THEORETICAL VERIFICATION OF THE SCALING RELATION TO DETERMINE SURFACE FRACTAL DIMENSION OF POROUS MEDIA

A simplified procedure is developed to acquire the surface fractal dimension of porous media utilizing the PSD information from mercury porosimetry or other analyses.The self similarity of the inner surface of Sierpinski sponge is analyzed,the result of which demonstrates that the inner surface of Sierpinski sponge is not scale invariant over the whole range of scale transformations.By applying the simplified procedure to analyze and treat the PSD information of Sierpinski sponge over the scale invariant range,it is found that the surface fractal dimension calculated by the scaling relation is in very good agreement with its theoretical value,which virtually provides a theoretical affirmation of the method.

Classification of forearm action surface EMG signals based on fractal dimension

Surface electromyogram （EMG） signals were identified by fractal dimension.Two patterns of surface EMG signals were acquired from 30 healthy volunteers＇ right forearm flexor respectively in the process of forearm supination （FS） and forearm pronation （FP）.After the raw action surface EMG （ASEMG） signal was decomposed into several sub-signals with wavelet packet transform （WPT）,five fractal dimensions were respectively calculated from the raw signal and four sub-signals by the method based on fuzzy self-similarity.The results show that calculated from the sub-signal in the band 0 to 125 Hz,the fractal dimensions of FS ASEMG signals and FP ASEMG signals distributed in two different regions,and its error rate based on Bayes decision was no more than 2.26%.Therefore,the fractal dimension is an appropriate feature by which an FS ASEMG signal is distinguished from an FP ASEMG signal.

Universality and Specificity of Fractal Dimension of Fractured Surfaces in Materials

After calculation on the fracture angles under various conditions of specific surface energies with different symmetry operations of rotation, the complicated behavior of dependence of fractal dimension on the structure of crystal is shown. It is found that the crack propagates along the weakest crystal plane no matter what the direction of the maximum stress is if the anisotropy is sufficiently strong; and then, the fractal dimension of the fractured surfaces might be determined by the approximate fractal structure already existed in the material. Specificity of the fractal dimension of fractured surfaces would be easy to appear in this case. Reversely, the crack propagates along the direction of the maximum stress no matter what direction of the weakest crystal plane is if the anisotropy is sufficiently weak. Universality of the fractal dimension of fractured surfaces would be possible to appear in this case. In many real materials, universality and specificity of the materials are associated. The fractal dimension measured may more or less be influenced by the structure of materials and it shows its universality through the specificity of materials.

Surface characteristics analysis of fractures induced by supercritical CO_(2)and water through three-dimensional scanning and scanning electron micrography

Morphology of hydraulic fracture surface has significant effects on oil and gas flow,proppant migration and fracture closure,which plays an important role in oil and gas fracturing stimulation.In this paper,we analyzed the fracture surface characteristics induced by supercritical carbon dioxide(SC-CO_(2))and water in open-hole and perforation completion conditions under triaxial stresses.A simple calculation method was proposed to quantitatively analyze the fracture surface area and roughness in macro-level based on three-dimensional(3D)scanning data.In micro-level,scanning electron micrograph(SEM)was used to analyze the features of fracture surface.The results showed that the surface area of the induced fracture increases with perforation angle for both SC-CO_(2)and water fracturing,and the surface area of SC-CO_(2)-induced fracture is 6.49%e58.57%larger than that of water-induced fracture.The fractal dimension and surface roughness of water-induced fractures increase with the increase in perforation angle,while those of SC-CO_(2)-induced fractures decrease with the increasing perforation angle.A considerable number of microcracks and particle peeling pits can be observed on SC-CO_(2)-induced fracture surface while there are more flat particle surfaces in water-induced fracture surface through SEM images,indicating that fractures tend to propagate along the boundary of the particle for SC-CO_(2)fracturing while water-induced fractures prefer to cut through particles.These findings are of great significance for analyzing fracture mechanism and evaluating fracturing stimulation performance.

Fractal characteristics of surface crack evolution in the process of gas-containing coal extrusion

In this paper, simulated experiment device of coal and gas outburst was employed to perform the experiment on gas-containing coal extrusion. In the experiment, coal surface cracks were observed with a high-speed camera and then the images were processed by sketch. Based on the above description, the paper studied the fractal dimension values from different positions of coal surface as well as their changing laws with time. The results show that there is a growing parabola trend of crack dimension value in the process of coal extrusion. Accordingly, we drew the conclusion that extruded coal crack evolution is a process of fractal dimension value increase. On the basis of fractal dimension values taken from different parts of coal masses, a fractal dimension of the contour map was drawn. Thus, it is clear that the contour map involves different crack fractal dimension values from different positions. To be specific, where there are complicated force and violent movement in coal mass, there are higher fractal dimension values, i.e., the further the middle of observation surface is from the exit of coal mass, and the lower the fractal dimension value is. In line with fractal geometry and energy theory of coal and gas outburst, this study presents the relation between fractal dimension and energy in the process of extruding. In conclusion, the evolution of crack fractal dimension value can signify that of energy, which has laid a solid foundation for the quantification research on the mechanism of gas-containing coal extrusion.

