Pore Distribution Function Research Articles

The Influence of Mechanical Stress Micro Fields around Pores on the Strength of Elongated Etched Membrane.

The investigation of the mechanical properties of polymer track-etched membranes (TMs) has attracted significant attention in connection with the extended region of their possible applications. In the present work, the mechanical stress fields around the pores of an elongated polyethylene terephthalate TM and around the 0.3 mm holes in model polymer specimens were studied in polarized light and with the finite element method. A break-up experiment showed the controlling role of stress field interaction in the forming of a microcrack system and the generation of a main crack with rupture of the TM (or model pattern). This interaction depended on the relative distance between the pores (holes) and their orientation. The results of the calculations of the pore distribution function over the surface of the TM via the net method and wavelet analysis are presented. The fractal character of pore distribution was established. The geometric characteristics of the TM pore system as initial defects are inherited by obtaining TM-based composites.

DIGITAL CLUSTER MODEL OF PORE SPACE AT FLOW OF THREE-PHASE FLOW IN POROUS MEDIUM

The work is devoted to one of the urgent problems of the oil and gas industry — the study of three-phase filtration. The creation of pore space models is an important stage in the study of the flow of oil and gas mixtures for the subsequent determination of the filtration and reservoir properties of reservoir rocks. The aim of the study is to develop a physical and mathematical model of a porous medium on the scale of a core sample. A digital cluster model for calculating the geometric parameters of the pore space is presented. The structure of the pore space of the cluster model is based on the distribution of pores by diameters obtained from capillary pressure curves (KCD). The core contains clusters consisting of a big channel (B) through which oil, water and gas move in a clear mode, average channels (A) with moving water and gas and small channels (S) with moving gas, as well as bridges between these channels. The division of the pore diameter distribution function into regions related to big, average and small channels is based on empirically determined relationships between the numbers of channels through which fluids move in the pore space in the above combinations. At the same time, the transition from the physical core model to the digital cluster model is carried out with the preservation of porosity, absolute permeability and taking into account the tortuosity of the channels. The dependence of the tortuosity of channels on their diameter is assumed according to a decreasing power law. The model presented in this paper is tested on two examples at different values of effective porosity and the number of intervals of the pore distribution function by diameter. The model has the potential for further development and calculation of the filtration flow of a three-phase mixture (oil, gas and water) on the scale of a core sample.

Comparison of Structure and Magnetic Properties of Ni/C Composites Synthesized from Wheat Straw by Different Methods

Synthesis of Ni/C nanostructured composites based on a natural raw material, i.e., wheat straw, is carried out in this work. The synthesis is performed by one- and two-stage methods using NiCl2 as the activating agent. The X-ray diffraction and EDS analyses reveal the presence of metallic nickel in the structure of the composites, whereas magnetic measurements showed that nickel was contained in the porous carbon matrix in the nanoparticle state. For nanocomposites synthesized by the one-stage method, the largest contribution to the formation of the porous structure might be attributed to pores with radii from 5 to 30 nm; for a nanocomposite synthesized in two stages, the pore distribution function exhibits a narrow isolated peak with a maximum of around 2.6 nm. Based on the obtained magnetic data, the coercive force, specific saturation magnetization and nickel content in nanocomposites are calculated. For the measured values of the coercive force, the average size of magnetic moment carriers is determined to be ~100 nm for the two-stage synthesis nanocomposite and ~100 ÷ 110 nm for the one-stage synthesis nanocomposites. The developed Ni/C nanocomposites might be used as a cheap material for energy storage applications or as magnetically controlled adsorbents.

