Multiscale Pore Research Articles

Multiscale Dynamic Diffusion Model for Ions in Micro- and Nano-Porous Structures of Fly Ash: Mineralization Experimental Research

The leaching concentration of alkaline ions plays a crucial role in the efficiency of the CO2 mineralization reaction in fly ash. The multi-scale structural characteristics of micro–nano pores in fly ash are the primary factors that control the leaching and diffusion rate of alkaline ions. However, the existing theoretical models do not account for the multi-scale pore structure, leading to challenges in accurately describing the ion diffusion in fly ash and predicting the reaction rate and efficiency of CO2 mineralization. To address this issue, a multi-scale dynamic diffusion model of ions was developed based on the micro–nano pore structure of fly ash. This model established the relationship between the ionic leaching rate and pore structure, as well as macroscopic changes over time, which were validated through experiments. Mineralization experiments with varying soaking times and uniaxial compression experiments on mineralized specimens were conducted to investigate the relationships among soaking time, ion leaching concentration, mineralization degree, and mechanical strength. The results elucidated the impact of alkaline ion concentration on the mineralization degree and mechanical strength of fly ash materials, offering theoretical insights to enhance mineralization and material properties.

A hybrid pore-network-continuum modeling framework for flow and transport in 3D digital images of porous media

Understanding flow and transport in multiscale porous media is challenging due to the presence of a wide range of pore sizes. Recent imaging advances offer high-resolution characterization of the multiscale pore structures. However, simulating flow and transport in 3D digital images requires models to represent both the resolved and sub-resolution pore structures. We develop a hybrid pore-network-continuum modeling framework. The hybrid framework treats the smaller pores below the image resolution as a continuum using the Darcy-scale formalism and explicitly represents the larger pores resolved in the images employing a pore network model. We validate the hybrid model against direct numerical simulations for single-phase flow and solute transport and further demonstrate its applicability for simulating two-component gas transport in a shale rock sample. The results indicate that the new hybrid model represents the flow and transport process in multiscale porous media while being much more computationally efficient than direct numerical simulation methods for the range of simulated conditions.

Multi-scale pore model construction and damage behavior analysis of SiCf/SiC composite tubes

SiCf/SiC composite materials are essential for spacecraft thermal protection, determining the safety of spacecraft. However, their complex structures and intricate fabrication processes have led to an unclear understanding of their failure mechanisms, limiting their application. In this study, circumferential compression experiments were conducted, and X-ray computed tomography (X-CT) was used to analyze the distribution characteristics of pore spaces. The experimental results indicate that damage manifests as secondary fracture phenomena based on temporal evolution characteristics. Specifically, after experiencing performance degradation of 24.73–60.96%, the material still maintained basic stability, exhibiting a performance recovery of 31.55–36.1% under the applied load until failure. To predict the dynamic damage behavior of materials at multiple scales, a multi-scale method combining statistical and microscopic approaches was proposed. A micro representative volume element (RVE) random fiber pore distribution model was established based on random processes and random medium theory. Finally, considering the CT data and the principle of minimum potential energy, a macroscopic finite element model of the micro-pores' structural characteristics in a three-dimensional wound tube was reconstructed. The results indicate that cracks initiate around pore defects and gradually propagate to form crack bands. The model closely matches the macroscopic damage and microscopic characteristics of the material. This work provides a new approach for the numerical simulation of pore defects in such materials.

