Complex Resistivity Data Research Articles

Experimental Study of Complex Resistivity Characteristics of a Sandstone Reservoir under Different Measurement Conditions

Due to the variability of fluid properties and saturation of reservoirs, large differences in formation temperature and pressure, and the diversity of rock and mineral compositions, the petrophysical response of reservoirs is often complex. This study explored a new method of reservoir fluid identification and evaluation based on the complex resistivity response characteristics of sandstone reservoirs under different measurement conditions. The complex resistivity of the five sandstone samples was measured under normal temperature and pressure and variable pressure, temperature, and formation conditions and under different oil saturations. Furthermore, the reservoir was comprehensively analyzed and evaluated based on the mineral composition, porosity, and permeability parameters. The results show that the resistivity of the sandstone increases logarithmically with pressure and oil saturation but decreases logarithmically with temperature and depth. The polarizability decreases slightly with increasing pressure and increases slightly with increasing temperature. With increasing depth, the polarizability decreases obviously, and with increasing oil saturation, the polarizability decreases moderately. Under different measurement conditions, the complex resistivity data for the sandstone reservoir and the IP parameters extracted through inversion are regular. The results of this study provide a new method for the identification and evaluation of complex reservoir fluids and have important reference value.

An Integrated Approach of Spectral Induced Polarization and Electromagnetic Coupling in Exploration Geophysics

Spectral induced electric polarization provides useful information on geoelectric parameters, which may allow mineral discrimination in exploration geophysics. Electromagnetic coupling between current and potential electrodes equally contributes to understanding the geology but represents the main source of noise in spectral induced electric polarization surveys. In this article, we propose an integrated analysis of these two phenomena in the context of complex resistivity data in order to evaluate their role in exploration geophysics taking into account their specificities. Deepening previous studies of forward modeling and inversion of mutual impedance in the frequency domain, in this present approach, we have employed an expanded apparent complex resistivity function, which includes the inductive effect in its parameters. We developed an integrated inversion of this function using the very fast simulated annealing and least-squares methods to estimate the geoelectric parameters. We also performed tests and applications on synthetic and real data, discussing the benefits of using the proposed complex resistivity model. The approach was applied to data from three profiles of the Copper District of Vale do Curaçá, Bahia, Brazil. The results show that it is possible to distinguish between spectral induced polarization and induction in terms of geoelectric parameters distributed in pseudosections and to identify patterns and behaviors for each of them. They constitute an important step toward mineral discrimination via analysis of analogous circuit parameters, a fundamental tool in searching metallic ores.

Reservoir evaluation method for complex resistivity using the borehole–surface electromagnetic method: A case study of an igneous reservoir in the K exploration area, China

Electrical well-logging techniques, combined with electrical conductivity models, have been widely used to estimate oil saturation levels in hydrocarbon reservoirs. For complicated and heterogeneous petroleum reservoirs, however, evaluation results are inevitably limited by well locations. Recent studies have indicated that the borehole–surface electromagnetic method (BSEM) can detect electrical characteristics distal from a well, and it can be applied to delineate the boundaries of complicated reservoirs. Therefore, in the study described here, a new method to estimate reservoir oil saturation, based on the BSEM, has been developed. In this work, we deployed the BSEM in a designated study area, obtaining complex resistivity and polarizability data, through the constrained inversion of the re-weighted regularized conjugate gradient method. Based on the petrophysical analyses, we developed a new saturation evaluation model, composed of a parallel circuit connection between formation water and the polarization induced by the porous medium containing clay minerals. The effectiveness of the new model was verified with a synthetic dataset generated using Archie's law and the improved Dias model. We found that the target reservoir oil saturation results calculated using the new oil saturation model were in good agreement with applicable nuclear magnetic resonance log data, thus verifying the validity of this new BSEM evaluation technique.

Using a combination of genetic algorithm and particle swarm optimization algorithm for GEMTIP modeling of spectral-induced polarization data

The generalized effective-medium theory of induced polarization (GEMTIP) is a newly developed relaxation model that incorporates the petro-physical and structural characteristics of polarizable rocks in the grain/porous scale to model their complex resistivity/conductivity spectra. The inversion of the GEMTIP relaxation model parameter from spectral-induced polarization data is a challenging issue because of the highly non-linear dependency of the observed data on the model parameter and non-uniqueness of the problem. To solve these problems as well as scape the local minima of the highly complicated cost function, the genetic algorithm (GA) can be applied but it has proven to be time-intensive computationally. However, this drawback can be resolved by incorporating a faster algorithm, e.g. particle swarm optimization (PSO). The aim of this work is to investigate whether recovering the model parameter of the ellipsoidal GEMTIP model from SIP data using the combined GA and PSO algorithms is possible. To achieve this aim, we set the best calculated individuals using GA as the search space of PSO, and then the best location achieved by PSO in each iteration is assigned as the updated model parameters. The results of our research work reveal that the model parameters can effectively be recovered using the approach proposed in this paper but the time constant of a noisy data that arises from the adverse dependency of this parameter on the ellipticity of a polarizable grain. Moreover, the execution time of the ellipsoidal GEMTIP modeling of complex resistivity data can be significantly improved using the proposed algorithm.

