Heterogeneous Pore Research Articles

The Control of Isolated Kerogen on Pore Structure and Heterogeneity in Marine-Continental Transitional Shale: A Case Study on the Taiyuan Formation, Northern Ordos Basin

Accurately determining the pore structure and heterogeneity characteristics of marine-continental transitional shale in the Taiyuan Formation is crucial for evaluating the shale gas resources in the northern Ordos Basin. However, the studies on pore characteristics and heterogeneity of marine-continental transitional shales and isolated kerogen are limited. This study collected Taiyuan Formation shale in the northern Ordos Basin, and corresponding kerogen isolated from shale and used N2 and CO2 adsorption experiment and Frenkel–Halsey–Hill and Volume-Specific Surface Area model to investigate the pore structure and heterogeneity of both. The results show that the isolated kerogen is dominated by micropores, and the micropore’s specific surface area and volume are 4.7 and 3.5 times the corresponding shale, respectively. In addition, the microporous heterogeneity of the isolated kerogen is stronger than that of shale, while the mesoporous heterogeneity is exactly the opposite. Meanwhile, the micropores fractal dimension Dm is positively correlated with organic matter (OM) content, while mesopores fractal dimension D1 and D2 are negatively linearly correlated with TOC content and have no significant relationship with clay mineral and quartz content (but show a significant positive correlation with illite and illite/smectite mixed layer). Isolated kerogen plays an important role in the pore (especially micropores) heterogeneity of shale, while other minerals (such as clay minerals) have a controlling effect on the mesopores heterogeneity of shale. Compared with marine shale, the marine-continental transitional shale of the Taiyuan Formation has a lower fractal dimension and better connectivity, which is conducive to shale gas seepage and migration. The final result can provide a significant basis for the reserve evaluation and the optimization of desert areas in the marine-continental transitional shale gas in the northern Ordos Basin.

Mesoscale simulation of granular materials under weak shock compaction–pore size distribution effects

This research established a systematic method to generate various pore-size distributions (PSDs) and studied the effect of PSDs on the shock compaction response of granular materials using two-dimensional mesoscale simulations under identical porosity. Simulations utilized various PSDs for three particle shapes (circle, ellipse, and square). Contacting particle configurations using three PSDs, characterized by spatially uniform distributed pores to heterogeneous distributed pores, and non-contacting particle configurations under a single case of PSD were tested. The PSD of generated particle sets was characterized using coordination number, mean diameter, and bimodality coefficient as statistical metrics. Mesoscale simulations showed that regardless of the conditions of pore distributions, shock compaction of granular materials consistently demonstrates a precursor, shock compaction front, and end. However, the shock compaction velocity of contacting particles was dependent on the PSDs despite the constant initial porosity. The compaction velocity was faster in particle configurations with relatively uniform pore distributions than in heterogeneous pore distributions, which our study demonstrated can be attributed to particle rearrangement during compaction. Circular-shaped particles had high sensitivity in shock compaction response to the various PSDs. Furthermore, a contacting particle configuration tended to propagate the shock compaction wave relatively faster than particles that were in a non-contact configuration. This study established the relative importance of considering PSD as a metric over the coordination number in studies of the shock compaction response of granular materials. Further, insights are provided on the evolving shock substructure to characterize the shock compaction response of granular materials.

The impact of pore heterogeneity on pore connectivity and the controlling factors utilizing spontaneous imbibition combined with multifractal dimensions: Insight from the Longmaxi Formation in Northern Guizhou

