Electrical Tortuosity Research Articles

Effect of microvariability on electrical rock properties

SUMMARY In petrophysics, physical rock properties are typically established through laboratory measurements of individual samples. These measurements predominantly relate to the specific sample and can be challenging to associate with the rock as a whole since the physical attributes are heavily reliant on the microstructure, which can vary significantly in different areas. Thus, the obtained values have limited applicability to the entirety of the original rock mass. To examine the dependence of petrophysical measurements based on the variable microstructure, we generate sets of random 2-D microstructure representations for a sample, taking into account macroscopic parameters such as porosity and mean grain size. For each microstructure produced, we assess the electrical conductivity and evaluate how it is dependent on the microstructure’s variability. The developed workflow including microstructure modelling, finite-element simulation of electrical conductivity as well as statistical and petrophysical evaluation of the results is presented. We show that the methodology can adequately mimic the physical behaviour of real rocks, showing consistent emulation of the dependence of electrical conductivity on connected porosity according to Archie’s law across different types of pore space (microfracture, intergranular and vuggy, oomoldic pore space). Furthermore, properties such as the internal surface area and its fractal dimension as well as the electrical tortuosity are accessible for the random microstructures and show reasonable behaviour. Finally, the possibilities, challenges and meshing strategies for extending the methodology to 3-D microstructures are discussed.

Tortuosity of pore channels in tight rocks as a key parameter in fluid flow ability

Tortuosity is a significant parameter in porous materials analysis. Not only, when it comes to rocks or soils but also cellular materials, alloys or cells, the multiple definitions exist for tortuosity and several purposes. Geometrical tortuosity describes the pore network paths; on the other hand thermal, diffusional, electrical and hydraulic tortuosity refers to the transport processes in the pore network. Computed X-ray tomography (CT) is the best solution in tortuosity estimation, thanks to the 3D images. In particular, computed X-ray tomography, together with mercury porosimetry (MICP), pulse- and pressure-decay permeability methods (PDP), as well as electrical parameter measurements (EPM), links and expands the information about the tortuosity into the greater meaning. The geological material was composed of tight, low-porosity and low-permeability gas-saturated rocks cored from the present depth of deposition below 3000 m, containing different lithologies, as sandstones, mudstones, limestones, and dolomites. The research presents the novel approach in the identification and analysis of the main pore channels based on 3D CT images. Algorithm of the central axis identifies and analyzes the whole main flow path and calculates tortuosity. High correlation was observed between the tortuosity and Swanson parameter from mercury porosimetry data. Moreover, the high correlation was detected between the tortuosity and saturation exponent from electrical parameter measurement in analyzed tight low-porosity and low-permeability deposits. Multilinear regression (MLR) allows estimating absolute permeability taking CT, MICP and EPM parameters into consideration. Combination of these parameters in one equation with high determination coefficient gives credence in estimating preliminary absolute permeability (PDP) based on the data which is executed as standard core analysis (MICP and EPM) and data from the non-invasive method (CT).

An Unsaturated Hydraulic Conductivity Model Based on the Capillary Bundle Model, the Brooks‐Corey Model and Waxman‐Smits Model

