Pore Fractal Dimension Research Articles

Experimental study on macro–micro-structural properties and strength prediction model of wastewater concrete

This study is intended to investigate the mechanical, durability, and drying shrinkage properties of concrete mixtures incorporating wastewater from ready-mixed concrete plants. The microstructural attributes were investigated by X-ray diffraction (XRD), scanning electron microscope (SEM) imaging, energy dispersive spectrometry (EDS), and mercury intrusion porosimetry (MIP). Meanwhile, rough set theory (RST) was used to analyze the influence of mean pore radius, porosity, fractal dimensions, and pore size distribution (PSD) on the compressive strength of wastewater concrete. The results showed that the seven-day cube compressive strengths for C20, C40, and C60 concrete specimens increased when wastewater was utilized, with the highest rise in the strength properties being observed as 16.84% for C40 mixture. Nevertheless, the 28-day cube compressive strengths of C20, C40, and C60 concretes were reduced by 4.85%, 9.33%, and 18.63%, respectively. The durability results showed that wastewater mixing reduced the frost resistance of C40 and C60 concrete, but improved for C20 concrete. The microstructural investigation revealed that mixing concrete with wastewater densifies the early-age concrete microstructure and refines the pore size. Nevertheless, the compactness of concrete microstructure at the later stage was reduced, and the pores in concrete were enlarged due to the poor cohesiveness of wastewater particles. The porosity and PSD have the greatest influence on the compressive strength of wastewater concrete. A strength and pore structure model of wastewater concrete was also developed and validated by considering PSD and porosity as bivariate parameters. Highlights The addition of wastewater can improve the early compressive strength of concrete. The addition of wastewater reduces the carbonization resistance of concrete. A high-precision model of wastewater concrete strength was established.

Fractal theory and dynamic contact angle-based imbibition model for two-phase flow in porous media

During the development of tight oil reservoirs, there are significant occurrences of spontaneous imbibition. Understanding the spontaneous imbibition behavior at the core scale of tight sandstone holds significant importance in improving the recovery rate. This study presents a novel mathematical model for characterizing the spontaneous imbibition phenomenon in tight porous media, drawing upon the fractal theory and the dynamic contact angle in capillary bundles. The proposed model has been verified by the results of core imbibition experiments in the literature. Furthermore, we conducted spontaneous imbibition simulation studies using core structures of different pore types extracted from real tight reservoirs to validate the applicability of the new mathematical model. Comparative analysis shows that the derived mathematical approach fits well with the simulation results, but the heterogeneity of the pore space can lead to certain errors between the model and the simulation results. The influencing factors analysis suggests that the higher the porosity, the higher the final recovery rate, whereas an increase in pore fractal dimension has little effect on the final recovery rate.

Pore structure of tight sandstones with differing permeability: The He 8 Member of the Middle Permian Lower Shihezi Formation, Gaoqiao area, Ordos Basin

AbstractTight sandstone has strong pore heterogeneity and complex pore structure, and the pore structure of tight sandstone varies with different permeability. To study the differences in the pore structure of tight sandstone with different permeability, this study investigated the tight sandstone of the He 8 Member in the Gaoqiao area of the Ordos Basin. Factors influencing pore formation are analyzed through experiments utilizing methods, such as distinguishing casting thin sections, scanning electron microscopy, high‐pressure mercury intrusion, and low‐temperature nitrogen adsorption. The results indicate that in this area, the pores of the tight sandstone are primarily dissolution and intercrystalline pores, with occasional intergranular pores and microcracks. Type Ⅱ samples (permeability > 0.2 × 10−3 μm2) are primarily composed of dissolution and intercrystalline pores, with a few visible intergranular and microcracks. In contrast, Type Ⅰ samples (permeability < 0.2 × 10−3 μm2) mainly consist of micropores and intercrystalline pores, where microcracks are observed locally. Pore size research demonstrates that Type Ⅰ samples have pore size under 1000 nm, with peaks primarily at 4–5 nm. There are also peaks between 10–1000 nm, but without a consistent pattern. For Type Ⅱ samples with sizes smaller than 1000 nm, pore distribution is evident. Peak values when the pore size exceeds 1000 nm. Type Ⅰ samples have fewer micron‐level pores, while Type Ⅱ samples are primarily dissolution pores. The nanopores of Type Ⅰ samples consist of flat pores with good connectivity, whereas those of Type Ⅱ samples are mainly blind pores with poor connectivity. Type Ⅰ samples have larger pore fractal dimensions, more intricate pore morphology, and rougher and irregular pore throat surfaces compared to Type II samples. Hence, the sedimentary environment, diagenesis, and mineral composition affect the pore distribution in tight sandstone. The research findings highlight the variations in the pore structure of tight sandstone with varying permeability, providing crucial guidance for classifying and assessing pore structure in tight sandstone reservoirs.