The heterogeneity of shale pores, a crucial factor in the occurrence and migration of shale gas, exerts a significant impact on the pore connectivity. Pores exhibiting a range of structural attributes to the complexity of pore connectivity. A comprehensive study into the impact of pore heterogeneity on pore connectivity in shale is lacking. This study aims to explore the impact of pore heterogeneity on pore connectivity in shale and the primary controlling factors of pore connectivity. Shale pore connectivity, pore structures, mineral composition, and geochemical parameters were assessed using various tests, including spontaneous imbibition, adsorption, mercury intrusion capillary pressure (MICP), focus ion beam-scanning electron microscopy (FIB-SEM), sulfur and carbon analysis, vitrinite reflectivity, and X-ray diffraction (XRD). Pore heterogeneity was quantitatively analyzed using the multifractal dimensions method. Results show that the increased heterogeneity of pore structure and surface roughness facilitating the potential for increased connectivity. The presence of well-developed micro-mesopores within the organic matter, alongside numerous disconnected and independent pores, contributes to an increase in pore heterogeneity. Micro-mesopore structures have a more pronounced impact on pore heterogeneity than macropores. The heterogeneity of the pores is predominantly influenced by variations in the PV and SSA of micro-mesopores. Furthermore, the heightened heterogeneity of pore structure (D1) and surface roughness (D2) leads to a more complex pore structure with increased roughness, promoting the potential for enhanced connectivity through additional throats and facilitating the formation of secondary microfractures. Shale cores characterized by high total organic carbon (TOC) content, porosity, and clay mineral content are conducive to improved pore connectivity. Conversely, the increase of thermal evolution maturity of shale in the over-mature stage is not conducive to the increase of pore connectivity. Thermal evolution maturity, TOC content, and clay mineral are key factors that control pore heterogeneity, further affecting the connectivity of shale pores. High pore connectivity is conducive to spontaneous imbibition capacity and the formation of hydraulic microfractures, promoting the migration of shale gas.

Matrix Compression and Pore Heterogeneity in the Coal-Measure Shale Reservoirs of the Qinshui Basin: A Multifractal Analysis

The application of high-pressure fluid induces the closure of isolated pores inside the matrix and promotes the generation of new fractures, resulting in a compressive effect on the matrix. To examine the compressibility of coal-measure shale samples, the compression of the coal–shale matrix in the high-pressure stage was analyzed by a low-pressure nitrogen gas adsorption and mercury intrusion porosimetry experiment. The quantitative parameters describing the heterogeneity of the pore-size distribution of coal-measure shale are obtained using multifractal theory. The results indicate that the samples exhibit compressibility values ranging from 0.154 × 10−5 MPa−1 to 4.74 × 10−5 MPa−1 across a pressure range of 12–413 MPa. The presence of pliable clay minerals enhances the matrix compressibility, whereas inflexible brittle minerals exhibit resistance to matrix compression. There is a reduction in local fluctuations of pore volume across different pore sizes, an improvement in the autocorrelation of PSD, and a mitigation of nonuniformity after correction. Singular and dimension spectra have advantages in multifractal characterization. The left and right spectral width parameters of the singular spectrum emphasize the local differences between the high- and low-value pore volume areas, respectively, whereas the dimensional spectrum width is more suitable for reflecting the overall heterogeneity of the PSD.

Factors Controlling Differences in Morphology and Fractal Characteristics of Organic Pores of Longmaxi Shale in Southern Sichuan Basin, China

