Electrical Formation Factor Research Articles

Relating permeability and electrical conductivity in partially saturated porous media by means of the Johnson–Koplik–Schwartz characteristic length

SUMMARY In this work, we revisit the seminal concept of Johnson–Koplik–Schwartz (JKS) length Λ, that is a characteristic length representing an effective pore size which controls various transport-related properties of porous media, such as, the permeability and the electrical conductivity. We present a novel closed-form equation that predicts the behaviour of Λ in partially saturated media, for different saturation states. Using previous models in the literature that predict the intrinsic and relative electrical conductivities under partially saturated conditions, we infer the JKS length Λ and the electrical formation factor F as functions of water saturation and properties associated with the pore-size distribution of the probed porous medium. The proposed method permits to estimate the effective permeability and the relative permeability directly from electrical conductivity measurements, thus opening new-avenues for the remote characterization of partially saturated media. We believe that this new model will prove useful for various characterization and modelling applications from reservoir (CO2 or hydrogen storage) to vadose zone studies.

Relationship between Chloride Migration, Bulk Electrical Conductivity and Formation Factor of Blended Cement Pastes

Abstract This study investigates the links between the non-steady-state chloride migration coefficient, the bulk electrical conductivity and the formation factor of blended cement paste specimens. 18 different binders were tested: two Portland cements (low- and high-alkali) in combination with limestone filler, fly ash, calcined clay, two biomass ashes, sewage sludge ash and crushed brick, as well as two Portland composite cements. In addition, the latter and the low-alkali Portland cement were tested in concrete as well for comparison. Mixes with high-alkali cement showed better resistance to chloride transport, and the effect of supplementary cementitious materials was found to be strongly linked with their reactivity. Moreover, the results showed a clear correlation of the migration coefficient with the bulk electrical conductivity and, to a lesser extent, with the formation factor. However, these relationships are strongly influenced by the methods used to determine conductivities and they need to be validated for higher maturities. Finally, the results suggested a fairly good correspondence between the results obtained on paste and concrete.

Dependence of electrical conduction on pore structure in reservoir rocks from the Beibuwan and Pearl River Mouth Basins: A theoretical and experimental study

The electrical conduction of reservoir rocks is crucial for estimating hydrocarbon and water saturation. The dependence of the electrical formation factor as a key parameter of electrical conduction on pore structure is analyzed through theoretical development, petrophysical experiments, error analysis, core-scale displacement experiments, and pore-scale numerical simulations. Through the tortuous fractal capillary bundle pore model, the electric formation factor is theoretically a function of three pore structure parameters: porosity, tortuosity fractal dimension, and pore fractal dimension. Through rock-electrical experiments from 46 reservoir rocks from the Beibuwan and Pearl River Mouth Basins, Thanh’s model can give a satisfactory performance with a suitable value for the ratio of minimum to maximum pore radius. Porosity-based formation factor models, including classical Archie’s law, have an unacceptable error at high formation factor. Our formation factor model provides better predictions with an error factor of ±10. The Archie’s cementation exponent can be expressed as the average tortuous degree of electrical conduction paths. The dependences of hydraulic and electrical conductions on pore structure are distinctly different. Hydraulic conductance has obvious pore-size dependence, the dominant flow channel, and threshold pressure, which are affected by displacement order. However, the case of electrical conduction is the opposite, in which electrical conduction has no dominant channel, and does not reflect the pore-size information under the same porosity.

