Topology Of Pore Space Research Articles

Surface-Constrained Metropolis Monte Carlo: Simulation of Reactions on Triply Periodic Minimal Surfaces.

Triply periodic minimal surfaces (TPMS) inspired by nature serve as a foundation for developing novel nanomaterials, such as templated silicas, graphene sponges, and schwarzites, with customizable optical, poroelastic, adsorptive, catalytic, and other properties. Computer simulations of reactions on TPMS using reactive intermolecular potentials hold great promise for constructing and screening potential TPMS with the desired properties. Here, we developed an off-lattice, surface-constrained Metropolis Monte Carlo (SC-MMC) algorithm that utilized a temperature quench process. The presented SC-MMC algorithm was used to investigate the process of graphitization reactions on the Schwarz primitive, Schwarz diamond, and Schoen gyroid TPMS, all with a cubic lattice parameter of 8 nm. We show that the optimized carbon TPMS exhibits a low energy, approximately -7.1 eV/atom, comparable to that of graphite and diamond crystals, along with a variety of topological defects. Furthermore, these structures showcase extensive and smooth surfaces characterized by a negative discrete Gaussian curvature, a distinctive feature indicative of an interconnected morphology. They possess specific surface areas of ∼2700 m2/g, comparable to graphene, and exhibit a significant porosity of around 90%. The theoretical X-ray correlation functions and nitrogen adsorption isotherms confirm that the constructed TPMS exhibit remarkably similar surface properties, although the pore space topology varies significantly.

A two-dimensional transient study on the impact of pore space connectivity on the immiscible two-phase flow in a water-wet, water–oil system

A multi-relaxation time lattice-Boltzmann model is employed to investigate the dynamic evolution of two immiscible phases through an artificial, randomly generated, porous structure. The flow is driven by a constant pressure gradient, in the absence of gravitational effects. Constraining attention to two dimensions, the impact of the morphological properties of the porous structure, generated using constant radius circular solid grains, on a water-wet, oil–water two-phase flow is studied. Variations in the pore space connectivity and topology are quantified by the Euler characteristic. It is found that the wetting phase saturation and the degree of pore network homogeneity have a significant impact on the dynamic evolution of the non-wetting phase topology, which is governed by a series of coalescence and snap-off events. It is also observed that the phenomenal macro-scale steady-state based on the velocity field does not also imply a temporal topological invariance of the displaced phases. The impact of the pore space morphology on the transient dynamics of the two-phase flow is monitored and quantified through a series of hydrodynamic and topological parameters that signify the underlying flow transport processes.

Investigation of Flow Characteristics of Landslide Materials Through Pore Space Topology and Complex Network Analysis

AbstractUnlike embankments, earth dams, and other man‐made structures, most landslide dams are formed by rapid accumulation of rock or debris rather than mechanical compaction; thus, they are loose and pose a great risk of seepage failure. Landslide materials usually have complex pore structures with randomly distributed pores of various sizes, making the flow and transport processes very complex. Aiming at these challenges, we systematically investigated the influences of pore structure on the micro‐and macro‐scale flow characteristics of landslide materials. First, landslide materials are simplified as spherical granular packings with wide grain size distributions. Then, we use the Finite‐difference method Stokes solver to simulate the fluid flow through granular packings and calculate their permeability. We characterize the pore structure using different topological measures, including these borrowed from complex network theory. Among these measures, tortuosity and global efficiency show clear relations with permeability. The pore network modeling indicates that pore size heterogeneity and pore connectivity significantly influence the flow characteristics. The correlation between pore‐scale velocity and throat diameters follows a power‐law scaling with an exponent close to two, suggesting that the Hagen–Poiseuille law would still be valid in complex porous media. The permeability and porosity, throat radius, and tortuosity of pore structure can be related by the equation proposed by Nishiyama and Yokoyama (2017, https://doi.org/10.1002/2016JB013793). The complex network analysis reveals that the assortative network is more permeable than the disassortative network. Furthermore, pores with larger closeness centrality have higher flow efficiency, resulting in higher macroscopic permeability.