AbstractSoil unsaturated hydraulic conductivity (K), which depends on water content (θ) and matric potential (ψ), exhibits a high degree of variability at the field scale. Here we first develop a theoretical hydraulic‐electrical conductivity (σ) relationship under low and high salinity cases based on the capillary bundle model and Waxman and Smits model which can account for the non‐linear behavior of σ at low salinities. Then the K‐σ relationship is converted into a K(θ, ψ) model using the Brooks‐Corey model. The model includes two parameters c and γ. Parameter c accounts for the variation of the term (λ + 2)/(λ + 4) where λ is the pore size distribution parameter in the Brooks‐Corey model, and the term m‐n where m and n are Archie's saturation and cementation exponents, respectively. Parameter γ is the sum of the tortuosity factor accounting for the differences between hydraulic and electrical tortuosity and Archie's saturation exponent. Based on a calibration data set of 150 soils selected from the UNSODA database, the best fitting log(c) and γ values were determined as −2.53 and 1.92, −4.39 and −0.14, −5.01 and −1.34, and −5.79 and −2.27 for four textural groups. The estimated log10(K) values with the new K(θ, ψ) model compared well to the measured values from an independent data set of 49 soils selected from the UNSODA database, with mean error (ME), relative error (RE), root mean square error (RMSE) and coefficient of determination (R2) values of 0.02, 8.8%, 0.80 and 0.73, respectively. A second test of the new K(θ, ψ) model using a data set representing 23 soils reported in the literature also showed good agreement between estimated and measured log10(K) values with ME of −0.01, RE of 9.5%, RMSE of 0.77 and R2 of 0.85. The new K(θ, ψ) model outperformed the Mualem‐van Genuchten model and two recently published pedo‐transfer functions. The new K(θ, ψ) model can be applied for estimating K under field conditions and for hydrologic modeling without need for soil water retention curve data fitting to derive a K function.

Electrical Tortuosity Index: A New Approach for Identifying Rock Typing to Enhance Reservoir Characterization Using Well-Log Data of Uncored Wells.

The world is gradually moving toward a severe energy crisis, with an ever-increasing demand for energy overstepping its supply. Therefore, the energy crisis in the world has shed important light on the need for enhanced oil recovery to provide an affordable energy supply. Inaccurate reservoir characterization may lead to the failure of enhanced oil recovery projects. Thus, the accurate establishment of reservoir characterization techniques is required to successfully plan and execute the enhanced oil recovery projects. The main objective of this research is to obtain an accurate approach that can be used to estimate rock types, flow zone indicators, permeability, tortuosity, and irreducible water saturation for uncored wells based on electrical rock properties that were obtained from only logging tools. The new technique is obtained by modifying the Resistivity Zone Index (RZI) equation that was presented by Shahat et al. by taking the tortuosity factor into consideration. When true formation resistivity (Rt) and inverse porosity (1/Φ) are correlated on a log-log scale, unit slope parallel straight lines are produced, where each line represents a distinct electrical flow unit (EFU). Each line's intercept with the y-axis at 1/Φ = 1 yields a unique parameter specified as the Electrical Tortuosity Index (ETI). The proposed approach was validated successfully by testing it on log data from 21 logged wells and comparing it to the Amaefule technique, which was applied to 1135 core samples taken from the same reservoir. Electrical Tortuosity Index (ETI) values show marked accuracy for representing reservoir compared with Flow Zone Indicator (FZI) values obtained by the Amaefule technique and Resistivity Zone Index (RZI) values obtained by the Shahat et al. technique, with correlation coefficients of determination (R2) values equal to 0.98 and 0.99, respectively. Hence, by using the new technique, the Flow Zone Indicator, permeability, tortuosity, and irreducible water saturation were estimated and then compared with the obtained results from the core analysis, which showed a great match with the R2-values of 0.98, 0.96, 0.98, and 0.99, respectively.

Comparative Study on Hydraulic and Electrical Transport Properties of Carbonate Rocks Based on Rock Typing