Formation factors for a class of deterministic models of pre-fractal pore-fracture networks

The main aim of this paper is to reveal effects of fractal features on the formation factors associated with different transport processes in scale invariant pore-fracture networks. Accordingly, we explore a class of deterministic infinitely ramified networks associated with pre-fractal standard Sierpinski carpets (including Sierpinski cubes and inverse Menger sponges). The focus is placed on the effects of network ramification, connectivity, and loopiness on the transport streamline constriction and tortuosity of transmission paths. The differences between the formation factors associated with the diffusibility, electrical conductivity, and hydraulic permeability are elucidated. Explicit expressions for the constrictivity and formation factors of deterministic pre-fractal networks are derived. In this regard, we stress that the electrical formation factor obeys the Archie law only if the random walk in the pre-fractal pore-fracture network is recurrent. We also note that the Archie's exponent can be either equal to, or less than the power-law exponent characterizing the scaling behavior of diffusibility. The notion of the structural formation factor is introduced. The values of scaling exponents characterizing the formation factors associated with different transport properties of the model networks are found to be within the ranges of field observations.

Impact of accelerating admixtures on the electrical properties of ordinary portland cement pastes

Electrical resistivity is a reliable concrete testing tool that agencies, researchers, and contractors have adopted to quickly assess the transport properties of cementitious systems. Like other electrically-based tests, resistivity measurements can be influenced, among other factors, by the ions dissolved in the pore solution of cementitious systems. To isolate the pore solution component, some researchers have suggested the implementation of the formation factor, which accounts for the system's pore solution. Among the mixture constituents potentially affecting the pore solution, accelerating admixtures are thought to have significant effects. Due to the lack of pore solution data, the community has come to mistrust any electrically-based test performed on concrete mixtures that include this kind of admixture. This study aims to improve the understanding of the effect that four different types of accelerating admixtures have on the electrical properties of an ordinary portland cement paste system. The data show that the influence of accelerating admixtures on the pore solution lessens over time. Moreover, development rates in the degree of hydration and the porosity of the system are found to be significantly affected by the chemistry of the admixture. Both electrical resistivity and formation factor are found to have high correlation with the total porosity of systems with and without accelerating admixtures.

Real-time monitoring the electrical properties of pastes to map the hydration induced microstructure change in cement-based materials

The effect of the supplementary materials (SCMs) on the moisture content and ion diffusivity at different hydration time is important for the service life modelling of modern concrete. This study designed a simple but valid method to monitor the microstructure change in pastes during hydration. A procedure easy to implement was proposed to detect the water content in pastes. The electrical conductivity of pore solution was evaluated by the evaporable water content in pastes and chemical composition in the binders. Results show that the electrical properties of pastes (conductivity, formation factor and its growth rate) can effectively indicate the hydration reactivity of binder, pore connectivity and volume of pore solution in the hardened pastes. The effect of water-binder ratio and SCMs on the structure of pastes are effectively indexed by the formation factor which is the conductivity of pore solution divided by that of paste. The inflection point of average growth rate of formation factor is a good index for the final setting of pastes. The relation between volume of evaporable water and formation factor is well demonstrated by the extended percolation theory. The real-time monitored electrical conductivity and formation factor of pastes can be used to calculate the chloride migration coefficient in hardened cement pastes.

Estimating biofuel contaminant concentration from 4D ERT with mixing models

We present the results of a lab-scaled feasibility study to assess the performance of electrical resistivity tomography for detection, characterization, and monitoring of fuel grade ethanol releases to the subsurface. Further, we attempt to determine the concentration distribution of the ethanol from the electrical resistivity tomography data using mixing-models. Ethanol is a renewable fuel source as well as an oxygenate fuel additive currently used to replace the known carcinogen methyl tert-butyl ether; however, ethanol is preferentially biodegraded and a cosolvent. When introduced to areas previously impacted by nonethanol-based fuels, it will facilitate the persistence of carcinogenic fuel compounds like benzene and ethylbenzene, as well as remobilize them to the ground water. These compounds would otherwise be retained in the soil column undergoing active or passive remediation processes such as soil vapor extraction or natural attenuation. Here, we introduce ethanol to a saturated Ottawa sand in a tank instrumented for four-dimensional geoelectrical measurements. Forward model results suggest pure phase ethanol released into a water saturated silica sand should present a detectable target for electrical resistivity tomography relative to a saturated silica sand only. We observe the introduction of ethanol to the closed hydraulic system and subsequent migration over the duration of the experiment. One-dimensional and three–dimensional temporal data are assessed for the detection, characterization, and monitoring of the ethanol release. Results suggest one-dimensional geoelectrical measurements may be useful for monitoring a release, while three-dimensional geoelectrical field imaging would be useful to characterize, monitor, and design effective remediation approaches for an ethanol release, assuming field conditions do not preclude the application of geoelectrical methods. We then attempt to use predictive mixing models to calculate the distribution of ethanol concentration within the measurement domain. For this study we examine four different models: a nested parallel mixing model, a nested cubic mixing model, the complex refractive index model (CRIM), and the Lichtenecker-Rother (L-R) model. The L-R model, modified to include an electrical formation factor geometry term, provided the best agreement with expected EtOH concentrations.