Pore-scale network modeling approach to study the impact of Microporosity's pore space topology

Carbonates present a significantly important area for the research as classical empirical methods applied for sandstones characterization, may easily mislead when applied to carbonates. The impact becomes more protuberant when considering low resistivity pay carbonate formations where Archie's equation may yield higher than actual water saturation values, which, however, underestimate the hydrocarbon reserves. Especially, the bimodal pore sizes distribution makes carbonates extremely complicated for characterization through traditional digital rock physics applications. Unlike sandstone, for a given carbonate sample, it is almost impossible to have pore digital 3D images with minimum elementary volume (REV) to generate a standard pore-network model (PNM) due to the resolution and computational processing power limitations.

Effects of pore topology on immiscible fluid displacement: Pore-scale lattice Boltzmann modelling and experiments using transparent 3D printed models

Waterflooding technology has been widely applied to mobilise the residual oil in petroleum reservoirs. It is crucial to quantitatively characterise the topology of pore space and recognise its influence on the development of preferential fluid displacement paths for enhancing oil recovery. However, understanding the sensitivity of the preferential fluid displacement path to the topological characteristics of pore space is rather limited. To address this, this study constructs digital pore models with various pore topologies using information extracted from natural sandstones. The multicomponent lattice Boltzmann method is used to predict the pore-scale immiscible water-oil displacement in the constructed pore structures under different wetting conditions. Displacement experiments are performed in the transparent models fabricated using three-dimensional printing technology to examine the numerical predictions. The results reveal that the pore topological skeleton is one of the key factors controlling the immiscible fluid displacement in pore space and has a strong impact on the fluid invasion patterns and preferential fluid displacement path. The pore-scale immiscible displacement dynamics are associated with not only pore topology but also fluid wettability. As the wetting condition changes from drainage to imbibition, we observe a transition of the Euler characteristic effect on the pore structures with similar pore characteristics: the moving characteristics and invading fluid occupancy decrease under drainage and approximately increase under imbibition, when the Euler characteristic of the pore topology increases. This study provides insights on the effect of pore topology and its coupled effect with fluid wettability on the immiscible fluid displacement in porous rocks.

Topology-based characterization of chemically-induced pore space changes using reduction of 3D digital images

We present an algorithm for the pore-scale simulation of the reactive transport in a 3D case. The algorithm is designed to facilitate the observation of pore space changes caused by chemical fluid-solid interaction. Additionally, the algorithm allows estimation of the main macroscopic properties evolution of the porous material, such as permeability, hydraulic tortuosity, and formation factor. Also, we develop an algorithm to compute the persistence diagrams for the independent cycles in the pore space, which quantitatively characterizes the changes in the pore space topology. Moreover, we speed up this algorithm by using the original digital image reduction approach. Applying the clustering technique to the persistence diagrams, we show that different matrix dissolution scenarios can be distinguished based on the persistence homology. These scenarios depend on the flow rate, reaction rate, and species concentration at the inlet. At the same time, the samples from the different clusters illustrate utterly different behavior of the cross-property (porosity-permeability) relations.This is extended version of our conference paper [1].

Cover Picture: Exploring residual CO2 trapping in Heletz sandstone using pore‐network modeling and a realistic pore‐space topology obtained from a micro‐CT scan (Greenhouse Gas Sci Technol 5/2021)

The cover image is based on the Original Article Exploring residual CO2 trapping in Heletz sandstone using pore-network modeling and a realistic pore-space topology obtained from a micro-CT scan by Kristina Rasmusson et al., https://doi.org/10.1002/ghg.2100.

Petro-mineralogical controls on coda attenuation in volcanic rock samples

SUMMARYSeismic attenuation measurements, especially those obtained from coda decay analysis, are becoming a key data source for the characterization of the heterogeneous Earth due to their sensitivity to small-scale heterogeneities. However, the relation between the scattering attenuation measured from coda waves and physical rock properties is still unclear. The goal of this study is to identify the main petrophysical and mineralogical factors controlling coda attenuation in volcanic rocks at the laboratory scale, as a necessary step before modelling seismic waves in real volcanic media. Coda wave attenuation was estimated from ultrasonic S-wave waveforms. To quantify the heterogeneity of the rocks and link them with this attenuation parameter, we performed several categorizations of the pore and grain systems of volcanic samples. Considering that seismic attenuation in rock samples can be modelled using the framework of wave propagation in random media, a statistical analysis of shear wave velocity fluctuations was performed: this analysis gives correlation lengths ranging from 0.09 to 1.20 mm, which represents the length scale of heterogeneity in the samples. The individual evaluation of the pore space and mineral content revealed that the pores of the samples (characterized by large vesicles) have a bigger effect than the grains on the heterogeneity level. We have developed a framework where intrinsic properties of the host rocks drive seismic attenuation by correlating the petro-mineralogical characteristics obtained from image data processing and analysis, with the coda attenuation measured at ultrasonic frequencies. There is conclusive evidence that porosity alone is not the primary controller of coda attenuation: it is also changed by the alteration level (i.e. oxidation, coating of the vesicles, secondary minerals) and the size of grains and pores. Among all the parameters analysed, it appears that the pore space topology is the main contributor to scattering attenuation in the volcanic samples.