The permeability (k) and electrical resistivity of carbonate rocks with similar porosity (ϕ) may exhibit multiple orders of magnitude differences due to the diversity of pore types and the multiscale characteristics of pore size. As a result, traditional permeability-porosity and resistivity-porosity models usually have strong limitations when applied to carbonate reservoirs, let alone evaluate permeability from electrical resistivity. In this study, a new rock typing parameter named relative transport quality index (RTQI) is proposed to categorize rock samples using permeability and formation resistivity factor (F). Samples with similar RTQI values tend to have similar relative capacities of hydraulic and electrical transport. Subsequently, the classification performance and microscopic differences between RTQI and other rock typing indices including flow zone indicator (FZI), current zone indicator (CZI), and electrical quality index (EQI) were compared and discussed based on the reported petrophysical data of 316 carbonate rock samples. The results indicate that the RTQI method significantly reduces the scattering of k and F by dividing the samples into distinct groups, and each RTQI group corresponds to a special k–F correlation with a high determination coefficient. However, the number of rock types identified by different rock typing indices is different, meaning that samples belonging to the same rock type in the k–F plot of the RTQI method may be classified into different rock types in the k–ϕ plot of the FZI method and the F–ϕ plots of the CZI and EQI methods, which may be caused by the microscopic differences of rock typing parameters. Different from the strong dependence of FZI on hydraulic tortuosity and CZI/EQI on electrical tortuosity, RTQI is mainly dominated by the ratio of electrical tortuosity to hydraulic tortuosity. Additionally, in view of the good correlation between petrophysical data after rock typing, two workflows are proposed to estimate the hydraulic and electrical parameters of carbonate rocks from log data.

Electrical, Diffusional, Hydraulic, and Geometrical Tortuosity Anisotropy Quantification Using 3D Computed Tomography Scan Image Data

Summary Sedimentary rocks display complex spatial distribution of both pore space and solid components, impacting the directional dependence of physical phenomena such as electrical conduction, fluid flow, heat transfer, and molecular diffusion. The complexity of the pore space is often quantified by the concept of tortuosity, which measures the sinuosity of the connecting paths in the pore space. Tortuosity is an important quantity in formation evaluation as it impacts petrophysical properties such as permeability and formation factor. However, the existence of various techniques can lead to nonuniqueness in assessment of tortuosity. Furthermore, spatial variation of the solid components of the rocks occurring at the core-scale domain reflected in the connectivity and distribution of the minerals is typically not quantified. The objectives of this paper are (a) to quantify tortuosity and tortuosity anisotropy of porous media through estimation of electrical, diffusional, hydraulic, and geometrical tortuosity at the pore scale and core scale and (b) to compare electrical, diffusional, hydraulic, and geometrical tortuosity. We estimate tortuosity in the pore space of microcomputed tomography (micro-CT) scan images and in the most connected and abundant solid phase of whole-core CT scan images. We conduct numerical simulations of electric potential distribution, diffusion, and fluid flow and velocity distribution to estimate electrical, diffusional, and hydraulic tortuosity, respectively. To calculate geometrical tortuosity, we use the segmented pore space from micro-CT scan images to extract a pore network model and compute the shortest path of all opposing pores of the samples. Finally, tortuosity values obtained with each technique are used to assess the anisotropy of the samples. We applied the documented workflow to core- and pore-scale images. The CT scan images in the core-scale domain belong to a siliciclastic formation. Micro-CT scan images in the pore-scale domain were obtained from Berea Sandstone, Austin Chalk, and Estaillades limestone formations. We observed differences in estimates of direction-dependent electrical, diffusional, hydraulic, and geometrical tortuosity for both types of images. The highest numerical differences were observed when comparing streamline electrical and hydraulic tortuosity with diffusional tortuosity. The observed differences were significant in anisotropic samples. Differences in tortuosity estimates can impact the outcomes of rock physics models for which tortuosity is an input. The documented comparison provides insight in the selection of techniques for tortuosity estimation. Use of core-scale image data provides semicontinuous estimates of tortuosity and tortuosity anisotropy, which are typically not attainable using pore-scale images. Additionally, the semicontinuous tortuosity anisotropy estimates from whole-core CT scan images provide a tool for selection of best locations to take core plugs.

