Pore Network Model Research Articles

3D imaging and flow analysis of sandstone pore structure

Abstract Micro CT technology can provide three-dimensional high-precision digital images with micrometer (or smaller) resolution, offering robust technical support for the study of the internal structure of rocks. Based on the data obtained from the CT scanning of Leopard sandstone, a series of image processes were carried out using the Avizo software to extract pore distribution. The watershed algorithm was employed to independently segment each pore, and the largest sphere algorithm was used to establish a sphere-tube model. Based on the constructed pore network model, quantitative analyses of the porosity, fractal dimensions, permeability, and other parameters of the sandstone sample were conducted. Moreover, the connectivity of the pores was analyzed using an automatic skeleton model. Results show: ① CT scanning digital core technology can not only visualize the three-dimensional connectivity and isolated pores of sandstone but also quantitatively characterize the pore structure parameters; ② The analyzed Leopard sandstone has a connected porosity of 13.76%, an isolated porosity of 0.53%, and the pore radius is mainly concentrated in the 0-70μm small pore range, occupying 76.1% of the total pore volume; ③ The lower the sample porosity, the higher the fractal dimension, indicating a more complex pore structure.

Comparing, slurry infiltration characteristics between calcareous and silica sands based on slurry infiltration column tests and CT scanning

Calcareous sand, also known as bioclastic deposits, has distinct composition and morphological characteristics compared to siliceous sand. The exploration of the South China Sea has revealed a high potential for slurry pressure balanced (SPB) shield tunnelling in coastal areas that pass through calcareous sand strata. However, the impact of the differences between calcareous sand and siliceous sand on filter cake formation remains unclear. This study aimed to investigate the slurry infiltration characteristics of calcareous sand and siliceous sand (with Fujian sand as a representative) with the same permeability coefficient through micro slurry infiltration column tests. The macroscopic differences in slurry infiltration between the two media were observed. The sand columns were scanned before and after slurry infiltration using a CT scanner, allowing for the reconstruction of both the original particles’ topology and the pore network of the sand column. A pore network model was established, and the Dijkstra algorithm was used to identify the dominant particle infiltration paths, with flow resistance serving as the weight criterion for evaluating pore connectivity performance. The study found that the differences in particle topology and connectivity of the pore network were the fundamental mechanisms underlying the macroscopic slurry infiltration behaviors between different types of sands. These differences also explained the influence of particle size on the slurry infiltration characteristics for the same type of sand. The findings shed light on the fundamental mechanisms driving the differences in slurry infiltration behaviors and provide insights into the influence of particle size on slurry infiltration characteristics within the same type of sand.

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.

Analysis and Characterization of Micro–Nano Pores in Coal Reservoirs of Different Coal Ranks

Coalbed methane represents a promising source of clean and efficient unconventional energy. The intricate network of micro–nano pores within coal serves as the primary adsorption space for gas, contributing to the complexity of gas migration channels. In this study, based on the box-counting method, three coal samples representing low, medium, and high ranks were subjected to high-precision micro-CT scanning and nano-CT scanning to generate three-dimensional (3D) pore network models using Avizo visualization software. This facilitated the accurate and quantitative characterization of the micro–nano pore structures within coal reservoirs. The results indicated that the face rate distribution range of each sample was large, indicating relatively strong heterogeneity in each sample. The volume fractal dimension of each sample, determined through micro–nano-CT scanning, was around 2.5, while the surface fractal dimension exhibited oscillatory characteristics with moderate uniformity. The pore equivalent radius and throat equivalent radius distributions were unimodal across all the samples, with the micro-CT scanning revealing a concentration primarily within the range of 100–400 μm for the pore equivalent radius and within 200 μm for the throat equivalent radius. Conversely, the nano-CT scanning exhibited concentrations primarily within the range of 500–2500 nm for the pore equivalent radius and within 2000 nm for the throat equivalent radius. The analysis of the 3D reconstruction structures indicated that the middle-rank coal exhibited more developed large–medium pores compared with the low-rank and high-rank coal, while the low-rank and high-rank coal exhibited relatively more micro–small pores. Furthermore, the low-rank coal exhibited the fewest number of pores but the largest average pore equivalent radius and throat radius. Additionally, the middle–high-rank coal exhibited a relatively larger number of pores. Despite the complex topological structures observed in each sample, a significant proportion indicated a coordination number of 0–20, indicating excellent connectivity within the coal samples. This study is conducive to the optimization of coalbed methane surface development blocks and the formulation of reasonable development plans.

