Induction Logging Tool Research Articles

Semi-Analytic Sensitivity of the MCIL Responses in Homogeneous Biaxial Anisotropic Media

We presented a semi-analytic solution for the sensitivity of the response tensor of the multi-component induction logging (MCIL) tool in a homogeneous biaxial anisotropic (BA) medium. By using the perturbation principle and the spectral representation of electromagnetic (EM) fields, the sensitivity was formulated as a seven-fold integral whose integrand involves two sets of spectral electric fields. Fortunately, such a complicated integral can be reduced to a three-fold integral, which consists of two parts: one is a definite integral over the spatial variable <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">z</i> that can be analytically integrated; the remaining is a two-fold integral over the spectral variable k that is computed by numerical quadrature. We verified our formulation by comparing it with the exact solution and the finite-difference (FD) approximation.

Modeling of triaxial induction logging responses in multilayered anisotropic formations

Triaxial induction logging tools have been widely applied to formation characterization due to their sensitivity to electric anisotropy. To model triaxial induction logs in multilayered general anisotropic formations, where the anisotropy can be arbitrary, an analytical method is applied to compute the tool responses. For the analytical method, Maxwell’s equations in the spectral domain are written into a compact first-order differential equation. The equation is solved to obtain the spectral-domain fields, which are transformed to the spatial domain through the inverse Fourier transform. The singular issue for the tool located in highly deviated wells is handled by subtracting the singular term in the spectral domain. The singularity treatment makes the integrands in the inverse Fourier transform decay faster, thus making the infinite integration computation faster. Formations with isotropic, transversely isotropic, biaxially anisotropic, and general anisotropic conductivity are modeled and compared to investigate the effects of anisotropy on the tool responses. For a tool in a general anisotropic formation, all of the [Formula: see text] components are nonzero. For a tool in a vertical well in transversely isotropic and biaxially anisotropic formations, only the diagonal components of [Formula: see text] are nonzero. For a tool located in a deviated well, the effects of tool deviation and electric anisotropy are coupled. The diagonal components are more sensitive to the electric anisotropy than the off-diagonal components, and the off-diagonal ones can clearly indicate bed boundaries.

The Calibration of an Array Induction Logging Tool in half-space

Array induction logging tools are currently relatively widely used resistivity logging tools. The scale of array induction logging tools includes workshop scale and half space scale. The main purpose of the workshop scale is to use the ring scale to determine the instrument constant (K value). The half-space scale determines the system error of the instrument coil, that is, the basic value. The longest sub-array of the array induction logging tool MIT has a detection depth of 2.5m in the air. Signals over 14m account for 10%, and signals over 28m account for 5%. The ground conductivity must be considered during the half-space calibration process. Influences. This topic studies the method of eliminating grounding conductivity and coil system errors. The completion of the subject will be of great significance to the accurate calibration of the instrument measurement signal.

Numerical Simulation and Analysis of Multicomponent Induction Logging Response in Anisotropic Formation

In this article, the response characteristics of multicomponent induction logging (MCIL) tool in anisotropic formation are analyzed. To solve the 1-D MCIL problems, we use a planar layered anisotropic medium (PLAM) Green's function (PLAMGF) method which is derived from the layered-medium Green's function (LMGF) and combined with MCIL excitation source and anisotropic formation environment, and then use it to investigate the equivalence of the MCIL tool responses in two models, i.e. the microscopic thin interbed formation and macroscopic anisotropic formation, and also analyze the effects of shoulder bed and formation dip on MCIL tools. In addition, in order to solve the complex 3-D problems, such as the effects of borehole, tool eccentricity and invasion on the tool response, we use the finite element method (FEM) based on a proposed new meshing scheme to simulate and analyze. This new meshing scheme includes two aspects: the use of cylindrical hexahedron element and the flexible meshing strategy combined with domain decomposition. Finally, some key detection performances of coaxial coils and coplanar coils of MCIL tool are studied. Numerical experiments are conducted to prove the effectiveness of our proposed method and provide the detailed results of the aforementioned aspects.