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.

Electrical formation factor versus porosity coarse-scale transforms from microscopic digital images: Example-based study

The question posed in this work is whether and how elemental data obtained on small and often sub-representative fragments of natural rock can be exploited to generate a physically valid transform between two physical properties useable at a coarser spatial scale, such as the reservoir scale. The pair of such properties targeted here is the porosity and electrical formation factor. We use the process-based upscaling to prove, by example, that a coarse-scale transform between these two variables can be obtained from a dataset computed on microscopic digital volumes of natural rock, including unconsolidated sand, medium-porosity sandstones, and low- and high-porosity carbonates. This upscaling method is based on constructing a coarse-scale (effective) rock volume from the elemental volumes with a subsequent simulation of a relevant physical process in this effective object, specifically the electrical current. A numerical simulation of Laplace equation governing electrical current is used to compute the effective resistivity. The effective porosity is simply the arithmetically averaged porosity of the elements. By using hundreds of random realizations of the effective object, we generate tight formation factor versus porosity transforms for each of the natural rock samples under examination. Because the proof offered here is by-example, it is not general. However, the method offered is general and, as such, can be used to address the same question as posed for various situations.

Correlation of Electrical Resistivity and Formation Factor with Chloride and Water Permeability of Recycled Aggregate Concrete

Among the methods of determining the permeability of concrete, electrical resistivity tests are the most rapid and one of the simplest techniques. Several studies have found a strong correlation between electrical resistivity and the other permeation properties, such as water permeability and rapid chloride penetrability. However, most of these comparisons used conventional concrete in which natural aggregates were used. Concrete with alternative aggregates such as recycled aggregate concrete (RAC) shows a different microstructure and higher permeability than conventional concrete. Thus, the existing correlations might not be applicable for concrete with recycled aggregates. This research measures the electrical resistivity (AASHTO T 358 & AASHTO TP 119), formation factor, rapid chloride permeability (ASTM C 1202), and water permeability (Germann water permeability test: GWT) of RAC. High chloride ion permeability was observed in all the samples. On the other hand, some samples were found to have low water permeability. It was observed that RAC could be evaluated as water-resistant when a low water/cement ratio was used. The bulk resistivity, surface resistivity, and formation factor were all found to be strongly correlated with rapid chloride permeability test and GWT measurements. Compared with the established correlation from other studies using conventional concrete, RAC shows a higher slope of electrical resistivity versus chloride permeability regression line. On the other hand, RAC can be assumed to have low water permeability when the bulk resistivity, surface resistivity, and formation factor are greater than 5.2 kΩ-cm, 9.6 kΩ-cm, and 528, respectively.