Shale gas is a prospective cleaner energy resource and the exploration and development of shale gas has made breakthroughs in many countries. Structure deformation is one of the main controlling factors of shale gas accumulation and enrichment in complex tectonic areas in southern China. In order to estimate the shale gas capacity of structurally deformed shale reservoirs, it is necessary to understand the systematic evolution of organic pores in the process of structural deformation. In particular, as the main storage space of high-over-mature marine shale reservoirs, the organic matter pore system directly affects the occurrence and migration of shale gas; however, there is a lack of systematic research on the fractal characteristics and deformation mechanism of organic pores under the background of different tectonic stresses. Therefore, to clarify the above issues, modular automated processing system (MAPS) scanning, low-pressure gas adsorption, quantitative evaluation of minerals by scanning (QEMSCAN), and focused ion beam scanning electron microscopy (FIB-SEM) were performed and interpreted with fractal and morphology analyses to investigate the deformation mechanisms and structure of organic pores from different tectonic units in Silurian Longmaxi shale. Results showed that in stress concentration areas such as around veins or high-angle fractures, the organic pore length-width ratio and the fractal dimension are higher, indicating that the pore is more obviously modified by stress. Under different tectonic backgrounds, the shale reservoir in Weiyuan suffered severe denudation and stronger tectonic compression during burial, which means that the organic pores are dominated by long strip pores and slit-shaped pores with high fractal dimension, while the pressure coefficient in Luzhou is high and the structural compression is weak, resulting in suborbicular pores and ink bottle pores with low fractal dimension. The porosity and permeability of different forms of organic pores are also obviously different; the connectivity of honeycomb pores with the smallest fractal dimension is the worst, that of suborbicular organic pores is medium, and that of long strip organic pores with the highest fractal dimension is the best. This study provides more mechanism discussion and case analysis for the microscopic heterogeneity of organic pores in shale reservoirs and also provides a new analysis perspective for the mechanism of shale gas productivity differences in different stress–strain environments.

The effect of stress barriers on unconventional-singularity-driven frictional rupture

Whether or not energy dissipation is localized in the vicinity of the rupture tip, and whether any distal energy dissipation far from the crack tip has a significant influence on rupture dynamics are key questions in the description of frictional ruptures, in particular regarding the application of Linear Elastic Fracture Mechanics (LEFM) to earthquakes. These questions are investigated experimentally using a 40-cm-long experimental frictional interface. Three independent pistons apply a normal load with a fourth piston applying a shear load, enabling the application of a heterogeneous stress state and stress barriers. After loading the frictional interface to a near-critical state, subsequent unloading of one normal-load piston leads to dynamic ruptures which propagate into the heterogeneous stress fields. The ruptures in these experiments are found to be driven by unconventional singularities, characterized by an ever-increasing breakdown work with slip, and as a result do not conform to the assumptions of LEFM. As these experimental stress barriers inhibit slip, they therefore also reduce the breakdown work occurring outside of the cohesive zone. It is shown that this distal weakening, far from the crack tip, must be considered for the accurate prediction of rupture arrest length. These experiments are performed in the context of a proposed stimulation technique for Enhanced Geothermal Systems (EGSs). It has previously been suggested, through theoretical arguments, that stress barriers could be induced through the manipulation of pore pressure such that there is reduced seismic hazard during the shear stimulation of EGSs. This stimulation technique, known as preconditioning, is demonstrated here to reduce the mechanical energy flux to the crack tip, G, while also increasing the fracture energy, Gc. Preconditioning is shown to be capable of arresting seismic rupture and reducing co-seismic slip, slip velocity, and seismic moment at preconditioning stresses which are reasonably achievable in the field. Due to the fully-coupled nature of seismic rupture and fault slip, preconditioning also reduces distal weakening and its contribution to the propagation of induced seismic ruptures. In a similar vein, heterogeneous pore pressure fields associated with some seismic swarms can be used to explain changes in stress drop within the swarm without recourse to material or total-stress heterogeneity.

Effect of water occurrence in coal reservoirs on the production capacity of coalbed methane by using NMR simulation technology and production capacity simulation

