Structural Parameters Of Porous Media Research Articles

EFFECTIVE GAS DIFFUSION COEFFICIENT OF FRACTAL POROUS MEDIA WITH ROUGH SURFACES BY MONTE CARLO SIMULATIONS

Gas diffusion coefficient is an important parameter in characterizing gas transport in porous media. Based on the fractal characteristics of microscopic capillaries, the effect of capillary surface roughness on gas diffusion is considered by the Monte Carlo technique. We proposed a probability model of the effective gas diffusion coefficient of the porous media with rough surfaces. This model is expressed as a function of the geometrical parameters of porous media, such as the porosity, the pore fractal dimension, the tortuosity fractal dimension, and the relative roughness. The simulated effective gas diffusion coefficient is compared with the available experimental data and a good agreement between them is obtained. The effect of the structural parameters of porous media on gas diffusion is analyzed in detail.

Multi-Scale Insights on the Threshold Pressure Gradient in Low-Permeability Porous Media

Low-permeability porous medium usually has asymmetric distributions of pore sizes and pore-throat tortuosity, thus has a non-linear flow behavior with an initial pressure gradient observed in experiments. A threshold pressure gradient (TPG) has been proposed as a crucial parameter to describe this non-linear flow behavior. However, the determination of this TPG is still unclear. This study provides multi-scale insights on the TPG in low-permeability porous media. First, a semi-empirical formula of TPG was proposed based on a macroscopic relationship with permeability, water saturation, and pore pressure, and verified by three sets of experimental data. Second, a fractal model of capillary tubes was developed to link this TPG formula with structural parameters of porous media (pore-size distribution fractal dimension and tortuosity fractal dimension), residual water saturation, and capillary pressure. The effect of pore structure complexity on the TPG is explicitly derived. It is found that the effects of water saturation and pore pressure on the TPG follow an exponential function and the TPG is a linear function of yield stress. These effects are also spatially asymmetric. Complex pore structures significantly affect the TPG only in the range of low porosity, but water saturation and yield stress have effects on a wider range of porosity. These results are meaningful to the understanding of non-linear flow mechanism in low-permeability reservoirs.

Numerical Investigation of Carbon Deposition Behavior in Ni/Al2O3-Based Catalyst Porous-Filled Solar Thermochemical Reactor for the Dry Reforming of Methane Process

Due to the utilization of concentrated solar energy, a more complex high-temperature thermal environment will be formed inside the solar thermochemical reactor, thereby resulting in complicated behaviors of chemical reactions. This paper numerically investigates the carbon deposition behaviors inside a Ni/Al2O3-based catalyst porous-filled solar thermochemical reactor for the dry reforming of methane (DRM) process under various operational conditions. The reaction kinetics for DRM including four side reactions are programmed via UDFs. The simulation results indicate that the optimal structural parameters of porous media for high-value syngas products with less carbon deposition are ϕ = 0.8 and dp = 2 mm, while the optimal feed ratio is CH4/CO2 = 1. Besides, the operating condition at vin = 100 mL/min and Plamp = 0.7 kW has the advantage of obtaining higher conversion rate while reducing the carbon deposition rate to some extent.

Gas slippage in fractal porous material

Gas flow through porous media in the slip flow regime is of great significance for the exploitation of underground natural gas and oil. The gas slip effect in porous media plays a very important role in different engineering fields, because gas slippage is involved in the determination of gas apparent permeability. In this study, the gas slip effect was investigated in model microporous materials: composite silica aerogels. We measured gas and water permeability in sets of nano composite silica aerogels, fractal materials with a high pore volume and tortuosity, and low permeability. The observed difference in gas and water permeability was analyzed from the point of view of the slip regime (Klinkenberg correction), b) and transition regime (Knudsen correction). The effect of structural parameters of porous media (pore volume, tortuosity, fractal features) on the Klinkenberg and Knudsen corrections are discussed and the different models proposed in the literature are tested. Experimental results showed that: (1) gas permeability is almost two orders of magnitude greater than water permeability, (2) Klinkenberg and Knudsen corrections increase with decreasing permeability, (3) the Knudsen corrections calculated from the literature models were almost one order of magnitude lower than experimental data, (4) we also tested the Klinkenberg approach for tortuous and fractal porous media, the fractal model with second-order slip improved the accuracy of the prediction and agree with the experimental results.