Effect of Binder Content on Silicon Microparticle Anodes for Lithium-Ion Batteries

Electrode formulation directly influences the resulting composite electrode structure and properties, ultimately impacting the electrode performance and durability. Although there have been many significant advancements in the development and understanding of novel and effective binder materials for silicon anodes1–4, few studies report more than one formulation, or ratio of active material to conductive additive to polymeric binder5,6.In this study, we focus on investigating the impact of polyimide binder weight ratio in silicon microparticle electrodes. Electrode adhesion to the current collector, cohesion, porosity, electrical resistivity, and electrical tortuosity were characterized in pristine electrodes. These properties were then correlated to electrode cycle life and rate performance in Si-NMC622 full cells. We show that there is an optimal binder weight ratio for a given type of polymer binder. Increasing binder weight ratio improves electrode adhesion and cohesion, resulting in improved cycle life. However, increased binder weight ratio decreases electrical conductivity and porosity, leading to poorer silicon particle utilization, capacity, and rate performance.In the formulations we investigated, the silicon to carbon weight ratio was fixed, while binder content was varied. The optimal binder ratio maximizes silicon particle utilization, achieving 1084 ± 25 mAh/gSi gravimetric capacity after the formation cycles. When binder content was increased three-fold, the discharge capacity decreased by 27%, which was correlated to lower electrode porosity and lower initial coulombic efficiency. We hypothesize that insufficient porosity limits lithium-ion access to the silicon particles, thus reducing the capacity at the given C-rate. We also hypothesize that the decreased coulombic efficiency indicates that the polyimide binder contributes to the consumption of available lithium.In contrast, capacity retention improved with additional binder content. This is partly due to increased electrode cohesion with the added binder and partly due to lower overall capacity in the silicon particles, resulting in less volumetric strain. In electrodes with the binder content reduced by one-third, capacity retention dropped dramatically. We hypothesize that there is a lower limit of binder content, below which the electrode lacks sufficient structural integrity to withstand volume strains during cycling.These findings point towards important design principles for the optimization of binder content in silicon electrode formulations.

Estimation of the Size and Type of Porosity in an Albian Carbonate Reservoir of the Campos Basin, Southeastern Brazil

Abstract —The Albian carbonates of the Quissama Formation in the Campos Basin, southeastern Brazil, are important oil reservoirs. They make part of a carbonate platform that formed along the eastern coast of Brazil and the western coast of Africa during the Albian, which resulted in the opening of the South Atlantic Ocean. Subsequently, this reservoir was subjected to different postdepositional diagenetic processes. The present study utilized geophysical well logs to estimate the porosity of this reservoir, based on density, neutron porosity, and sonic logs. The estimates do not show good results when compared with the laboratory measurements. Then, exploring the fact that these logs are obtained with different physical principles, a multiple linear regression and an artificial neural network with Bayesian stochastic approach were applied, which resulted in a better porosity estimate. As porosity is a petrophysical parameter considered significant in the characterization of reservoirs, it was used, hereafter, to estimate permeability and water saturation of the reservoir, applying empirical equations. From there, it was not enough just to estimate the porosity, but was necessary to know what type it is. For this purpose, the concepts of the electrical formation factor, cementation coefficient, tortuosity, and anisotropy were used. With them, the zones with primary intergranular and interparticle porosity as well as secondary porosity, such as fractures, fissures, and vugs, were mapped. It was concluded that, with studies of this type, it is also possible to identify the connected and nonconnected porosities, which permits estimation of the effective porosity along the well.

Application of electrical rock typing for quantification of pore network geometry and cementation factor assessment

Rock typing with its various applications reduces the required time and cost for petrophysical analysis by categorizing similar rocks into distinct groups. Rock typing is divided into different categories, one of which, is electrical rock typing. An application of static electrical rock typing is cementation factor prediction which significantly affects fluid saturation estimation. Many factors, such as pore geometry, affect cementation factor in various means. Hence, achieving an explicit correlation to compute it as a function of these affecting factors is difficult. However, examining petrophysical properties which influence cementation factor is feasible. In this study, two definitions of formation resistivity factor are merged to achieve the cementation factor correlation as a function of effective cross-sectional area, porosity, and electrical tortuosity. To determine effective cross-sectional area and electrical tortuosity in wellbore through a time-efficient and inexpensive method, electrical rock typing is used. The results of this study reveal that Kozeny's factor is perfectly correlated with effective cross-sectional area and electrical tortuosity. Therefore, effective cross-sectional area and electrical tortuosity are computed throughout the wellbore. Moreover, investigating the relation between flowing porosity and rock capacity for transmitting electricity shows that they are directly related. Cementation factor and stagnant porosity also have a direct relationship. The findings of this study aid the assessment of porous media for attaining a clear understanding of petrophysical properties relationships, and their impact on porous media capability for storing and transferring fluid and transmitting electricity. Determining petrophysical properties continuously in wellbore leads to a better comparison between different segments of the reservoir. Regarding the fact that all presented methods are mainly based on log responses, they are easy to apply. However, the availability of enough samples is essential to initiate the analysis. • Obtaining effective cross-sectional area continuously through wellbore. • Developing a method to determine electrical tortuosity through wellbore. • High EQI Samples have a higher flowing porosity, and a lower cementation factor. • As electrical tortuosity increases, m rises due to reduction in flowing porosity.

