Cumulative Pore Size Distribution Research Articles

Microstructural characterization of DEM-based random packings of monodisperse and polydisperse non-convex particles.

Understanding of hard particles in morphologies and sizes on microstructures of particle random packings is of significance to evaluate physical and mechanical properties of many discrete media, such as granular materials, colloids, porous ceramics, active cells, and concrete. The majority of previous lines of research mainly dedicated microstructure analysis of convex particles, such as spheres, ellipsoids, spherocylinders, cylinders, and convex-polyhedra, whereas little is known about non-convex particles that are more close to practical discrete objects in nature. In this study, the non-convex morphology of a three-dimensional particle is devised by using a mathematical-controllable parameterized method, which contains two construction modes, namely, the uniformly distributed contraction centers and the randomly distributed contraction centers. Accordingly, three shape parameters are conceived to regulate the particle geometrical morphology from a perfect sphere to arbitrary non-convexities. Random packing models of hard non-convex particles with mono-/poly-dispersity in sizes are then established using the discrete element modeling Diverse microstructural indicators are utilized to characterize configurations of non-convex particle random packings. The compactness of non-convex particles in packings is characterized by the random close packing fraction fd and the corresponding average coordination number Z. In addition, four statistical descriptors, encompassing the radial distribution function g(r), two-point probability function S2(i)(r), lineal-path function L(i)(r), and cumulative pore size distribution function F(δ), are exploited to demonstrate the high-order microstructure information of non-convex particle random packings. The results demonstrate that the particle shape and size distribution have significant effects on Z and fd; the construction mode of the randomly distributed contraction centers can yield higher fd than that of the uniformly distributed contraction centers, in which the upper limit of fd approaches to 0.632 for monodisperse sphere packings. Moreover, non-convex particles of sizes following the famous Fuller distribution of the power-law distribution of the exponent q = 2.5, have the highest fd (≈0.761) with respect to other q. In contrast, the particle shapes have an almost negligible effect on the four statistical descriptors, but they are remarkably sensitive to particle packing fraction fp and size distribution. The results can provide sound guidance for custom-design of granular media by tailoring specific microstructures of particles.

Modeling of effect of fly ash amount on microstructure and chloride diffusivity of blended fly ash-cement systems

Reasonable utilization of industrial fly-ash wastage in concrete engineering has been regarded as an effective way to reduce carbon emissions. By adding the reasonable dosage of fly ash to cement paste, the compactness and microstructure characteristics of the blended cement systems can be significantly improved, thereby effectively enhancing the durability of concrete structures. The vector hydration model of blended fly ash-cement systems with the interference effects of different hydration layers of fly ash and cement particles, the solubility equilibrium of solid phases and the electrical neutrality of the pore solution involved is established. By fully comparing with the experimental data of hydration degree, capillary porosity and CH content, the accuracy of the developed hydration model is verified. Based on the hydration model, the effect of fly ash content on the concentration of different ions and pH in the pore solution with curing time is discussed. Additionally, the evolution characteristic of hydration degree, capillary porosity and CH content with curing time at different fly ash content is also analyzed. Based on the reconstructed microstructure of blended systems, the rolling sweep (RS) technique is used to determine the pore size distribution of capillary pores. The effect of fly ash content on cumulative pore size distribution and differential pore size distribution at different curing time is quantitatively evaluated and discussed. By utilizing the first-passage cube, the dual-probability-Brownian motion method is constructed to predict the chloride diffusivity of blended cement systems. After diffusion model is verified by multi-group experimental data, the optimal dosage of fly ash at different water-binder ratio is calculated, which can provide theoretical guidance for practical applications in concrete engineering.

Impact of sand to aggregate ratio on mechanical properties and micro-structures of waste crumb rubber concrete

