Spatial Distribution Of Electrical Resistivity Research Articles

Nanoparticle Assisted EOR during Sand-Pack Flooding: Electrical Tomography to Assess Flow Dynamics and Oil Recovery.

Silica nanoparticles have been shown to exhibit many characteristics that allow for additional oil to be recovered during sand-pack flooding experiments. Additionally various imaging techniques have been employed in the past to visually compare flooding procedures including x-ray computed tomography and magnetic resonance imaging; however, these techniques require the sample to be destroyed or sliced after the flooding experiment finishes. Electrical resistance tomography (ERT) overcomes these limitations by offering a non-destructive visualization method allowing for online images to be taken during the flooding process by the determination of spatial distribution of electrical resistivity, thus making it suitable for sand-packs. During the scope of this research a new sand-pack system and methodology was created which utilized ERT as a monitoring tool. Two concentrations, 0.5 wt% and 1.0 wt%, of SiO2 nanoparticles were compared with runs using only brine to compare the recovery efficiency and explore the ability of ERT to monitor the flooding process. Electrical resistance tomography was found to be an effective tool in monitoring local recovery efficiency revealing 1.0 wt% SiO2 to be more effective than 0.5 wt% and brine only runs during the scope of this research. A new method involving the slope function in excel was used to compare the effects of nanofluids on resistivity trends also revealing information about the rate of recovery against time. SiO2 nanofluid recovery mechanisms such interfacial tension reduction and viscosity enhancement were then considered to explain why the nanofluids resulted in greater oil recovery.

Interpretation of deep directional resistivity measurements acquired in high-angle and horizontal wells using 3-D inversion

The interpretation of resistivity measurements acquired in high-angle and horizontal wells is a critical technical problem in formation evaluation. We develop an efficient parallel 3-D inversion method to estimate the spatial distribution of electrical resistivity in the neighbourhood of a well from deep directional electromagnetic induction measurements. The methodology places no restriction on the spatial distribution of the electrical resistivity around arbitrary well trajectories. The fast forward modelling of triaxial induction measurements performed with multiple transmitter–receiver configurations employs a parallel direct solver. The inversion uses a pre-conditioned gradient-based method whose accuracy is improved using the Wolfe conditions to estimate optimal step lengths at each iteration. The large transmitter–receiver offsets, used in the latest generation of commercial directional resistivity tools, improve the depth of investigation to over 30 m from the wellbore. Several challenging synthetic examples confirm the feasibility of the full 3-D inversion-based interpretations for these distances, hence enabling the integration of resistivity measurements with seismic amplitude data to improve the forecast of the petrophysical and fluid properties. Employing parallel direct solvers for the triaxial induction problems allows for large reductions in computational effort, thereby opening the possibility to invert multiposition 3-D data in practical CPU times.

Solution of the Time-Domain Inverse Resistivity Problem in the Model Reduction Framework Part I. One-Dimensional Problem with SISO Data

Many time-domain problems in engineering applications can be described by means of parameter-dependent time-invariant dynamic systems. We are interested in parameter estimation, by fitting available transient measurements using the nonlinear least square method. As the main application, we consider the control source electromagnetic (CSEM) method of geophysical exploration governed by the diffusion Maxwell system, where the unknown parameters describe the spatial distribution of electrical resistivity. We propose a novel model reduction approach for constructing an efficient approximation of the Jacobian. The reduction is based on subspace projection of the state variable, and it allows us to split the time and space dependence of the derivative. We examine several popular rational Krylov subspaces and single out the $H_2$-optimal subspace that not only minimizes the approximation error but completely annuls its influence on the inversion result. Preliminary numerical experiments with a simplified one-dimensional, single-input/single-output CSEM setting are reported to validate our strategy.