Digital image reduction for the analysis of topological changes in the pore space of rock matrix

The paper presents an original algorithm for reducing three-dimensional digital images to improve the computing performance of persistence diagrams. These diagrams represent changes in pore space topology during essential or artificial changes in the structure of porous materials. The algorithm has linear complexity because during reduction, each voxel is checked not more than seven times. This check, as well as the removal of voxels, takes a constant number of operations. We illustrate that the algorithm’s efficiency depends on the complexity of the original pore space and the size of filtration steps. The application of the reduction algorithm allows the computation of one-dimensional persistence Betti numbers for models of up to 5003 voxels by using a single computational node. Thus, it can be used for routine topological analysis and the topological optimization of porous materials.

Capillary rise in vuggy media

Carbonates can be highly heterogeneous formations with large variations in pore size distribution and pore space topology, which results in complex multiphase flow behavior. Here we investigate the spontaneous imbibition behavior of fluids in vuggy carbonates. Glass beads of 1.0 mm diameter, with dissolvable vug placeholders, are sintered to form multiple configurations of heterogeneous vuggy core with variations in matrix porosity, vug size, vug spatial location, and number of vugs. The core fabrication process is repeatable and allows the impact of vug textural properties to be investigated in a controlled manner.Capillary rise experiments are conducted in these proxy vuggy carbonate core and compared with the homogeneous non-vuggy core as reference. Continuous optical imaging is performed to track the position of the air-water interface in the cores. To understand the change in capillary height in the presence of a vug, a volume-of-fluid two-phase numerical simulation is performed in a parallel set of connected and disconnected tubes. Finally x-ray tomography scans are performed to identify the shape of the air-water interface in a select few cores.The results can be summarized as follows: disconnected vugs result in higher capillary rise compared to non-vuggy porous media. The vugs act as capillary barriers, diverting fluid flow to the adjacent connected channels, which ultimately results in a higher overall capillary rise. The results of this work highlight that radius of spontaneous invasion of aqueous phases, such as fracture fluid and hazardous wastes, are affected by vug porosity but not their distribution.

Characterizing coal pore space by gas adsorption, mercury intrusion, FIB–SEM and µ-CT

Understanding multiphase flow properties is essential for assessing and exploiting coals. These properties depend on the 3D pore space information, i.e. geometry and topology. However, determining the geometric and topological properties in coals are still challenging due to the complicated pore structures comprising several length scales. Studying pore scale structures in coals in a continuous range across over several length scales and integrating these information are necessary to increase the understanding of the role of pore structure on transport properties. Most of the current modeling methods are usually based on one or two experimental methods with limited and insufficient information. In this work, CO2 adsorption, N2 adsorption, MIP, X-ray µ-CT and FIB–SEM are used to study the pore structure characteristics of coal samples cored from the No. 9 coal seam of upper Permian Longtan formation at the Longfeng mine, China. The porosity, pore surface area, pore size distribution, connectivity and pore shapes measured by different methods are analyzed. We show that a combination of these techniques provides a richer picture of pore structure in coals. The obtained 3D pore structure can be applied to predict transport properties which are important to capture coal mine methane (CMM) and optimize field development. The results will also be helpful for the gas control in coal mines.