Application and Research of Multi-Scale Dynamic Diffusion Permeability Model in Different Coal Ranks

The spatial scale of coal mining and rock layer control is distributed between 10-10 and 107, spanning 17 orders of magnitude. There are multi-scale pore cracks from millimeter to micro and nanometers in the coal, and the pore size can reach one million times, which makes the coal permeability also show a multi-scale characteristics of millions and time. For the permeability of the coal seam, it is necessary to test and analyze the distribution of micro and nano pores and cracks in the coal [1]. CBM mining is accompanied by the dynamic change of adsorption pressure in coal and the complex deformation of multi-scale heterogeneous structure of coal, and the multi-scale deformation feature of pore fissure structure plays an important role in the transport of methane [2]. However, existing studies focus on treating coal as a homogeneous isotropic medium, without considering the influence of coal multiscale pore structure on permeability. The variation of heterogeneous degree of coal structure with structural scale and its influence on dynamic diffusion and permeability are rarely reported. Li Zhiqiang et al. [3] conducted an experimental-model-mechanism study of CBM gas micro-nano series multi-scale dynamic diffusion permeability. On this basis, the dynamic diffusion and permeability of different coal scales.

Hydrogen Geostorage in Organic-Rich Shales: Critical Insights Into the Role of Cushion Gas in Hydrogen Accumulation within Organic Nanoporous Systems

Summary Depleted shale formations have the potential for hydrogen geostorage. The storage mechanisms, however, are complex and influenced by several factors including mineralogy, pore size distribution, residual hydrocarbons in place, and the choice of cushion gas. This study aims to investigate hydrogen distribution within this multiscale pore system, with a focus on understanding how hydrogen accumulates in the organic nanoporous network. Such insights are critical for the long-term storage and recovery assessments. Using molecular simulations, representative organic matter comprising nanoporous kerogen and nanopores of different sizes was constructed. Hydrogen intake of the organic system in the presence of residual amount of natural gas was quantified, considering multiple hydrogen injection scenarios. Despite stronger chemical affinity toward natural gas, hydrogen accumulated in all pore sizes, even the smallest, potentially beneficial for long-term storage but hindering rapid recovery. Moreover, the study was extended to investigate the role of cushion gas in the accumulation of hydrogen in organic structures. It was found that introducing cushion gases, such as methane and carbon dioxide, reduces hydrogen intake in the nanopores, with carbon dioxide being the most effective due to its stronger attraction to kerogen. Nitrogen, on the other hand, had relatively lower impact. The results were consistent with the observed trends in the analysis of the nonbonding energy of all systems. The results reported in this study provide critical insights into the factors influencing hydrogen accumulation in the organic constituents of shale formations for an optimized design of hydrogen geostorage in depleted shale gas reservoirs.

Homogenized color-gradient lattice Boltzmann model for immiscible two-phase flow in multiscale porous media

In this paper, a homogenized multiphase lattice Boltzmann (LB) model is established for parallelly simulating immiscible two-phase flow in both solid-free regions (pore scale) and porous areas (continuum scale). It combines the color-gradient multiphase model with the Darcy–Brinkman–Stokes method by adding a term that includes surface force and drag force of porous matrix to multiple-relaxation-time LB equation in moment space. Moreover, an improved algorithm is proposed to characterize and implement the apparent wettability in the locally homogenized porosity field. Validations and test cases are given to demonstrate the accuracy and robustness of this new model, as well as its applicability for trans-scale fluid simulation of transport and sorption behavior from porous (Darcy flow) area to free (Stokes flow) area. For practicality, the two-phase seepage flow in a composite rock structure with multiscale pores is simulated by this new model, and the effects of viscosity ratio and wettability on the displacement process are discussed.

Lightweight polyimide/silica aerogel composite foams and their derived carbon foams for excellent flame retardancy, thermal insulation and EMI shielding performance