A Study on the Pore Structure and NMR Fractal Characteristics of Continental Shale in the Funing Formation of the Gaoyou Sag, Subei Basin

The continental shale oil resource in China exhibits significant potential and serves as a crucial strategic alternative to the country’s conventional oil and gas reserves. The efficacy of shale oil exploration and production is heavily contingent upon the heterogeneity of the pore structure within the reservoir. However, there remains a scarcity of research pertaining to the pore structure of continental shale and the factors that influence it. The objective of this study is to provide a quantitative characterization of the heterogeneity exhibited by the continental shale of the Funing Formation in the Gaoyou Sag. In this study, the research focus is directed toward the continental shale of the Funing Formation located in the Gaoyou Sag of the Subei Basin. This paper examines the correlation between the fractal dimension of nuclear magnetic resonance (NMR) and various factors including the total organic carbon (TOC), mineral composition, geochemical parameters, and physical properties, utilizing the principles of fractal dimension theory. The findings indicate that the primary pore types observed in the Funing Formation continental shale are inorganic matrix pores, which encompass dissolution pores, clay mineral intergranular pores, and a limited number of pyrite intergranular pores. By employing a relaxation time cutoff, the NMR fractal dimension can be categorized into two distinct dimensions: the bound-fluid-pore fractal dimension (0.5795~1.3813) and the movable-fluid-pore fractal dimension (2.9592~2.9793). The correlation between mineral composition and the fractal dimension indicates a negative relationship between the fractal dimensions of bound-fluid pores and movable-fluid pores and the content of quartz. The correlation between clay minerals and the fractal dimension indicates a significant negative relationship between the fractal dimensions of bound-fluid pores and movable-fluid pores with illite. There exists a negative correlation between the pore fractal dimension of bound fluid and the content of organic matter, whereas a positive correlation is observed between the pore fractal dimension of mobile fluid and the content of organic matter. The range of maturity of organic matter within the Funing Formation exhibits a relatively limited span, as indicated by the vitrinite reflectance (Ro) values falling between 0.8% and 0.9%. This narrow range of maturity does not exert a substantial influence on the two fractal dimensions. The NMR fractal dimension exhibits a negative correlation with permeability in relation to reservoir physical properties, while the bound-fluid-pore fractal dimension demonstrates a negative correlation with the total porosity. The findings suggest that the NMR fractal dimension can serve as a valuable indicator for evaluating the physical characteristics of reservoirs. The present study successfully examined the pore structure of continental shale through the utilization of nuclear magnetic resonance technology. This innovative technique provides a novel avenue for the assessment of continental shale reservoirs and the investigation of pore heterogeneity on a global scale.

Evolution of organic pores in Permian low maturity shales from the Dalong Formation in the Sichuan Basin: Insights from a thermal simulation experiment

Shale oil and gas exploration is greatly impacted by the development and evolution of organic pore structures. In order to study the evolution of shale pore structures over maturities, we conducted thermal simulation experiments on low-mature organic-rich shale (Ro = 0.73%, TOC = 9.57%) obtained from the Dalong Formation. Various maturity stages were covered in these experiments, from low to over-maturity. By analyzing mineral composition, organic geochemistry, and characteristics of pore structures at various temperatures used for thermal simulation, we examined how organic matter pores generate and evolve during the formation of shale hydrocarbons. As a result, an integrated model of the evolution of pore structures in organic-rich shale was developed. Our study revealed the following insights: With increasing thermal simulation temperature, shale pore development exhibited three distinct stages: initial development, rapid development, and slow development. These stages correspond respectively to the three stages of organic matter thermal evolution. The distribution of pores in the shale transitioned from a unimodal structure dominated by larger pores to a bimodal structure with both micropores and macropores. Decomposition of organic matter and pressure compaction play a controlling role on organic porosity. Pore structure parameters and fractal dimensions of the pores were primarily influenced by organic matter decomposition, residual liquid hydrocarbons, and diagenetic processes. Additionally, kerogen type, morphology of organic matter debris, symbiosis of minerals-organic matter also impacted pore development.