Influence of binder content on gas-water two-phase flow and displacement phase diagram in the gas diffusion layer of PEMFC: A pore network view

Understanding the gas-water flow dynamics in the gas diffusion layer (GDL) is one of the keys to improving the proton exchange membrane fuel cell's (PEMFC) overall performance and avoiding water flooding. Yet, the relationship between the two-phase flow and micro-scale GDL structures (including binder, PTFE, and fiber skeleton) is not well understood. In this study, three-dimensional GDL structures with different fractions of binder contents (φb=0%∼50%) and a fixed porosity of 75.6 % are confidently reconstructed based on high-resolution images from the confocal microscope, implying that the addition of binder will increase the number of large pores and cause a bimodal throat size distribution through morphology analysis. Thereafter, drainage simulations are performed under a wide range of capillary number (−9 < log Ca <0) and viscosity ratio (−3 < log M < 2) by the pore network model (PNM), which robustly predicts the displacement phase diagram of viscous fingering, capillary fingering, stable displacement, and transitional regime. In the viscous fingering and stable displacement regime, the nonwetting phase saturation (Snw) is nearly the same for different φb, implying the fluid invading pathway does not change much with the addition of binder. However, in the capillary fingering regime (refer to the actual operating conditions), Snw increases rapidly with φbat the breakthrough time and its transient value continues to increase until the steady state, which may be attributed to the increased fractions of pores above the capillary threshold attributed by the bimodal throat size distribution. In addition, the effective water permeability increases sharply with φb, whereas the gas permeability remains almost constant, which means such pore structure alteration by adding the binder is beneficial to water disposal in PEMFC. This research provides insights into delineating the effect of pore and throat size distribution alteration by adding binder on two-phase dynamics in GDL.

Pore unit cell network modeling of the thermal conductivity dynamics in unsaturated sandy soils: Unveiling the role of spanning‐wetting phase cluster

AbstractAs the world struggles with climate change and energy crises, understanding the role of soil in the food–water–energy nexus becomes increasingly critical. Accurately estimating the soil thermal conductivity drying curve is essential for assessing the impacts of temperature on soil biota and crop growth, environmental changes due to forest fires and global warming, and for designing geo‐energy extraction techniques such as geothermal energy piles. Existing empirical models often fail to accurately estimate the soil thermal conductivity (TC), particularly in pendular soil moisture regimes where they do not capture sharp changes in TC. This study introduces a novel approach using a pore unit cell network model to more accurately describe the dynamics of TC in variably saturated soils. A quadratic parallel scheme within each soil pore unit cell links the TCs of solid, water, and air to the overall effective conductivity. By modeling air invasion in the pore network model and employing the proposed equation, we determined the unsaturated soil TC based on varying local conductivities. The model effectively captures the significant decrease in conductivity in the pendular saturation regime, associated with the shrinkage of the spanning‐wetting cluster. Quantitative analyses showed a substantial improvement in prediction accuracy compared to existing models, especially under varying moisture conditions. Our findings have significant implications for better characterizing soil thermal and hydraulic properties, which are crucial for resource management in a changing climate and advancing geo‐energy technologies.