Effects of pores on nonlinear vibration and post buckling behavior of functionally graded material pipes conveying fluid

Functionally graded material (FGM) has an important application prospect in aircraft engineering, especially in smart aircraft. The dynamic behavior of FGM has been widely investigated so far but more work is needed for the porous FGM pipes conveying fluid. In this paper, a sensible pore distribution function related with the volume fraction of metal and ceramic is proposed for the dynamic modeling of porous FGM pipes conveying fluid. The maximum porosity and its corresponding position are taken into account in the present mechanical model. The material properties of the porous pipes are temperature dependent and can be affected by pore distribution. The governing equation of the porous FGM pipe is derived and then the exact solution of post buckling is obtained. The nonlinear primary resonance is determined by the multiple scale method. It is shown that the effect of the pore distribution is very significant on the post buckling behavior and nonlinear primary resonance of the porous FGM pipes. The current work is very helpful in understanding the influence of pore distribution on static and dynamic behavior of pores FGM structures in engineering practice.

Model of Forming Isotropic and Anisotropic Graphite Under High Temperatures and Fluences Neutron Irradiation

A model is proposed for describing the shape change of isotropic and anisotropic graphite under the influence of high temperatures and high neutron radiation fluences. The model is based on a new approach, which uses the following provisions: description of the near-pore neighborhood in graphite as a solid solution using the theory of phase transformations of the first kind; consideration of a new phase as a spheroidal pore of small eccentricity, flattened along the direction of greatest stress; taking into account the clustering of carbon atoms at fluences of more than . The graphite non-isotropy is characterized by different pore sizes, different diffusion coefficients, the lengths of the paths of graphite atoms along and across volume of the sample, which in turn depend on the temperature of the sample. It is proposed that the initial element on the basis of which a new phase will be formed is the spheroidal pore of small eccentricity, flattened along the direction of the highest tension. A kinetic equation that describes the diffusion of pores under the influence of high temperatures and intense neutron fluxes is obtained. Initially, the pores are in a field of predetermined stresses oriented along and across the sample. The contribution of diffusion processes is due to the term proportional to the pore distribution function in the sample, and the effect of the neutron flux is described by an additional term in the kinetic equation. The obtained kinetic equation for anisotropic graphite can be transformed for isotropic graphite. For isotropic and anisotropic graphite, model solutions have been obtained that characterize the change in its volume with time under the influence of a neutron flux and high temperature. It is shown that the magnitude of the change in the relative volume of reactor graphite for isotropic graphite exceeds a similar value for anisotropic graphite. Theoretical confirmation of the laws governing the swelling of anisotropic graphites under the influence of large neutron fluences and in the high-temperature field, previously obtained by other authors, is obtained: longitudinal compression of anisotropic graphite samples corresponds to a change in the linear dimensions of isotropic graphites; the transverse compression of anisotropic graphite samples is less than the change in the longitudinal linear dimensions of isotropic graphites.

Nanoscale pore structure characterization of the Bakken shale in the USA

Understanding the pore structures of unconventional reservoirs such as shale can assist in estimating their elastic transport and storage properties, thus enhancing the hydrocarbon recovery from such massive resources. Bakken Shale Formation is one of the largest shale oil reserves worldwide located in the Williston Basin, North America. In this paper, we collected a few samples from the Bakken and characterized their properties by using complementary methods including X-ray diffraction (XRD), N2 and CO2 adsorption, and Rock-Eval pyrolysis. The results showed that all range of pore sizes: micro (<2nm), meso (2–50nm) and macro-pores (>50nm) exist in the Bakken shale samples. Meso-pores and macro-pores are the main contributors to the porosity for these samples. Compared with the Middle Bakken, samples from Upper and Lower Bakken own more micro pore volumes. Fractal dimension analysis was performed on the pore size distribution data, and the results indicated more complex pore structures for samples taken from the Upper and Lower Bakken shales than the Middle Bakken. Furthermore, the deconvolution of the pore distribution function from the combination of N2 and CO2 adsorption results proved that five typical pore size families exist in the Bakken shale samples: one micro-pore, one macro-pore and three meso-pore size families. The studies on the correlations between the compositions and the pore structures showed that mostly feldspar and pyrite affect the total pore volume of samples from Middle Bakken Formation whereas clay dominates the total pore volume of samples from Upper/Lower Bakken Formation. TOC and clay content are the major contributors to the micro-pore size family in the Upper/Lower Bakken. Also, it was observed that the increase of hard minerals could increase the percentage of macro-pore family in the Middle Bakken Formation.