The replacement of natural river sand with crumb rubber (CR) in crumb rubber concrete (CRC) has attracted attention for its remarkable toughness and environmentally friendly properties. Sand to aggregate ratio (SAR) needs special attention as an important parameter in the mix proportions design of CRC as the CR volume fraction will vary with the SAR, affecting the particle packing within the CRC and therefore having a significant impact on the CRC properties, such as workability, mechanical properties and micro-structures. Thus, present study discusses the impact of SAR on both fresh and hardened properties of CRC. Relationship between SAR and workability, strength (including compressive and flexural-tensile), dynamic elastic modulus and damping ratio are analyzed. Cumulative pore size distribution and micro-morphology for each mixture were assessed using mercury intrusion porosimetry (MIP) and scanning electron microscopy (SEM) technology. Results show that the workability increases slightly and then decreases significantly with increasing SAR, and the best workability is demonstrated at a SAR of 40%. Wet packing density, compressive strength, and dynamic elastic modulus showed a monotonically decreasing trend with SAR from 30% to 70% due to the weaker bonding properties of the CR particles. Flexural-tensile strength and damping ratio exhibited an initial increase followed by a decrease with SAR, reaching peak values at 50%, measured at 9.75 MPa and 1.91%, respectively. Cumulative pore volume increased from 0.3244 to 0.4315 as SAR rose from 30% to 70%, potentially contributing to the decline in compressive strength and elastic modulus. Additionally, the micro morphology appeared to be more loose with the increase in SAR. Relationship between SAR and the above indicators is modelled. Radar charts were created to analyze the influence of SAR on the overall performance of CRC. The relative area shows a significant decrease when SAR exceeds 50%.

Characterizing unfrozen water content of saline silty clay during freezing and thawing based on superposition of freezing point reduction

Soil freezing point and unfrozen water content are essential parameters for the design of an artificial ground freezing (AGF) system. Previous studies on AGF technology mainly focused on soils in non-saline areas and unfrozen water content characteristic of soils in saline areas with different initial water contents was rarely investigated. Through a series of freezing point and nuclear magnetic resonance (NMR) tests, this paper investigated the influences of salt type (i.e. NaCl and Na2SO4), salt content, and initial water content on the freezing point of saline soils during freezing, unfrozen water content and pore size distribution during freezing and thawing. NaCl saline soils showed a salt content-dependent freezing point, deviating from Na2SO4 saline soils. Hysteresis effects were evident in the phase transition point, unfrozen water content, and pore size distribution during the full freeze-thaw cycle. NaCl saline soils exhibited a gradual reduction in dominant pore size with decreasing temperature during freezing and thawing, while Na2SO4 saline soils was associated with wider range of pore size. The Clapeyron equation was adopted and modified to accurately predict the freezing point and unfrozen water content of saline soils with different salt and initial water contents under different temperatures with help of newly introduced correction coefficients (i.e. a, b, k3, k4, and kt). Furthermore, the accuracy of the existing model in predicting cumulative pore size distribution was improved with help of a newly correction coefficient (i.e. β) through an regression analysis.

Characterization of void space, large-scale structure, and transport properties of maximally random jammed packings of superballs

Dense, disordered packings of particles are useful models of low-temperature amorphous phases of matter, biological systems, granular media, and colloidal systems. The study of dense packings of nonspherical particles enables one to ascertain how rotational degrees of freedom affect packing behavior. Here, we study superballs, a large family of deformations of the sphere, defined in three dimensions by $|{x}_{1}{|}^{2p}+|{x}_{2}{|}^{2p}+{|{x}_{3}|}^{2p}\ensuremath{\le}1$, where $p\ensuremath{\in}(0,\ensuremath{\infty})$ is a deformation parameter indicating to what extent the shape deviates from a sphere. As $p$ increases from the sphere point ($p=1$), the superball tends to a cuboidal shape and approaches a cube in the $p\ensuremath{\rightarrow}\ensuremath{\infty}$ limit. As $p\ensuremath{\rightarrow}0.5$, it approaches an octahedron, becomes a concave body with octahedral symmetry for $p<0.5$, and approaches a three-dimensional cross in the limit $p\ensuremath{\rightarrow}0$. Previous characterization of superball packings has shown that they have a maximally random jammed (MRJ) state, whose properties (e.g., packing fraction $\ensuremath{\phi}$, average contact number $\overline{Z}$) vary nonanalytically as $p$ diverges from unity. Here, we use an event-driven molecular dynamics algorithm to produce MRJ superball packings with $0.85\ensuremath{\le}p\ensuremath{\le}1.50$. To supplement the previous work on such packings, we characterize their large-scale structure by examining the behaviors of their structure factors $S(Q)$ and spectral densities ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\chi}}}_{{}_{V}}(Q)$, as the wave number $Q$ tends to zero, and find that these packings are effectively hyperuniform for all values of $p$ examined. We show that the mean width $\overline{w}$ is a useful length scale to make distances dimensionless in order to compare systematically superballs of different shape. Moreover, we compute the complementary cumulative pore-size distribution $F(\ensuremath{\delta})$ and find that the pore sizes tend to decrease as $|1\ensuremath{-}p|$ increases. From $F(\ensuremath{\delta})$, we estimate how the fluid permeability, mean survival time, and principal diffusion relaxation time vary as a function of $p$. Additionally, we compute the diffusion ``spreadability'' $\mathcal{S}(t)$ [Torquato, Phys. Rev. E 104, 054102 (2021)] of these packings and find that the long-time power-law scaling indicates these packings are hyperuniform with a small-$Q$ power law scaling of the spectral density ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\chi}}}_{{}_{V}}(Q)\ensuremath{\sim}{Q}^{\ensuremath{\alpha}}$ with an exponent $\ensuremath{\alpha}$ that ranges from 0.64 at the sphere point to 0.32 at $p=1.50$, and decreases as $|1\ensuremath{-}p|$ increases. Each of the structural characteristics computed here exhibits an extremum at the sphere point and varies nonanalytically as $p$ departs the sphere point. We find the nonanalytic behavior in $\ensuremath{\phi}$ on either side of the sphere point is nearly linear, and determine that the rattler fraction ${\ensuremath{\phi}}_{R}$ decreases rapidly as $|1\ensuremath{-}p|$ increases. Our results can be used to help inform the design of colloidal or granular materials with targeted densities and transport properties.