Improving watershed-based pore-network extraction method using maximum inscribed ball pore-body positioning

Pore-scale modeling is a rapidly evolving area of research because modeling multiphase flow directly on 3D pore geometries is of utmost importance in wide variety of research areas, including oil and gas development, hydrology and material sciences. Although there are numerous methods to model flow, only so-called pore-network models are computationally effective enough to perform simulations in large modeling domains, and they are orders of magnitude faster than direct modeling approaches. However, pore-network models require a simplification of the 3D pore geometry to perform simulations, which are usually referred to as pore-network extraction. Such extraction poses a separate problem because it must provide an accurate description of the pore space geometry and topology. Different methods have been proposed in the literature. Recently, watershed-based approaches have been popular due to their effectiveness in working with porous media images of any porosity. A watershed algorithm requires seed placement to segment the space into distinct pores. We propose a hybrid algorithm combining the power of watersheds in finding intersections between pores with the advantages of the maximum inscribed ball technique, which is very effective in finding pore centers. We rigorously verify and test our novel methodology on artificial and X-ray microtomography images of wide variety of porous materials: sphere packings, carbonate, soil, ceramic and sandstone samples. Comparison against a purely watershed-based method and results based solely on the maximum inscribed balls–based method (in terms of pore/throat total number, pore size distributions and connection statistics, and multiphase flow properties including capillary curves and relative permeabilities) revealed the accuracy of our novel technique, consistency with existing classical techniques and great potential in analysing 3D pore images of any complexity. On the other hand, comparison of extracted pore-network topology (as based on Euler number) revealed significant differences between different methodologies, which is rather surprising considering the similarities in two-phase flow properties. While analysing permeability results, we also compared two popular pore-throat partitioning models and advocated in favor of the weight model usually utilized within watershed-based extracted pore networks. Our results illuminate problems in current pore-network models and outline some potential ways to improve their accuracy in future research.

Impact of mineralogy and wettability on pore-scale displacement of NAPLs in heterogeneous porous media

Subsurface formations often contain multiple minerals with different wettability characteristics upon contact with nonaqueous-phase liquids (NAPLs). Constitutive relationships between microstructure heterogeneity and NAPL fate and transport in these formations are difficult to predict. Several studies have used pore-scale network models with faithful representations of rock pore space topology to predict macroscopic descriptors of two-phase flow, however wettability is usually considered as a spatially random variable. This study attempts to overcome this limitation by considering more realistic representations of rock mineralogy and wettability in these models. This is especially important for heterogeneous rocks where properties vary at the pore-scale. The work was carried out in two phases. First, pore-fluid occupancy maps during waterflooding were obtained by X-ray microtomography to elucidate the impact of pore wall mineralogy and wettability on water preferential flow paths and NAPL trapping within a heterogeneous aquifer sandstone (Arkose). Then, microtomography images of the rock were used to generate a hybrid pore network model (PNM) that incorporated both pore space topology and pore wall mineralogy. In-situ contact angles (CA) measured on the surface of different minerals were assigned to the network on a pore-by-pore basis to describe the exact wettability distribution of the rock (Pore-by-pore model). The equivalent network was used as input in a quasi-static flow model to simulate waterflooding, and the predictions of residual NAPL saturation and relative permeabilities were compared against their experimental counterparts. To examine the sensitivity of the model to the underlying fluid-solid interactions, we also used traditional methods of wettability characterization in the input data and assigned them randomly to the PNM. Wettability in this case was assessed from macroscale CA distribution of oil droplets on the surface of unpolished Arkose substrates released by spontaneous imbibition of water (Arkose model) and from pendant drop measurements on polished quartz (Quartz model). Our results revealed that the Pore-by-pore model predicted waterflooding with the highest accuracy among all three cases. The Arkose model slightly overestimated NAPL removal whereas the Quartz model failed to predict the experiments. More in-depth analysis of the Pore-by-pore and Arkose models showed that macroscopic transport quantities are less dependent to microstructure heterogeneity if minerals are distributed uniformly across the rock. The predictions herein indicate the importance of incorporating mineralogy and wettability maps to improve the prediction capabilities of PNMs especially in systems with high mineral heterogeneity, where minerals are nonuniformly distributed, or selective fluid-mineral interactions are targeted.