First in situ tests of a new electrostatic resistivity meter

If field applications of the electrostatic method are limited to roughly the first ten metres due to the necessity of staying in a low‐induction number domain, the possibilities it opens in urban area surveying, dry hole resistivity logging, non‐destructive testing and laboratory studies of the complex resistivity justify the design of a new multi‐frequency resistivity meter presenting a very low‐input capacitance and high‐phase sensitivity. After a first series of sample measurements in the laboratory, the new resistivity meter was tested in two different field contexts: the mapping of building remains in a Gallo‐Roman archaeological site under a flat meadow and the assessment of the thickness of anthropogenic layers in a town. The first test allowed a direct comparison with previous galvanic resistivity measurements and proved a very good agreement between the magnitude and spatial distribution of electrical resistivity. The second test established its reliable measuring abilities in a disturbed environment.

Effects of Surfactant-Emulsified Oil-Based Mud on Borehole Resistivity Measurements

SummaryWe quantify the influence of oil-based mud (OBM)-filtrate invasion and formation-fluid properties on the spatial distribution of fluid saturation and electrical resistivity in the near-wellbore region. The objective is to appraise the sensitivity of borehole resistivity measurements to the spatial distribution of fluid saturation resulting from the compositional mixing of OBM and in-situ hydrocarbons.First, we consider a simple two-component formulation for the oil phase (OBM and reservoir oil) wherein the components are first-contact miscible. A second approach consists of adding water and surfactant to a multicomponent OBM invading a formation saturated with multiple hydrocarbon components. Simulations also include presence of irreducible, capillary-bound, and movable water. The dynamic process of OBM invasion causes component concentrations to vary with space and time. In addition, the relative mobility of the oil phase varies during the process of invasion because oil viscosity and oil density are both dependent on component concentrations.Presence of surfactants in the OBM is simulated with a commercial adaptive implicit compositional formulation that models the flow of three-phase multicomponent fluids in porous media. Simulations of the process of OBM invasion yield 2D spatial distributions of water and oil saturation that are transformed into spatial distributions of electrical resistivity. Subsequently, we simulate the corresponding array-induction measurements assuming axial-symmetric variations of electrical resistivity.We perform sensitivity analyses on field measurements acquired in a well that penetrates a clastic formation and that includes different values of density and viscosity for mud filtrate and formation hydrocarbon. These analyses provide evidence of the presence of a high-resistivity region near the borehole wall followed by a low-resistivity annulus close to the noninvaded resistivity region. Such an abnormal resistivity annulus is predominantly caused by high viscosity contrasts between mud filtrate and formation oil. The combined simulation of invasion and array-induction logs in the presence of OBM invasion provides a more reliable estimate of water saturation, which improves the assessment of in-place hydrocarbon reserves.

Time-Lapse Variations of Multi-Component Electrical Resistivity Measurements Acquired In High-Angle Wells

Measurements of electrical conductivity anisotropy are becoming increasingly common in LWD and open-hole environments. At the same time, field experience indicates that invasion and time of logging can have a significant effect on multi-component induction measurements acquired in high-angle wells, specifically in the presence of highly permeable formations and large fluid density and viscosity contrasts. Some efforts have been made to study these effects, but the actual spatial distribution of fluid saturation due to invasion has not been considered previously. We use a commercial multiphase fluid-flow simulator to reproduce invasion behavior in high-angle wells. Simulations provide an effective and reliable environment to study time-lapse effects of different geometrical and petrophysical parameters on the ensuing spatial distribution of fluid saturation. The study considers the effects of both water- and oil-base muds invading hydrocarbon-bearing formations in interbedded sand-shale sequences. Simulations show that gravity segregation causes off-centered and asymmetric spatial distributions of electrical resistivity in high-angle wells. Further, no-flow boundary conditions at impermeable shale boundaries cause high local concentrations of mud-filtrate. These effects can vary significantly with time. Depending on the time of measurement acquisition, three-dimensional (3D) effects due to invasion can distort multi-component apparent resistivity estimates. Consequently, inversion techniques should not be blindly used to synthesize all the measurements into estimates of conductivity anisotropy. It is necessary that 3D effects, including those due to invasion, be diagnosed in the analysis prior to estimating anisotropic conductivity parallel and perpendicular to bedding plane. Our work suggests that cross-coupled components of opposite sign and non-monotonic time variations in the coplanar components could diagnose time dependent invasion effects on multi-component induction measurements.