Correlating rock packing index, tortuosity, and effective cross-sectional area with electrical quality index

In Archie's formula, cementation factor (m) is an important parameter that plays a key role in calculating fluid saturation and characterizing reservoir. Rock geometrical attributes, e.g. electrical tortuosity, particle's specific surface area, packing index, effective cross-sectional area, and porosity, considerably affect m. Natural heterogeneities of reservoir rocks cause enormous challenges in determining the aforementioned properties in particular cross-sectional area, electrical tortuosity, and packing index. To overcome this challenge while avoiding time-consuming experiments, categorizing rocks based on an appropriate criterion is a proper solution. In this study, rock classification was performed using an electrical criterion called Electrical Quality Index (EQI), which indicates the quality of rock for transmitting electricity. Since this capacity is controlled by rock geometry, EQI must be related to petrophysical properties. To correlate EQI with the effective cross-sectional area (ψ), packing index (PI), and electrical tortuosity (τe), 23 samples were analyzed. First, samples were categorized into four electrical rock types (ERTs) with different ranges of EQI. Then, the average ψ, PI, and τe of samples belong to each ERT was computed and plotted versus the average EQI of the corresponding ERT. It was ascertained that there are clear linear relations between ψ, PI, τe and EQI average values with determination coefficient values of over 0.96. This implies considerably low dispersion around the straight trendlines that provides linear functions for predicting ψ, PI, and τe of new ERTs. The developed method is a prediction module for purposes like assessing rock geometry, and fluid saturation in hydrocarbon reservoirs. Applying this algorithm to a big dataset including a high number of samples belong to a particular reservoir leads to the better assessment of reservoir heterogeneity and rock quality. Using an analogy between electrical and hydraulic rock typing, rock geometry is investigated without the necessity of performing costly and time-consuming experiments.

Importance of Microstructure in Carbonate Rocks: Laboratory and 3D-Imaging Petrophysical Characterization

Carbonate rocks are considered to be essential reservoirs for human development, but are known to be highly heterogeneous and difficult to fully characterize. To better understand carbonate systems, studying pore-scale is needed. For this purpose, three blocks of carbonate rocks (chalk, enthrocal limestone, and dolomite) were cored into 30 samples with diameters of 18 mm and lengths of 25 mm. They were characterized from pore to core scale with laboratory tools. These techniques, coupled with X-ray micro-tomography, enable us to quantify hydrodynamic properties (porosity, permeability), elastic and structural properties (by acoustic and electrical measurements), pore distribution (by centrifugation and calculations). The three rocks have similar properties to typical homogeneous carbonate rocks but have specific characteristics depending on the rock type. In the same rock family, sample properties are different and similarities were established between certain measured properties. For example, samples with the same hydrodynamic (porosity, permeability) and structural (formation factor, electrical tortuosity) characteristics may have different elastic properties, due to their cohesion, which itself depends on pore size distributions. Microstructure is understood as one of the essential properties of a rock and thus must be taken into account to better understand the initial characteristics of rocks.