The occurrence of gas and water is a critical factor affecting the production capacity of coalbed methane. Therefore, occurrence and dynamic interaction between gas and water in coal reservoirs need to be studied. T2 spectrum of all the samples were studied by NMR technique at 0, 5, 9, and 28 h of natural evaporation. Then, multifractal model was used to characterize water distribution heterogeneity, and a novel evaluation coefficient was proposed to characterize distribution heterogeneity of water content, the correlation among evaluation coefficient, water distribution heterogeneity and pore structure parameters was analyzed. The results are as follows. In the saturated state, the moisture distribution of three types is heterogeneous. Type A of adsorption pore-developed exhibits strong moisture variation heterogeneity of small pores, in contrast to the uniform moisture variation in large pores. Type B of fracture-developed has the highest coefficient of variation in moisture distribution. The coefficient of variation A1 for moisture content can determine the speed of moisture transport and evaporation in the pore structure. A lower A1 indicates a greater moisture transport volume and faster moisture transport rate over the same time. The coefficient of variation A2 for moisture distribution represents the heterogeneity of moisture content variation in the pore structure. That is, a smaller A2 indicates better heterogeneity in the distribution of moisture content in the pore structure. Numerical simulation indicates the average gas production and the peak gas production time increase and decrease with the initial moisture content (Sgrw) increases, respectively. These findings provide practical guidance for coalbed methane development, especially in optimizing coalbed methane production capacity prediction and improving recovery efficiency.

Fractal research on pores in oil and gas reservoirs - Inspirations from over 700 high pressure mercury injection experiments

Pore fractal has now become an important research method to study reservoir pore heterogeneity and complexity, and is widely used in unconventional reservoir research. However, its guiding significance for reservoir research and the relationship between fractal dimension and reservoir pore structure parameters are not yet clear. This undoubtedly hinders the further development of fractal in reservoir research. This time, comprehensive research, including pore fractals, was conducted on over 700 high-pressure mercury injection experiments, providing guidance for reservoir pore fractal research. The research results indicate that there are significant differences in the application of fractals in different oil fields. Generally, the curves of high-pressure mercury injection experiments present 1–4 segment fractals, among which the 2 and 3 segment fractals are the most common, and the 4 segment fractals are the least common. There is a correlation between the number of the fractal segments with permeability and pore throat sorting coefficient. The lower the permeability, the more obvious the multi-segment fractal features. The more fractal segments, the greater the fractal dimension corresponding to each segment. The number of fractal segments can characterize the distribution of reservoir pore size. The fractal dimension of large pore-throats is greater than that of small pore-throats. On the whole, there is a negative correlation between fractal dimension and permeability, porosity, and pore throat radius. But this correlation is unstable in different oilfields. And the average value of the overall correlation coefficient is only about 0.5. Different fractal segments in a multi-segment fractal represent different types of pores. The application of pore fractal dimension needs to be combined with pore types.

Heterogeneity properties and permeability of shale matrix at nano-scale and micron-scale

Heterogeneity of shale pores at nano-scale and micrometer-scale is of great significance to gas transport properties. In this study, the pore structure of shale samples from lower Silurian Longmaxi Formation in the Sichuan basin is investigated by field emission-scanning electron microscopy (FE-SEM) and x-ray micro-computed tomography (Xμ-CT) technology. Based on fractal theory, the lacunarity is introduced to describe the clustering degree of pores in shale matrix, which can compensate for the limitations of fractal dimension. Combining lacunarity with fractal dimension allows for quantification of subtle differences in pore spatial distribution. For FE-SEM images at nano-scales, the fractal dimension changes in a “U” shape, while lacunarity changes in a “∩” shape. For Xμ-CT images at micrometer-scale, both the fractal dimension and lacunarity change in a logarithmic function. Lacunarity at both nano-scale and micrometer-scale linearly decreases with the increase in fractal dimension. By three-dimensional (3D) pore network modeling analysis, the structure properties of the connected pores, such as the number of pores and throats, pore diameter, pore volume, pore surface, throat length, and coordination number, are quantitatively calculated, and these structure parameters show strong heterogeneity. The average coordination number of the connected pores ranges in 2.92–4.36. This indicates that these pores in shale matrix have poor connectivity. The permeability varies from 0.06 to 0.17 μm2 in two-dimensional (2D) Xμ-CT images but from 3.20 to 34.99 μm2 in a 3D structure. The permeability in the 3D structure is about two order higher in magnitude than that in the 2D Xμ-CT images.