Beyond Carbon Steel: Detecting Wellbore Shape and Cavities, and Cement Imperfections in Cased Wells

The non-corrosive, electrically resistive fiberglass casing materials may improve the economics of oil and gas field projects. At moderate temperatures (&lt;120 °C), fiberglass casing is superior to carbon steel casing in applications that involve wet CO2 injection and/or production, such as carbon capture and storage, and CO2-based enhanced oil recovery (EOR) methods. Without a perfect protective cement shell, carbon steel casing in contact with a concentrated formation brine corrodes and the fiberglass casing is superior again. Fiberglass casing enables electromagnetic logging for exploration and reservoir monitoring, but it requires the development of new logging methods. Here we present a technique for the detection of integrity of magnetic cement behind resistive fiberglass casing. We demonstrate that an optimized induction logging tool can detect small changes in the magnetic permeability of cement through a non-conductive casing in a vertical (or horizontal) well. We determine both the integrity and solidification state of the cement-filled annulus behind the casing. Changes in magnetic permeability influence mostly the real part of the vertical component of the magnetic field. The signal amplitude is more sensitive to a change in the magnetic properties of the cement, rather than the signal phase. Our simulations showed that optimum separation between the transmitter and receiver coils ranged from 0.25 to 0.6 m, and the most suitable magnetic field frequencies varied from 0.1 to 10 kHz. A high-frequency induction probe operating at 200 MHz can measure the degree of solidification of cement. The proposed method can detect borehole cracks filled with cement, incomplete lift of cement, casing eccentricity, and other borehole inhomogeneities.

An iterative inversion of Dual Induction Tool logs from thin-bedded sandy\u2013shaly formations of the Carpathian Foredeep using a modified simulated annealing method

In thin-bedded sandy–shaly Miocene formations of the Carpathian Foredeep, the main source of errors in gas saturation evaluation is the underestimation of resistivity of thin, hydrocarbon-bearing beds, which is the result of the low vertical resolution of induction logging tools. This problem is especially visible in older boreholes drilled in times where the Dual Induction Tool (DIT) was the primary induction tool used for determining the formation resistivity, and in shallowest depth intervals of newer boreholes where the DIT was used instead of newer array tools for cost-saving reasons. In this paper, we show how a global inversion algorithm was used to improve the vertical resolution of DIT logs. Our implementation of an iterative inversion utilizes a one-dimensional formation model, vertical response functions of the DIT, and a modified simulated annealing algorithm to determine the true vertical distribution of the formation resistivity. The algorithm was tested on resistivity logs recorded in a borehole drilled in the Carpathian Foredeep in Poland, where the DIT and the High-Resolution Array Induction (HRAI) tool were run in the same depth interval.

Investigation of borehole effects on azimuthal resistivity measurements using novel pseudo‐analytic formulas

ABSTRACTDownhole resistivity measurements provide valuable information for geosteering and formation evaluation. It is important to understand and correct the environmental effects, such as the borehole, the tool eccentricity and the resistivity anisotropy effects, of the measurements based on fast and accurate modelling methods. A new pseudo‐analytic solution for eccentric coaxial and tilted‐coil antennas in the cylindrically multilayered medium with transverse isotropic conductivity was developed. This method can take the eccentric tool, the borehole, the mud invasion and the resistivity anisotropy into account. These formulas enable us to simulate the responses of the downhole induction logging tools, including induction wireline and azimuthal propagation logging‐while‐drilling measurements. Instead of using the prior fictitious boundary, the generalized reflection coefficients are proposed to construct the linear matrix functions to deal with the tool eccentricity. The cylindrical functions are reorganized and presented in forms of ratios. Thus, the proposed formulas obviate the overflow issue in the computation and are more stable and efficient. The proposed approach is compared and validated with other well‐established methods. Simulations and case studies show that: (1) the responses of azimuthal resistivity logging‐while‐drilling tool are affected by the tool's eccentricity in both isotropic and anisotropic medium; (2) sine curve behaviours exist for the phase difference and amplitude ratio of azimuthal resistivity measurements along with different eccentricity azimuth.

Pseudoanalytical Formulations for Modeling the Effect of an Insulating Layer in Electromagnetic Well Logging

In this paper, we present a set of compact formulations to model the response of the electromagnetic well-logging tools in eccentric multilayered medium. Different from previous models, the coil antennas are imbedded in an insulating protection layer (IPL) rather than expose to the borehole directly, which agrees much better with some real tools, e.g., the array induction logging tool. The effects of both metal mandrel and an IPL are considered in eccentric scenarios. Our formulations are derived on the basis of the ratios of cylindrical functions, which obviate the notorious overflow issues during numerical computation. Numerical results show that the effect of IPL gradually appears with the increase of the eccentric distance.