Pore-Scale Modeling of Electrokinetics in Geomaterials

Pore-scale finite-volume continuum models of electrokinetic processes are used to predict the Debye lengths, velocity, and potential profiles for two-dimensional arrays of circles, ellipses and squares with different orientations. The pore-scale continuum model solves the coupled Navier–Stokes, Poisson, and Nernst–Planck equations to characterize the electro-osmotic pressure and streaming potentials developed on the application of an external voltage and pressure difference, respectively. This model is used to predict the macroscale permeabilities of geomaterials via the widely used Carmen–Kozeny equation and through the electrokinetic coupling coefficients. The permeability results for a two-dimensional X-ray tomography-derived sand microstructure are within the same order of magnitude as the experimentally calculated values. The effect of the particle aspect ratio and orientation on the electrokinetic coupling coefficients and subsequently the electrical and hydraulic tortuosity of the porous media has been determined. These calculations suggest a highly tortuous geomaterial can be efficient for applications like decontamination and desalination.

Electric energy dissipation and electric tortuosity in electron conductive cement-based materials

The emergence of multifunctional cement-based materials in the construction industry has the potential to shift the paradigm from strength-only performance to new functionalities enabled by electron conducting capabilities in one of the most material- and energy-intensive industry sectors worldwide. To enable such developments, we present results of a hybrid experimental-theoretical investigation of the electrical conductivity and resistive (Joule) heating of highly heterogeneous nanocarbon (nCB)--cement-based composites (pastes and mortars). By analogy with diffusivity, we find that electrical conductivity is determined by the electric tortuosity of a ``volumetric wiring'' permeating a highly heterogeneous matrix from percolation to saturation. From a combination of electrical conductivity and Joule heat rate measurements, we show that the electric energy dissipation at the origin of the Joule heating originates from spatial electric-field fluctuations, reminiscent of the fluctuation-dissipation theorem. We report that these fluctuations---in first order---are well captured by functional relations of the electric tortuosity of the composite material, and synthesize these observations into a first-order dissipation-tortuosity model. We suggest that harvesting the benefits of electron conducting cement-based materials, such as resistive heating, electromagnetic shielding, and energy storage, will ultimately focus on settling the competition between conductor concentration and electric tortuosity. Given the global environmental footprint of concrete, the results open venues for the sustainable development of concrete for existing and emerging green technology applications.

Tortuosity of kerogen pore structure to gas diffusion at molecular- and nano-scales: A molecular dynamics simulation

The tortuosity of kerogen pore structures is a vital parameter in the quantification of the gas diffusion ability and production of shale reservoirs. In this study, we perform a molecular dynamics simulation on the gas diffusion in the molecular- and nano-scale pores of shale kerogen to evaluate the tortuosity of the kerogen pore structure to gas diffusion. A novel diffusion model is proposed to evaluate the tortuosity by considering gas adsorption affinity, transportation regime, and probe gas atomic size. The results indicate that the tortuosity of the kerogen pore structure to gas diffusion is not a constant; instead, it highly depends on the probe gas atomic size and gas adsorption ability. The diffusive tortuosity is overestimated when the effect of gas adsorption ability is ignored. We find that the electrical tortuosity is lower than the diffusive tortuosity. This confirms that the tortuosity is underestimated when considering a purely geometric effect.

Calculation of Cementation Exponent and Multiplier Using P-Wave Velocity and Porosity for Sandstone Reservoirs

