Pore Size Distribution Function Research Articles

Pore structure characterization and permeability estimation with a modified multimodal Thomeer pore size distribution function for carbonate reservoirs

Pore structure of carbonate reservoirs is complex and multimodal. In order to characterize the pore structure of complex carbonate, a modified multimodal Thomeer pore size distribution (PSD) function was developed, which was based on the multimodal Gaussian density function and three controlling parameters including peak position, peak height and full width at half maximum (FWHM). The Expectation-Maximization algorithm for Gaussian mixture model was utilized to obtain three controlling parameters for the calculation of Thomeer parameters, namely the extrapolated displacement pressure, the percent bulk volume occupied by mercury at infinite capillary pressure and the pore geometrical factor. Three permeability models were proposed based on the Thomeer parameters and compared with the previous models. The results show that PSD curve of 55% samples need more than two Gaussian density function, which illustrates the multimodal characteristic. Thomeer parameters relate to the controlling parameters of Gaussian density function. The peak position moved toward larger capillary pressure with the increase of extrapolated displacement pressure and pore geometrical factor. The peak height has positive correlation with the percent bulk volume occupied by mercury at infinite capillary pressure and negative correlation with pore geometrical factor respectively. FWHM has positive correlation with pore geometrical factor. The extrapolated displacement pressure derived from the first Gaussian density function has a high correlation with permeability, which demonstrates that permeability is mainly controlled by the maximum pore throat radius. We found that when the sample has the percentage occupied by the first porous system larger enough than 21.64%, its permeability is dominated by the first porous system with the maximum pore throat radius; otherwise, it would be influenced by the second porous system. The comparative study shows that permeability models that has considered the influence of second porous system could improve the accuracy of permeability estimation for the complicated carbonate samples.

Framework to estimate the soil-water characteristic curve for soils with different void ratios

The soil-water characteristic curve (SWCC) contains information regarding the geometric pore space in a soil and is commonly used to estimate unsaturated soil properties, such as unsaturated hydraulic conductivity and unsaturated shear strength. Soil volume change can significantly affect the SWCC and the engineering properties of soil. Different SWCCs can be obtained if the soil specimens are prepared with different initial void ratios. The volumetric shrinkage curve (VSC) is commonly used to convert the SWCC in the form of gravimetric water content (w-SWCC) into a curve that is in the form of degree of saturation (S-SWCC). In this paper, a framework is developed in which different S-SWCCs are generated based on the measured w-SWCC of soil in a relatively loose condition and the VSC. The proposed framework is based on the concept of the pore size distribution function (PSDF). The estimated SWCCs corresponding to different initial void ratios from the proposed framework were verified by using experimental data from published studies.

Theoretical and experimental study of the frost heaving characteristics of the saturated sandstone under low temperature

The pore structure and unfrozen water film have a significant influence on the frost heave of saturated porous media. The freezing process and frost heaving characteristics of saturated sandstones have been studied in this research by theoretical and experimental approaches. A developed micromechanical model has been proposed, considering the distribution function of pore size, the effect of unfrozen water film, and the interfacial free energy. The distribution of pore size in sandstone can well satisfy a dual-pore structure model, including the thin pores and coarse pores. Besides, four typical thickness functions are used to investigate the influence of the thickness of unfrozen water film on the disjoining pressure and frost heaving strains. The exponential equation suggested by Fagerlund (1973) may be better to quantify the thickness of this film by comparing with the experimental results. In addition, the frost heaving strains are also very close to the experimental values if ignoring the unfrozen water film. This calculation results may give the reasons why a satisfactory results can also be obtained with the absence of the unfrozen water film in the previous models. This study provides a better understanding of the frost heaving mechanism of saturated porous materials.

Analysis of the mechanism of temperature influencing methane adsorption in coal from perspective of adsorbed layer thickness theory

Temperature is an important factor influencing gas content in coal seam. The adsorbed layer thickness in coal has not been quantitatively analyzed under different temperatures. To probe the temperature evolvement and its effect on methane adsorbed layer thickness in coal, the adsorbed layer thickness equation is established based on thermodynamic principles. The adsorbed layer thickness increases with decreasing temperature and increasing equilibrium pressure. The low temperature can promote methane adsorption and increase the number of adsorbed layers. When the pore size is larger than the pore radius at which capillary condensation occurs, the adsorbed layer thickness will decrease as the pore radius increases. This phenomenon shows a negative exponential function. If the pore radius increases to a certain extent, the number of adsorbed layers does not change with the increasing pore radius. The number of adsorbed layers in the micropores and mesopores are greater than that in the macropores. The adsorbed methane quantity can be calculated by the pore size distribution function and adsorbed layer thickness function under different temperatures. The adsorbed layer thickness theory not only reveals the mechanism of temperature influencing methane adsorption in coal but also can be used to predict the adsorption isotherms at different temperatures and pressures if the pore size distribution is known.