Correlation analysis for spread-spectrum induced-polarization signal processing in electromagnetically noisy environments

In induced-polarization (IP) surveys, the raw data are usually distorted significantly by the presence of electromagnetic (EM) interferences, including cultural noise. Several methods have been proposed to improve the signal-to-noise ratio of these data. However, signal processing in an electromagnetically noisy environment is still a challenging problem. We have determined a new and simple technique based on the analysis of the correlation between the measured potential and the injected primary current signals. This processing is applied to the data acquired using a new frequency-domain IP method called the spread-spectrum induced-polarization (SSIP) approach. In this approach, we use a pseudorandom m-sequence (also called the maximum length sequence) for the injected primary current. One of the advantages of this sequence is to be essentially spectrally flat in a given frequency range. Therefore, complex resistivity can be determined simultaneously at various frequencies. A new SSIP data set is acquired in the vicinity of Baiyin mine, Gansu Province, China. The correlation between potential difference and transmitting current signals for each period can be used to assess data quality. Only when the correlation coefficient between the two signals is greater than 0.5 can the SSIP data be used for subsequent processing and tomography. We determine what threshold value should be used for the correlation coefficient to extract high-quality apparent complex resistivity data and eliminate EM-contaminated data. We then compare the pseudosections with and without using the correlation analysis. When the correlation analysis is used, the noisy data are filtered out, and the target anomaly obtained through tomography is clearly enhanced. The inversion results of the apparent complex resistivity (amplitude and phase) for the survey area are consistent with some independent geologic and drilling information regarding the position of the ore body demonstrating the effectiveness of the approach.

3D complex resistivity tomography on cylindrical models using EIDORS

ABSTRACTComplex resistivity imaging is a relatively new geophysical technique, developed in the last few decades mainly for hydrogeological and environmental applications. The aim of this work is to present an EIDORS application of the 3D complex resistivity tomography on cylindrical laboratory models. EIDORS is an open‐source numerical environment developed with the aim of sharing data and promoting collaboration between groups working in these fields. In spite of being a well‐recognised software for forward modelling and inversion for medical tomographies, EIDORS still needs to be adapted for geophysical purposes. We discuss the role played by the mesh choice and the contact impedances on the accuracy of the finite‐element solution achieved by tetrahedral elements. When a 3D tomography is performed on a standard machine with limited local memory, the dual reconstruction can help to retain a sufficient accuracy without increasing the allocated memory. Although for medical applications on the human body a linear inversion can effectively represent the slight changes in resistivity magnitude, when a subsoil has to be investigated resistivity can vary substantially. Thus we develop an algorithm to add to the non‐linear inversion for complex resistivity data, through the integration of the EIDORS basic functions. The algorithm has been validated through four synthetic examples. The reconstructed models, having a growing degree of complexity, are similar to the true ones. We highlight the role played by phase and resolution to detect the anomalies. When the dipole length is enlarged and the embedded anomalies decrease in size, the reconstruction becomes more difficult. We show that EIDORS could act as a base code for tomographic inversion of frequency‐domain data (and also of time‐domain real‐valued data) for laboratory problems, because of its high flexibility and reliability reached by the forward and inversion routines.

2D tomographic inversion of complex resistivity data on cylindrical models

ABSTRACTThe resistive and capacitive response of a multiphase subsoil can be analysed by amplitude and phase models of the electrical complex resistivity. The main goal of this work is to extend the 2D transformed formulation used for electrical site investigations for cylindrical laboratory models, solving the complex resistivity forward problem starting from the Complete Electrode Model approach. This formulation is tested by a comparison with the full 3D solution and is proven to be stable and accurate. Inversion of complex resistivity data is achieved through a Matlab interface included in the EIDORS environment, with the addition of numerous new functions. Three synthetic examples are discussed, to understand the potential and limits of this approach in comparison with the 3D inversion. Laboratory experiments on a cylindrical laboratory model with a horizontal cross‐section of 10 electrodes validated synthetic results. The model having a height of 1 m and a diameter of 500 mm is made by sand contaminated from the top by an engineered fluid with electrical properties similar to chlorinated solvents.