Multiscale pore‐network reconstruction of a fine‐textured heterogeneous soil

AbstractDigital samples offer many opportunities to study subsurface fluid flow and contaminant transport processes. The pore size distribution of especially fine‐textured porous media often covers many orders of magnitude in the length scale, which makes accurate microCT scanning and modeling of the underlying processes difficult. When a single‐resolution image is not capable of capturing all relevant details of a sample, one should scan the sample, or selected parts of it, at different resolutions. Combining multiple resolutions into one single sample for subsequent pore‐scale modeling is generally not possible due to limitations in computer memory and speed, thus making it necessary to create a simpler sample containing relevant information from the parent networks. We imaged four samples using different resolutions to capture the multiscale heterogeneity of a fine‐textured soil and combined them into one overall digital sample based on the original pore networks. The parent networks were characterized using their geometrical properties, correlations between these properties, and connectivity functions describing the network topologies. Our approach creates stochastic networks of arbitrary size with the same flow properties as the parent network. The method, implemented using the PoreStudio pore network model, repeatedly integrates information at two subsequent scales, with the resulting digital sample having the same hydraulic properties as the original samples. The procedure leads to more useful three‐dimensional digital models, facilitating basic analyses of underlying pore size distributions. Porosity calculations were compared with direct measurements, while those for the hydraulic conductivity were compared with estimates based on the particle size distribution and nearby field data.

Non-monotonic effect of compaction on longitudinal dispersion coefficient of porous media

Utilizing the discrete element method and the pore network model, we numerically investigate the impact of compaction on the longitudinal dispersion coefficient of porous media. Notably, the dispersion coefficient exhibits a non-monotonic dependence on the degree of compaction, which is distinguished by the presence of three distinct regimes in the variation of dispersion coefficient. The non-monotonic variation of dispersion coefficient is attributed to the disparate effect of compaction on dispersion mechanisms. Specifically, the porous medium tightens with an increasing pressure load, reducing the effect of molecular diffusion that primarily governs at small Péclet numbers. On the other hand, heightened pressure loads enhance the heterogeneity of pore structures, resulting in increased disorder and a higher proportion of stagnant zones within porous media flow. These enhancements further strengthen mechanical dispersion and hold-up dispersion, respectively, both acting at higher Péclet numbers. It is crucial to highlight that hold-up dispersion is induced by the low-velocity regions in porous media flow, which differ fundamentally from zero-velocity regions (such as dead-ends or the interior of permeable grains) as described by the classical theory of dispersion. The competition between weakened molecular diffusion and enhanced hold-up dispersion and mechanical dispersion, together with the shift in the dominance of dispersion mechanisms across various Péclet numbers, results in multiple regimes in the variation of dispersion coefficients. Our study provides unique insights into structural design and modulation of the dispersion coefficient of porous materials.

The impact of porous structure on oil–water two-phase flow under CO2 environment in continental shale reservoirs

CO2 applications for enhanced oil recovery and storage in continental shale reservoirs are promising, and there is a need to evaluate the impact of porous structure on oil–water two-phase flow under CO2 environment. In this study, first, digital cores of quartz-rich, carbonate-rich, and clay-rich shales are established using Focused Ion Beam Scanning Electron Microscopy scanning data processed through generative adversarial networks. Subsequently, the pore networks generated by digital cores are quantitatively analyzed using the generalized extreme value distribution. Finally, pore network modeling is carried out to elucidate the effect of porous structural differences on oil–water flow considering CO2 dissolution and capillary forces. The results show that quartz-rich shale, characterized by nanopore intergranular dominance and the highest pore network connectivity, demonstrates the highest relative permeability of the oil phase. Carbonate-rich shale exhibits intermediate relative permeability of oil phase, while clay-rich shale exhibits the worst. The dissolution of CO2 reduces oil–water interfacial tension and oil viscosity, enhances oil mobilization within nanopores, and notably increases the relative permeability of the oil phase. The permeability of the oil phase is governed by pore structure, displaying positive correlations with core heterogeneity, pore radius, coordination number, and throat length, and negative correlations with throat radius.