Isothermal drying of plant-based food material: An approach using 2D polydimethylsiloxane (PDMS) micromodels

The aims of this study were to build PDMS micromodels that simulated plant-based food material, and use them to investigate the drying mechanisms at pore-scale, the drying front morphologies and the drying curves during the isothermal drying process. Micromodels were built using a modified photolithographic technique. Three normal pore size distribution functions were developed to simulate the plasmodesma, intercellular space, and cell wall. Micromodels were impregnated with a pyranine aqueous solution and placed on a balance illuminated with ultraviolet light. Isothermal drying was developed by natural convection (20 °C). Drying front morphologies displayed a hierarchical behavior in which pores with the largest diameter dried first. Drainage and surface evaporation sequences and internal evaporation controlled the drying of PDMS micromodels. The micromodels were useful to simulate plant-based food material and study isothermal drying of such porous media. The results led to the proposal of some drying mechanisms that were involved.

Physical assessment of a Haplohumox soil under integrated crop-livestock system

Soil structure characterization in both macro and micro scales is very complex. The soil porous system (SPS) is responsible for numerous functions in soil, such as water infiltration, retention, redistribution, gas exchange, root growth and other processes related to the SPS. Indices, hydraulic functions and micromorphological measures of soil physical quality (SPQ) were carried out to evaluate the structure of a Haplohumox under integrated crop-livestock system (ICLS). Two soil depths were analyzed (0–10 and 10–20 cm) in four tillage systems: conventional tillage (CT), minimum tillage (MT), no-tillage (NT) and chiseled no-tillage (CNT), taking into account the annual ryegrass cropped during the winter for grazing (G) and silage (S) use. Soil water retention curve (SWRC), pore size distribution function (PSD), SPQ indices and the aeration hydraulic-energy function were associated together with other parameters obtained via micromorphological analysis of soil structure. Areal porosity (AP) was determined to classify the shape of pores as rounded (R), elongated (E) and complex (C). The size of pores was chosen based on their function and classified as storage pores (0.5–50 μm), transmission pores (50–500 μm) and fissures (>500 μm). The number of pores (NPo) was also estimated considering the disconnected pores. Results indicated that the top layer is most affected by tillage. Rounded pores were predominant for all evaluated systems, whereas complex pores such as fissures presented the largest contribution to AP at the deeper surface layer for all treatments. The plowing operation affected soil infiltration and water retention processes in MT and CT as well as AP and NPo in the NT system. NT and CNT required less energy to drain water in both surface layers evaluated. In the top layer MT/S yielded the largest energy to release water, exhibiting small values of AP and a homogeneous SPS. Strong correlation was found between absolute aeration index and some shape parameters of PSD, evidencing the physical relation between these indices. The micromorphological analysis supported the understanding of the other SPQ indices and aeration function for the tillage systems evaluated here.

Pore-scale model for estimating the bimodal soil–water characteristic curve and hydraulic conductivity of compacted soils with different initial densities

This paper proposed a pore-scale model to simulate the effect of initial soil density on the bimodal soil water characteristic curve (SWCC) of compacted soils. The pore-scale model is developed based on the bimodal pore-size distribution. Soils with bimodal pore-size distribution is assumed to have dual porosity, namely the macropore structure and the micropore structure, and hypothesized that the micropore structure is hard to be compressed under mechanical loading. The water stored in the macropore structure is divided into two parts, the bulk water and the meniscus water, respectively. The deformation of soil (bulk water flow) is obtained by horizontal shifting and vertical scaling of the pore-size distribution (PSD) function. A toroidal model is used to describe the influence of initial density on the meniscus water. The pore structure of compacted coal gangue was qualitatively imaged as an evidence of the pore structure changes, and the SWCC of the compacted coal gangue was quantitatively analyzed. Finally, a numerical method is advised for simulating bimodal permeability function by using the proposed model with Mualem function. Laboratory test results in published literature are employed to validate the proposed model and permeability function, and the model predictions showed good agreement with the experimental data in the literature.