Residual oil saturation following gas injection in sandstones: Microfluidic quantification of the impact of pore-scale surface roughness

Micro- and nanoscale surface roughness within subsurface rocks is ubiquitous due to weathering and diagenesis. To assess the impacts of surface roughness on non-wetting gas flooding operations, we conducted immiscible drainage experiments in glass micromodels representing single-scale rock matrices with identical pore topology but varying degrees of surface roughness. The experiments were performed in capillary-dominated regimes where air was the non-wetting phase and crude oil was the wetting phase, emulating an enhanced oil recovery or non-aqueous phase liquid phase remediation process. We find that, for approximately constant pore-space topology, surface roughness (quantified with the average hillock height to pore depth ratio, Ω) has minor impact on sweep efficiency when Ω < 5.5%. However, once a critical threshold value of Ω > 12.5% is reached, recovery becomes consistently 10% higher and gas breakthrough occurs at later times. In addition, the roughest micromodel displays the highest repeatability of dendrite pathways validating diagenetic controls on gas flood sweep efficiency. We also find that surface roughness does not considerably affect the morphology of non-wetting phase dendrites and phase topology versus air saturation curves.Sub-pore scale visualizations in the micromodels indicate that contact-line pinning, the phenomenon responsible for higher sweep and greater dendrite tortuosity, only occurs in the roughest micromodel with Ω > 12.5%, whereas pendular rings and grain-lining thin films occur in all of the micromodels. Non-local snap-off occurs in micromodels regardless of roughness. The effects of isolated fracture surface roughness on capillary trapping saturations is found to be negligible for both drainage and imbibition saturation cycles. However, the presence of an isolated fracture diverts gas dendrites from sweeping the matrix and therefore increases oil trapping by approximately 10–30% compared to the micromodels without fractures. The workflow and experimental results in this paper provide benchmarking opportunities for direct numerical simulation algorithms for porous geomaterials. In addition, the paper aims to highlight the nontrivial implications of surface roughness for reservoir quality assessment and various subsurface operations.

Disorder characterization of porous media and its effect on fluid displacement

Depending on topology of pore space, different patterns of multiphase flow in porous media are observed. By analyzing pore-scale mechanisms, a phase diagram is constructed showing that wettability and structural disorder collectively affect displacement efficiency and fluid-fluid interfacial area.

Modifications of chalk microporosity geometry during burial – An application of mathematical morphology

Abstract The diagenetic evolution of chalk during burial has previously been established and can be summarized as follows: (1) ooze deposition and dewatering (burial 1000 m). Moreover, chalk particles tend to increase in size as a result of diagenesis, i.e. recrystallization or cementation. As a result of compaction and cementation, the shape, size and connectivity of chalk microporosity evolve during burial. However, if the evolution of bulk porosity during burial is well quantified, actual modifications of pore space topology are less understood. Quantifying pore space properties such as pore and throat sizes, aspect ratio and spatial distribution usually require costly instruments as well as long and complex experimental procedures. Instead, this study documents the application of mathematical morphology to investigate chalk microporosity from two-dimensional (2D) scanning electron microscope (SEM). Chalk samples (n = 105) have been collected from onshore quarries and offshore oil and gas reservoirs. Six chalk lithotypes are defined based on their mineralogical composition, i.e. clay and silica content, as well as the average size of chalk particles, and their apparent diagenetic impact, which appears strongly related to the mean grain size. The latter is used as a proxy for the diagenetic overprint, while the burial-diagenetic model offers a framework for the different lithotypes and their respective pore space properties. During intermediate burial ( 1000 m), pressure solution and cementation become pervasive and produce large clusters of coalescent calcite crystals (3–10 μm; mean = 5.13 μm). Total porosity is strongly reduced as a result (6–11%) while pore body and throat dimensions drop to 1.58 and 0.03 μm, respectively. A high aspect ratio (88.1) and lower proportion of rough porosity relative to total image porosity suggest that throats are proportionally more affected than pore bodies. Cementation leads to less dendritic, more globular and isolated pores. Where processes such as overpressure and oil charge have helped preserve porosity during deep burial (20–30%), pore and throat dimensions were locked to moderately high values (>2.0 and 0.1 μm, respectively), even in silica- and clay-rich chalk. Since the geometry of microporosity exerts a major control on fluid flow, reservoir modelling and recovery predictions could benefit from a better understanding on the geological controls on chalk microporosity. Not only can mathematical morphology quantify pore space properties that are fundamental in pore network and flow modelling, but by being applicable on large datasets, it could provide a new insight into the geological modifications of chalk microporosity during burial.