Modeling sub‐resolution porosity of a heterogeneous carbonate rock sample

AbstractAccurately estimating the petrophysical properties of heterogeneous carbonate rocks across various scales poses significant challenges, particularly within the context of water and hydrocarbon reservoir studies. Digital rock analysis techniques, such as X‐ray computed microtomography and synchrotron‐light‐based imaging, are increasingly employed to study the complex pore structure of carbonate rocks. However, several technical limitations remain, notably the need to balance the volume of interest with the maximum achievable resolution, which is influenced by geometric properties of the source–detector distance in each apparatus. Typically, higher resolutions necessitate smaller sample volumes, leading to a portion of the pore structure (the sub‐resolution or unresolved porosity), that remain undetected. In this study, X‐ray microtomography is used to infer the fluid flow properties of a carbonate rock sample having a substantial fraction of porosity below the imaging resolution. The existence of unresolved porosity is verified by comparisons with nuclear magnetic resonance (NMR) data. We introduce a methodology for modeling the sub‐resolution pore structure within images by accounting for unresolved pore bodies and pore throats derived from a predetermined distribution of pore throat radii. The process identifies preferential pathways between visible pores using the shortest distance and establishes connections between these pores by allocating pore bodies and throats along these paths, while ensuring compatibility with the NMR measurements. Single‐phase flow simulations are conducted on the full volume of a selected heterogeneous rock sample by using the developed pore network model. Results are then compared with petrophysical data obtained from laboratory measurements.

Determination of a pedotransfer function for specific air–water interfacial area in sandy soils: A pore network‐informed multigene genetic programming approach

AbstractUnderstanding specific air–water interfacial area (SAWIA) is essential for characterizing and modeling various phenomena in vadose zone hydrology, such as virus and colloid transport, contaminant dissolution, evaporation, and the hydro‐mechanical behavior of unsaturated soils. Traditional measurement methods, including X‐ray imaging and tracer techniques, often encounter challenges, leading to a scarcity of studies that provide a reliable relationship for SAWIA. Currently, no pedotransfer function in the literature links SAWIA with saturation and suction using readily measurable soil properties such as median grain size and porosity. In this study, we initially developed a pore network model capable of predicting SAWIA by calibrating it with corresponding soil‐water retention curves (SWRCs). We then used these models to compile a comprehensive database of SAWIA for six sandy soils, for which experimental SWRCs were available, covering a range of median grain sizes and porosities. Utilizing this database, we established a pedotransfer function through multigene genetic programming. The accuracy of this function was validated against experimental data not previously used in its training and testing. Our parametric study indicated that increases in either porosity or median particle size led to a decrease in the regions exhibiting higher SAWIA in terms of saturation and suction.

Study on multi‐cycle gas‐water displacing mechanism in underground gas storage of low‐permeability reservoir based on PNM

AbstractA deep understanding of the pore‐scale multi‐cycle two‐phase seepage mechanism of gas‐water systems in low‐permeability reservoirs is crucial for enhancing oil and gas recovery and optimizing the operating conditions of underground gas storage. A pore network model was reconstructed using micro‐CT images of low‐permeability core samples from the Dagang Oilfield, China. The mathematical models of gas‐water flow in the pore‐scale models were established based on Poiseuille's law and the quasi‐static displacement theory, considering the gas compressibility and slip effects. The porosity, pore size, absolute permeability, and relative permeability (Kr) of oil‐water and gas‐water were calculated using pore network simulations and validated against experimental benchmark data of the same samples. The effects of multi‐cycle displacement, rock wettability, and average pore pressure on the gas‐water two‐phase flow were simulated and analyzed. The results showed that the relative permeability of gas (Krg) at the same water saturation level significantly increased when the gas compressibility and slip effects were considered. With an increase in the number of gas‐water displacement cycles, Krg at the same water saturation level showed a decreasing trend, indicating a reduction in the gas seepage capability. Krg decreased with increasing water contact angle. With an increase in the average pore pressure, Krg decreased and gradually increased when the average pressure exceeded 25 MPa.

Super-localization of spatial network models

Spatial network models are used as a simplified discrete representation in a wide range of applications, e.g., flow in blood vessels, elasticity of fiber based materials, and pore network models of porous materials. Nevertheless, the resulting linear systems are typically large and poorly conditioned and their numerical solution is challenging. This paper proposes a numerical homogenization technique for spatial network models which is based on the super-localized orthogonal decomposition (SLOD), recently introduced for elliptic multiscale partial differential equations. It provides accurate coarse solution spaces with approximation properties independent of the smoothness of the material data. A unique selling point of the SLOD is that it constructs an almost local basis of these coarse spaces, requiring less computations on the fine scale and achieving improved sparsity on the coarse scale compared to other state-of-the-art methods. We provide an a posteriori analysis of the proposed method and numerically confirm the method’s unique localization properties. In addition, we show its applicability also for high-contrast channeled material data.