The role of pore-size distribution function on the estimation of engineering properties of unsaturated soil

The role of pore-size distribution function on the estimation of engineering properties of unsaturated soil

Structural transformations during periodic deformation of low-porosity amorphous materials

Atomistic simulations are employed to study microstructural evolution of pore ensembles in binary glasses under periodic shear deformation with varied amplitude. The consideration is given to porous systems in the limit of low porosity. The initial ensembles of pores are comprised of multiple pores with small sizes, which are approximately normally distributed. As periodic loading proceeds, the ensembles evolve into configurations with a few large-scale voids and significantly reduced number of small pores. These structural changes are reflected in skewed shapes of the pore-size distribution functions and the appearance of a distinct peak at large length scales after hundreds of shear cycles. Moreover, periodic shear causes substantial densification of solid domains in the porous systems. The structural evolution of pore ensembles is found to stem from the formation of shear band like regions of enhanced particle mobility after a number of transient cycles. The spatial extent of regions with increased atomic mobility depends strongly on the strain amplitude. A simple theoretical model is developed to qualitatively describe the transformation of the initial configurations of small-size voids into larger-scale void agglomerates.

Role of the pore-size distribution function on water flow in unsaturated soil

The hydraulic properties of soil (i.e. soil-water characteristic curve (SWCC) and coefficient of permeability) govern the moisture flow in it. Previous research has indicated that the hydraulic properties of soil are dependent on its pore-size distribution. An improved capillary model is now proposed to explain the concept of the pore-size distribution in soil and its relationship to SWCC. A new model, the “valve model”, is also proposed as the explanation for water flow in unsaturated soil. The pore-size distribution function is incorporated in the “valve model” and is used to calculate the relative coefficient of permeability for unsaturated soil. In this paper, the role of the pore-size distribution function in the estimation of SWCC and the permeability function are explained. Equations are proposed for estimating the pore-size distribution function from the experimental data of relative coefficient of permeability. The results from the proposed equations agree with the experimental data from laboratory measurement and published data.

STRESS EFFECT ON CEMENTATION FACTOR OF SANDSTONE ROCKS TYPE EVIDENCE FOR A VARIABLE ARCHIE POROSITY EXPONENT “m”

Ancient sandstones include important reservoirs for hydrocarbons (oil and gas). This research provides an experimental investigation on the influence of variations in confining pressure on cementation factor of two wells located in Sirt basin. Measurements of formation resistivity factor versus cementation factor for sandstone samples which were collected from both wells at different confining pressures were carried out. The Effects of confining stress on the electrical properties of the rock samples were studied and analyzed. The results showed that the confining pressure variations depend on the pore structure of the studied rock. Furthermore, it can be concluded that the electrical resistivity of rocks is function of pore size distribution and how the fluids were distributed in the pore spaces. The effect of overburden pressure and the porosity variation on cementation factor is also investigated for different rock types. It has been concluded that the compaction due to overburden pressure generally causes a considerable increase in resistivity, especially in poorly cemented rocks. In low-porosity rocks, resistivity measurements determined under representative overburden pressures that are strongly recommended to improve well log interpretation.

A pore-size distribution function based method for estimation of hydraulic properties of sandy soils

Hydraulic property of soil is key information required for understanding the groundwater flow in the soil (including saturated and unsaturated zone). The water flow in soil is governed by the geometrical pore-space characteristics of soil structure (i.e., pore-size distribution function). Even though the concept of pore-size distribution function had been proposed decades ago, the pore-size distribution function is rarely used to estimate the hydraulic properties in engineering practice. In practice, the effective particle size (i.e., d10) and void ratio (e) are commonly used for the estimation of saturated coefficient of permeability, ks, for sandy soils. Neither d10 nor e can accurately represent the geometrical pore space in soil. With the development of unsaturated soil mechanics, it is observed that the pore-size distribution function can be expressed in another form which is named as soil-water characteristic curve (SWCC). In this study, the coefficients of permeability of sandy soils were estimated using the concept of “pore-size distribution function” (or SWCC). The comparison between the estimated results using the proposed equation and the measured data from laboratory tests in Nanyang Technological University (NTU) showed that the proposed equation in this note provided good estimation of ks.