Effect of nanopore network connectivity on the phase behavior of confined associating fluids

We investigate the phase behavior of associating fluids inside heterogeneous slit pores. Two distinct phase transitions are observed for connected pores of two slit widths for both hard and attractive walls. In the case of the hard wall, the wider pore undergoes the vapor-liquid transition earlier than the narrower pore due to its weaker confinement and increased fluid interactions. In the case of an attractive pore surface, the narrower pore undergoes the vapor-liquid transition earlier than the wider pore. This can be attributed to the enhanced surface interactions in the narrower pore, which promote the condensation of the fluid phase. The x-density profile of the systems reveals that the interfacial fluid molecules play an essential role in early/delayed phase transition in the respective pores of the heterogeneous systems.

Dynamic fractionation of methane carbon isotope during mass transport in coal with bidisperse pore structures: Experiments, numerical modeling, and applications

Gas-in-place (GIP) content and the in-situ free/adsorbed gas ratio are crucial factors for evaluating resource potential and optimizing production strategies of deep coalbed methane (CBM). While the prevailing notion that adsorbed gas predominates is widely accepted in shallow CBM, this idea has been contested in deep CBM. Various numerical models for calculating GIP content based on gas volume data from canister degassing experiments commonly suffer from low accuracy, strong multiplicity, and inability to evaluate critical parameters of free/adsorbed gas ratio. Isotope fractionation is an important tool for studying the occurrence state and transport mechanism of natural gas, and numerical modeling that considers both cumulative degassing content and carbon isotope data has proven effective in determining the GIP content and adsorbed gas ratio in shale. However, the applicability of the existing isotope fractionation models in deep CBM has yet to be demonstrated experimentally and theoretically. In this study, four coal samples from the Shanxi and Taiyuan formations in Ordos Basin were subjected to canister degassing, gas metering, and methane isotopic composition testing. The results revealed significant multi-stage carbon isotope fractionation characteristics throughout deep CBM degassing, reflecting the strong heterogeneous pore structure characteristics within the coal. Existing carbon isotope fractionation (CIF) models are unable to effectively characterize this complex phenomenon. Based on these findings, we innovatively developed a CIF model that considers bidisperse pore structures and multiple transport mechanisms. The model can better characterize the complex isotope fractionation behavior and reveal the mechanisms of carbon isotope transport in series structures of multi-scale pores. Using the model, we calculated the GIP content of four experimental samples from the Shanxi and Taiyuan formations on the southeastern edge of the Ordos Basin, ranging from 27.78 m3/t to 39.13 m3/t, with an average of 31.68 m3/t, and the in-suit free gas ratio ranges from 13.30 % to 32.89 %, with an average of 19.45 %. These research findings provided new insights for assessing the resource potential of deep CBM, screening sweet spots, and predicting gas well performance.

Image-based quantitative probing of 3D heterogeneous pore structure in CBM reservoir and permeability estimation with pore network modeling

Coalbed methane (CBM) recovery is attracting global attention due to its huge reserve and low carbon burning benefits for the environment. Fully understanding the complex structure of coal and its transport properties is crucial for CBM development. This study describes the implementation of mercury intrusion and μ-CT techniques for quantitative analysis of 3D pore structure in two anthracite coals. It shows that the porosity is 7.04%–8.47% and 10.88%–12.11%, and the pore connectivity is 0.5422–0.6852 and 0.7948–0.9186 for coal samples 1 and 2, respectively. The fractal dimension and pore geometric tortuosity were calculated based on the data obtained from 3D pore structure. The results show that the pore structure of sample 2 is more complex and developed, with lower tortuosity, indicating the higher fluid deliverability of pore system in sample 2. The tortuosity in three-direction is significantly different, indicating that the pore structure of the studied coals has significant anisotropy. The equivalent pore network model (PNM) was extracted, and the anisotropic permeability was estimated by PNM gas flow simulation. The results show that the anisotropy of permeability is consistent with the slice surface porosity distribution in 3D pore structure. The permeability in the horizontal direction is much greater than that in the vertical direction, indicating that the dominant transportation channel is along the horizontal direction of the studied coals. The research results achieve the visualization of the 3D complex structure of coal and fully capture and quantify pore size, connectivity, curvature, permeability, and its anisotropic characteristics at micron-scale resolution. This provides a prerequisite for the study of mass transfer behaviors and associated transport mechanisms in real pore structures.