The determination of surface relaxivity and application to coal spontaneous imbibition

Experimental researches on spontaneous imbibition are of great significance for improving the recovery rate of coalbed methane and preventing gas disasters. The determination of microstructure is a prerequisite for studying pore seepage behaviors. The transverse surface relaxivity must be known first before obtaining the pore size distribution (PSD) by nuclear magnetic resonance (NMR). In this paper, a method for determining the transverse surface relaxivity of low-permeability coal was improved by correlating the NMR cumulative PSD curves and the corrected mercury intrusion porosimetry (MIP) capillary pressure curves. The MIP data was calibrated for the matrix compression effect in the high-pressure part only by MIP experiment and for the surface cavity effect in the low-pressure part. Then the transverse surface relaxivity obtained was applied to study the time and space evolution behaviors of water imbibition volume and water content in pores of different scales during spontaneous imbibition. The results indicate that the pore volume only accounts for 31.64%-66.47% of the measured mercury volume. Besides, in the rapid rising stage and the prior period of the slow rising stage of spontaneous imbibition, micropores dominate water imbibition and are the first to reach a water-saturated state. As time increases, the contributions of mesopores and macropores to water imbibition become significant gradually. After water enters coal samples, a small part of water advances along the connected path with low capillary resistance and reaches the outlet first, forming the dominant channel. However, most of the water diffuses laterally to the same horizontal plane. When the pores in this horizontal plane approach a saturated state, water migrates upward.

Quantitative Analysis of Pore Space Structure in Dry and Wet Soil by Integral Geometry Methods

We present a methodology for a numerical analysis of three-dimensional tomographic images in this paper. The methodology is based on integral geometry, topology, and morphological analysis methods. It involves calculating cumulative and non-cumulative pore size distributions of Minkowski functionals and Betti numbers. We investigated 13 samples in dry and wet (saturated beyond the field capacity) conditions within different horizons of the Phaeozem albic. For samples of the arable horizon, an increase in the Euler characteristic was observed in the process of wetting. For samples from the A2, AB and B2 horizons, the Euler-Poincare characteristic decreased during wetting. It has been proven that both Betti numbers (number of isolated pores and number of “tunnels”) decrease with swelling of the AB and B2 horizons at a depth of 20–90 cm. For samples from the arable horizon, another dependence was observed: A Betti number of zero increased first but decreased during wetting. Based on the change in topological characteristics, two methods of changing the topology of the void space of the soil were demonstrated. The above-described quantitative changes of proposed parameters of pore space tomographic images prove the possibility and progressiveness of their usage for the pore space transformation estimate.