Multifunctional porous materials demonstrate ubiquitous applications in the fields of flame retardancy, thermal insulation and electromagnetic interference (EMI) shielding. In this work, a series of lightweight polyimide/silica aerogel (PIF/SiA) foams with exceptional thermal stability, flame retardancy and thermal insulation performance were prepared by employing microwave-assisted foaming and thermal imidization treatment, using polyester ammonium salt/silica aerogel (PEAS/SiA) powders as the derivative precursors. The limiting oxygen index and fire growth rate reached as high as 58.2 % and as low as 0.1 kW/(m2·s) for PIF/SiA composite foams, respectively, which was a result of the formation of micro/nano multi-scale pore structure of PIF skeleton and the “pearl-necklace-like” skeletal network of nano SiA. In addition, the PIF/SiA composite foams exhibited excellent thermal insulation and infrared stealth performance, which demonstrate a potential for long service life in fire protection use. Furthermore, the carbonized PIF/SiA (i.e., PICF/SiA) foams possessed enhanced mechanical (improvement of 117.6 %) and EMI shielding performance (specific EMI shielding effectiveness: 8541.9 dB/(g/cm2)) when compared with the original PIF/SiA composite foams. To sum up, a facile method was proposed to fabricate multifunctional PIF-based composite foams and their derived carbon foams for flame retardancy, thermal insulation and EMI shielding applications in high-end engineering sectors.

Multi-scale pore structure characteristics of coal under alternating hydraulic intrusion pressure

Multi-scale pore structure characteristics of coal under alternating hydraulic intrusion pressure

Study on the evolution of solid–liquid–gas in multi-scale pore methane in tectonic coal

Study on the evolution of solid–liquid–gas in multi-scale pore methane in tectonic coal

Fabrication of magnesium-doped biphasic calcium phosphate granules with sea urchin spine-derived porous structure

In bone regeneration, synthetic materials are required to replace autogenous bone grafts. The shape, composition, surface, and porous structure of the material are key factors in bone formation and material resorption. In this study, we describe the fabrication of Mg-doped biphasic calcium phosphate (Mg-BCP) granules comprising hydroxyapatite (HAp) and beta-tricalcium phosphate (β-TCP) by exploiting the structural and chemical characteristics of sea urchin spines. The Mg-BCP granules were cylinders with a 1.2–1.8 mm diameter and height of 1.4–1.7 mm. The β-TCP/HAp ratio and Mg content in the Mg-BCP granules were controlled within the ranges of 0.36–0.45 and 2.40–6.21 mol%, respectively. Controlling the β-TCP/HAp ratio and Mg content may contribute to controlling the material resorption rate and promoting osteogenesis and angiogenesis. The Mg-BCP granules maintained the structural characteristics of the sea urchin spines. The granules comprised radial wedges termed septa, and a meshwork termed stereom. The interseptal gaps, or micropores, decreased from the granular exterior (24–29 μm) to the interior (14–28 μm). The septa in the outermost layer provide concavities on the sides of the cylindrical granules. The stereom meshworks in the core and outer layers involved micropores in the ranges of 3–15 and 3–10 μm, respectively. These multiscale pores and surface undulations may improve cell penetration and attachment, bodily fluid permeability, and protein adsorption. The compressive strengths of the Mg-BCP granules were in the range of 45.2–46.1 MPa, which are useful as bone grafts. Due to their rounded shapes, the Mg-BCP granules filled a mold more densely than the clinically used and irregularly shaped granules. These findings demonstrated that Mg-BCP granules are promising materials for bone regeneration.

Multiscale Pore Structure Evolution of Different Rank Coals Induced by Chelating Agent Intrusion

Summary China’s coalbed methane (CBM) reservoirs are characterized by low permeability (<1 md). Stimulation with conventional acids is facing the problems of secondary precipitation, high corrosion rates, and fines migration. Chelating agent intrusion was proposed as a promising alternative for conventional acids, while the pore structure evolution induced by it needs to be further clarified. In this study, coal samples with three different ranks were selected and treated with L-glutamic acid N, N-diacetic acid (GLDA). Low-temperature Ar and N2 adsorption tests, mercury intrusion porosimetry (MIP), and scanning electron microscope (SEM) analyses were applied to investigate nanoscale to macroscale pore structure changes. X-ray fluorescence (XRF) spectroscopy tests were conducted to determine the mineralogical change of coal. The results show that chelating agent intrusion can widen fracture width, connect micropores, and create void space in macropores by dissolving carbonate minerals, while the nanoscale pore volumes (PVs) showed a slight decrease due to clay minerals collapse. The fractal dimensions Dm calculated by the MIP results of lignite, bituminous coal, and anthracite coal decreased by 0.2735, 0.1734, and 0.1444, respectively. It is indicated that a pore structure with a diameter of >100 nm of the coal became more unified, which favors the seepage of gas/water. The chelating agent intrusion shows a significant effect on lignite, followed by bituminous and anthracite coal. However, the metal element reduction rate of anthracite coal presents the highest, followed by bituminous coal and lignite. There can be a risk that a long intrusion time would loosen the skeleton of lignite, leading to further reservoir damage. Therefore, bituminous and anthracite coal samples are preferred, as the skeletons of higher-rank coals are more compact. These research findings introduced a potential stimulation method for enhancing CBM recovery and provided references for field application.