Genesis and reservoir preservation mechanism of 10 000‐m ultradeep dolomite in Chinese craton basin

AbstractThe 10 000‐m ultradeep dolomite reservoir holds significant potential as a successor field for future oil and gas exploration in China's marine craton basin. However, major challenges such as the genesis of dolomite, the formation time of high‐quality reservoirs, and the preservation mechanism of reservoirs have always limited exploration decision‐making. This research systematically elaborates on the genesis and reservoir‐forming mechanisms of Sinian–Cambrian dolomite, discussing the ancient marine environment where microorganisms and dolomite develop, which controls the formation of large‐scale Precambrian–Cambrian dolomite. The periodic changes in Mg isotopes and sedimentary cycles show that the thick‐layered dolomite is the result of different dolomitization processes superimposed on a spatiotemporal scale. Lattice defects and dolomite embryos can promote dolomitization. By simulating the dissolution of typical calcite and dolomite crystal faces in different solution systems and calculating their molecular weights, the essence of heterogeneous dissolution and pore formation on typical calcite and dolomite crystal faces was revealed, and the mechanism of dolomitization was also demonstrated. The properties of calcite and dolomite (104)/(110) grain boundaries and their dissolution mechanism in carbonate solution were revealed, showing the limiting factors of the dolomitization process and the preservation mechanism of deep buried dolomite reservoirs. The in situ laser U‐Pb isotope dating technique has demonstrated the timing of dolomitization and pore formation in ancient carbonate rocks. This research also proposed that dolomitization occurred during the quasi‐contemporaneous or shallow‐burial periods within 50 Ma after deposition and pores formed during the quasi‐contemporaneous to the early diagenetic periods. And it was clear that the quasi‐contemporaneous dolomitization was the key period for reservoir formation. The systematic characterization of the spatial distribution of the deepest dolomite reservoirs in multiple sets of the Sinian and the Cambrian in the Chinese craton basins provides an important basis for the distribution prediction of large‐scale dolomite reservoirs. It clarifies the targets for oil and gas exploration at depths over 10 000 m. The research on dolomite in this study will greatly promote China's ultradeep oil and gas exploration and lead the Chinese petroleum industry into a new era of 10 000‐m deep oil exploration.

Experimental Study on CO2 Flooding Characteristic in Low-Permeability Sandstone Considering the Influence of In-Situ Stress

Summary The pore network controlled by in-situ stress significantly influences the CO2 flooding in low-permeability reservoirs. In this study, the CO2/oil distribution and response of pore structure were monitored online using low-field nuclear magnetic resonance (LF-NMR), and the in-situ stress dependence of oil recovery was analyzed. The results show that the pore structure consists of adsorption pore (AP < 1 millisecond), percolation pore (1 millisecond < PP < 10 milliseconds), and migration pore (10 milliseconds < MP). Oil recovery was primarily influenced by AP and MP at lower in-situ stress, while PP and MP are the main contributors at higher in-situ stress. The matrix experienced compression deformation, microfracture generation, and shrinkage of pore, combined with an increase and followed by a decrease in oil recovery, responding to the increase of in-situ stress from 5 MPa to 15 MPa and from 15 MPa to 20 MPa. The reduction in gas channels promotes a piston-like advancement of oil displacement, resulting in an initial increase in oil recovery, while subsequent decline is linked to heightened pore heterogeneity caused by high in-situ stress. Increased heterogeneity reduces gas displacement stability, hampers CO2 sweep efficiency, and results in a granular distribution of residual oil. The findings provide insight on CO2-enhanced oil recovery (EOR) in low-permeability reservoirs.