Influence of Superplasticizer Type and Dosage on Early-age Drying Shrinkage of Cement Paste with Consideration of Pore Size Distribution and Water Loss

We introduced a parameter rs (the radius of the pores where the meniscus forms), which is composed of two factors, i e, water loss and cumulative pore size distribution (PSD), to provide a better explanation of the influence of superplasticizers(SPs) on early-age drying shrinkage. In our experiments, it is found that the addition of three types of SPs leads to a significant increase in the early-age drying shrinkage of cement paste, and drying shrinkage increases with the dosage of SPs. Based on the results above, we further studied the mechanism of the effects of SPs on the early-age drying shrinkage of cement paste by PSD and water loss, which are two components of rs. The experimental results indicate that rs can be a better index for the early-age drying shrinkage of cement-based materials with SPs than a single factor. In addition, the effects of SPs on other factors such as hydration degree and elastic modulus were also investigated and discussed.

Inverse model of capillary pore distribution of fly ash mixed cement materials

In order to study the pore structure of cementitious materials, an inverse model of the capillary distribution considering fractal dimension is proposed based on the Lucas-Washburn equation. X-ray computed tomography (XCT) is used to characterize the capillary absorption process non-destructively. The pore size distribution is inferred from the water content distribution, and the feasibility of the technique is verified by the split test and titration test. The model is applied to the cementitious materials with 10% fly ash. The results show that the larger the capillary pore diameter, the faster the water in the capillary rises, and in the early stage of capillary water absorption, the higher the water in capillary rises. The cumulative pore size distribution is derived from the model, and the correlation between the results and the cumulative pore volume measured by the mercury intrusion porosimetry is 0.942 6, which proves the accuracy of the inverse model.

Inverse modeling deduction of pore distribution in cement materials from capillary absorption features

The moisture transport performance of concrete is a vital factor that affects its durability, and this performance is closely related to the pore structures of the porous materials. In this study, water content profiles of capillary absorption were obtained using X-ray computed tomography technology. Based on the Lucas–Washburn equation, an inverse model was established to deduce the pore size distribution from the water content profiles. The feasibility of the proposed method was demonstrated using a size distribution model of the cement samples with different water-to-cement ratios. The obtained results were compared with the cumulative pore size distribution measured by mercury intrusion porosimetry, which indicated that the two methods exhibited satisfactory consistency.

Influence of evaporation rate on pore size distribution, water loss, and early-age drying shrinkage of cement paste after the initial setting

The influence of the water evaporation rate on early-age drying shrinkage of cement paste is investigated. To measure shrinkage, three mixed groups with different water–cement ratios (w/c’s) were studied over a period of 72 h. The 72-h early-age drying shrinkage, starting from the initial setting time, was measured. The pore size distribution (PSD) was measured using mercury intrusion porosimetry. The results show that the increase of the evaporation rate leads to a large increase in the early-age drying shrinkage. During the first six hours, each group had a good positive relationship between the shrinkage ratio and water loss ratio, and the shrinkage ratio was slightly greater than water loss ratio. Different water evaporation rates influence the most probable pore diameter of cement paste, which increases as the water evaporation rate increases. However, the porosity of the bulk paste and volume of mesopores was not consistent with the rule of the most probable pore diameter. A higher water evaporation rate resulted in a lower pore volume within 26 nm. Therefore, a parameter rs, which can explain the contradiction between the increase of shrinkage and volume of mesopores, was calculated from the water loss and cumulative PSD. The total volume of mesopores may not be the dominant factor in early-age shrinkage, but the most probable pore diameter, parameter rs, and relationship between them can provide a better index of drying shrinkage for the early-age of cement-based materials. Furthermore, in the paste with a w/c of 0.28, rs and drying shrinkage show a linear relationship.

A Fractal Model of Hydraulic Conductivity for Saturated Frozen Soil

In cold regions, hydraulic conductivity is a critical parameter for determining the water flow in frozen soil. Previous studies have shown that hydraulic conductivity hinges on the pore structure, which is often depicted as the pore size and porosity. However, these two parameters do not sufficiently represent the pore structure. To enhance the characterization ability of the pore structure, this study introduced fractal theory to investigate the influence of pore structure on hydraulic conductivity. In this study, the pores were conceptualized as a bundle of tortuous capillaries with different radii and the cumulative pore size distribution of the capillaries was considered to satisfy the fractal law. Using the Hagen-Poiseuille equation, a fractal capillary bundle model of hydraulic conductivity for saturated frozen soil was developed. The model validity was evaluated using experimental data and by comparison with previous models. The results showed that the model performed well for frozen soil. The model showed that hydraulic conductivity was related to the maximum pore size, pore size dimension, porosity and tortuosity. Of all these parameters, pore size played a key role in affecting hydraulic conductivity. The pore size dimension was found to decrease linearly with temperature, the maximum pore size decreased with temperature and the tortuosity increased with temperature. The model could be used to predict the hydraulic conductivity of frozen soil, revealing the mechanism of change in hydraulic conductivity with temperature. In addition, the pore size distribution was approximately estimated using the soil freezing curve, making this method could be an alternative to the mercury intrusion test, which has difficult maneuverability and high costs. Darcy’s law is valid in saturated frozen silt, clayed silt and clay, but may not be valid in saturated frozen sand and unsaturated frozen soil.