Effect of nanosize BaZrO3 inclusions on vortex parameters in YBa2Cu3O7−x

We report on the field dependence of the microwave complex resistivity data in YBa2Cu3O7−x/BaZrO3 films grown by PLD at various BaZrO3 content. The data, analyzed within a recently developed general framework for the mixed-state microwave response of superconductors, yield the field dependence of the fluxon parameters such as the vortex viscosity and the pinning constant. We find that pinning undergoes a change of regime when the BaZrO3 content in the target increases from 2.5 mol.% to 5 mol.%. Simultaneously, the vortex viscosity becomes an increasing function of the applied magnetic field. We propose a scenario in which flux lines are pinned as bundles, and a crossover from dilute point pins to dense c-axis correlated defects takes place between 2.5 and 5 mol.% in the BZO concentration. Our data are inconsistent with vortices occupying mainly the BaZrO3 sites at low fields, and suggest instead that vortices occupy both BaZrO3 sites and interstitials in the YBa2Cu3O7−x matrix, even at low fields.

Inversion of 2-D DC resistivity data using rapid optimization and minimal complexity neural network

Abstract. The backpropagation (BP) artificial neural network (ANN) technique of optimization based on steepest descent algorithm is known to be inept for its poor performance and does not ensure global convergence. Nonlinear and complex DC resistivity data require efficient ANN model and more intensive optimization procedures for better results and interpretations. Improvements in the computational ANN modeling process are described with the goals of enhancing the optimization process and reducing ANN model complexity. Well-established optimization methods, such as Radial basis algorithm (RBA) and Levenberg-Marquardt algorithms (LMA) have frequently been used to deal with complexity and nonlinearity in such complex geophysical records. We examined here the efficiency of trained LMA and RB networks by using 2-D synthetic resistivity data and then finally applied to the actual field vertical electrical resistivity sounding (VES) data collected from the Puga Valley, Jammu and Kashmir, India. The resulting ANN reconstruction resistivity results are compared with the result of existing inversion approaches, which are in good agreement. The depths and resistivity structures obtained by the ANN methods also correlate well with the known drilling results and geologic boundaries. The application of the above ANN algorithms proves to be robust and could be used for fast estimation of resistive structures for other complex earth model also.

A state‐space Bayesian framework for estimating biogeochemical transformations using time‐lapse geophysical data

We develop a state‐space Bayesian framework to combine time‐lapse geophysical data with other types of information for quantitative estimation of biogeochemical parameters during bioremediation. We consider characteristics of end products of biogeochemical transformations as state vectors, which evolve under constraints of local environments through evolution equations, and consider time‐lapse geophysical data as available observations, which could be linked to the state vectors through petrophysical models. We estimate the state vectors and their associated unknown parameters over time using Markov chain Monte Carlo sampling methods. To demonstrate the use of the state‐space approach, we apply it to complex resistivity data collected during laboratory column biostimulation experiments that were poised to precipitate iron and zinc sulfides during sulfate reduction. We develop a petrophysical model based on sphere‐shaped cells to link the sulfide precipitate properties to the time‐lapse geophysical attributes and estimate volume fraction of the sulfide precipitates, fraction of the dispersed, sulfide‐encrusted cells, mean radius of the aggregated clusters, and permeability over the course of the experiments. Results of the case study suggest that the developed state‐space approach permits the use of geophysical data sets for providing quantitative estimates of end‐product characteristics and hydrological feedbacks associated with biogeochemical transformations. Although tested here on laboratory column experiment data sets, the developed framework provides the foundation needed for quantitative field‐scale estimation of biogeochemical parameters over space and time using direct, but often sparse wellbore data with indirect, but more spatially extensive geophysical data sets.

Characterization of bimodal facies distributions using effective anisotropic complex resistivity: A 2D numerical study based on Cole-Cole models

Subsurface heterogeneity characteristics are of major importance in hydrologic modeling, and likely result in anisotropic electrical properties. We computed the anisotropic effective complex resistivity of 2D bimodal facies distributions numerically. Complex resistivities of individual facies are described in terms of the Cole-Cole relaxation model. First, we determined that effective DC resistivities of the distributions can be reasonably well described by power averaging the properties of individual facies. We found a clear relationship between the mixing parameter and correlation lengths of the facies distributions with respect to horizontal and vertical directions. Then, we used the power-law mixing model to invert for individual Cole-Cole model parameters by fitting predicted electrical responses to simulated spectral effective complex-resistivity data for the two perpendicular directions. Thus, it is possible to derive the electrical properties of individual facies as well as structural parameters describing bimodal facies distribution by means of a noninvasive measurement approach. In particular, anisotropy of the spectral complex-resistivity response provides information on correlation lengths of the distribution. This finding is relevant for all applications of electrical-impedance spectroscopy where anisotropy might be encountered.

