Modification of the RLA model for presenting a cluster system of a composite material with a fractal filler structure

The paper proposes a modification of the diffusion-limited aggregation model to study the properties of a cluster system. A computational experiment to determine the mutual influence of the sticking probability and the volume concentration of particles on the formation of fractal clusters in a cluster system was carried out in accordance with the second-order orthogonal central compositional plan (OCCP). As a result of a computational experiment in accordance with the OCCP, an equation was obtained for the dependence of the mass fractal dimension of clusters on the volume of particle concentration and the probability of adhesion of diffusing particles and cluster particles in the adhesion zone. This dependence was obtained in a range of volume concentration of particles from 2 to 5 % and the probability of adhesion of diffusing particles and particles of clusters in the adhesion zone from 0.2 to 1.

Experimental Study on the Riverbed Coarsening Process and Changes in the Flow Structure and Resistance in the Gravel Riverbed Downstream of Dams

Following the construction of a reservoir, sediment is intercepted, which greatly reduces the sediment concentration in the discharged flow. This reduction causes riverbed scouring and flow structure adjustments downstream, thereby impacting the river habitat. This study used the generalized flume test with different bed sand compositions and discharge rates to simulate the scouring adjustment process of a sand pebble riverbed channel downstream of a reservoir. The results show that the bed sediment composition affects the water surface gradient, scour depth, turbulence intensity, and sand resistance directly after final scouring. Coarse-grained bed sediment demonstrated the greatest final turbulence intensity and sand resistance, while bed sediments with reduced coarseness exhibited a greater scouring degree; the resistance for sand grains of moderate coarseness showed the greatest change. Sand resistance was exponentially and positively correlated with the median grain size and the fractal dimension of bed sediment mass. The mass fractal dimension expression was suitable for the analysis of bed sand grain-size distribution; it contributed to the calculation of grain resistance with fewer hydraulic parameters. The relationship between the mass fractal dimension and the adjusted grain resistance was also established, which can aid the calculation of the resistance changes in sandy gravel-bed river reaches downstream of reservoirs, enabling the prediction of their effects on aquatic habitats.

An Analytical Flow Model for Heterogeneous Multi-Fractured Systems in Shale Gas Reservoirs

The use of multiple hydraulically fractured horizontal wells has been proven to be an efficient and effective way to enable shale gas production. Meanwhile, analytical models represent a rapid evaluation method that has been developed to investigate the pressure-transient behaviors in shale gas reservoirs. Furthermore, fractal-anomalous diffusion, which describes a sub-diffusion process by a non-linear relationship with time and cannot be represented by Darcy’s law, has been noticed in heterogeneous porous media. In order to describe the pressure-transient behaviors in shale gas reservoirs more accurately, an improved analytical model based on the fractal-anomalous diffusion is established. Various diffusions in the shale matrix, pressure-dependent permeability, fractal geometry features, and anomalous diffusion in the stimulated reservoir volume region are considered. Type curves of pressure and pressure derivatives are plotted, and the effects of anomalous diffusion and mass fractal dimension are investigated in a sensitivity analysis. The impact of anomalous diffusion is recognized as two opposite aspects in the early linear flow regime and after that period, when it changes from 1 to 0.75. The smaller mass fractal dimension, which changes from 2 to 1.8, results in more pressure and a drop in the pressure derivative.

ULTRA SMALL-ANGLE X-RAY SCATTERING STUDY OF FLOCCULATION IN SILICA-FILLED RUBBER

ABSTRACT The flocculation of silica during vulcanization is monitored using the ultra small-angle X-ray scattering technique for two different types of silica: a highly dispersible silica (HD) and a conventional silica (CV), mixed into a blend of S-SBR and BR rubbers. The cutoff length of the silica aggregate Rss and the mass fractal dimension Dm, which indicate the degree of flocculation of aggregates, are estimated according to the modified unified equation. The aggregate radius Ra is estimated to be related to the lower cutoff length Rss, indicating the radius of gyration of the mass-fractal structure. For both silicas, Ra increases during vulcanization. For the CV silica, an increase of Dm is observed, whereas no significant increase of Dm can be seen for the HD silica. The Ra of CV is relatively high compared with that of HD. On the other hand, the CV silica shows a relatively lower Dm compared with that of HD. These results indicate that CV has a larger size of aggregates and lower degree of agglomeration of its aggregates. The presence of di(tri-ethoxy-silyl-propyl)tetrasulfide (TESPT) as coupling agent between the silica and rubber decreases the aggregate radius of silica. However, in the absence of TESPT, a low mass-fractal dimension, which means a low degree of agglomeration of aggregates, is observed. This results from a lower mobility of silica aggregates, depending on the size of the aggregates. The silica loading also has an influence on the flocculation process. The aggregate radius increases as the silica loading is increased. At the same time, a higher mass-fractal dimension, and therefore also a higher degree of agglomeration, can be seen at higher silica loading.

Fractal Characteristics of Soil Particle-Size Distributions under Different Landform and Land-Use Types

It can provide theoretical guidance for the prevention of soil erosion and planting structure adjustment to study on fractal characteristics of soil particle-size distributions under different landform and land-use types. Soil particle-size distribution (PSD) is one of the most important physical attributes due to its strong influence on soil properties related to water movement, productivity and soil erosion. The fractal and multifractal measures were useful tools in identifying soil PSD with different taxonomy. Land-use type, as one of important factors to affect soil PSD was paid little attention in the previous research. In this paper, the theory of soil particle-size fractal was applied to characterize PSD in soils with the same taxonomy and different land-use types. Then the effects of land use on the fractal and multifractal parameters were analyzed. The study was conducted on the loess hilly areas of the Loess Plateau in Nanxiaohegou basin of Gansu. Soil was sampled from 18 land use types. The soil PSDs were obtained by sieving and pipette methods. The result showed that: (1) the mass fractal dimension of soil particles was significant correlated with the soil mass clay content; （2）both the soil mass clay content and the mass fractal dimension of soil particles showed the same tendency of increasing with the soil layer， and the mass fractal dimension relates to the land uses and topographic feature. Thus they could be potential parameters to reflect soil physical properties influenced by land use. More significant result is required in the future study to test the applicability of fractal parameters in characterizing land use effect on soil particle-size distributions.

Influence of thresholding in mass and entropy dimension of 3-D soil images

With the advent of modern non-destructive tomography techniques, there have been many attempts to analyze 3-D pore space features mainly concentrating on soil structure. This analysis opens a challenging opportunity to develop techniques for quantifying and describe pore space properties, one of them being fractal analysis. Undisturbed soil samples were collected from four horizons of Brazilian soil and 3-D images at 45 μm resolution. Four different threshold criteria were used to transform computed tomography (CT) grey-scale imagery into binary imagery (pore/solid) to estimate their mass fractal dimension (Dm) and entropy dimension (D1). Each threshold criteria had a direct influence on the porosity obtained, varying from 8 to 24% in one of the samples, and on the fractal dimensions. Linear scaling was observed over all the cube sizes, however depending on the range of cube sizes used in the analysis, Dm could vary from 3.00 to 2.20, realizing that the threshold influenced mainly the scaling in the smallest cubes (length of size from 1 to 16 voxels). Dm and D1 showed a logarithmic relation with the apparent porosity in the image, however, the increase of both values respect to porosity defined a characteristic feature for each horizon that can be related to soil texture and depth.