An experimental study on microstructure of leachate-polluted stabilized clay

Clay-solidified grouting curtain (CSGC) is a new kind of vertical barrier for remediating unregulated waste disposal sites in China that combines vertical-barrier and cement-based solidification-stabilization treatment techniques. The cement, stabilizing agents and landfill leachate clearly influence penetration. Although CSGC is becoming widely used because it is effective and economical, little is known about how it works. There is no clear consensus on the penetration mechanism, especially under actual continuous leachate percolation. The present work, therefore, studies the microstructure of CSGC under actual continuous leachate percolation. The cement and self-development stabilizing agents (CERSM-B) and their combined effect on the cumulative intrusion and pore size distribution were investigated using mercury intrusion porosimetry and scanning electron microscope images. The experimental results demonstrated that the unhydrated cement particles first create a large pore space. With increasing cement content, cementation products fill the large pores, thus decreasing the total pore volume. Fine-needle hydration ettringite crystal and calcium silicate hydrate gels are found when the cement content is below 15%. Stabilizing agents (CERSM-B) play an important role in the microstructure of CSGC. A close structure of flaky crystals with small, infrequent pores can be observed in samples treated with stabilizing agents (CERSM-B). However, adding too many stabilizing agents (CERSM-B) may increase the continuity of macropores. The peak pore size distribution and corresponding pore size increase with increasing dosage of stabilizing agents (CERSM-B). In engineering applications, the recommended range of cement and stabilizing agents (CERSM-B) is 15–20% percent clay and 7.5–10% cement.

Particle size effects on soil reflectance explained by an analytical radiative transfer model

Experimental evidence points to an intimate link between soil reflectance, R, and particle/aggregate diameter, D. Based on this strong correlation, various statistical methods for remote and proximal sensing of soil texture and hydraulic properties have been developed. In this paper, we derive a more fundamental and physically-based analytical radiative transfer model that yields a closed-form functional R(D) relationship for dry soils. Despite several simplifying assumptions, the proposed model shows good agreement with measured spectral reflectance (350–2500 nm) data of six soils covering a broad range of textures, colors, and mineralogies. The proposed S-shaped R(D) function resembles cumulative particle and pore size distributions as well as the soil water characteristic function. These analogies may potentially lead to new avenues for developing novel physical models for extracting important soil properties from remotely sensed reflectance data.

Porcolation: An Invasion Percolation Model for Mercury Porosimetry

Mercury porosimetry is utilized primarily in the oil industry to determine the pore size distribution of rock samples. During the process, mercury is forced into the sample with gradually increasing pressure and the volume of the injected mercury is measured vs. the applied pressure (the saturation curve). In practice, the saturation curve is assumed to be directly related the cumulative pore size distribution. However, this distribution does not coincide with the real one because of the “nonaccessibility” of pores at a given pressure. This motivates our goal to determine a more accurate cumulative pore size distribution. To achieve this, we treat the propagation of mercury as a percolation process (dubbed “porcolation” after PORosimetry perCOLATION). Porcolation is an external pressure-driven access-limited invasion percolation model where resistance values are assigned to sites/vertices. As pressure increases, the invading mercury occupies sites with smaller resistance values along paths that are connected to the “boundaries” of the network. Simulations are carried out on regular lattices, as well as on random graphs with prescribed degree distributions (representing the pore network of rock samples). An assumed pore size distribution is considered as an input/parameter of the simulations resulting in an output saturation curve. We determine the input–output mapping (homeomorphism) and utilize its inverse to correct the discrepancies between the assumed and actual pore size distributions. The results show nice agreement between experimental saturation curves and those obtained from our homeomorphism method.