CR1Dinv: A Matlab program to invert 1D spectral induced polarization data for the Cole–Cole model including electromagnetic effects

An inversion code has been constructed using Matlab, to recover 1D parameters of the Cole–Cole model from spectral induced polarization data. In a spectral induced polarization survey, impedances are recorded at various frequencies. Both induced polarization and electromagnetic coupling effects occur simultaneously over the experimental frequency bandwidth, and these become progressively more dominant when the frequency increases. We used the CR1Dmod code published by Ingeman-Nielsen and Baumgartner [2006]. This code solves for electromagnetic responses, in the presence of complex resistivity effects in a 1D Earth. In this paper, a homotopy method has been designed by the authors to overcome the local convergence problem of normal iterative methods. In addition, in order to further condition the inverse problem, we incorporated standard Gauss–Newton (or quasi-Newton) methods. Graphical user interfaces enable straightforward entering of the data and the a priori model, as well as the cable configuration. Two synthetic examples are presented, showing that the spectral parameters can be recovered from multifrequency, complex resistivity data.

Experimental Monitoring of Cr(VI) Bio-Reduction Using Electrochemical Geophysics

Many Department of Energy (DOE) sites are contaminated with highly carcinogenic hexavalent chromium (Cr(VI)). In this research, we explore the feasibility of applying complex resistivity to the detection and monitoring of microbially-induced reduction of hexavalent chromium (Cr(VI)) to a less toxic form (Cr(III)). We hope to measure the change in ionic concentration that occurs during this reduction reaction. This form of reduction promises to be an attractive alternative to more expensive remedial treatment methods. The specific goal of this research is to define the minimum and maximum concentration of the chemical and biological compounds in contaminated samples for which the Cr(VI)-Cr(III) reduction processes could be detected via complex resistivity. There are three sets of experiments, each comprised of three sample columns. The first experiment compares three concentrations of Cr(VI) at the same bacterial cell concentration. The second experiment establishes background samples with, and without, Cr(VI) and bacterial cells. The third experiment examines the influence of three different bacterial cell counts on the same concentration of Cr(VI). A polarization relaxation mechanism was observed between 10 and [Formula: see text]. The polarization mechanism, unfortunately, was not unique to bio-chemically active samples. Spectral analysis of complex resistivity data, however, showed that the frequency where the phase minimum occurred was not constant for bio-chemically active samples throughout the experiment. Significant shift in phase minima occurred between [Formula: see text] from the initiation to completion of Cr(VI) reduction. This phenomenon was quantified using the Cole-Cole model and the Marquardt-Levenberg nonlinear least square minimization method. The data suggest that the relaxation time and the time constant of this relaxation are the Cole-Cole parameters most sensitive to changes in biologically-induced reduction of Cr(VI).

Effects of Drying on the Low-Frequency Electrical Properties of Tournemire Argillites

Nearly water-saturated argillite samples (initial water content near 3.4 wt%) were cored from an undisturbed area of an underground facility of the French Institute for Radioprotection and Nuclear Safety (IRSN), located at Tournemire (Aveyron, France). These samples were subjected to the following desiccation path: (a) A desaturation phase during which the samples were dried at ambient temperature conditions, relative humidity equal to 43% in average and (b) a heating phase during which the same samples were heated at four temperature levels from 70°C up to 105°C. During both phases, the low-frequency complex resistivity (0.18Hz–12 kHz) was recorded by a four-electrode device. The amplitude of the complex resistivity was extremely sensitive to water content change. At the end of the isotherm desaturation phase, it was multiplied by a factor of 3 to 5. During the heating phase, the resistivity increased by more than two orders of magnitude compared to the initial state. The percentage of Frequency Effect shows a low sensitivity to water content changes during the desaturation stage while it increased by two orders of magnitude during the heating phase. This result confirms that low-frequency spectral signature is extremely sensitive to textural changes (i.e., thermal-induced microcracking in this case) that occurred during heating. Moreover, the complex resistivity of the samples shows a strong anisotropy (a ratio of 10 between both amplitudes measured in the perpendicular directions). The classical Cole-Cole model cannot be used to fit the experimental data obtained in the heating phase. A generalized formulation of this model is required and was successfully applied to represent the complex resistivity data.