Natural bentonite as an internal curing agent in the production of eco-friendly ultra-high performance concrete with low autogenous shrinkage

This study investigated the use of natural bentonite as a green internal curing agent to prepare eco-friendly ultra-high performance concrete (UHPC) with low autogenous shrinkage and excellent heavy metal ions solidification properties. A method based on the pore fractal dimension analysis was used for assessing the performance of UHPC. Results showed the use of bentonite as a replacement of cement could effectively reduce the autogenous shrinkage through its internal curing effect without compromising the compressive strength and workability of UHPC. The UHPC containing 4% bentonite showed the best volume stability and durability, with a 26.9% reduction in the autogenous shrinking compared to the control UHPC. The addition of bentonite further improved ion penetration resistance and solidification of heavy metal ion owing to its ion exchange capacity. However, the enhancement effect decreased when the bentonite content was too high due to the volume change of bentonite. Two kinds of pore classification dimensions, Dmin and Dmax, were obtained from NMR results to build good correlations with the autogenous shrinkage and durability, respectively. Finally, the ecological evaluation demonstrated that the designed UHPC with bentonite had relatively low environmental impact compared to other internal curing material, which was promising to generate a cleaner product in the near future.

Theoretical analysis of shape factor of gas hydrate sediments under stress dependence

The Kozeny-Carman (KC) equation is used extensively to characterize the effective permeability of gas hydrate sediments. However, most existing modeling approaches ignore the changes in the effective stress, hydrate saturation, and pore structures of porous media, which significantly affect the extraction and exploration of gas hydrates. In addition, theoretical models that can accurately describe shape factors during the imbibition process and predict the effective permeability of gas hydrate sediments are rarely reported. This paper proposes a theoretical stress-dependent shape factor model to study the physical relations between the shape factor and relevant parameters (e.g., effective stress, hydrate saturation, effective porosity, and pore fractal dimension). Then, the derived model is extended to study the shape factor during the imbibition process. The two main novel features of the proposed model are: (1) it takes the effective stress, hydrate saturation, and pore structures into account; and (2) it can be used to study the evolution of shape factors during the imbibition process in gas hydrate sediments. The predictions from the developed model provide a good agreement with experimental results, which validates the model. In addition, based on the derived model, the effects of relevant parameters on shape factors are studied theoretically. From a practical standpoint, the model can not only estimate the effective permeability of gas hydrate sediments under stress dependence but also provide insight into the evolution of shape factor, pore structures (e.g., capillary total number, pore fractal dimension, tortuosity fractal dimension, and effective porosity) and hydrate pore habits during the extraction of hydrates.

Nano-scale pore distribution characterisation of coal using small angle X-ray scattering

In the process of coal seam fracturing with liquid nitrogen (LN2), the change of coal pore structure has an important influence on the efficiency of coalbed methane (CBM) extraction. The nano-scale pore size distribution (PSD) in coal particles before and after freezing with LN2 are experimentally studied in this work. Coal samples are collected from four coal mines, where coal and gas outburst accidents have occurred. Small angle X-ray scattering technology (SAXS) and scanning electron microscopy (SEM) are used to study the pore structure changes of coal samples quantitatively and qualitatively. It is found that the scattering intensity of coal samples increases after freezing. The PSD of all samples significantly changes in the range of 0.8–7 nm, showing new pore spaces in 0.8–4 nm and fewer pores in the 4–7 nm range. Both the pore fractal dimension and the radius of gyration of coal samples increase after freezing and are mainly affected by the changes in pores and the anisotropy of the coal matrix. Crack expansion and pore connections are observed in the surface structure of the coal sample using SEM. This study provides a better understanding of the nano-scale mechanism of coal seam fracturing with LN2 for the prevention of coal and gas outbursts.