The formation resistivity factor is important as reservoir property because it is required to calculate volume of hydrocarbon in reservoir rocks. It depends on Winsauer’s multiplier (a) which is a function of fluid tortuosity and cementation exponent (m). Cementation exponent is a major source of uncertainty in the calculation of hydrocarbon saturation for a given reservoir condition. A small error in the cementation exponent and/or multiplier could give a huge error in the formation factor and have serious consequences. The empirical relationships between reservoir parameters such as P-wave velocity and formation factor depend on local conditions such as environment of deposition, rock type, mineralogy, and diagenesis. For promoting hydrocarbon reservoir development; numerous petrophysical parameters are required. Some of them are measured but the others are sometimes assumed such as cementation exponent (m) and the multiplier (a) of Archie’s general equation. The present work offers some empirical models and charts to be used for resolving the cementation exponent and the Winsauer’s multiplier. Thirty-nine core samples obtained from the Upper Cretaceous reservoir zones; Gebel Nazzazat, Western central Sinai (Raha, Wata and Matulla formations) were laboratory analyzed for porosity, density, electrical resistivity, and ultrasonic wave velocity. They are composed mainly of clean sandstone, with some limestone and dolomitic limestone. This paper introduces seven innovative charts to estimate formation factor parameters using electrical quality index concept (EQI). They are classified according to the value of multiplier (a = 0.5 – 4.0) which is a function of electric tortuosity. The first chart estimates the multiplier (a) from P-wave velocity. The other six charts estimate the cementation exponent (from m = 1.0 up to 3.0) using fractional porosity and P-wave velocity at the previously determined multiplier (a). The present charts are based on a reliable empirical relationship (R2 = 0.82) connecting elastic-electrical parameters as formation resistivity factor and P-wave velocity. The model reliability verification is accomplished using 82 laboratory measurements of porosity and P-wave velocity for sandstone core samples from the Bahariya Formation side by side with 51 empirical estimated multiplier and cementation exponent for different lithofacies (sandstones and carbonates) and obtained from several geographic locations.

Electrical conductivity and tortuosity of solid foam: Effect of pore connections.

Numerical and analytical methods at both micro- and mesoscales are used to study how the electrical resistivity and the high-frequency tortuosity of solid foam are modified by the presence of membranes that partially or totally close the cell windows connecting neighbor pores. Finite-element-method simulations are performed on two pores connected by a single-holed membrane and on well-ordered Kelvin foam. For two pores connected by a single-holed membrane, we show that the equation for pore access resistance obtained by Sahu and Zwolak [Phys. Rev. E 98, 012404 (2018)2470-004510.1103/PhysRevE.98.012404] can predict, after a few modifications, the electrical resistivity at the membrane scale for a large range of membrane apertures. Considering these analytical results, we build a pore-network model by using two kinds of conductances at the pore scale: interpore conductance and intrapore conductance. Local interpore resistances govern foam electrical conductivity at small membrane aperture size, but when the membrane aperture has the same order of magnitude as the pore size, the intrapore resistances are no longer negligible. An important success of this pore-network model is that it can be used to study the effects of percolation on the foam electrical conductivity by using pore-network simulations on larger samples containing a few thousand pores and having different proportions of closed membrane randomly distributed over the sample. The tortuosity is found to be drastically larger than one in foam containing membranes with small apertures or a significant fraction of closed membranes.

(Invited) Impact of Mesoscale Morphology on Electrode Performance through Multi-Physics Simulations

While lithium-ion battery electrodes are manufactured in large-scale, high-speed, roll-to-roll manufacturing processes, it is the morphology of the particle and conductive binder structures that greatly affect macroscale properties and can vary significantly as a function of manufacturing conditions. This relationship is particularly true in the extremely fast (dis)charge environments relevant for electrification of our vehicle fleet, where the short time scales probe ever smaller length scales and increase the impact of ionic and charge transport limitations. To explore the process-structure-property relationship, we employ mesoscale finite element simulations of the three-phase particle-conductive binder-electrolyte composite of NMC cathodes. Particle and conductive binder domain mesostructures are derived from both x-ray computed tomography imaging and simulated using discrete element methods. The Conformal Decomposition Finite Element Method is applied to create conformal three-phase finite element discretizations of these mesostructures. Effective properties including electrical conductivity, tortuosity, and mechanical modulus are calculated and compared to experimentally measured values. Coupled electrochemical-mechanical simulations of cathode discharge are performed and validated against half-cell experimental data. We focus on how the conductive binder domain morphology affects electrode performance. Sandia National Laboratories is a multi-mission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

Permeability Prediction in Rocks Experiencing Mineral Precipitation and Dissolution: A Numerical Study