Do Pores Exist?—Foundational Issues in Pore Structural Characterisation

This work reviews a range of fundamental theoretical considerations in pore structural characterisation. The pore concept is essential for providing a better understanding of physical processes arising within porous media than purely phenomenological approaches. The notion of a pore structure is found to be independently valid and invariant during theory change concerning said physical processes, even for structural models obtained via indirect methods. While imaging methods provide a more direct characterisation of porous solids, there is often a surfeit of information beyond that which can be wielded with current computing power to predict processes sufficiently accurately. Unfortunately, the pore network model extraction methods cannot decide in advance the level of simplification necessary to obtain the optimum minimal idealisation for a given physical process. Pore network models can be obtained with differing geometrical and topological properties, but similar mass transfer rates, for reasons that are often not clear. In contrast, the ‘pore-sifting’ strategy aims to explicitly identify the key feature of the void space that controls a mass transport process of interest.

Fluid entrapment during forced imbibition in a multidepth microfluidic chip with complex porous geometry

Understanding and controlling fluid entrapment during forced imbibition in porous media is crucial for many natural and industrial applications. However, the microscale physics and macroscopic consequences of fluid entrapment in these geometric-confined porous media remain poorly understood. Here, we introduce a novel multidepth microfluidic chip, which can mitigate the depth confinement of traditional two-dimensional (2-D) microfluidic chips and mimic the wide pore size distribution as natural-occurring three-dimensional (3-D) porous media. Based on microfluidic experiments and direct numerical simulations, we observe the fluid-entrapment scenarios and elucidate the underlying complex interaction between geometric confinement, capillary number and wettability. Increasing depth variation can promote fluid entrapment, whereas increasing capillary number and contact angle yield the opposite effect, which seemingly contradicts conventional expectations in traditional 2-D microfluidic chips. The fluid-entrapment scenario in depth-variable microfluidic chips stems from microscopic interfacial phenomena, classified as snap-off and bypass events. We provide theoretical analyses of these pore-scale events and validate corresponding phase diagrams numerically. It is shown that increasing depth variation triggers snap-off and bypass events. Conversely, a higher capillary number suppresses snap-off events under strong imbibition, and an increased contact angle inhibits bypass events under imbibition. These macroscopic imbibition patterns in microfluidic porous media can be linked with these pore-scale events by improved dynamic pore-network models. Our findings bridge the understanding of forced imbibition between 2-D and 3-D porous media and provide design principles for newly engineered porous media with respect to their desired imbibition behaviours.

Permeability anisotropy analysis of two-phase flow during hydrate dissociation process

Natural gas hydrate (NGH) is a versatile and energy source. But in the actual extraction process, NGH in the reservoir will be out of phase equilibrium conditions and dissociate. This will induce alterations in permeability characteristics of reservoir and will exert a significant influence on the assessment of hydrate reservoir capacity. In the research, an innovative CT triaxial system was used to obtain the micro-structure of sediment specimen during hydrate dissociation. The anisotropy of absolute permeability (k), capillary pressure (Pc) and relative permeability (kr) were also analyzed using the pore network model (PNM). As demonstrated by the results, k increases gradually in all three directions during the dissociation. Pc gradually decreases. The degree of anisotropy of both Pc and gas-water relative permeability (krg and krw) gradually decreases. The impact of hydrate dissociation on the kr anisotropy during primary gas flooding surpasses that observed during secondary water flooding. As hydrate saturation decreases, the krw increases and the krg decreases in the horizontal directions. The krw does not change significantly and the krg increases in the vertical direction. Along the length of the sample, the distribution of hydrate and pore space exhibits heterogeneity across the sections. This inhomogeneous distribution will lead to anisotropy in permeability.