Estimation of Dry-Rock Elastic Moduli Based on the Simulation of Mud-Filtrate Invasion Effects on Borehole Acoustic Logs

Summary Reliable estimates of dry-rock elastic properties are critical to the accurate interpretation of the seismic response of hydrocarbon reservoirs. We describe a new method for estimating elastic moduli of rocks in-situ based on the simulation of mud-filtrate invasion effects on resistivity and acoustic logs. Simulations of mud-filtrate invasion account for the dynamic process of fluid displacement and mixing between mud-filtrate and hydrocarbons. The calculated spatial distributions of electrical resistivity are matched against resistivity logs by adjusting the underlying petrophysical properties. We then perform Biot-Gassmann fluid substitution on the 2D spatial distributions of fluid saturation with initial estimates of dry-bulk (kdry) modulus and shear rigidity (µdry) and a constraint of Poisson's ratio (?d) typical of the formation. This process generates 2D spatial distributions of compressional and shear-wave velocities and density. Subsequently, sonic waveforms are simulated to calculate shear-wave slowness. Initial estimates of the dry-bulk modulus are progressively adjusted using a modified Gregory-Pickett (1963) solution of Biot's (1956) equation to estimate a shear rigidity that converges to the well-log value of shear-wave slowness. The constraint on dynamic Poisson's ratio is then removed and a refined estimate of the dry-bulk modulus is obtained by both simulating the acoustic log (monopole) and matching the log-derived compressional-wave slowness. This technique leads to reliable estimates of dry-bulk moduli and shear rigidity that compare well to laboratory core measurements. Resulting dry-rock elastic properties can be used to calculate seismic compressional-wave and shear-wave velocities devoid of mud-filtrate invasion effects for further seismic-driven reservoir-characterization studies.

Three-dimensional electrical resistivity imaging of a gold heap

A case study is presented for an electrical resistivity geophysical survey, conducted on a gold leach pad of low-grade ore. The electrical resistivity method maps the spatial distribution of electrical resistivity, which is an intrinsic property of material that measures the resistance of electrical current flow through a medium. The property is influenced by moisture content, ionic strength of the porewater, and mineralization. The geophysical method was applied to the leach pad to discern patterns of high and low moisture from past infiltration into the heap. A total of 12 survey lines were run in parallel over an 8 ha portion of the pad. The results showed that the high electrical resistivity areas, which are likely related to low moisture, could be explained by the physics of unsaturated fluid flow or evapotranspiration. The low electrical resistivity areas were thought to be related to high moisture from preferential flow along highly permeable regions of the heap. Validation of electrical resistivity was accomplished by correlating co-located geophysical data and rock samples of moisture content and total gold concentration. On an individual point-by-point basis, the correlation between the two datasets was low, due to the mismatch in measurement scales of the two characterization methods. Averaged resistivity data within discrete bins of the independent variable (rock sample), however, produced high correlations and empirical models were developed from a linear regression of averaged behavior.

Fast 2D inversion of large borehole EM induction data sets with an efficient Fréchet-derivative approximation

