Pore Size Fractal Dimension Research Articles

Macro–micro correlation analysis on the loess from Ili River Valley subjected to freeze–thaw cycles

The Ili River Valley in Xinjiang, China, is a typical seasonal frozen area where loess landslide disasters have become increasingly common during the freeze–thaw periods in recent years. This study analyzed the macroscopic mechanical strength and microstructure changes of the Ili loess under different freeze–thaw cycles (FTCs) through the post-freeze–thaw triaxial compression test on the unsaturated soil in laboratory. Apart from the scanning electron microscopy (SEM), and the nuclear magnetic resonance (NMR), the macro–micro correlation analysis and the cluster-principal component analysis were applied for the theoretical discussion. The results indicated that the cohesive force of the loess exhibits an initial decreases, followed by the increases, and eventually keep stable after various FTCs, while the internal friction angle showed the opposite developing trend before the final constant. Similar to the strong correlation between the cohesive force and the particle abundance, the internal friction angle is also closely related to the abundance and orientation fractal dimension of the loess particles. However, the principal component analysis results showed that cohesive force strongly correlates with the average maximum pore size and the pore size fractal dimension, for which the internal friction angle most strongly affected by the average maximum particle size. The possible reason is that the extracted principal components represent a class of microscopic parameters with the same or similar change trend, although there may be a certain offset between them. The mechanical deterioration of loess is attributed to the repeated frost heaving force and the migration potential caused by FTCs. The alterations of the microstructure accelerated the deterioration of the macroscopic mechanical properties of the loess, which further widens the understanding of the mechanism behind the deterioration of loess mechanical strength in the Ili River Valley under FTCs, and contributes to the prevention and management of the local landslide disasters.

COUPLED THERMAL-REACTIVE FLOW SIMULATION STUDY ON IN-SITU CONVERSION PROCESS OF LOW-MEDIUM MATURITY FRACTURED SHALE OIL RESERVOIR

The low-medium maturity shale oil in China has large resource potential. The occurrence state of such resource is mainly retained hydrocarbon and unconverted organic substance, making the in-situ conversion process a requisite technology. Meanwhile, the naturally fractured shale reservoir has multiple types of pore space, making the hydrothermal coupling process more complex. In this paper, a coupled thermal-reactive compositional flow model and numerical solution method is proposed. Specifically, the apparent permeability of fractured shale oil reservoir is derived based on fractal theory. Besides, the multistage parallel chemical kinetic reactions during in-situ conversion process and evolution of reservoir fluid composition and shale porosity are incorporated. Then the accuracy of the proposed model is tested through numerical cases. Finally, the impact of key operation parameters and fractal parameters on shale oil exploitation is analyzed, such as heating temperature, heating spacing, pore size fractal dimension, fracture length fractal dimension and tortuosity fractal dimension. The proposed model is capable of accurate and efficient prediction of the fractured low-medium maturity shale oil reservoir production.

Pore size fractal dimension for characterizing Au/TiO2 catalyst

The quality and assessment of a catalyst can be documented in detail by the application of pore size. This research aims to calculate fractal dimension from the relationship among pore size, maximum pore size and wetting phase saturation and to confirm it by the fractal dimension derived from the relationship among the ratio between surface area per unit pore volume, entry surface area per unit pore volume and wetting phase saturation. In this research, pore size was measured on Au/TiO2 using Brunauer–Emmett–Teller (BET) surface area. Two equations for calculating the fractal dimensions have been employed. The first one describes the functional relationship between wetting phase saturation, pore size, maximum pore size and fractal dimension. The second equation implies to the wetting phase saturation as a function of surface area per unit pore volume, entry surface area per unit pore volume and the fractal dimension. Two procedures for obtaining the fractal dimension have been utilized. The first procedure was done by plotting the logarithm of the ratio between pore size and maximum pore size versus logarithm wetting phase saturation. The positive slope of the first procedure = 3 − Df (fractal dimension). The second procedure for obtaining the fractal dimension was determined by plotting the logarithm of the ratio between surface area per unit pore volume, entry surface area per unit pore volume versus the logarithm of wetting phase saturation. The negative slope of the second procedure = Df − 3. It was found that the plasma + thermally treated Au/TiO2 has the highest fractal dimension value owing to possibility of having holes and channels. The results also show similarity between pore size fractal dimension and surface area per unit pore volume fractal dimension. In our case, as conclusions, the higher the fractal dimension, the better the catalytic activity.