Model of the radial distribution function of pores in a layer of porous aluminum oxide

An empirical formula is derived to describe the quasi-periodic structure of a layer of porous aluminum oxide obtained by anodization. The formula accounts for two mechanisms of the transition from the ordered state (2D crystal) to the amorphous state. The first mechanism infers that vacancy-type defects arise, but the crystal lattice remains undestroyed. The second mechanism describes the lattice destruction. The radial distribution function of the pores in porous aluminum oxide is obtained using the Bessel transform. Comparison with a real sample is performed.

Effect of the Pore Size Distribution on the Displacement Efficiency of Multiphase Flow in Porous Media

Abstract Due to the complexity of porous media, it is difficult to use traditional experimental methods to study the quantitative impact of the pore size distribution on multiphase flow. In this paper, the impact of two pore distribution function types for three-phase flow was quantitatively investigated based on a three-dimensional pore-scale network model. The results show that in the process of wetting phase displacing the non-wetting phase without wetting films or spreading layers, the displacement efficiency was enhanced with the increase of the two function distribution’s parameters, which are the power law exponent in the power law distribution and the average pore radius or standard deviation in the truncated normal distribution, and vice versa. Additionally, the formation of wetting film is better for the process of displacement.

Investigation of pore size and energy distributions by statistical physics formalism applied to agriculture products

In this paper, we present a new investigation that allows determining the pore size distribution (PSD) in a porous medium. This PSD is achieved by using the desorption isotherms of four varieties of olive leaves. This is by the means of statistical physics formalism and Kelvin’s law. The results are compared with those obtained with scanning electron microscopy. The effect of temperature on the distribution function of pores has been studied. The influence of each parameter on the PSD is interpreted. A similar function of adsorption energy distribution, AED, is deduced from the PSD.

Temporal changes of soil physical quality under two residue management systems

AbstractAlthough crop residue management is known to affect near‐surface soil physical quality, little is known about the temporal variability of these indicators over short time intervals. This study evaluates the temporal changes of nine indicators of soil physical quality. These are organic carbon content, structural stability index, bulk density, macroporosity, air capacity, relative field capacity, plant available water capacity, Dexter's S‐index and saturated hydraulic conductivity. A second set of soil physical indicators, based on the distribution of soil pore volume, was also evaluated. The indicators were determined in three different times during the growing cycle of winter durum wheat cultivated within a long‐term field research carrying out in Southern Italy and comparing two types of crop residue management, that is, burning (B) and soil incorporation (I). Only the bulk density changed over time for both treatments, although the air capacity also changed for the incorporation of wheat residues. Residual effects of the autumnal soil tillage and soil compaction were a common source of variability, irrespective of which treatment was used. Based on the existing guidelines for evaluating the physical quality of these agricultural soils, optimal or near‐optimal values were detected in about half of the cases under consideration. This suggests that both B and I create sufficiently good conditions for crop growth during the crop cycle. The comparison between observed and optimal soil pore distribution function was always poor. The pore volume distributions showed lower densities of small pores and relatively higher densities of large pores than the proposed optimal distribution. This study also suggests that the considered optimal or references curves probably cannot be applied successfully to a wide range of agricultural soils.

Dispersion transition and the nonergodicity of the disordered nanoporous medium-nonwetting liquid system