Formation Factor Concept for Non-Destructive Evaluation of Concrete's chloride diffusion coefficients

Estimation of chloride diffusion coefficient (Drcm) is an integral part of service life assessment of vulnerable concrete structures due to chloride induced corrosion. This study focuses on the suitability of an alternate non-destructive, low-cost approach of estimating diffusion coefficients through electrical resistivity and formation factor as a replacement of conventional destructive migration tests. The variation in formation factor for 60 concrete mixes with different Supplementary Cementitious Materials (SCM) types (fly-ash, slag) and proportions (0–40%) along with multiple mix parameters (w/cm ratio and target slump) were studied after 365 days of curing. Drcm values predicted from formation factor approach were found to be in close proximity to the coefficients obtained from migration test but however, required certain modifications to ensure conservative estimations. Tentative modification factors were developed for each binder separately as well as for all blended mixes. Based on the obtained factored Drcm values using the modification factor, it was demonstrated that it is possible to ensure reliable and conservative estimation of corrosion initiation time of any mixes without the requirement of destructive testing.

Electrical formation factor of clean sand from laboratory measurements and digital rock physics

Abstract. Electrical properties of rocks are important parameters for well-log and reservoir interpretation. Laboratory measurements of such properties are time-consuming, difficult, and impossible in some cases. Being able to compute them from 3-D images of small samples will allow for the generation of a massive amount of data in a short time, opening new avenues in applied and fundamental science. To become a reliable method, the accuracy of this technology needs to be tested. In this study, we developed a comprehensive and robust workflow with clean sand from two beaches. Electrical conductivities at 1 kHz were first carefully measured in the laboratory. A range of porosities spanning from a minimum of 0.26–0.33 to a maximum of 0.39–0.44, depending on the samples, was obtained. Such a range was achieved by compacting the samples in a way that reproduces the natural packing of sand. Characteristic electrical formation factor versus porosity relationships were then obtained for each sand type. 3-D microcomputed tomography images of each sand sample from the experimental sand pack were acquired at different resolutions. Image processing was done using a global thresholding method and up to 96 subsamples of sizes from 2003 to 7003 voxels. After segmentation, the images were used to compute the effective electrical conductivity of the sub-cubes using finite-element electrostatic modelling. For the samples, a good agreement between laboratory measurements and computation from digital cores was found if a sub-cube size representative elemental volume (REV) was reached that is between 1300 and 1820 µm3, which, with an average grain size of 160 µm, is between 8 and 11 grains. Computed digital rock images of the clean sands have opened a way forward for obtaining the formation factor within the shortest possible time; laboratory calculations take 5 to 35 d as in the case of clean and shaly sands, respectively, whereas digital rock physics computation takes just 3 to 5 h.

Variations in Elastic and Electrical Properties of Crustal Rocks With Varying Degree of Microfracturation

AbstractThis work aims at investigating the effect of varying degrees of microfracturing on the joint elastic and electrical transport properties of rocks. Different crustal rocks were subjected to thermal treatment, expected to induce microfracturing, up to different target temperatures from 100 up to 900 °C. The rocks bulk and pore volumes, P and S wave velocities, and frequency‐dependent electrical impedance were measured before and after the treatment. As the temperature of treatment increased, P and S wave velocities and the electrical formation factor drop and pore and bulk volumes increase. As indicated by the microscopic images, this is consistent with the creation of microcracks. These created microcracks do not affect the properties in the exact same manner, and a strong effect of the initial porosity is observed for electrical formation factor. Extrapolating to low‐frequency field‐scale measurements in water‐saturated reservoir rocks highlights an interesting observation: Both seismic and electrical properties at the field scale might highlight similar variations with increasing damage in all rocks. The maximum amount of decrease expected for all rocks is about 1 order of magnitude in electrical formation factor and 40% decrease in P and S wave velocities. Finally, temperature proved to affect very differently the rocks of varying porosity and mineral content, in ways not fully covered by existing works. Porosity, by increasing the matrix compressibility, damps the degree of microfracturing and crack opening. The distinct behavior in calcite‐pure marble evidences a dominance of anisotropic of thermal expansion over isotropic expansion mismatch.