Upscaling the reaction rates in porous media from pore- to Darcy-scale

Modeling and prediction of reactive transport in porous media are challenging due to the complexity of the characterization of reactions across spatial and time scales. The application of reaction rates obtained from batch experiments to porous media is not valid because it disregards the influences of flow pathways, distribution of residence time, transport limitations within the porous media, as well as neglecting the impact of surface mineralogy heterogeneity. In this study, we presented how the pore-scale modeling can help to improve the Darcy-scale simulations. First, the reactive transport was simulated in a pore-network model and was validated against the experiments. Then, the pore-network results were averaged to obtain the effective reaction rates as a function of pore velocity, the inlet concentration, and the resident concentration. The upscaled function was incorporated into the Darcy-scale model and showed a significant improvement in predicting the concentration profiles. Notably, the use of batch reaction rates in the Darcy model (ADRE-batch) led to significant underestimation, up to 93%, of the required pore volume injection for complete contaminant removal from the simulation domain.

Fabrication of controlled porous and ultrafast dissolution porous microneedles by organic-solvent-free ice templating method

Porous Microneedles (PMNs) have been widely used in drug delivery and medical diagnosis owing to their abundant interconnected pores. However, the mechanical strength, the use of organic solvent, and drug loading capacity have long been challenging. Herein, a novel strategy of PMNs fabrication based on the Ice Templating Method is proposed that is suitable for insoluble, soluble, and nanosystem drug loading. The preparation process simplifies the traditional microneedle preparation process with a shorter preparation time. It endows the highly tunable porous morphology, enhanced mechanical strength, and rapid dissolution performance. Micro-CT three-dimensional reconstruction was used to better quantify the internal structures of PMNs, and we further established the equivalent pore network model to statistically analyze the internal pore structure parameters of PMNs. In particular, the mechanical strength is mainly negatively correlated with the surface porosity, while the dissolution velocity is mainly positively correlated with the permeability coefficient by the correlation heatmap. The poorly water-soluble Asiatic acid was encapsulated in PMNs in nanostructured lipid carriers, showing prominent hypertrophic scar healing trends. This work offers a quick and easy way of preparation that may be used to expand PMNs function and be introduced in industrial manufacturing development.

Permeability Prediction in Nonwoven Geotextiles Using Mathematical Modeling and Numerical Simulation

The vertical permeability coefficient is a pivotal hydraulic index of needle-punched nonwoven geotextiles. The accurate determination of the permeability coefficient is important for assessing engineering properties. This study employed mathematical modeling, numerical simulations, and physical experimentation to investigate the permeability behavior of nonwoven geotextiles. Mathematical modeling relies on the fiber and pore size characteristics of the geotextiles extracted through two-dimensional image analysis. The numerical simulation method was based on a pore network model acquired through three-dimensional image analysis. The results of the physical experiments served as benchmarks for evaluating the precision of the two methods. These findings underscore the efficacy of mathematical modeling and numerical simulation in predicting the permeability characteristics of nonwoven geotextiles.

Study on meso-macroscopic ionic conductivity of hydrogels and construction of prediction model

The utilization of hydrogels in biological devices has seen a significant expansion, necessitating a thorough investigation into their conductivity. In this regard, we conducted a comprehensive examination of the impact of crosslinkers on pore radius and distribution. When the crosslinker proportion was augmented by a factor of 10, the pore radius exhibited a reduction of nearly 3.7 times, resulting in a more uniform pore distribution. Notably, our findings indicated a direct proportionality between conductivity and mesoscopic porosity, coupled with an inverse relationship with crosslinking density. To advance our understanding, we proposed an equivalent pore network model that omits considerations of curvature to predict the ionic conductivity of hydrogels. Intriguingly, as the proportion of crosslinker increased, the mesoscopic pores of hydrogels demonstrated a correlation with macroscopic features. Upon comparison with experimental data, the model exhibited a commendable alignment with the observed trends. Through mutual refinement with experimental results, a novel prediction equation emerged, yielding an average prediction error less than 2 %. Beyond trend prediction, our model achieved relative quantitative predictions, providing valuable insights for the regulation of conductivity in electronic biological devices. This research contributes to the advancement of knowledge in the field, offering a nuanced perspective on the interplay between crosslinkers, pore characteristics, and the conductivity of hydrogels.