Development of Compaction Localization in Leitha Limestone: Finite Element Modeling Based on Synchrotron X‐Ray Imaging

AbstractThe mechanical behavior and failure mode of porous rocks vary with their microstructures. The formation of compaction bands (CBs) has been captured with high precision via in situ synchrotron CT and kinematic characteristics can be attained by image analysis. However, the stress characteristics cannot be directly evaluated from images, and how porosity heterogeneity triggers local instability and leads to the formation of CBs is not yet fully understood. To address this problem, we established a finite element (FE) model of the solid skeleton of a Leitha limestone sample based on X‐ray μCT data, considering the heterogeneity of pores and plastic hardening, and reproduced the evolution of strain localization and CBs. Our results revealed that the heterogeneity of porosity has a profound influence on the formation and propagation of CBs. Precursory stresses always appear very early around the pores where compaction bands develop, and the stress state of most points in CBs is quasi‐uniaxial compression, which has significantly high maximum principal stress σ1 in a direction subparallel to the sample axis, causing yield then compaction failure. Also, using a simplified FE mesh and ignoring the fracture of particles underestimate the extreme stress and porosity reduction—these can be improved by using fine mesh and involving grain‐scale fracture mechanics. Our study proves the feasibility and reliability of the CT‐FE simulation scheme, which can be extended to investigating the stress distribution and evolution of different rock types with a spectrum of failure modes if in situ CT data of rock deformation is available.

Effect of porosity and pore heterogeneity on heat transfer performance of polyimide aerogels

The effects of porosity and pore distribution on the heat transfer performance of polyimide (PI) aerogel under natural convection were investigated through a combination of experimental and numerical simulations. The governing equations of heat transfer were analyzed in detail. A novel heterogeneity factor (η) was introduced to quantify internal pore distribution. PI aerogels exhibiting a range of porosities and heterogeneity factors were synthesized and characterized. The natural convection heat transfer coefficient of PI aerogels was measured experimentally, providing empirical data. A porous model was developed by integrating Voronoi technique with a two-scale generation method, allowing for comprehensive numerical simulations of heat transfer. The numerical results demonstrated strong concordance with the experimental data, validating the model’s accuracy. The results revealed that the heat transfer performance of the aerogels diminished markedly with increasing porosity when heterogeneity was held constant. Conversely, with fixed porosity, the heat transfer performance improved significantly with greater heterogeneity. Numerical simulations further enabled the visualization of internal temperature and flow fields, elucidating that the effect of porosity and heterogeneity on natural convection heat transfer performance is predominantly driven by variations in internal permeability.

A heterogeneous pore design algorithm for material extrusion additive manufacturing

Material extrusion additive manufacturing offers great potential for customizing matters with complex external contours, and filament diameter-adjustable 3D (FDA-3D) printing strategy provides fresh impetus to create heterogeneous porous structures inside these complex matters. However, the absence of supporting algorithms to implement FDA-3D printing severely hinders its widespread use. In this paper, we develop a heterogeneous pore design (HPD) algorithm aimed at advancing the development of FDA-3D printing for producing heterogeneous porous matters. The HPD algorithm consists of three sub-algorithms: model design, collapse compensation, and fabrication file (G-codes) generation. As proofs of concept, we utilize this algorithm to 3D print radial gradient and letter-embedded gradient materials following specific steps: (1) designing the heterogeneous porous models with collapse compensation in Grasshopper® and displaying them in Rhinocores®; (2) customizing and writing the corresponding G-codes files by following the material extrusion 3D printer's control rules; (3) upgrading a commercial extrusion printer to FDA-3D print the design models via the customized G-codes. Micro-computed tomography-based 3D reconstruction and quantified pore size maps for the fabricated objects demonstrate the high capability of this HPD algorithm. Overall, the HPD algorithm holds the potential to revolutionize material extrusion 3D printers cost-effectively, creating new possibilities for material extrusion of heterogeneous materials.