The experiments in which a nonwetting liquid does not flow from a disordered nanoporous medium are described. The outflow is shown to depend on the degree of filling of the porous medium and its temperature in a critical manner. A physical mechanism is proposed where the transition of a system of liquid nanoclusters in a confinement into a metastable state in narrow filling and temperature ranges results from the appearance of a potential barrier due to the fluctuations of the collective “multiparticle” interaction of liquid nanoclusters in neighboring pores of different sizes at the shell of a percolation cluster of filled pores. The energy of a metastable state forms a potential relief with numerous maxima and minima in the space of a porous medium. The dispersed liquid volume in a metastable state is calculated with an analytical percolation theory for a ground state with an infinite percolation cluster. The outflow time distribution function of pores is calculated, and a power law is obtained for the decrease in nonwetting liquid volume retained in a porous medium with increasing time. The relaxation of the system under study is a multistage process accompanied by discontinuous equilibrium and overcoming of numerous local maxima of a potential relief. The formation of the metastable state of retained nonwetting liquid results from the nonergodicity properties of a disordered porous medium. The proposed model can describe the detected dependences of dispersed liquid volume on the degree of filling and temperature.

Kinetics of the dispersion transition and nonergodicity of a system consisting of a disordered porous medium and a nonwetting liquid

An approach has been proposed for the description of the dispersion transition of a nonwetting liquid in confinement. This approach describes intrusion and extrusion processes for the ground state of a disordered porous medium, which is characterized by the formation of a fractal percolation cluster. The observed transition of the system of liquid nanoclusters in confinement to a metastable state in a narrow range of degrees of filling and temperatures has been explained by the appearance of a potential barrier owing to fluctuations of the collective "multiparticle interaction" of liquid nanoclusters in neighboring pores of different sizes on the shell of the fractal percolation cluster of filled pores. The energy of the metastable state forms a potential relief in the space of the porous medium with many maxima and minima. The volume of the dispersed liquid in the metastable state has been calculated within the analytical percolation theory for the ground state with the infinite percolation cluster. The extrusion-time distribution function of pores has been calculated. It has been found that the volume of the nonwetting liquid remaining in the porous medium decreases with time according to a power law. Relaxation in the system under study is a multistep process involving discontinuous equilibrium and overcoming of many local maxima of the potential relief. The formation of the metastable state of the trapped nonwetting liquid has been attributed to the nonergodicity of the disordered porous medium. The model reproduces the observed dependence of the volume of the dispersed liquid both on the degree of filling and on the temperature.

Analysis on Collapsibility and Microstructure of Unsaturated Loess Using Fractal Geometry

This paper studies the microstructure of 16 group samples from three different sites of North-west region in P. R. China. Pictures of microstructure were processed with imaging processing program to acquire the geometer parameter and fractal dimension of pores. The range of pores’ fractal dimension is between 1.816~1.936. The pore distribution function of unsaturated soil is established based on fractal geometry theory. The pore water distribution of loess under natural moisture is analyzed. The relationships of collapsibility coefficient with fractal dimension and porosity of unsaturated pores are analyzed with the method of regression analysis. A larger fractal dimension represents a more complex pore-structure. The collapsibility coefficient of loess increases with the increase of fractal dimension and porosity of unsaturated pores.

Modeling of Chemical Vapor Infiltration Rate Considering a Pore Size Distribution

To analyze chemical vapor infiltration (CVI) rates, a simulation model (PC model) was proposed, which is capable of considering difficulties of densification in the internal regions of porous bodies and the pore closure phenomena. In the model, a fictitious tapered pore is constructed based on the pore size distribution of the preform body, and variation of the pore shape during the process is calculated. For simulation study, fictitious tapered pores were constructed using different pore size distribution functions of Gaussian, δ‐function, and flat distribution, and their shapes and characteristics were compared. In the case of the Gaussian flat distribution (large dispersion), the fraction of fine pores was large and these pores became closed near their mouths. Reconversion of temporal fictitious pore shape into the pore distribution function was attempted and the PC model was successfully applied to monitor variations in the pore size distributions during the CVI process.

Characterization of Hydrophobic Microporous Membranes from Water Permeation

This paper deals with the characterization of four hydrophobic microfiltration membranes from water permeation measurements. A method proposed by McGuire et al. is used. The method uses a mathematical technique of smoothing spline fit in order to obtain a smooth pore distribution function without the need of a priori assumptions about the nature or shape of the distribution. Good agreement between the discrete distribution determined by a classical method and the continuous distribution determined from the McGuire method was obtained.