Electromagnetic Waves in Multilayered Generalized Anisotropic Media

This paper presents the formulations for calculating the electromagnetic (EM) fields in multilayered generalized anisotropic media. Maxwell’s equations are written into a first-order differential (in $z$ ) equation concerning the transverse electric and magnetic field components in the spectral domain. The equation can be solved to obtain the EM fields in a homogeneous anisotropic medium. For fields in layered anisotropic media, the local transmission and reflection matrices, the global reflection matrices, and the recursion relations of the wave amplitudes at interfaces are derived and used to express the EM fields in arbitrary layers. The electric and magnetic dipole sources can locate in arbitrary layers, and the medium can have both full-tensor magnetic and dielectric anisotropy. The singular behavior of the solution in the close vicinity of the dipole source is subtracted to make the integrands decay rapidly as functions of $k_{x}$ and $k_{y}$ . The contributions of the subtracted part are calculated analytically. A three-layer anisotropic medium is modeled to show the convergence of the integrals with the singularity subtraction. To validate the algorithm for multilayered generalized anisotropic media, a five-layer medium is modeled and compared with finite element method results. The algorithm is also applied in geophysical EM well logging by modeling the triaxial induction logging tool. The responses in vertical and deviated wells are computed and compared with finite element results. The good agreement between the two results further validates the algorithm and demonstrates its capability to model induction logging tools in multilayered generalized anisotropic media.

Accelerated Computation of Triaxial Induction Tool Response for Arbitrarily Deviated Wells in Planar-Stratified Transversely Isotropic Formations

In this letter, a new formulation for calculating an induction logging tool response in a multilayered transversely isotropic (also called uniaxial anisotropic) dipping formation is proposed. Using transmission line theory, only five independent integrals are necessary to form all the components of the dyadic Green’s function in order to calculate the tool response, resulting in a more succinct and efficient formulation. The fast Hankel transform (FHT) is then employed to calculate these spectral integrals efficiently. In special cases, such as horizontal and vertical wells where the direct FHT fails, alternative approaches are proposed. A singularity extraction is implemented to handle the divergent integrals for a horizontal well, whereas the double-exponential integration rule is implemented for a vertical well. In order to speed up the computation, the spectral transmission line currents and voltages are precalculated and then stored in memory, and parallel computing using OpenMP is employed. Numerical examples demonstrate a speedup factor of more than two orders of magnitude compared with other reported results based solely on the FHT.

Experiments and simulations of a prototype triaxial electromagnetic induction logging tool for open-hole hydraulic fracture diagnostics

The monitoring and diagnostics of induced fractures are important for the real-time performance evaluation of hydraulic fracturing operations. Previous electromagnetic-based studies show that single backbone triaxial induction logging tools are promising candidates for real-time monitoring and diagnosis of fractures in noncased wells. With a fast-forward solver and reliable parametric inversion techniques, it may be possible to estimate many features of the propped fracture geometry (e.g., area, dip, conductivity) from the measured induced voltages. To support the development of field deployable tools, the concept must be tested in experiments, in a controllable environment, before it is tested under field-like conditions. To this end, we have designed and built a prototype induction tool and performed two sets of tests to compare with numerical simulation results. The experimental setup consists of triaxial transmitter and receiver coils in coaxial, coplanar, and cross-polarized configurations. Thin (highly conductive) metallic targets of various sizes, shapes, and orientations are used to emulate various fracture geometries. The laboratory and shallow earth measurements are shown to be in good agreement with simulations for all examined cases. The average relative and maximum discrepancies of the measured signals from the simulated ones are lower than 3% and 10%, respectively. With the prototype tool, strong signals sensitive to the fracture’s surface area and dip are measured in a coaxial coil configuration, whereas weaker signals sensitive to the fracture’s aspect ratio are observed in a coplanar configuration. Cross-polarized signals are also shown to be strong and sensitive to the fracture’s dip. The results suggest that a tool of similar specifications can be used for the detection and extraction of the parameters of fractures propped with sufficiently electrically conductive proppant.

