio in the cerium hexaboride crystals with the purpose of developing the selection criteria of samples used in creating a single-photon thermoelectric detector of UV and X-ray ranges.