Numerical modelling of complex resistivity effects on a homogenous half‐space at low frequencies

ABSTRACTThe many different existing models describing the spectral behaviour of the resistivity of geological materials at low frequency, combined with the lack of available field data, render the interpretation of complex resistivity (CR) data very difficult. With a recent interest in CR‐measurements for environmental applications and thanks to technological progress, the use of wide‐band frequency equipment seems promising, and it is expected to shed light on the different results among the published solutions to the electromagnetic (EM) coupling problem. We review the theory of EM‐coupling over a homogeneous half‐space with CR‐effects and study some aspects of the complex coupling function. We advocate the use of the CR‐based coupling function in the interpretation process, in order to obtain a better understanding of the physical processes involved in CR‐effects. Application of the model to real field data shows systematic good agreement in two simple cases, even over wide ranges of frequencies. Interpretation with a double Cole–Cole model is applied for comparison, and in spite of good fits to the data, large differences are observed in the interpreted low‐frequency dispersion. We conclude that the use of a second Cole–Cole model to describe EM‐coupling may corrupt the interpretation of the low‐frequency dispersion, even when only the normal range of frequencies (<100 Hz) is considered, and that the use of the actual EM‐coupling expression is essential when the goal is a better understanding of interaction between CR‐effects and EM‐coupling.

Direct inversion of the apparent complex‐resistivity spectrum

Cole‐Cole model parameters are widely used to interpret electrical geophysical methods and are obtained by inverting the induced polarization (IP) spectrum. This paper presents a direct inversion method for parameter estimation based on multifold least‐squares estimation. Two algorithms are described that provide optimal parameter estimation in the least‐squares sense. Simulations demonstrate that both algorithms can provide direct apparent spectral parameter inversion for complex resistivity data. Moreover, the second algorithm is robust under reasonably high noise.

Interpretation of multifrequency complex resistivity data for a layered Earth model

A method is proposed for interpreting data obtained by measuring mutual impedances of dipole-dipole configurations on the surface of a layered Earth. Such data are assumed to be available over a sufficiently broad band of temporal frequencies and dipoles interspacing. For a given grounded transmitting dipole, two receiving grounded dipoles of selected different orientations are used. The electromagnetic circuit coupling is effectively cancelled at any given frequency by appropriate Bessel transform operation on the measured complex impedances versus spacing. The next step is to infer the complex resistivities of the Earth's layers at each frequency. From such inferred data at a sufficient number of spot frequencies, the dispersive behavior of the resistivity of each layer is deduced. This proposed procedure is demonstrated by applying it to computer-simulated data on a two-layer Earth with encouraging results.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Forward and Inverse Cole-Cole modelling in the analysis of frequency domain electrical impedance data

An interactive computer program to model frequency domain complex resistivity data has been developed using the Cole?Cole model. This simple, well established model, based on the mathematical response of an electrical circuit, is effective in modelling the electrical impedance of a mineralized rock, particularly sulphide mineralization. Model parameters: Resistivity R; chargeability, m; frequency dependence, c; and time constant r, are estimated by forward modelling. An inversion technique, ridge regression, is used to obtain the parameters corresponding to the best fit curve. The program, written in Turbo Basic, is designed to run on any IBM PC/XT/AT or close compatible. It incorporates a well structured approach with ease of operation, employing simple to use menus and descriptive error messages. Input is via the keyboard or through a file system. Output is tabular and graphical, showing the measured and predicted data, and a least squares error estimate.

Physical model for the complex resistivity of the Earth

We show that the empirical Cole-Cole model used to inter-pret low-frequency complex resistivity data does have a physical basis. Such a configuration is a homogeneous conductor loaded by a sparse distribution of spheroidal metallic particles with a polarisable surface layer which can be characterised by an interface impedance.

Electrical conductivity/microstructural relationships in aged CaO and CaO + MgO partially-stabilized zirconia

Samples of CaO and CaO + MgO partially-stabilized zirconia (PSZ), solution treated at 1830° C and aged at 1400° C to produce a fine dispersion of tetragonal precipitates, were subjected to a.c. electrical measurements in the frequency range 10−3 to 106 Hz, at a temperature of 300° C. The component of resistivity due to the grain interiors, obtained from plots of complex resistivity, showed three stages of behaviour, attributed to equilibration, coarsening and finally transformation of a tetragonal precipitate into a more resistive monoclinic phase. A model of the electrical response of a dispersion of particles was used to estimate the conductivities of the constituent phases of the PSZ ceramic and to simulate the complex resistivity data obtained.