Fractal study on permeability characteristics in rough and dense porous media

The research in this paper explores the roughness of pores in rough and dense porous media using the model of rough capillary bundles. By taking into account the influence of boundary layer effects and microscale phenomena on fluid flow, a fractal model is derived to determine the efficient permeability of fluid flow in rough dense porous media. The connection between effective permeability and relative roughness and pore microstructure structure is discussed. It is revealed that the effective permeability exhibits an inverse proportionality to the relative roughness and viscosity, while concurrently displaying a direct proportionality to the pore fractal dimension. Furthermore, through the validation of experimental data and a comparative analysis with existing research models, it is evident that the model studied in this paper aligns more closely with real-world conditions.

Investigating effects of pore-scale variables and pore geometries on the thermal behaviors of porous concretes

Thermal behaviors play significant roles in the design of porous concretes. However, the effects of pore geometries on microscopic thermal behaviors are not still well understood. This work aims to propose a microscopic analysis framework to construct different microstructure models and to study the effects of pore geometries on the thermal behaviors of porous concretes. The microstructures with pore and cement phases are generated using the random generation algorithm (RGA) and compared with realistic microstructures. Digital numerous simulations are conducted to investigate the temperate distribution and heat transfer properties in the pixelated microstructures. Pore-scale variables, such as pore fractal dimension, pore size and porosity, are defined to understand their effects on the thermal behaviors of concretes. Results show that the transient temperature variation behaviors occur in the microstructures, which may be caused by the non-equilibrium heat transfer in the transient time scale. The effective thermal conductivity (ETC) decreases with increasing the pore radius, circularity, porosity and pore number, and it increases as pore fractal dimension increases. The microstructures with square pores have the largest ETC than those microstructures with pentagon, hexagon, and circle pore geometries. Totally, the numerical ETC agrees well with the analytical ETC, showing the accuracy of the proposed microscopic analysis framework. The proposed microscopic concrete analysis framework can provide effective tools to the fire resistance design of concrete constructions used for the green buildings and deep projects such as the deep bury of nuclear wastes.

(Invited) Using Molecular Dynamics Simulations to Relate Morphology to Water and Ion Dynamics in Hydrated Ion-Conducting Polymers

Hydrated ion-containing polymer membranes are used as electrolytes in a variety of applications, including in fuel cells and in alkaline batteries. Achieving high conductivity in hydrated, ion-conducting polymers typically requires the hydrophobic backbone of the polymers to be nano-phase separated from the hydrophilic domains so that the ions (protons or hydroxide ions) have well-defined water domains for efficient transport. The ion transport thus depends strongly on the hydration level and on the detailed morphology of the hydrophilic domains. It is often difficult to determine the morphology of these domains experimentally. I will present results from atomistic molecular dynamics (MD) simulations that reveal the domain morphology in various ionic polymers. Increasing water content generally leads to an increase in the characteristic spacing between hydrophilic domains. However, this swelling can be obscured in X-ray scattering due to a loss of scattering contrast between the hydrophobic and hydrophilic domains. The MD simulations reveal that the systems are nano-phase separated, even when X-ray scattering appears to indicate otherwise. Calculated and measured scattering profiles are in good qualitative agreement. I will discuss several methods to characterize the water domain morphology in more detail, including various measures of pore size distributions, surface areas, and fractal dimension. Water and ion diffusivities calculated from the MD simulations follow the experimentally-measured trends in conductivity and are consistent with changes in the nanoscale morphology with changing water content. I will discuss the implications of the results for the future design of ion-conducting polymers for use as membranes in electrochemical devices.This work was performed, in part, at the Center for Integrated Nanotechnologies, an Office of Science User Facility operated for the U.S. Department of Energy (DOE) Office of Science. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International, Inc., for the U.S. DOE’s National Nuclear Security Administration under contract DE-NA-0003525. Figure 1

Investigation of the relationship between gel strength and microstructure of surimi gel induced by dense phase carbon dioxide based on quantitative analysis