Water vapour sorption on mudrocks

Abstract High-resolution water sorption isotherms were measured on 13 representative mudrock samples in order to assess the mechanisms of water vapour sorption and their relationship to the pore structure of mudrocks. The isotherm measurements were performed at 303 K on a gravimetric, dynamic vapour sorption device. Experimental data were interpreted by traditional physisorption models for which the validity was evaluated by relating model parameters to those obtained from nitrogen physisorption measurements. No direct relationships with the pore structure were observed, except for the Gurvich total pore volumes and the corresponding porosity data. Specific surface areas from Brunauer–Emmett–Teller theory are ambiguous and do not relate to nitrogen data, suggesting that water molecules do not adsorb as (multi-) layers covering pore walls. The volume filling theory (Dubinin–Astakhov equation) fits the water sorption data well but no relationship to the nitrogen data was observed in the studied sample set. A lower affinity of water for micropores was evident from the higher filling pressures of N 2 -based micropore volumes. The Barret–Joyner–Hallenda theory combined with N 2 physisorption measurements on moist mudrocks revealed that capillary condensation prevails close to saturation but not below about 0.94 relative pressure ( p / p 0 ). A distinct low-pressure hysteresis was observed from hysteresis scanning that was attributed to surface chemistry since capillary condensation occurs only at very high relative pressures. Analysis of mineralogical composition, total organic content (TOC) and organic maturity in relation to water sorption revealed only a weak correlation with the total clay content. In contrast, cation-exchange capacity (CEC) strongly correlates with water uptake, which evidences a surface-chemistry-controlled sorption mechanism. Tests of the influence of the exchangeable cation were inconclusive because pore system alteration due to cation-exchange probably superimposed the effect. To further assess the sorption mechanisms of water, nitrogen physisorption isotherms were measured on moisture-equilibrated mudrocks (11, 52, 75, 94% relative humidity at 298 K). Micropore analysis and cumulative pore-size distributions denote that water blocks pore throats rather than fills pore volumes at lower relative humidities. Over the entire humidity range, no direct relationship between water sorption and pore size was observed. These findings imply that water adsorption does not sequentially fill pores with increasing radii in mudrocks as relative humidity increases, as would be expected from water sorption by capillary condensation. This conclusion has important implications for the interpretation and measurement of geomechanical and petrophysical properties of mudrocks. Capillary pressures, particularly at low water saturations, are often calculated from water saturation using a concept based on the Kelvin equation for capillary condensation. Since water sorption in mudrocks seems to be controlled by surface chemistry rather than pore size, this approach is questionable. The observations reported here suggest that the water distribution in mudrock pore systems resulting from vapour equilibration differs from that obtained by fluid displacement (i.e. capillary drainage or imbibitions). A further consequence is that water vapour equilibration is a convenient, but not necessarily representative, method to obtain partially water-saturated mudrock samples for laboratory measurement of saturation-dependent geomechanical or petrophysical properties.

Local 3D segmentation of soil pore space based on fractal properties using singularity maps

Over the last decade, major technological advances in X-ray computed tomography (CT) have allowed for the investigation and reconstruction of three-dimensional (3D) natural porous media architectures at very fine scales. Soil scientists can use the internal structure information to develop predictive models for a range of physical, chemical and biological processes in soil. Image segmentation and thresholding are crucial steps when applying these methods to extract complex pore space geometry information from images. Traditional thresholding algorithms face challenges related to the heterogeneity of soil samples, noise and artefacts introduced during the image acquisition process.This study proposes a new segmentation method using local greyscale value (GV) concentration variabilities based on fractal concepts. Singularity maps were created to measure the GV concentration at each point. The C-V method was combined with the singularity map approach (Singularity-CV method) to define thresholds that can be applied to binarize CT images.This study also introduces a new method for creating 3D synthetic soil images based on truncated multifractals that simulate low-contrast and non-bimodal GV histograms. A synthetic soil image was created with the objective to compare traditional segmentation methods (Otsu and maximum entropy) with the Singularity-CV method. We obtained better results in porosity and more amount of pores at all scales than traditional methods, although some small pores were incorrectly identified due to the ability to amplify every anomalous GVs. Misclassification error (ME) was low and similar to Otsu.Two different 3D CT soil images were also used in this analysis, corresponding to samples of the same soil with 1.2 and 1.6gcm−3 bulk densities. After applying the Singularity-CV method to the GV images, the results were compared with the aforementioned traditional segmentation methods. The image comparison was based on the porosity, pore size distribution (PSD) and cumulative pore size distribution (CPSD). The Otsu method achieves a higher porosity than the Singularity-CV method because it defines the largest pores. However, the Singularity-CV method detected more pores at all sizes. The maximum entropy method always yielded the lowest porosity.