Fractal analysis of the effect of rough surface morphology on gas slip flow in micro- and nano- porous media

Gas slip flow in micro- and nano- porous media with rough surfaces is investigated by the fractal geometry theory with a focus on the effect of surface roughness of capillaries. Based on the assumption that the pore size distribution of the porous media and rough elements of the wall surfaces of capillaries follow the fractal scaling law, apparent gas permeability and gas slippage factor are derived. According to the Klinkenberg equation, the key to the calculation of apparent gas permeability is the determination of gas slippage factor. In this paper, we established an analytical relationship between the gas slippage factor and the structural parameters of porous media. We first validated the model with available experimental data, then analyzed the effect of the relative roughness, porosity, the tortuosity fractal dimension and the pore fractal dimension on the gas slippage factor. With our fractal model, the physical mechanisms of gas slip flow are better elucidated.

Study on flow parameters of fractal porous media in the high-velocity fluid flow regime

High-velocity fluid flow, which will result in the region of the wellbore or fracture, is generally in the turbulent flow regime and has drawn tremendous attention in petroleum engineering field. Turbulent factor is the key parameter, which is widely used to describe high-velocity flow in porous media. In this work, a theoretical model for turbulent factor in fractal porous media in the high-velocity fluid flow regime is developed. Moreover, a novel analytical expression for the permeability in porous media based on Wu's resistance model is also derived. Then, the analytical Kozeny-Carman constant with no empirical constant is obtained. The predictions of permeability-porosity relation by the current mathematical models have been validated by comparing with available experimental data. Furthermore, the effects of structural parameters of porous media on the curve of velocity and pressure drop are discussed in detail.

Probing the water distribution in porous model sands with two immiscible fluids: A nuclear magnetic resonance micro-imaging study

The effect of the structural heterogeneity of porous networks on the water distribution in porous media, initially saturated with immiscible fluid followed by increasing durations of water injection, remains one of the important problems in hydrology. The relationship among convergence rates (i.e., the rate of fluid saturation with varying injection time) and the macroscopic properties and structural parameters of porous media have been anticipated. Here, we used nuclear magnetic resonance (NMR) micro-imaging to obtain images (down to ∼50μm resolution) of the distribution of water injected for varying durations into porous networks that were initially saturated with silicone oil. We then established the relationships among the convergence rates, structural parameters, and transport properties of porous networks. The volume fraction of the water phase increases as the water injection duration increases. The 3D images of the water distributions for silica gel samples are similar to those of the glass bead samples. The changes in water saturation (and the accompanying removal of silicone oil) and the variations in the volume fraction, specific surface area, and cube-counting fractal dimension of the water phase fit well with the single-exponential recovery function {f(t)=a[1-exp(-λt)]}. The asymptotic values (a, i.e., saturated value) of the properties of the volume fraction, specific surface area, and cube-counting fractal dimension of the glass bead samples were greater than those for the silica gel samples primarily because of the intrinsic differences in the porous networks and local distribution of the pore size and connectivity. The convergence rates of all of the properties are inversely proportional to the entropy length and permeability. Despite limitations of the current study, such as insufficient resolution and uncertainty for the estimated parameters due to sparsely selected short injection times, the observed trends highlight the first analyses of the cube-counting fractal dimension (and other structural properties) and convergence rates in porous networks consisting of two fluid components. These results indicate that the convergence rates correlate with the geometric factor that characterizes the porous networks and transport property of the porous networks.

A complex model for the permeability and porosity of porous media

Transport phenomenon in porous media is essential in various scientific and engineering fields. The permeability and porosity of porous media serve important functions in transport phenomena. In this study, a complex model that considers the characters of pore microstructure and fluid in porous media is developed for the permeability and porosity of porous media. The flow rate expressions of this model are compared with those of previous models. As the proposed models relate the properties of fluids to the structural parameters of porous media, the various expressions of the developed model can reveal the phenomena of all types of fluid flow in a variety of porous media. The predicted permeabilities and porosities show good agreement with the available experimental data and illustrate that the proposed model can be used to characterize flow in porous media.

Evolution of the effective permeability for transient and pore-scale two-phase flow in real porous media

Permeability is one of the key parameters to model and predict the infiltration or transport process of fluid through a porous media. However, most models and approaches that have been developed experimentally, theoretically or numerically to determine the saturated permeability for steady flow are indirect or based on predefined or virtual porous media models. To the best of our knowledge, the variation behavior of the effective permeability with the infiltration length or time in unsaturated flow based on a real porous media has rarely been considered and is little understood. Herein, we propose a simple numerical method of modelling the infiltration processes of a liquid though a porous media preform based on a real porous media obtained from an experimental scanning electron microscopy (SEM) image and validate it by comparing the simulated results with experimental data. Then, we calculate the unsaturated permeability using Darcy’s law based on the results of numerical simulation without any structural parameters of porous media. The evolution of the effective permeability with the time or flow front is then presented, and the relationship between the saturation degree and permeability is also considered. The numerical results indicate that (i) the maximum infiltration length along the macroscopic flow direction globally characterizes the variations of the flow front better than the other parameters; (ii) the effective permeability of an unsaturated porous media decreases exponentially with time and the advancing of the flow front and decreases with the degree of saturation following a power-law trend; and (iii) the saturation evolution may have great effects on the effective permeability of a liquid through a porous media.