Electrical Resistivity and Formation Factor of Air-Entrained Concrete

Electrical Resistivity and Formation Factor of Air-Entrained Concrete

On Permeability Prediction From Complex Conductivity Measurements Using Polarization Magnitude and Relaxation Time

AbstractGeophysical length scales determined from complex conductivity (CC) measurements can be used to estimate permeability when the electrical formation factor F is known. Two geophysical length scales have been proposed: (1) the specific polarizability normalized by the imaginary conductivity and (2) the time constant multiplied by a diffusion coefficient . The parameters and account for the control of fluid chemistry and/or varying minerology on the geophysical length scale. We evaluated the predictive capability of two CC permeability models: (1) an empirical formulation based on or normalized chargeability and (2) a mechanistic formulation based on . The performance of the CC models was evaluated against measured ; and further compared against that of well‐established estimation equations that use geometric length scales. Both CC models predict permeability within one order of magnitude for a database of 58 sandstone samples, with the exception of samples characterized by high pore volume normalized surface area . Variations in and likely contribute to the poor model performance for the high samples, which contain significant dolomite. Two observations favor the implementation of the ‐based model over the ‐based model for field‐scale estimation: (1) a limited range of variation in relative to and (2) field measurements are less time consuming to acquire relative to . The need for a reliable field‐estimate of limits application of either model, in particular the model due to a high power law exponent associated with .

Connectivity, formation factor and permeability of 2D fracture network

The purpose of this paper is to investigate the effects of fracture connectivity and length distributions on the electrical formation factor, F, of random fracture network using percolation theory. We assumed that the matrix was homogeneous and low-permeable, but the connectivity and length distributions of fracture system were randomly variable. F of fracture network is analyzed via finite element method. The main result is that: different from the classical percolation “universal” power law for porous-type rocks, F of fracture network obeys a normalized “universal” scaling relation using the length-scale 〈l〉/L (〈l〉 is fracture mean length, and L is the domain size). Our proposed formation factor model, derived from the normalized “universal” scaling relationship, is valid in fracture network with constant fracture length and length distributions, showing that the normalized “universal” scaling law is independent of fracture patterns. The normalized scaling relation is also successfully used to derive the permeability model of 2D random fracture network using the previously published dataset, which obtained better fitting results than before.

Thermal conductivity of partially saturated microstructures

The growing importance of tight reservoirs exacerbates the necessity of pore-scale studies to characterize porous media from the pore-level point of view. Accurate prediction of pore-scale effective thermal and electrical conductivities leads to proper thermophysical and petrophysical characterization of partially saturated media. In this paper, a numerical framework is offered to predict electrical and thermal conductivities of two-phase saturated microstructures. The immiscible displacement scenarios within the microporosities are conducted utilizing a direct pore morphology-based technique; a set of rules to construct the fluid-fluid interfaces under capillary-driven flows. Subsequently effective thermal and electrical conductivity curves are predicted using steady state diffusion equation. Two sets of microstructures are used as the pore space geometries; real and synthetic. The real media under consideration include binary images of oil/water-wet sandstone and carbonate formations and the fluid systems contain steam-oil and water-oil equilibriums. The swelling spheres algorithm is adapted to generate two-dimensional granular synthetic media based on a typical particle size distribution of Alberta's unconsolidated oil sand. The result packages, including thermal diffusivity and conductivity, electrical conductivity, formation factor, and apparent diffusion coefficient are generated and discussed considering rock types and fluid configurations. The thermal and electrical conductance of well-connected consolidated microstructures appear to be weak functions of water saturation and are mainly controlled by porosity and solid phase configuration.

Directional-Permeability Assessment in Formations With Complex Pore Geometry With a New Nuclear-Magnetic-Resonance-Based Permeability Model