Method of determination of equilibrium moisture content of building materials of fencing structures

When studying the thermal condition of the enclosing structures, it is necessary to have the values of the equilibrium moisture content Wp of the material of the design corresponding to the given temperature T and the relative humidity φ of the environment. Typically, the isotherms of sorption are empirical ratios, which approximates experimentally obtained graphs Wp = f (φ, T). The methods of experimental determination of equilibrium moisture content are quite complex in terms of ensuring the long-term maintenance of the stationary state of the surrounding gas environment and the accuracy of measuring the change in the mass of moisture material. In addition, each experiment produces only one value of Wp for certain T and φ, that is, obtaining the equilibrium moisture content of a particular porous material throughout the range of changes in relative humidity at this temperature takes a significant time interval. Below is an algorithm for numerical determination of the sorption isotherms based on the data on the pore size distribution function for a given capillary-porous material with the use of a formula for the equilibrium thickness δ of a condensate layer on a solid surface located in the gas medium with the corresponding parameters T and φ. This formula is obtained by Professor N. I. Nikitenko on the basis of his molecular-radiation theory of the heat and mass transfer, in accordance with which the energy transfer, as well as mass of matter or field, is carried out by material carriers that are continuously released or absorbed by particles of substance. The molecular-radiation theory explains the differences between the classical theory of thermal conductivity and experimental data, and on the verge it passes into the Fourier equation. Numerous experiments with different capillary-porous materials were carried out and verification of the obtained results was carried out. They confirm that the proposed algorithm allows us to determine the equilibrium moisture content of any porous materials for which the pore size distribution function is known throughout the range φ at a given temperature.

Super-sieving effect in phenol adsorption from aqueous solutions on nanoporous carbon beads

Removal of aromatic contaminants, like phenol, from water can be efficiently achieved by preferential adsorption on porous carbons which exhibit molecular sieving properties. Here, we present nanoporous carbon beads exhibiting an outstanding sieving effect in phenol adsorption from aqueous solution at neutral pH, which is evidenced experimentally and theoretically. The molecular sieving with pure phenol adsorbed phase is achieved by tuning the pore size and surface chemistry of the adsorbent. This study elucidates the essential role of hydrophobic interactions in narrow carbon micropores in removal and clean-up of water from organic pollutants. Furthermore, we suggest a new theoretical approach for evaluation of phenol adsorption capacity that is based on the Monte Carlo simulation of phenol adsorption with the relevance to the pore size distribution function determined by the density functional theory method from low temperature nitrogen adsorption.

A predictive model of the effective tensile and compressive strengths of concrete considering porosity and pore size

Pores, voids correspond to inevitable products in the formation of concrete and significantly affect its macroscopic effective strength. A lot of researches show that both porosity and pore structure have significant influence on the concrete strength and differences exist with respect to those influences on the tensile and compressive strengths. In this paper, first, the relationships between the effective tensile and compressive strengths of concrete and porosity are expressed respectively from the proposed simplified center pore model. Second, in order to further consider the influence of the pore structure, the pore size is chosen as the representative index of pore structure and an influence function related to the pore size is proposed based on the correlation analysis. The total influence coefficient of pore size is obtained by combining the pore size distribution function and influence function. Taking the total influence coefficient into account in the relation between the effective strength and porosity, explicit formulae of porous concrete effective tensile and compressive strengths are finally deduced. Through comparing the present approach with a few classical analytical solutions and experimental observations, the results indicate the reliability and accuracy of the proposed approach and the derived equations are simple and convenient to use. Analysis and discussion suggest that the effect of porosity on the compressive strength of concrete exceeds that of the tensile strength and that the effective concrete strength with the same porosity can be improved by decreasing the pore size.

Quantitative analysis porous structure of activated carbon with classical density functional theory

Towards development of a more reliable theoretical procedure, we apply a modified classical density functional theory for porous analysis on solid heterogeneity. Such novel theoretical procedure has been used to analyze the pore size distribution (PSD) of five activated carbon samples and to predict the adsorption isotherms of these materials. As for the characterization sensitive with the adopted numerical algorithms, we evaluate the representative of the required PSD by three numerical methodologies with their predictive capability. It is notable that P1 method with B-spline function as prior PSD function form is suitable for the pore-size analysis of activated carbon for its smallest average deviation on isotherm fitting and prediction. Moreover, the effect of hypothesis form on solid heterogeneity is also discussed according to its contribution on the accuracy and stability of the numerical procedure. According to the proposed feature pore width range theory, we discuss the relationship between the numerical procedure and the predictive capability of the characterized PSD. With the fluctuated experimental temperature into consideration, we also make predictive calculation on adsorption capacity of activated carbon within certain error range, which is meaningful for the development of predictive functional in PSD model.