Positronium Decay in Silica Sol-Gels

ABSTRACTPositronium lifetimes inside porous silica are measured and discussed in terms of surface interactions, oxygen and nitrogen induced quenching and pore sizes. Surface interactions are studied for silica gels having surfaces covered solely with hydroxyl or methoxy groups. A rapid decay of positronium inside the pores filled with gaseous or liquid oxygen is reported and explained in terms of quenching mechanisms. An increase in the measured lifetimes for pores filled with nitrogen is attributed to the change in the pore distribution function.

Membrane heteroporosity and the probability function correlation

The probability function correlation [1, 2] of sieving data for membranes is examined in the light of heteroporosity theory. Four pore area distribution functions for arrays of circular pores are used to calculate sieving coefficients, s , as a function of the solute radius ratio, a s/ a m, where a s and a m are the solute radii corresponding to any sieving coefficient, s , and to s = 0.5, respectively. Probability log plots of s vs. a s/ a m show very little effect of structure over the region 0.85 > s > 0.3; only for s < 0.01 does the pore distribution function substantially effect the dependence of s on a s/ a m. It is inferred from these computer-generated data that probability plots should give good correlation of sieving data from membranes with widely differing structures, and they cannot be expected to yield much structural information, except in the region of very small sieving coefficients.

The pore tree structure of porous char

A theory is presented which describes the tree-like pore structure of carbon char. Eachpore that reaches the exterior surface of a char particle is depicted as the trunk of a tree. A statistically derived and empirically verified pore distribution function specifies the size distribution of the tree trunks on the particle surface. A continuous branching description of the pore tree predicts the number and size of the pores as a function of the skewed distance into the pore tree. The pore structure is completely specified through measured values of the porosity θ, internal surface area s p , and the particle radius a . The oxidation rate of carbon char is shown to be sensitive to the structure of the pore tree and the present theory is shown to accurately model the oxidation data base.

Application of a stochastic network pore model to oil-bearing rock with observations relevant to oil recovery

Mercury porosimeter experiments have been traditionally used to investigate the pore structure of oil bearing rocks, although interpretation based upon the oversimplified parallel-bundle model is inadequate to explain many practical aspects of oil recovery. A technique for stochastically assigning the sizes of tubular pore segments placed in a network configuration of interconnected pores has been used to model pore structure and a trial and erro procedure has been devised which gives directly the size distribution of segments comprising the network which will exactly reproduce any observed merc porosimeter penetration curve. The theory is applied to porosimeter tests on a core sample from the Agha Jari Field (Iran). It is evident that the pore distribution function according to a network interpretation comprises a very much greater proportion of larger pores than is inferred from the parallel model. This distortion of the pore size distribution is shown to arise from the inaccessibility of larger segments when surrounded by small pores, a phenomenon that cannot be represented by the parallel-bundle approach. As a quantified interconnecting pore model, the network analysis has potential for investigating oil retention mechanisms in a reservoir, and the probable micro-scale water displacement behaviour of the pore network deduced to rep the core sample is described. Low recovery factors seem to be related to water flowing preferentially through pathways made of larger pores. Entrapment likely in large pores isolated by surrounding smaller ones.

Char Gasification: Part I. Transport Model

Abstract A general model is developed to describe the mass transport and heterogeneous chemistry which occurs during the gasification of porous coal char. The pore branching sequence depicts that each pore that reaches the exterior surface of the particle is the trunk of a tree. The gasification rate per pore tree is obtained analytically. The effects of Knudsen diffusion, continuum diffusion, and both adsorption and desorption kinetics are included. Each physical mechanism may limit the gasification rate within some range of pore size, particle size, gas temperature and gas pressure. The gasification rate per pore tree is integrated over a pore distribution function to determine the total gasification rate. In general, no single mechanism controls the entire gasification process. However, the known results of existing models are recovered in the extreme limits of kinetic and diffusion controlled gasification.