Summary This paper proposes a new method for directional-permeability assessment with nuclear-magnetic-resonance (NMR) measurements. Conventional techniques for permeability assessment from NMR measurements include empirical correlations such as SDR (Schlumberger-Doll-Research) and Coates models. However, carbonate rocks are known for lack of good correlations between pore-body-size and pore-throat-size, which makes it challenging and often unreliable to estimate permeability from NMR T2 (spin-spin relaxation time) distribution in carbonate formations with complex pore structure. It also was proposed that conventional permeability models can be improved by incorporating an estimated pore-connectivity factor. However, none of the previously introduced techniques reflects the anisotropic characteristics of rock permeability. The new NMR-based directional-permeability model, introduced in this paper, incorporates a directional pore-connectivity factor into a conventional NMR-based permeability model. We introduce two approaches to quantify the directional pore-network connectivity of rock samples with pore-scale images. The first approach calculates directional pore connectivity in 3D pore-scale images with a topological technique. The second approach combines image analysis and electrical formation factor. The new NMR-based permeability model enables assessment of rock permeability in any desired direction. We successfully calibrated and tested the introduced NMR-based permeability model on carbonate, sandstone, and sandpack samples with complex pore geometry or anisotropic permeability. The anisotropic permeability used for calibration and test purposes was obtained by the lattice Boltzmann method (LBM) simulations on microcomputed tomography (CT) images of rock samples. The comparison between the permeability estimates with our new NMR model and conventional NMR models (e.g., SDR and Coates models) demonstrated that the NMR-based directional-permeability model significantly improves assessment of rock permeability, by reflecting rock's anisotropic characteristics and minimizing calibration efforts. The outcomes of this research can significantly improve permeability assessment in complex carbonate reservoirs and anisotropic sandstone reservoirs, and can be extended further to organic-rich mudrock formations.

Application of critical path analysis for permeability prediction in natural porous media

Critical path analysis (CPA), originally developed to describe electrical conductance in semiconductors, has been shown recently to hold some promise in describing transport properties of porous media. I applied some previously developed concepts in CPA and percolation theory to predict permeability in a suite of sandstone, carbonate, and clay-rich samples. I assumed that the pore sizes in my samples exhibited fractal scaling and expressed the electrical formation factor as a function of porosity using universal scaling from percolation theory. The resulting CPA permeability predictions match the measured values very well. In addition, I show how considering the scale-dependence of the percolation threshold yields two characteristic length scales for transport properties: the critical pore size, and the sample size. This work suggests that the CPA framework is appropriate for describing transport properties of natural porous media, and provides a theoretical basis for understanding the permeability of tight rocks like shale in which laboratory permeability measurements are difficult.

Pore Space Connectivity and the Transport Properties of Rocks

Pore connectivity is likely one of the most important factors affecting the permeability of reservoir rocks. Furthermore, connectivity effects are not restricted to materials approaching a percolation transition but can continuously and gradually occur in rocks undergoing geological processes such as mechanical and chemical diagenesis. In this study, we compiled sets of published measurements of porosity, permeability and formation factor, performed in samples of unconsolidated granular aggregates, in which connectivity does not change, and in two other materials, sintered glass beads and Fontainebleau sandstone, in which connectivity does change. We compared these data to the predictions of a Kozeny-Carman model of permeability, which does not account for variations in connectivity, and to those of Bernabe et al . (2010, 2011) model, which does [Bernabe Y., Li M., Maineult A. (2010) Permeability and pore connectivity: a new model based on network simulations, J. Geophys. Res. 115 , B10203; Bernabe Y., Zamora M., Li M., Maineult A., Tang Y.B. (2011) Pore connectivity, permeability and electrical formation factor: a new model and comparison to experimental data, J. Geophys. Res. 116 , B11204]. Both models agreed equally well with experimental data obtained in unconsolidated granular media. But, in the other materials, especially in the low porosity samples that had undergone the greatest amount of sintering or diagenesis, only Bernabe et al. model matched the experimental data satisfactorily. In comparison, predictions of the Kozeny-Carman model differed by orders of magnitude. The advantage of the Bernabe et al. model was its ability to account for a continuous, gradual reduction in pore connectivity during sintering or diagenesis. Although we can only speculate at this juncture about the mechanisms responsible for the connectivity reduction, we propose two possible mechanisms, likely to be active at different stages of sintering and diagenesis, and thus allowing the gradual evolution observed experimentally.