The microstructure of a surimi product determines its quality. Dense phase carbon dioxide (DPCD) can induce surimi gel formation, and the gel strength of the product are significantly better than that of heat-induced gels. The study analysed the changes of the surimi from golden pompano gel strength during the process of DPCD-induced gelation, and the changes of microstructure based on quantitative analysis of scanning electron microscope (SEM) image using ImageJ 1.42 software. The correlations between gel strength and microstructure was investigated. The results showed that the DPCD treatment significantly increased the cross-linking degree (CLD) and gel strength of surimi, compared with the raw surimi. The CLD and gel strength of surimi increased with the increase of DPCD treatment pressure, temperature and time. Quantitative microscopic analysis revealed that the number of pores (n) in the surimi gels increased and then decreased. The apparent porosity (ƞa), average pore area (Aa), average pore perimeter (Pa), fractal dimension (Df) and pore equivalent diameter (d) increased with the increase of DPCD treatment pressure, temperature and time. Correlation analysis showed that the CLD, ƞa, Aa, Pa, Df, d and median pore perimeter (Pc-50) were strongly positively correlated with the gel strength. In contrast, lacunarity (L) is strongly negatively correlated with the gel strength. The linear correlation coefficients between the CLD, ƞa and Df and the gel strength are 0.97, 0.95 and 0.96, respectively. These results provide a technical basis for DPCD to process high-quality surimi products. These findings also offer a novel approach for the testing and evaluating of the quality of surimi products.

Study on the Characteristics of Composite Recycled Aggregate Concrete Based on Box–Behnken Design Response Surface Model

This study investigates the influence of recycled fine aggregates (RFA) and waste concrete powder (WCP) on the compressive strength of concrete. The response surface methodology is employed, considering three factors: the content of WCP, the water–cement ratio, and the replacement ratio of recycled fine aggregates. Compressive tests are conducted at different ages (3 days, 28 days, and 90 days). A statistical approach is used to establish a response surface model for compressive strength and to verify its fitting with experimental results. By combining qualitative and quantitative analyses, including morphological analysis of SEM images, stratified binarization statistics, and fractal dimension calculations, the mechanisms of the effects of singly and doubly mixed RFA and WCP on the compressive strength of concrete are analyzed. The results show that an increase in the content of WCP from 5% to 15% gradually improves the compressive strength of the concrete. The water–cement ratio significantly affects the compressive strength, with an optimal ratio of 0.43. Replacement with less than 33% fine aggregates does not significantly reduce the compressive strength of the concrete. The concrete specimens with singly mixed fine aggregates exhibit the largest pore area after stratified grayscale binarization, while those with doubly mixed aggregates have the largest area of hydrated calcium silicate. Fractal analysis of the binarized images confirms a positive correlation between the fractal dimension of hydrated calcium silicate and compressive strength and a negative correlation between the fractal dimension of pores and compressive strength.

Effect of clinoptilolite on properties and fractal characteristic of pore structure of polypropylene fiber-reinforced cement-based composite

To further analyze the effect mechanism of clinoptilolite on the macro-mechanics and microstructure of polypropylene fiber-reinforced cement-based composite, the samples with 0, 5%, 10%, 15%, 20% and 25% clinoptilolite contents were investigated by compression test, flexural test, X-ray diffraction (XRD), scanning electron microscope (SEM) and mercury intrusion porosimetry (MIP), and the pore structure characteristics were quantitatively analyzed by fractal theory. Results showed that: With the increase of clinoptilolite content, the compressive strength, flexural strength and porosity of samples first increased and then decreased. The addition of clinoptilolite reduced the 7-day strength but increased the 28-day compressive strength, 60-day compressive strength, 28-day flexural strength and 60-day flexural strength of the samples by about 6%, 14.3%, 13.9% and 19.1%. It was recommended that the clinoptilolite content should not exceed 15%. Due to the filling effect and pozzolanic effect of clinoptilolite, adding clinoptilolite into the matrix could promote a hydration reaction to produce more C-S-H gels and reduce the proportion of more harmful pores and harmful pores, effectively improving the internal pore structure of the matrix. Meantime, it was found that the evolution law of pore structure based on fractal dimension calculated by the thermodynamic fractal model was consistent with the variation law of the pore size distribution curves and pore volume measured by MIP. Furthermore, a polynomial relationship model between clinoptilolite content, the quantitative fractal characteristic of pore structure and the macroscopic mechanical behaviors was established, which indicated that the pore fractal dimension could quantitatively describe the effect of clinoptilolite content on the pore microstructure.