A new model for the electrical conductivity of cement-based material by considering pore size distribution

Electrical conductivity is one of the most important indicators of the durability, impermeability and frost resistance of cement-based materials (CBMs). It is also a main performance parameter for some special CBMs such as insulating concrete and electrically conductive concrete. The aim of this study was to examine the relationship between electrical conductivity and saturation degree of CBMs more deeply by considering the pore size distribution (PSD), which is described in a new way. The distribution of the pore solution (the main conducting medium) in CBMs was analysed by considering the PSD function, the Kelvin equation and theories of capillary and surface adsorption. According to the pore solution distribution and conductivity theory, a conducting tube network model was established. The curves obtained by the proposed model were found to fit the experimental data well. The conducting tube network model was then used to analyse the factors influencing the electrical conductivity of CBMs. The conclusions obtained from this study were that the electrical conductivity of CBMs varies with the relative ratio of large and small pores and the mean value and standard deviation of large pores, and that the electrical conductivity of CBMs is proportional to the pore solution conductivity and porosity of the CBM.

Multiscale Simulation of Porous Ceramics Based on Movable Cellular Automaton Method

The paper presents a model for simulating mechanical behaviour of multiscale porous ceramics based on movable cellular automaton method, which is a novel particle method in computational mechanics of solid. The initial scale of the proposed approach corresponds to the characteristic size of the smallest pores in the ceramics. At this scale, we model uniaxial compression of several representative samples with an explicit account of pores of the same size but with the random unique position in space. As a result, we get the average values of Young’s modulus and strength, as well as the parameters of the Weibull distribution of these properties at the current scale level. These data allow us to describe the material behaviour at the next scale level were only the larger pores are considered explicitly, while the influence of small pores is included via the effective properties determined at the previous scale level. If the pore size distribution function of the material has N maxima we need to perform computations for N − 1 levels in order to get the properties from the lowest scale up to the macroscale step by step. The proposed approach was applied to modelling zirconia ceramics with bimodal pore size distribution. The obtained results show correct behaviour of the model sample at the macroscale.

Hygrothermal modeling and evaluation of freeze-thaw damage risk of masonry walls retrofitted with internal insulation

For historical buildings with a worth-preserving appearance, internal wall insulation can be the only possible solution to improve the building energy efficiency. However, the application of an internal insulation layer changes significantly the hygrothermal performance of the building envelope. For masonry walls, such intervention may lead to freeze-thaw damage of the brickwork. In this study, a hygrothermal model is developed. The model takes into account moisture and heat transport in porous medium and tracks the occurrence of freezing and thawing in function of pore size distribution and as well as the ice content. Freezing and melting of water in porous medium is implemented based on the theory of freezing point depression, as freezing temperature of water in porous medium depends on pore size, i.e. water in the smaller pores freezes at temperatures lower than 0 °C. The numerical model results are compared with a porous medium freezing experiment and good agreement is found. Traditional hygrothermal assessment uses the number of zero crossings on a Celsius scale as the number of freeze-thaw cycles. We propose a method that uses the number of actual ice growth and melt cycles as an indicator more accurately accounting for the freeze-thaw process. In addition, we develop an index, called FTDR Index, to assess freeze-thaw damage risk. We perform simulations of uninsulated and internally retrofitted masonry walls using two Swiss climatic conditions. The study clearly shows increase of freeze-thaw cycles and ice content after internal retrofitting in both climates. Thus, FTDR Index increases after internal retrofitting.

Characterization of activated carbons with low-temperature hydrogen adsorption

Low-temperature nitrogen adsorption isotherms are widely used for characterization of carbon materials. However, quite complex physical mechanism of interaction of nitrogen with graphite and micropores hinders a reliable pore size distribution (PSD) analysis. This situation is worsening by a strong regularization procedure which effect on the PSD function is basically unknown. In the present paper we propose a new method of the PSD analysis of activated carbons in the micropore range using hydrogen adsorption isotherms at 77 K. We relied on the kinetic Monte Carlo simulation and accurately accounted for the McLachlan surface mediation, quantum correction of the H2 – C potential, and the reduced carbon collision diameter (0.26 nm) determined previously (Ustinov E. Carbon 2016; 100: 52). Analysis of PSDs of several samples of activated carbons has shown that the microporous structure of investigated materials consists of discrete number of slit micropores of specified width. We noted that a population of micropores having width of 0.67–0.69 nm is often observed. This suggests that this group of pores can appear due to burn-off of one layer in the graphite lattice. The kernel for the PSD analysis is presented in the form of regression equation which can be used by researches independently.