The fractal characteristic change in the Huanghe River Estuary due to the hydrodynamic conditions’variation

The study area lies in the subaqueous delta, which came into being in 1964 - 1976. Oneoil-field road has been built for exploring petroleum to form a wave barrier. The hydrodynarnic conditions on the north side of the road are relatively violent, on the contrary the hydrodynarnic conditions on the south side of the road are nearly placid. This makes the study area a natural laboratory for studying the influence of the hydrodynarnic conditions on the fractal characteristics of the tidal flat. Selecting an area is named Case Ⅰ on the side of stronger hydrodynarnic activities and an area is named Case Ⅱ on the other side. Measuring the topography and sampling and analyzing the granulometrical composition, it is found that the hydrodynarnic conditions have fatal influence on the surface fractal dimensions and the granulometrical fractal dimensions of the area. In Case Ⅰ , which has strong hydrodynarnic conditions, the surface fractal dimensions are obviously larger than those of Case Ⅱ , and the granulometrical fractal dimensions are relatively smaller than those of Case Ⅱ , the surface fractal dimensions of Case Ⅰ decrease quickly with the increase of grid size; the granulometrical fractal dimensions are disperse, while the hydrodynarnic conditions of Case Ⅱ are just reverse. A sampling line and a core sampling on each side of the road are selected. It is found that on the south side of the road the granulometrical fractal dimensions vary regularly in the line and with the depth, the farther apart from the road, the smaller the fractal dimensions, and the deeper the sampling position the larger the fractal dimensions, while granulometrical fractal dimensions on the north side of the road have no such regularity pattern. The mechanism of the influence of the hydrodynarnic conditions on the fractal characteristics is discussed.

Influence of Drying Methods on Fractal Geometric Characteristics of Mesoporous Silica Aerogels

Chemical modification/ambient drying method and freeze drying method were introduced to research the synthesis of mesoporous silica aerogels. By analyzing N2 gas adsorption/desorption isotherms, the fractal geometric characteristics of gels were focused. The overall surface fractal dimensions were determined by analyzing N2 gas adsorption branch and a Frenkel-Halsey-Hill （FHH） equation was empolyed to determine surface fractal dimension Df It is found that, during ambient drying process, VTMCS/VWetgel ratio plays a crucial role in the changes of geometric feature, the key point is 50%, when the ratio is lower, and surface roughness increases with the ratio, when it exceeds 50%, the surface is almost unaffected by the modification. While freeze drying always tends to get larger Df freeze drying process could cause a rough surface of the gels. Compared with traditional porosity and specific surface area analyses, fractal geometry may be expected to be favorable for mesoporous structural analyses of materials.

Real-time pore structure evolution difference between deep and shallow coal during gas adsorption:A study based on synchrotron radiation small-angle X-ray scattering

Coal seam CO_(2) sequestration is an important option to address global warming.A better knowledge on coal pore structure evolution during gas adsorption can provide guidance for coal seams CO_(2) seques-tration.However,few investigations on the pore structure evolution differences between the deep and shallow coal were conducted during gas adsorption.In this study,based on the real-time synchrotron radiation small-angle X-ray scattering(SAXS)observation,the average pore diameter and pore surface fractal dimension evolution differences between deep and shallow coal were investigated from the as-pects of coal compositions and stress history.Two types of coal deformation(inner-swelling and outer-swelling)coexist during gas adsorption.Coal compositions have significant impact on the dominance of deformation type.The dominance of inner-swelling in deep coal is induced by the higher ash contents,and there is the decrease of average pore diameter during gas adsorption.The impact of stress-history(burial depth)on adsorption-induced deformation is more prominent than that of gas adsorption ca-pacity.In deep coal,the surface fractal dimension evolution presents a negative correlation with the evolution of pore diameters.In shallow coal,the surface fractal dimension evolution presents a Langmuir-type correlation with the adsorption time.

Bed roughness adjustments determined from fractal measurements of river-bed morphology

The flow resistance in rivers is an old and partly unsolved problem. In this study, the bed surface fractal dimension（BSFD） is used to describe the bed morphology, and combined with the bed roughness, a general model experiment is developed. The results show that there is a positive relationship between the BSFD and the bed roughness, which can be further applied to estimate the roughness changes in rivers. These findings will also guide further studies of the mobile-bed flow resistance.