The gas effective permeability of porous media with Klinkenberg effect

Gas transport properties in micro and nano-scale porous media are of significance for low-permeability reservoirs. Gas slippage and gas molecular diffusion in micro- and nano-pores take important effect on the gas permeability of porous media. Therefore, gas effective permeability of micro and nano-scale porous media over the entire Knudsen regime is presented by a fractal model. The analytical expression for gas effective permeability with Klinkenberg effect which is a function of structural parameters of porous media (porosity, fractal dimensions and pore diameter) and gas property (mean free path of gas molecule) is derived based on the microflow model and fractal capillary model. In order to further address the local flow field characteristics, numerical simulations are also performed on a fractal Sierpinski carpet. The fractal model is validated by comparison with available experimental results, and the effect of gas slippage on the gas permeability is discussed also. The present results indicate that gas effective permeability with slippage effect increases with the increase of fractal dimension for pore size distribution and decreases as the fractal dimension for tortuosity increases. And the gas slip factor increases with the decrease of pore size, it can be also increased by increased fractal dimension for pore size distribution under fixed maximum pore size and porosity. The current fractal model can characterize the multi-scale microstructures in porous media, and every parameter in the proposed gas effective permeability model has specific physical meaning.

GAS DIFFUSION COEFFICIENT OF FRACTAL POROUS MEDIA BY MONTE CARLO SIMULATIONS

Gas diffusion behavior in fractal porous media is simulated by Monte Carlo technique in this work. Based on the fractal character of pore size in porous media, the probability model of the effective gas diffusion coefficient is derived. The proposed model of the effective gas diffusion coefficient is explicitly expressed as a function of structural parameters of porous media, such as porosity, pore size, the fractal dimensions for pore area and tortuosity. The effect of structural parameters of porous media has been studied in detail. The results show that the present results from the Monte Carlo simulations present a good agreement with those from the available analytical model and the available experimental data. The proposed Monte Carlo simulation technique may have the potential in predictions of other gas transport properties in fractal porous media.

A fractal model for spherical seepage in porous media

The characters of spherical/radial seepage in porous media have attracted steadily attention in many sciences and technologies such as in oil/water exploration, nuclear waste disposal, and heat and mass transfer in aerospace materials, biological tissue and organs. Considering the effects of capillary pressure, in this work we study the effective radial permeability and relative permeability for spherical seepage in porous media by applying the fractal theory and technique for porous media. The proposed models are related to the structural parameters of porous media, such as fractal dimensions, porosity, tortuosity and fluid properties. The validity of the proposed model is verified by comparing the model predictions with the available model and the existing experimental data. The present results show that the effective radial permeability and radial porosity decrease with the increase of radial distance. The parametrical effects on the radial permeability are also studied. It is found that the relative permeability for spherical seepage of wetting phase increases with the increase of wetting phase saturation, and the relative permeability of the non-wetting phase decreases with the increase of the wetting phase saturation. The contributions for permeability and relative permeability for spherical/radial seepage from capillary pressure can be negligible when pc,av/pm<0.01, otherwise, the effect of capillary pressure on the seepage in porous media should be taken into account.

Seepage Characteristics Study on Rabinowitch Fluid through Porous Media

Fractal expressions for flow rate, velocity and effective permeability of Rabinowitch fluid flow in porous media are derived based on the fractal properties of porous media and capillary model. Each parameter in the proposed expressions does not contain any empirical constant and has clear physical meaning and the proposed fractal models relate the flow properties of Rabinowitch fluid with the structural parameters of porous media. The presented analytical expressions help to understand the physical principles of Rabinowitch fluid through porous media.

Numerical modeling for solid–liquid phase change phenomena in porous media: Shell-and-tube type latent heat thermal energy storage

In this paper, a numerical model is established to predict the phase change material (PCM) melting process in porous media. The heat transfer enhancement technique using metal foam in a shell-and-tube type latent heat thermal energy storage (LHTES) unit is investigated. The solid–liquid phase change phenomenon is solved with the enthalpy porosity theory. The computational fluid dynamic technology is adopted to predict the flow and heat transfer for the liquid PCM and heat transfer fluid (HTF). The appropriate source terms accounting for the pressure drop caused by the presence of solid PCM and porous media are added to the momentum equations. The solid–liquid interface position and the temperature distribution are predicted to describe the melting process. The effects of the structural parameters of porous media and the inlet conditions of HTF on the thermal characteristics of LHTES unit are analyzed. The numerical model can be further extended to investigate the thermal performance of different types of storage units in LHTES system.