AbstractIn this study, we focus on the electrical tortuosity‐based permeability model k = reff2/8F (reff is an effective pore size, and F is the formation factor) and analyze its applicability to rocks experiencing mineral precipitation and dissolution. Two limiting cases of advection‐dominated water‐rock reactions are simulated, that is, the reaction‐limited and transport‐limited cases. At the pore scale, the two precipitation/dissolution patterns are simulated with a geometrical model and a phenomenological model. The fluid and electric flows in the rocks are simulated by directly solving the linear Stokes equation and Laplace equation on the representative elementary volume of the samples. The numerical results show that evolutions of k and F differ significantly in the two limiting cases. In general, the reaction‐limited precipitation/dissolution would result in a smooth variation of k and F, which can be roughly modeled with a power function of porosity ϕ with a constant exponent. In contrast, the transport‐limited precipitation/dissolution mostly occurs near the pore throats where the fluid velocity is high. This induces a sharp change in k and F despite a minor variation in ϕ. The commonly used power laws with constant exponents are not able to describe such variations. The results also reveal that the electrical tortuosity‐based permeability prediction generally works well for rocks experiencing precipitation/dissolution if reff can be appropriately estimated, for example, with the electrical field normalized pore size Λ. The associated prediction errors are mainly due to the use of electrical tortuosity, which might be considerably larger than the true hydraulic tortuosity.

The effect of various lengths of pores and throats on the formation resistivity factor

Pore geometry, quantified by the length and size of the pore space, affects the electrical resistivity of the porous media. However, the length described by the geometrical tortuosity and pore topology effect on the resistivity of the model does not thoroughly consider the existing pore geometrical models, which only investigate the pore size, throat length and throat size of the models. A modified capillary model including a pore body and several throats derived the formation factor from the coordination number, the cross-sectional area ratio and geometrical tortuosity of the pores and throats in the model. The derived relationship between the formation factor and porosity of the capillary model compared with the formation factor versus porosity for the various rock types was shown in a plot. The geometrical tortuosity of each rock type almost followed the electrical tortuosity of the related rock type, and the electrical tortuosity was larger than the geometrical tortuosity caused by the variation in the size of the pore and throat. For low porosity, the resistivity of the real porous media was lower than the resistivity of the Archie equation due to the low values of the pore-to-throat cross-sectional area ratio and geometrical tortuosity. The sandstones and interparticle carbonates presented a porosity exponent close to 2.0 and an electrical tortuosity from 1.5 to 4.0 on the plot of the porosity exponent versus electrical tortuosity. The fractured carbonate showed a porosity exponent from 1.0 to 1.6 and an electrical tortuosity ranging from 1.0 to 3.0, while the vuggy carbonates were widely distributed, with a porosity exponent larger than 2.0 and an electrical tortuosity ranging from 2 to 8. This new model correlates the formation factor and porosity to the combination of the coordination number with the geometrical tortuosity and the throat and pore cross-sectional area ratios, thus enhancing the understanding of the pore geometry and topology effect on the electrical resistivity of a porous media with various pore types.

Mass diffusivity determination of various building materials based on inverse analysis of relative humidity evolution at the back face of a sample

In this study, we use a novel method to determine the mass diffusion coefficients of hygroscopic materials. The experiment involves subjecting one face of the sample to relative humidity (RH) variations over time and measuring the RH at the back face. The imposed RH and temperature are measured during the experiment, and they are used as boundary conditions in a comprehensive computational code to address heat and mass transfer in porous media. This new method is utilized to characterize the following building materials: autoclave aerated concrete, plaster, poplar wood, pine wood, medium-density fiberboard and low-density fiberboard. This paper provides the details regarding the determination of the sorption isotherms of the selected materials that are required for the determination of mass diffusivity. The obtained electrical tortuosity values are compared with geometrical tortuosity values determined via microtomography and three-dimensional image processing. The agreement between the two tortuosity values is applicable only for porous media with narrow pore size distribution.