Estimating Permeability of Porous Media from 2D Digital Images

Digital rock physics (DRP) has been widely used as an effective approach for estimating the permeability of porous media. However, conventional implementation of DRP requires the reconstruction of three-dimensional (3D) pore networks, which suffer from intensive memory and underlying uncertainties. Therefore, it is highly significant to develop an approach only based on two-dimensional (2D) cross-sections of parent samples without 3D reconstruction. In this study, we present a novel approach that combines the Kozeny–Carman equation with fractal theory to derive a bridge function that links 2D cross-sectional images and 3D pore structures of parent samples in flow equivalence. Using this bridge function, we predicted the physical properties of the parent samples, including the permeability, bulk porosity, tortuosity, and pore fractal dimension. To validate our model, we performed Lattice Boltzmann (LB) simulations on nine carbonate samples and compared the LB simulation results with our model’s predictions. We also compared our predicted results with available data on various porous materials, such as sandstone, glass beads, and carbonate, in the literature. Our findings demonstrate that without reconstructing 3D pore networks, our method provides a reliable estimation of sample permeability using 2D cross-sectional images. This approach not only simplifies the determination of sample permeability in heterogeneous porous media but also sheds new light on the inherent correlations between 2D cross-sectional information and 3D pore structures of parent samples. Moreover, the derived model may be conducible to a better understanding of flow in reservoirs during the extraction of unconventional onshore and offshore oil/gas.

Response and Mechanism of Coal Fine Production to Differential Fluid Action in the Baode Block, Ordos Basin

The Baode Block in the Ordos Basin is currently one of the most successfully developed and largest gas field of low–medium rank coal in China. However, the production of coal fine has affected the continuous and stable drainage and efficient development of this area. The special response and mechanism of differential fluid action during the drainage process is one of the scientific issues that must be faced to solve this production problem. In view of this, the evolution laws of a reservoir’s macro–micro physical characteristics under different fluid conditions (fluid pressure, salinity) have been revealed, and the response mechanism of coal fine migration-induced reservoir damage has been elucidated through a nuclear magnetic resonance online displacement system. The results indicated that pores at different scales exhibited varying patterns with increasing displacement pressure. The proportion of the mesopore and transition pore is not affected by salinity and is positively correlated with displacement pressure. When the salinity is between 3000 mg/L and 8000 mg/L, the proportion of macropore and micropore showed parabolic changes with increasing displacement pressure, and there was a lowest point. The evolution law of pore fractal dimension and permeability change rate under the action of different fluids jointly showed that there was an optimal salinity for the strongest reservoir sensitivity enhancement effect. The mechanical and chemical effects of fluid together determined the damage degree of coal reservoir induced by coal fine migration.

Study on the Response Law of Coal Pore Structure and Permeability Affected by Acidification Time.

In order to study the pore alteration and permeability of coal affected by acid liquor, samples were collected from the Yuwu coal mine in the Qinshui basin, Shanxi Province, and taken as the study object. Hydrochloric acid (HCl) with a 10% volume concentration was used to treat these coal samples. The pore structure characteristics and gas permeability of this coal with different treatment times were measured by laboratory experiments. The fractal theory was introduced to analyze the complexity of the sample pore and the changing rules of coal permeability. The research results show that acid liquor has a significant influence on the pore structure of YW coal. Under the effect of acid treatment, the micropore volume of the coal sample is reduced, but both the mesopore and macropore volume are increased. The fractal dimension of acidulated coal samples changes in the range of 2.57-2.81, and it is exponentially decreased with the increase of the treatment time. This indicates that the acid treatment can make the YW coal surface become smooth, and the pore structure tends to be smooth. The acidification method is able to effectively enhance the coal permeability with a maximum increment of about 9.43 times. After 30 h of acid treatment, the total pore volume, fractal dimension, and gas permeability of this coal tend to be stable. The acid treatment time should be controlled at around 30 h.