New segmentation method based on fractal properties using singularity maps

To improve our understanding of the factors that control a number of critical soil processes, it is important to properly identify pore space zones. Computed tomography (CT) images provide increasingly reliable information about the geometry of pores and solids in soils at very small scales and are a non-invasive technique. However, the low contrast between voids and pores and the non-bimodal greyscale value (GV) histograms observed in the CT images present a problem with respect to pore identification.In this work, we propose a new segmentation method based on the local GV concentration variability when using singularity maps. We also introduce a new method for creating synthetic CT soil images based on truncated multifractals that simulate low-contrast and non-bimodal GV histograms.From three different bidimensional CT soil images and one synthetic soil image, singularity maps were created to measure the GV concentration at each point by defining areas with self-similar properties that were shown as power-law relationships in Concentration-Area plots (C-A method). The C-A method together with a singularity map (the “Singularity-CA” method) was used to define thresholds that were applied to binarize the CT images. Promising results were obtained when the greyscale images were overlapped with the borders of the binarized images.Once these black and white images were obtained, we compared them with commonly used segmentation methods: the Otsu, Iterative and Maximum Entropy methods. The image comparison was based on the total porosity, cumulative pore size distribution (CPSD), cumulative pore size–area distribution (CPSAD) and misclassification error (ME). We found that the Otsu and the Iterative methods overestimated the size of large pores compared to the ground-truth image, which overestimated the porosity. Conversely, the Singularity-CA method extracted medium and large pores with a good fit compared to the ground-truth image. It was observed that whereas the Otsu and Iterative methods obtained the large pores, the “Singularity-CA” method detected an aggregate of small pores, although many of these small pores were incorrectly identified. This was due to the latter's high sensitivity when detecting anomalous GV values. The Maximum Entropy method always resulted in the lowest porosity in the real CT soil samples and the greatest porosity in the synthetic soil image samples.

Fluid flow in complex porous media: Experimental data and IFU model predictions for water vapour permeability

In this research work, an Intermingled Fractal Units' model (IFU's model) has been proposed with the aim of predicting water vapour permeability characteristics of porous rock, normally studied in gas reservoir field. IFU modelling approach commences with the reproduction of experimental pore size distribution with the help of diverse fractal base units mixed together. This procedure allows simulating the porous microstructure in terms of pore cumulative curve or pore size distribution. An analytical procedure is used for obtaining the permeability values. The studied rocks include limestone from South Sardinia quarries and have similar characteristics of those studied in gas reservoir field. They have been taken from four different parts (systems A, B, C and D) of the quarry for the assessment of the heterogeneity of this rock. From the experimental tests, the average water vapour permeability values are equal to 7.22 ± 1.22, 4.21 ± 1.51, 10.09 ± 1.11 and 10.12 ± 2.4210−12 kg m−1 s−1 Pa−1 respectively for systems A, B, C and D, whereas predictions by IFU are respectively equal to 7.15 ± 1.55, 4.25 ± 1.45, 10.12 ± 1.22 and 9.98 ± 2.1810−12 kg m−1 s−1 Pa−1. The comparison shows a good capacity of IFU procedure to predict water vapour permeability values.

A new method for obtaining the rock pore structure eigenvalue

To obtain the pore structure eigenvalue, the following two methods are usually applied: the graphical method and the trapezoidal method. Both methods have intrinsic disadvantages. For the graphical method, the pore size distribution curve must satisfy the normal distribution and some of the data from the cumulative pore size distribution curve are selected and averaged; this makes the method inflexible and causes inevitable computation errors. For the trapezoidal method, the saturation range is restricted, which causes the obtained results to deviate from the true value. To overcome these disadvantages, we propose a new method that is based on the trapezoidal method. The software 1stOpt is applied to get the capillary pressure function by fitting with the measured data. By substituting the pore radius function derived by the capillary pressure function into the computed formula of the new method, we obtain the pore structure eigenvalues. In comparison to the conventional methods, the results obtained by the new method are closer to the true value because this method takes into account the entire saturation range for integrating. In addition, it can be applied in all kinds of pore size distributions.