Characterization and mechanism of multi-scale pore changes in scCO2-water injection into different porosity coal specimen

The process of supercritical CO2 (scCO2) injection into the coal body induces inhomogeneous changes in pore, which has a significant effect mechanical changes of the geological storage of CO2 coal seams. In this study, the effect of scCO2-water intrusion on coal samples with different porosity was investigated by NMR equipment and the change in the mechanical properties were tested by uniaxial compression and acoustic emission techniques after treatment. Results showed that during the treatment of scCO2-water, the pores of different scales showed an exponential change trend of y = a·xb, with the macropore of low-porosity coal samples continuously increasing and the macropore of high-porosity coal samples continuously decreasing. The pore changes after treatment mainly occurred in the micropore range, and the changes of low-porosity coal samples were more than 6%, while the changes of high-porosity coal samples were less than 2.3%. The changes in the fractal dimension of low-porosity coal samples exceeded those observed in high-porosity. The geochemical impact, effective stress of scCO2-water mixed fluid, and the adsorption and expansion mechanism of matrix macromolecules are influenced by varying porosity. This study helps to understand the internal multi-scale pore coupling mechanism and the effect on the coal mechanical properties after CO2 injection.

A computationally efficient modeling of flow in complex porous media by coupling multiscale digital rock physics and deep learning: Improving the tradeoff between resolution and field-of-view

Digital rock physics is at the forefront of characterizing porous media, leveraging advanced tomographic imaging and numerical simulations to extract key rock properties like permeability. However, fully capturing the heterogeneity of natural rocks necessitates imaging increasingly larger sample volumes, presenting a significant challenge. Direct numerical simulations at these scales become either prohibitively expensive or computationally unfeasible due to limitations in resolution and field of view (FOV). This issue is particularly pronounced in carbonate rocks, known for their complex, multiscale pore structures, which exacerbate the resolution-FOV tradeoff. To address this, we introduce a machine learning strategy that merges multiscale imaging data from various resolutions with a 3D convolutional neural network (CNN) model. This approach is innovative in its ability to identify cross-scale correlations, thereby enabling the estimation of transport properties in larger volumes—properties that are difficult to simulate directly—using trainable proxies. The integration of multiscale imaging with deep learning allows for accurate permeability predictions at scales beyond those feasible with traditional direct simulation methods. By employing transfer learning across different scales during the training phase, our multiscale machine learning model achieves robust performance, with an R² exceeding 0.96 when evaluated on diverse lower-resolution domains with larger FOVs. Notably, this method significantly enhances computational efficiency, reducing the computational time by orders of magnitude. Originally developed for the intricate pore structures of carbonate rocks, our approach shows promise for application to a wide range of multiscale porous media, offering a viable solution to the longstanding tradeoff between imaging resolution and FOV in digital rock physics.