Pore structure and fractal dimension analysis of ancient city wall bricks in China

Comprehensive quantitative characterization of the pore structures of ancient city wall bricks is important for predicting the durability of historical masonry buildings. However, in most previous studies, only one or two methods were used to analyse the pore structures of fired clay bricks. In this study, mercury intrusion porosimetry (MIP), low-temperature nitrogen adsorption (LTNA), and low-field nuclear magnetic resonance (LF-NMR) were used to characterize the pore structure and fractal dimension of nine different ancient city wall bricks. The results show that the surface relaxivity of ancient bricks measured via the Hahn spin echo (HSE) in LF-NMR ranged from 1.55 to 1.75 μm/s. Furthermore, the porosity of the blue bricks measured via LF-NMR were much lower than that obtained via the gravimetric method owing to a higher number of paramagnetic iron mineral phases. LTNA was not suitable for describing pore size distribution of ancient bricks as the pore diameters were mainly concentrated in the range of 100–1000 nm. The pore structures of ancient bricks in dried and water-saturated states were different, the pore size of the white bricks obtained via LF-NMR was smaller than the MIP-derived pore-throat size by a factor of approximately 2.

Study of the Macro and Micro Characteristics of and Their Relationships in Cemented Backfill Based on SEM

Nuclear magnetic resonance can only quantitatively obtain porosity and pore size distribution, but as a conventional microstructure observation technology, scanning electron microscope (SEM) can select different magnifications to observe the microstructure of backfill materials. However, the processing of SEM images is not deep enough. In this paper, Image-Pro Plus 6.0 software was used to extract the data from SEM images, and the parameters of the area, and the perimeter, aspect ratio and roundness of the pores in the SEM images were obtained. The fractal characteristics of the pores in the SEM image were obtained by using the slit island method fractal theory. The concretization and quantification analysis of the pores’ complexity were achieved. A functional relationship model for the strength and pore parameters was constructed; thus, the influence law of pore characteristics on strength was quantitatively analyzed. The conclusions included: (1) Pore parameters indicate that most pores in backfill are irregular, and only a few pores are regular—however, the whole structure has good fractal characteristics (R2 > 0.96). (2) The fractal dimension of pores is directly proportional to the roundness, the aspect ratio, and the pore content of pores—which indicates that the complexity of pores is related to both pore shape and pore content. (3) The strength had a linear inverse relationship with the roundness, aspect ratio, pore content, and fractal dimension—which indicates that all characteristics of pores have a certain influence on the strength.

New insights into pore fractal dimension from mercury injection capillary pressure in tight sandstone

Mercury injection capillary pressure (MICP) has been widely used for pore fractal dimension determination and thus leads to a variety of calculation models with different results. Here, taking the tight sandstone gas reservoir of Shaximiao Formation in Jinhua-Zhongtaishan area, central Sichuan Basin as the object, the theory, method and application of pore fractal dimension determination from MICP are explored. Based on Yu-Xia model and Washburn equation, rigorous analytical expressions on fractal dimension, capillary pressure and mercury saturation are deduced. After pre-processing including validation, consistency correction and shape-preserving interpolation, the fractal turning point is located with the local maximum of the front-back moving variance ratio of mercury saturation, and then the global, macropore and micropore fractal dimensions are determined respectively by nonlinear fitting. As suggested by the data processing results of the 39 MICP samples, there is no significant direct correlation between pore fractal dimensions and petrophysical properties represented by permeability. However, the combination of fractal model related parameters, especially global fractal dimension and entry pressure, can identify effectively reservoir quality ranks. Meanwhile, for gas layers with relatively high permeability, larger global fractal dimensions may imply roughly more favorable pore structure and better reservoir quality, while the total quality of the relatively low-permeability gas layers is poor and nearly independent of the fractal dimensions. The representative MICP-based pore fractal models, He-Hua and Shen-Li, are critically reviewed. The theoretical simplification and calculative approximate of these two models lead to some degree of error in pore fractal dimension determination, despite their slight correlation in the fitting results with those of the present model. This study may improve the understanding of the pore fractal dimension determined from MICP and provide reference for pore structure evaluation, reservoir quality classification and capillary pressure modeling.