Analysis of Electromagnetic Induction for Hydraulic Fracture Diagnostics in Open and Cased Boreholes

In this paper, the sensitivity and detectability of an electromagnetic induction tool for hydraulic fracture detection are analyzed by calculating the electromagnetic response from an orthogonal transverse fracture (OTF) in an open or cased borehole using the improved numerical mode matching method. The OTF is modeled as a slim circular disk, which is axially symmetric with respect to the borehole axis and filled with a conductive or magnetic proppant. The feasibility of the induction tool for fracture diagnostics was validated via scaled-down experimental measurements. We then quantitatively analyze the induction response sensitivity to different proppant parameters, such as conductivity and permeability, to evaluate the effectiveness of the induction logging tool for fracture detection. The analysis reveals that the short-spaced receiver can accurately locate the fracture position and distinguish small-sized fractures, while the long-spaced receiver can differentiate fractures with large dimension. Casings with different thicknesses, conductivities, and permeabilities are modeled together with the fracture to investigate their effects in fracture detection. Finally, the application of the induction tool to a fracture network is evaluated.

Radiation of Arbitrary Magnetic Dipoles in a Cylindrically Layered Anisotropic Medium for Well-Logging Applications

We present a set of stable and efficient formulas to compute the electromagnetic radiation of arbitrary magnetic dipoles in a cylindrically layered anisotropic medium. This set of formulas is derived on the basis of the generalized reflection and transmission coefficients. By expressing our new formulas by the ratios of Bessel or Hankel functions, rather than directly by these special functions, the notorious overflow problem for numerical computation is successfully obviated. Our formulas can be easily implemented for any number of layers, as well as for arbitrary locations and orientations of the transmitter and the receiver. Numerical experiments have demonstrated their correctness and stability. They are then utilized to investigate the influence of the eccentricity distance, the eccentricity angle, and the formation anisotropy on the response of a multicomponent induction logging tool.

Transient electromagnetic fields of a buried horizontal magnetic dipole

Electromagnetic surveys using a vertical transmitter loop are common in land, marine, and airborne geophysical exploration. Most of these horizontal magnetic dipole (HMD) systems operate in the frequency domain, measuring the time derivative of the induced magnetic fields, and therefore a majority of studies have focused on this subset of field measurements. We examine the time-domain electromagnetic response of a HMD including the electric fields and corresponding smoke rings produced in a conductive half-space. Cases of a dipole at the surface and buried within the earth are considered. Results indicate that when the current in the transmitter is rapidly switched off, a single smoke ring is produced within the plane of the vertical transmitter loop, which is then distorted by the air-earth interface. In this situation, the circular smoke ring, which would normally diffuse symmetrically away from the source in a whole space, is approximately transformed into an ellipse, with a vertical major axis at an early time and a horizontal major axis at a late time. As measured from the location of the transmitter, the depth of investigation and lateral footprint of such a system increases with burial depth. It is also observed that the electric field measured in the direction of the magnetic dipole only contains a secondary response related to the charge accumulation on any horizontal conductivity boundaries because the primary field is always absent. This field component can be expressed analytically in terms of a static and time-varying field, the latter term adding spatial complexity to the total horizontal electric field at the earth surface at early times. Applications of this theoretical study include the design of time-domain induction-logging tools, crossborehole electromagnetic surveys, underground mine expansion work, mine rescue procedures, and novel marine electromagnetic experiments.

Calibration response simulation of a triaxial induction tool with a metal mandrel

The calibration of triaxial induction logging tools is commonly performed in large water tanks, which are costly and complicated to use. In contrast, calibration with a metal loop is relatively economical and convenient. A tilted metal loop is introduced to calibrate all the components of a triaxial induction tool simultaneously. We have evaluated and optimized parameters such as radius, resistance, azimuthal angle, and position of the calibration loop with the 3D finite-element method. For validation, the accuracy of the simulation method is verified with analytical solutions with consideration of the metal mandrel effect. A quantitative agreement is found between the simulation results and the measurements of a realistic triaxial induction tool with a metal mandrel. Numerical simulation results demonstrate that the presence of the metal mandrel causes the nine components of the tool to change nonlinearly with the formation conductivities in the double logarithmic coordinate. This nonlinear effect can be reduced by eliminating the background signals from the metal mandrel. After the optimization of the parameters of the calibration loop, the responses of the triaxial induction tool can be calibrated accurately.