Singular value decomposition for single-phase flow and cluster identification in heterogeneous pore networks

Pore networks play a key role in understanding and quantifying flow and transport processes in complex porous media. Realistic pore-spaces may be characterized by singular regions, that is, isolated subnetworks that do not connect inlet and outlet, resulting from unconnected porosity or multiphase configurations. The robust identification of these features is critical for the characterization of network topology and for the solution of the set of linear equations of flow and transport. We propose a robust method based on singular value decomposition to solve for network flow and locate isolated subnetworks simultaneously. The performance of the method is demonstrated for pore networks of different complexity.

Multifractal characteristics on pore structure of Longmaxi shale using nuclear magnetic resonance (NMR)

The efficient exploration and extraction of shale gas is essential for China's energy structure as a replacement for natural gas. In this research, shale samples from the Longmaxi Formation in Changning, Sichuan Province were investigated for their pore structure. To achieve this, X-ray diffraction (XRD) and nuclear magnetic resonance (NMR) experiments were performed on the samples. Fractal theory was employed to characterize the pore structure and fractal features of the shale reservoirs. The fractal characteristics of reservoir rocks were correlated with physical parameters and mineral components to identify the controlling factors for the multifractal dimension. The results indicate the following: ① Quartz predominates in the mineral composition of shale in the study area, while clay minerals are the least abundant. ② The primary pore types observed in the samples are bound fluid pores, primarily controlled by mesopores (2 nm ≤ r ≤ 50 nm). ③ The calculated multifractal parameters show that the heterogeneous pore structure exhibits multifractal characteristics. ④ The low probability multifractal parameters Dmin-D0 and αmax-α0 were found to be negatively correlated with reservoir porosity, permeability, and clay mineral content, while the high probability multifractal parameters D0-Dmax and α0-αmin were found to be positively correlated with them. The comprehensive fractal characterization of reservoir rocks demonstrates the applicability of multifractal dimensions in characterizing the heterogeneity of shale reservoir pore structures, which holds potential promise for coal methane exploration.

Study on full-scale pores characterization and heterogeneity of coal based on low-temperature nitrogen adsorption and low-field nuclear magnetic resonance experiments

The characteristics and heterogeneity of coal pores are crucial for understanding the production mechanism of coalbed methane (CBM). In this study, coal samples with varying degrees of metamorphism (0.58% ≤ RO, max ≤ 3.44%) were collected. The characteristics of pore development and the heterogeneous properties of pores were revealed through low-temperature nitrogen adsorption (LTNA) and low-field nuclear magnetic resonance (NMR) experiments. The results indicate that pores with varying diameters exhibit favorable development in low-rank coals, along with favorable pores connectivity. The micropores composition of middle-rank coals was found to be 73.56%, however, the connectivity among transitional, meso, and macropores was observed to be poor. In high-rank coals, the proportion of micropores was 92.74%, with numerous micropores being closed or semi-closed. This resulted in inferior connectivity between micropores and transitional pores. As coal metamorphism progressed, the DL1 (characterizing the roughness of adsorption pores (AP) surface, ranging from 2.13 to 2.45) and DL2 (characterizing the complexity of AP structure, ranging from 2.56 to 2.77) initially decreased and then increased, whereas the DN (characterizing the heterogeneity of seepage pores (SP), ranging from 2.92 to 2.95) consistently improved. Furthermore, the roughness of pore surface and the complexity of pore structure in AP increased as the specific surface area and volume of pores increased. On the contrary, as the SP content increased, the uniformity of the pore structure improved. When the volume of SP remained constant, the complexity of the pore structure decreased due to increased pore connectivity.