Reconstruction of 3D porous media using multiple-point statistics based on a 3D training image

To date many methods of constructing porous media have been proposed. Among them, the multiple-point statistics (MPS) method has a unique advantage in reconstructing 3D pore space because it can reproduce pore space of long-range connectivity. The Single Normal Equation Simulation (SNESIM) is one of most commonly used algorithms of MPS. In the SNESIM algorithm, the selection of training image is vital because it contains the basic pore structure patterns. In the previous reconstructions of 3D porous media using SNESIM, a 2D slice was usually employed as the training image. However, it is difficult for a 2D slice to contain complex 3D pore space geometry and topology patterns. In this paper, a 3D training image is used in order to provide more realistic 3D pore structure features. Besides, a multi-grid search template is applied for the purpose of capturing the pore structures of different scales and speeding up the reconstruction process. Two sandstone cores are taken as test examples and the 3D porous media are reconstructed. The two-point correlation function, pore network structure parameters and absolute permeability are applied as the evaluation indexes to validate the accuracy of the reconstructed models. The comparison result shows that the reconstructed models are in good agreement with the real model obtained by X-ray computed tomography scanning in the pore throat geometry and topology and transport property, which justifies the reliability of the proposed method.

Formation factor in Bentheimer and Fontainebleau sandstones: Theory compared with pore-scale numerical simulations

Accurate quantification of formation resistivity factor F (also called formation factor) provides useful insight into connectivity and pore space topology in fully saturated porous media. In particular the formation factor has been extensively used to estimate permeability in reservoir rocks. One of the widely applied models to estimate F is Archie's law (F=ϕ−m in which ϕ is total porosity and m is cementation exponent) that is known to be valid in rocks with negligible clay content, such as clean sandstones. In this study we compare formation factors determined by percolation and effective-medium theories as well as Archie's law with numerical simulations of electrical resistivity on digital rock models. These digital models represent Bentheimer and Fontainebleau sandstones and are derived either by reconstruction or directly from micro-tomographic images. Results show that the universal quadratic power law from percolation theory accurately estimates the calculated formation factor values in network models over the entire range of porosity. However, it crosses over to the linear scaling from the effective-medium approximation at the porosity of 0.75 in grid models. We also show that the effect of critical porosity, disregarded in Archie's law, is nontrivial, and the Archie model inaccurately estimates the formation factor in low-porosity homogeneous sandstones.

Scale-dependent diffusion anisotropy in nanoporous silicon

Nanoporous silicon produced by electrochemical etching of highly B-doped p-type silicon wafers can be prepared with tubular pores imbedded in a silicon matrix. Such materials have found many technological applications and provide a useful model system for studying phase transitions under confinement. This paper reports a joint experimental and simulation study of diffusion in such materials, covering displacements from molecular dimensions up to tens of micrometers with carefully selected probe molecules. In addition to mass transfer through the channels, diffusion (at much smaller rates) is also found to occur in directions perpendicular to the channels, thus providing clear evidence of connectivity. With increasing displacements, propagation in both axial and transversal directions is progressively retarded, suggesting a scale-dependent, hierarchical distribution of transport resistances (“constrictions” in the channels) and of shortcuts (connecting “bridges”) between adjacent channels. The experimental evidence from these studies is confirmed by molecular dynamics (MD) simulation in the range of atomistic displacements and rationalized with a simple model of statistically distributed “constrictions” and “bridges” for displacements in the micrometer range via dynamic Monte Carlo (DMC) simulation. Both ranges are demonstrated to be mutually transferrable by DMC simulations based on the pore space topology determined by electron tomography.

Fractality of The Geysers

Heat convection at pore-scale, which is strongly dependent on the topology of pore space, remains poorly understood for geothermal reservoirs. This is despite fundamental advances made in modeling heat transfer in nano- and micro-scale conduits. With this in mind, we analyze the fractality of the pore space of The Geysers to fully characterize its topology. We consider circular and slit-like throat geometries to represent aspect ratios close to unity and infinity, respectively. Our study shows that the effective length of pore space follows the general fractal rule. This study can have major implications for understanding heat convection at pore-scale by presenting a representative fractal model for The Geysers.