A fractal model for gas slippage factor in porous media in the slip flow regime

Gas slip effect in porous media in the slip flow regime is very important in various scientific and engineering fields. It has been shown that gas slippage factor plays an important role in determination of gas apparent permeability. In this work, a novel predictive model for gas slippage factor in micro-porous media with low permeability in the slip flow regime is developed based on the fractal theory. Every parameter in the proposed model has clear physical meaning. The predictions of gas slippage factor by the proposed model show the same variation trend with the available experimental data. Based on the proposed gas slippage factor, it is found the ratio of the gas permeability to the intrinsic/liquid permeability under mean pressure has the same variation trend with empirical correlations. The effects of structural parameters of porous media on the gas slip factor are discussed in detail.

A fractal model for the starting pressure gradient for Bingham fluids in porous media embedded with randomly distributed fractal-like tree networks

An analytical expression is derived for the starting pressure gradient for Bingham fluids in porous media embedded with randomly distributed fractal-like tree networks based on fractal theory and technique. The proposed model relates the flow rate and the starting pressure gradient to the structural parameters of porous media and microstructural parameters of fractal-like tree networks, the yield stress and fractal dimensions of porous media and maximum mother diameter of randomly distributed fractal-like tree networks. The results show that the starting pressure gradient decreases with the increase of porosity of matrix material, fractal dimension for mother diameters, diameter ratio and permeability, and the starting pressure gradient increases with the increase of the length ratio and the yield stress. The model predictions from the present model for the starting pressure gradient are in good agreement with the available expression.

A fractal model for the starting pressure gradient for Bingham fluids in porous media embedded with fractal-like tree networks

In this paper, a fractal model is presented for the starting pressure gradient for Bingham fluids in porous media embedded with fractal-like tree networks. The proposed model relates the starting pressure gradient to the structural parameters of porous media and microstructural parameters of the fractal-like tree networks, the yield stress and fractal dimensions. The model predictions from the present model for the starting pressure gradient are compared with the available expression. Good agreement is obtained between the predictions by the proposed expression Eq. (17) for the starting pressure gradient with those from the available expression.

Fractal analysis of Casson fluid flow in porous media

Fractal models for flow rate, velocity, starting pressure gradient and effective permeability for Casson fluid in porous media are proposed based on the fractal properties of porous media and capillary model. The proposed models are expressed as functions of fractal dimension, porosity, maximum pore size and representative length of porous media. All parameters in the proposed expressions have clear physical meaning, and the proposed models relate the properties of Casson fluid to the structural parameters of porous media. The velocity, starting pressure gradient and effective permeability versus different parameters are discussed, and the analytical expressions reveal the physical principles for flow velocity, starting pressure gradient and effective permeability in porous media.

Fractal analysis of Herschel–Bulkley fluid flow in porous media

The Herschel–Bulkley (HB) fluid is the representative fluid which may be reduced to the power-law fluid, Bingham and Newtonian fluids in appropriate conditions. In this paper, fractal models for velocity and the starting pressure gradient for HB fluid in porous media are derived based on fractal characteristics of porous media and capillary model. The proposed models are expressed as a function of fractal dimensions, porosity, maximum pore size and representative length of porous media. Every parameter in the proposed expressions has clear physical meaning, and the proposed models relate the flow characteristics of HB fluid to the structural parameters of porous media. The variation trends of fractal velocity and starting pressure gradient versus different impact factors are shown, and the analytical expressions reveal the physical principles for flow velocity and starting pressure gradient in porous media.

A fractal model for the starting pressure gradient for Bingham fluids in porous media

In this paper, we present a fractal model for the starting pressure gradient for Bingham fluids in porous media based on the fractal characteristics of pores in the media and on the capillary pressure effect. Every parameter in the proposed models has clear physical meaning, and the proposed model relates the starting pressure gradient of Bingham fluids to the structural parameters of porous media, the yield stress, the capillary pressure parameters and the fractal dimensions of porous media. The model predictions from the present model for the starting pressure gradient are in good agreement with the available expression Eq. (2). The results also show that at smaller radii ( r ¯ < 0.3 mm ) and low porosity ( ϕ < 0.3), the capillary pressure has the significant influence on the starting pressure gradient in porous media and thus cannot be neglected. However, at high porosity, the starting pressure gradient is primarily produced by the shear stress and the contribution to the starting pressure gradient from the capillary pressure is negligible.