Incorporation of Sub‐Resolution Porosity Into Two‐Phase Flow Models With a Multiscale Pore Network for Complex Microporous Rocks

AbstractPorous materials, such as carbonate rocks, frequently have pore sizes which span many orders of magnitude. This is a challenge for models that rely on an image of the pore space, since much of the pore space may be unresolved. In this work, sub‐resolution porosity in X‐ray images is characterized using differential imaging which quantifies the difference between a dry scan and 30 wt% potassium iodide brine saturated images. Once characterized, we develop a robust workflow to incorporate the sub‐resolution pore space into a network model using Darcy‐type elements called microlinks. Each grain voxel with sub‐resolution porosity is assigned to the two nearest resolved pores using an automatic dilation algorithm. By including these microlinks with empirical models in flow modeling, we simulate single‐phase and multiphase flow. By fine‐tuning the microlink empirical models, we match permeability, formation factor (the ratio of the resistivity of a rock filled with brine to the resistivity of that brine), and drainage capillary pressure to experimental results. We then show that our model can successfully predict steady‐state relative permeability measurements on a water‐wet Estaillades carbonate sample within the uncertainty of the experiments and modeling. Our approach of incorporating sub‐resolution porosity in two‐phase flow modeling using image‐based multiscale pore network techniques can capture complex pore structures and accurately predict flow behavior in porous materials with a wide range of pore size.

Multi-Scale Pore Structure Heterogeneity in Tuff Reservoirs Investigated with Multi-Experimental Method and Fractal Dimensions in Chang 7 Formation, Southern Ordos Basin

Multi-Scale Pore Structure Heterogeneity in Tuff Reservoirs Investigated with Multi-Experimental Method and Fractal Dimensions in Chang 7 Formation, Southern Ordos Basin

Modeling of multilayer water adsorption and condensation in slits of cement minerals by molecule simulation and adsorption isotherm

The interactions between water and multiscale pores affect significantly most of the physical and chemical properties of cementitious materials such as cement mortar, paste, and concrete. In this paper, molecular mechanism of multilayer water adsorption and condensation in micropores of typical cementitious minerals, the dicalcium silicate (C2S) and calcium silicate hydrate (C-S-H), were investigated by molecular simulations. Classical adsorption isotherm models were examined for their applicability to describe the adsorption law in molecular scales. Besides, the Kelvin equation was modified to satisfy the description of condensation at the microscale. Calculation results show that the most commonly used Brunauer-Emmett-Teller (BET) model can only describe the isotherms within a limited range of low water vapor pressures. In comparison, the modified Brunauer-Emmett-Teller-Pickett (BETP) model can describe the adsorption of water molecular on the surface of C2S and C-S-H more precisely, due to considering the adsorption layers as finite at saturation pressure and the reduced escape probability of the outermost layer of adsorbed water molecules. As for the condensation of water molecules in C2S and C-S-H slits, the traditional Kelvin equation is not applicable. Therefore, a refined Kelvin equation was proposed to describe the relationship between pore size and the pressure required for condensation accurately by considering the critical pore size, adsorption thickness, and decay rate of adsorption potential energy. Further analysis suggests that C2S releases more first-layer adsorption heat and thus shows stronger adsorption of water molecules compared to C-S-H.

Study on CO2 and CH4 Competitive Adsorption in Shale Organic and Clay Porous Media from Molecular- to Pore-Scale Simulation

Summary The elucidation of the competitive adsorption behaviors between CO2 and CH4 holds great importance in the context of improving natural gas recovery in shale reservoirs. Shale rock, as a complex porous medium, exhibits a highly interconnected multiscale pore network with pore size spanning from several to tens of nanometers. Nevertheless, accurately capturing the adsorption effects and studying the CO2/CH4 competitive adsorption within a large-scale, realistic, 3D nanoporous matrix remains a significant challenge. In this paper, we proposed a novel lattice Boltzmann method (LBM) coupled molecular simulation to investigate CO2/CH4 competitive adsorption in 3D shale nanoporous media. The initial step involves conducting Grand Canonical Monte Carlo (GCMC) simulations to simulate the competitive adsorption behaviors of CO2 and CH4 in kerogen and illite slit pores, with the aim of obtaining the atomic density distribution. Subsequently, a Shan-Chen-based lattice Boltzmann (LB) simulation is used under identical conditions. By coupling the molecular simulation results, the fluid-solid interaction parameters are determined. Finally, LB simulations are performed in designed 3D porous media, utilizing the fluid-solid interaction parameters. The effects of mineral type, CO2 concentration, and pore structure on competitive adsorption behaviors are discussed carefully. Our research offers significant contributions to the improvement of gas recovery and carbon geological sequestration through the examination of CO2/CH4 competitive adsorption in nanoporous media. Additionally, it serves as a link between molecular and pore-scale phenomena by leveraging the benefits of both molecular simulations and pore-scale simulations.