A semianalytic solution to the response of a triaxial induction logging tool in a layered biaxial anisotropic formation

We have developed a forward-modeling method to compute the response of a triaxial induction logging tool in a layered biaxial anisotropic dipping formation without borehole and invasion zones. The purpose of this development is to provide a fast-forward computation algorithm to handle cracks in transverse isotropic (TI) formations in oil exploration, which is a mathematically challenging problem for log data inversion. We solve for the spectral-domain transverse electromagnetic (EM) field equations, propagation matrix, and reflection matrix in a biaxial anisotropic planarly layered media. The EM fields in the space domain are obtained by a 2D inverse Fourier transform. We derive formulations of the EM fields generated by three orthogonal transmitting coils in a fully anisotropic layered media. The proposed formulations are based on arbitrary relative dipping and azimuthal and tool angles; thus, we obtain the full coupling matrix connecting source excitations and magnetic fields anywhere along the tool axis. Computation results using this method in the response of triaxial induction tools in several cases were compared with published data in TI formations and biaxial layered formations. Our results agreed very well with the published data.

A fast algorithm to forward model the triaxial induction logging response in layered transversely isotropic dipping formations

We have developed a new analytic method to compute the response of triaxial induction logging tools in layered transverse isotropic (TI) dipping formations without borehole and invasion zones. A triaxial induction tool is composed of one or more sets of three orthogonal transmitter coils and three orthogonal receiver coils arranged along the tool axis. The tool axis may intercept a formation with dip, azimuthal, and rotation angles. Based on the electromagnetic (EM) field in planarly layered media, formulations of the EM fields generated by these three transmitting coils are derived. A fast-forward-modeling algorithm to compute the responses of an induction tool was developed. Compared with the algorithm using the coefficient propagator method previously developed, the proposed algorithm calculates the generalized reflection and transmission coefficients only once for each layer regardless of the position of the transmitters, and therefore, it greatly speeds up the computation. The simulation code solves for all nine components of the magnetic field in a TI layered medium. Results of this new method were developed for several formation models, which agreed very well with the published data. For a dipping or nondipping case in a 28-layer formation, the proposed method was about 37 times faster, which was more appropriate to be used in an inversion algorithm.

Characteristics of the Sum of Cross-Components of Triaxial Induction Logging Tool in Layered Anisotropic Formation

There are two nonzero cross-components of a triaxial induction logging tool in the medium coordinate system in a transversely isotropic (TI) formation. The sum of the cross-components holds dependence on only the horizontal conductivities with little nonlinearity and small shoulder bed effect in a horizontally layered formation. Based on the generalized reflection coefficient method, simplified formulas of the sum are derived to analyze its response characteristics. Numerical results show that the apparent conductivity obtained from the sum is a square-looking log with high vertical resolution. Moreover, the readings almost equal to the true horizontal conductivity of the formation beds. These characteristics can be applied to reconstruct the horizontal conductivity and the formation boundaries with triaxial induction logging data.

Integral equation of relationship on the apparent conductivity and true conductivity in induction logging

This paper investigates the relation between the induced electromotive force measured by induction logging tool and the apparent conductivity, and the relation between the apparent conductivity and the formation true conductivity. Assuming the conductivity in Green’s function to be the function of the field point coordinate, the apparent conductivity expression of electric-field intensity is derived using Green’s formula, and the integral equation has been established representing the relationship of the apparent conductivity with the true conductivity under this condition. The integral equation is analyzed and then leads to the conclusion that the equivalent conductivity is the apparent conductivity and the values of the apparent conductivity function contain the true conductivity, and the method derived the true conductivity from the apparent conductivity around the well axis is put forward. The validity of the approach given in this paper is verified through numerical calculation. On the basis of above means, the transmitter coil produces an electric-field distribution in formation at every point where the induction logging tool moves along a wellbore, and a number of the receiving coils obtain an apparent conductivity distribution; this is what induction electric-field logging is.

Forward modelling of multi-component induction logging tools in layered anisotropic dipping formations

Multi-component induction logging provides great assistance in the exploration of thinly laminated reservoirs. The 1D parametric inversion following an adaptive borehole correction is the key step in the data processing of multi-component induction logging responses. To make the inversion process reasonably fast, an efficient forward modelling method is necessary. In this paper, a modelling method has been developed to simulate the multi-component induction tools in deviated wells drilled in layered anisotropic formations. With the introduction of generalized reflection coefficients, the analytic expressions of magnetic field in the form of a Sommerfeld integral were derived. The fast numerical computation of the integral has been completed by using the fast Fourier–Hankel transform and fast Hankel transform methods. The latter is so time efficient that it is competent enough for real-time multi-parameter inversion. In this paper, some simulated results have been presented and they are in excellent agreement with the finite difference method code's solution.