In addition to reliability and stability, the efficiency and expediency of inversion methods have long been a strong concern for their routine applications by well-log interpreters. We have developed and successfully validated a new inversion method to estimate 2D parametric spatial distributions of electrical resistivity from array-induction measurements acquired in a vertical well. The central component of the method is an efficient approximation to Fréchet derivatives where both the incident and adjoint fields are precomputed and kept unchanged during inversion. To further enhance the overall efficiency of the inversion, we combined the new approximation with both the improved numerical mode-matching method and domain decomposition. Examples of application with synthetic data sets show that the new methodis computer efficient and capable of retrieving original model re-sistivities even in the presence of noise, performing equally well in both high and low contrasts of formation resistivity. In thin resistive beds, the new inversion method estimates more accurate resistivities than standard commercial deconvolution software. We also considered examples of application with field data sets that confirm the new method can successfully process a large data set that includes 200 beds in approximately [Formula: see text] of CPU time on a desktop computer. In addition to 2D parametric spatial distributions of electrical resistivity, the new inversion method provides a qualitative indicator of the uncertainty of estimated parameters based on the estimator’s covariance matrix. The uncertainty estimator provides a qualitative measure of the nonuniqueness of estimated resistivity parameters when the data misfit lies within the measurement error (noise).

Assessment of Permeability from Well Logs Based on Core Calibration and Simulation of Mud-Filtrate Invasion

This paper describes the application of a new methodology to estimate the permeability of clastic rock formations based on numerical simulation of the physics of mud-filtrate invasion. The methodology assumes a key well with a complete suite of well logs and laboratory core measurements of porosity, permeability, capillary pressure, and relative permeability. For additional wells in the same field, absolute permeability is estimated by matching shallow resistivity logs with the electrical resistivity in the flushed zone yielded by the simulation of mud-filtrate invasion. We describe the application of this methodology to the estimation of permeability in three wells penetrating the same over-pressured tight gas sands of the East Texas Bossier Formation. Conventional core porosity and permeability measurements, along with capillary pressure, are used to determine rock types and flow units in the cored key well. Estimates of permeability based on a modified version of Winland's equation agree with the measured permeability of the available core samples. Simulations of mud-filtrate invasion account for the dynamic process of immiscible flow between mud filtrate and in-situ gas as well as for salt mixing between mud filtrate and connate water. Moreover, the simulations properly reproduce the effect of mudcake buildup along the borehole wall. Two-dimensional spatial distributions of water saturation and salt concentration obtained from the simulations are used to calculate spatial distributions of electrical resistivity. The latter are checked against the measured shallow, medium, and deep resistivity logs to calibrate time of invasion and Archie's saturation and cementation exponents. Based on the analysis in the key well (Well 1), petrophysical assessment of flow units is performed in two nearby wells (Wells 2 and 3) within the same gas field. Initial Winland permeability values are progressively adjusted until the calculated spatial distributions of electrical resistivity agree with the shallow array-induction resistivity readings. We find that for Well 2, the estimated permeability is equal to the initial guess, whereas for Well 3 the estimated permeability is approximately 50-80% higher than the initial guess.

Flow pathways in porous media: electrical resistance tomography and dye staining image verification

Electrical resistance tomography permits the determination of the spatial distribution of electrical resistivity by non-destructive means. The technique may be applied to the study of flow through porous media by following the changes in resistivity distribution within a soil or rock core as an electrolytic tracer is passed through the specimen. Image reconstruction of the electrical resistance tomography data may be achieved by robust regularized nonlinear inverse methods provided data errors are suitably characterized. The procedure is reported here for a natural (undisturbed) soil core using four planes of 16 electrodes placed around the boundary of the core. The experiment was performed with a dye tracer that provided, by destructive slicing, visual verification of the flow pathways observed with the tomographic imaging.

Comments on distinguishability in electrical impedance imaging.

In Electrical Impedance Imaging (EII), the spatial distribution of electrical resistivity of a volume conductor is reconstructed from measurements of potential which result from an externally applied electric field. The ability of such a system to distinguish a target inhomogeneity and the discussion of several measures of distinguishability has been a subject of a recent study. In this communication a few comments are added to those of. The medical device safety regulations limit the maximum total input current which can be applied to the human thorax. Based on the currently existing safety regulations, if the input current to the thorax is limited and constant, patterns applied between opposite electrodes result in higher distinguishability of a centered target than the cosine current patterns as suggested by.