Research on the Multiscale Microscopic Pore Structure of a Coalbed Methane Reservoir

Coal rock pores are the space in which coalbed gas is stored and flows. Accurately characterizing the pore structure of coalbed gas is the foundation of coalbed gas reserve assessment and production forecasting. Traditional experimental methods are unable to characterize the multi-scale pore structure characteristics of coal rock. In this paper, a multi-scale pore structure characterization method is proposed by coupling various experimental methods, including low-pressure nitrogen gas adsorption experiments, X-ray computed tomography (XCT) imaging technology, and scanning electron microscopy (SEM). Using Zhengzhuang coalbed gas as an example, the micro-pore structure of coalbed gas reservoirs is characterized and depicted from a multi-scale perspective. The results indicate that a single experimental approach can only partially reveal the microstructure of coal rock pores. The combined use of multiple methods can accurately reveal the full-scale microstructure of coal rock pores. The pore structure of the experimental coal rock samples exhibits multi-scale characteristics, with a complex variety of pore types, including inorganic pores, organic pores, and fractures. Organic pores are predominant, with a small number of inorganic pores, and their sizes range from 2 nm to 50 μm. Mineral particles and fractures are observed at both the nanoscale and microscale, exhibiting typical multi-scale characteristics, with quartz being the predominant mineral.

Optimal selection of inversion method for gas-adsorption pore characterization of shales in Wufeng and Longmaxi Formation, Sichuan Basin

The pore space in gas shale spans multiple scales, ranging from nanometers to micrometers with an extremely complex structure and strong microscopic heterogeneity. Existing low-temperature gas adsorption (LTGA) pore size distribution (PSD) analysis models are based on the assumption of a one-dimensional tubular model and there is a lack of sufficient basis for selecting the most appropriate inversion model among the various types available. In this study, a comprehensive characterization of numerous samples from the Wufeng and Longmaxi Formation in the southern Sichuan Basin was conducted using different methods and inversion models. Based on multiple dimensions, such as fitting errors, the correlation between different methods including low-temperature CO2 adsorption (LTCA), nitrogen adsorption (LTNA), and large-scale mosaic Scanning Electron Microscopy (LAM-SEM), the most suitable one-dimensional models for LTCA and LTNA PSD analysis for the studied shale samples are determined. The simulation of gas condensation processes on LAM-SEM images yielded pore volume (PV) in the range of 32–48 nm comparable to the PV characterized by LTNA. Furthermore, the differences observed in PSDs between the gas condensation simulation procedure and the equivalent circular area diameter method indicate that irregular corner regions within larger pores are attributed to the volume of smaller-sized pores during gas adsorption characterization. It is revealed that the correlation between stitched surface area (SA) and maximum methane adsorption is stronger than individual characterizations, indicating that both micropores and mesopores contribute significantly to adsorption, and both characterization methods need to be employed to obtain SSA that influences methane adsorption. The research findings are helpful to the improvement of the multi-scale pore characterization level and evaluation of shale reservoirs.

Strength, Permeability and Multiscale Pore Characteristics of Cement-Based Materials with High-Volume Fly Ash Contents and Different Water-Binder Ratios

Strength, Permeability and Multiscale Pore Characteristics of Cement-Based Materials with High-Volume Fly Ash Contents and Different Water-Binder Ratios