A study on capillary actions of power-law fluids in porous fibrous materials via W-M function

The study of fluid diffusion is an important aspect of heat and mass transfer of the porous fibrous materials. This work established a fractal model for the diffusion of power-law fluids in porous fibrous materials by considering the pore size distribution and the tortuosity of the capillary. Adopting the Darcy’s law and the Hagen–Poiseuille’s law, the diffusion coefficient of power-law fluids is derived as a function of the tortuosity fractal dimension, the pore size fractal dimension and the flow behavior index, in which the phase transition and the adsorption effect of fiber as well as the influence of gas diffusion and temperature change are taken into consideration. And the Weierstrass–Mandelbrot (W-M) function is applied to manifest the detailed fractal characters of the pores. Focusing on an analytical expression of the diffusion of power-law fluids in porous fibrous materials, the changes of liquid volume fraction, gas concentration and temperature distribution subjected to the specification initial and boundary conditions are simulated numerically. The test of this approach on the height of fluids when the bottom of cotton fabrics is immersed in the water display the clear diffusion of fluid in fiber. Our preliminary results indicate the important roles that the porosity and flow behavior index play in the fluids transfer in the porous fibrous materials: the fluids with lower power law index rise higher heights and diffuse more rapidly, meanwhile, the height increases with the porosity.

FRACTAL MODEL OF GAS DIFFUSION IN FRACTURED POROUS MEDIA

Understanding gas transport behavior though fractured porous media is essential in many fields including fiber science, energy science, soil science, environmental engineering, chemical engineering, etc. In this paper, a fractal model is developed to characterize gas diffusion through fractured porous media, where a bundle of fractal-like tree branching networks is used to represent the fracture system according to fractal scaling laws. The analytical expression for relative gas diffusion coefficient of fractured porous media is derived. The proposed fractal model has been validated by the available experimental data and empirical correlations. From the parametrical study, it can be seen that structural parameters of fractured porous media (for example porosity, the fractal dimension, the diameter ratio, the length ratio and the branching angle) have a significant effect on equivalent gas transport properties. Gas relative diffusion coefficient has a positive correlation with the porosity, the pore size fractal dimension, or the diameter ratio, whereas it has a negative correlation with the length ratio, the branching levels, or the branching angle. The proposed fractal model does not only shed light on gas transport physics of fractured porous media, but also reveals more mechanisms than experimental measurements.

DERIVATION OF PERMEABILITY–PORE RELATIONSHIP FOR FRACTAL POROUS RESERVOIRS USING SERIES–PARALLEL FLOW RESISTANCE MODEL AND LATTICE BOLTZMANN METHOD

Permeability of porous reservoirs plays a significant role in engineering and scientific applications. In this study, we investigated the relationship between pore size fractal dimension (Df) and its porosity, as well as that between Dfand the pore structure parameters, and consequentially developed an algorithm to generate pore spaces with arbitrary fractal dimension characterizing the pore size distribution. Using the series–parallel flow resistance model and lattice Boltzmann method (LBM) in combination, we then systematically analyzed the effects of physical properties on the fluid flows in two-dimensional (2D) context, and quantitatively derived a permeability–pore relationship for fractal porous media. The new relationship shows that: (i) the permeability of a fractal porous medium is proportional to the square of its maximum pore size λmax; (ii) the larger the fractal dimension Dfof a pore space, the smaller the flow resistance of the porous medium; (iii) porosity φ to the power of (4 - Df)/(2 - Df) is proportional to the permeability of a porous medium; (iv) similar to the Kozeny–Carman (KC) equation, the tortuosity τ has its square inversely proportional to the permeability; more importantly, it is found to be a function of porosity approximately satisfying the relationship τ = φDf-2in a fractal porous medium. Moreover, we demonstrated that the newly derived fractal permeability–pore relationship is equivalent to KC equation and Poiseuille's law respectively, at Df= 1 and Df= 2.