Multicomponent Induction Logging Research Articles

Multi-component induction logging detection characteristics of the fracture azimuth and dip angles and the fast extraction methods of fracture distribution parameters

In the field of log interpretation of tight sandstone and shale reservoirs, it is difficult to quantitatively evaluate the fracture distribution parameters (fracture azimuth angle and fracture dip angle) near the borehole. Multi-component induction logging can measure the apparent resistivities of the reservoir in different directions by an orthogonal coil system, which lays a foundation for the quantitative evaluation of the fracture distribution parameters near the borehole. First, we derive the finite element equations for numerical calculation from the Maxwell equations for the time-harmonic field and construct a three-dimensional (3D) vector finite element numerical algorithm for the fractured formation. Second, we quantitatively analyze the multi-component induction logging detection characteristics of the fracture azimuth and dip angles. Third, we establish a fast extraction method of the fracture azimuth angle based on coordinate system rotation and an analytical calculation method of the fracture dip angle using the combination of cross components and coplanar components of multi-component induction logging. Finally, we use field data to test the fracture distribution parameter extraction method, and the fracture dip and azimuth angles calculated by multi-component induction logging are consistent with those calculated by borehole imaging logging, which realizes the fast extraction of the distribution parameters of fractures in tight sandstone and shale reservoirs.

Using the multi-component induction logging data to evaluate the geometric parameters of the hydraulic fracture

Abstract Hydraulic fracturing technology can effectively improve the seepage capacity of low-porosity and -permeability reservoirs. Geometric parameters evaluation (height, aperture and length) of hydraulic fracture is essential at different stages of fracturing. This paper presents a new method to evaluate the three parameters of small-scale fractures by multi-component induction logging based on numerical simulations. First, the model of calculation of the induced electric field with vertical hydraulic fractures is established using a three-dimensional finite element method (3D FEM), and the algorithm is verified correctly by comparing it with the analytical solution. Five coil systems of xx, xz, yy, yz and zz that are sensitive to the geometric parameters of the fracture are determined. The relationships between the geometric parameters of the fracture and the measurement signals of five coils are then investigated. The results show that the length and aperture of the fracture have a power exponent relationship with the measurement voltage, while the height parameter is closely related to the logging curves. Based on the relationships, the calculation models of the geometric parameters are established and the applicable range of it is analyzed. It is demonstrated that the complete characterization of fracture geometric can be realized by combining multi-spacing and multi-coil systems. Finally, the influence of the borehole and surrounding formation on the measurements is also considered, and the results indicate that the resistivity of the formation has less influence on the signals than the resistivity of the mud. Compared to the current instrument, the new method can evaluate all three geometric parameters of the hydraulic fracture.

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.

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.

Enhanced real-time determination of resistivity anisotropy and dip using multifrequency and multicomponent induction logging

Multicomponent induction (MCI) logging is able to provide a wealth of measurements at multiple subarrays and frequencies that can be used to evaluate complex subsurface formations. Real-time and postprocessing inversion methods have been introduced by various researchers for determining formation resistivity anisotropy (horizontal and vertical resistivity or conductivity), dip, and dip azimuth/strike using MCI measurements. The majority of these methods are based on single-frequency information. We have developed an enhanced real-time method and relevant workflow for determining formation resistivity anisotropy, dip, and dip azimuth using multifrequency MCI information. This enhanced method can be used to improve accuracy in formation evaluation applications, such as reservoir identification, hydrocarbon/water saturation calculation, and geologic and structural interpretation. Enhancements over the present single-frequency data processing include: (1) optimal harmonization of multiple single-frequency inverted logs, (2) robust determination of dip and dip azimuth angle for low-resistivity anisotropy ratios, (3) practical data-quality evaluation that takes into account the effects of formation resistivity, anisotropy ratio, and dip parameters, and (4) a new integrated workflow that can be used to determine formation anisotropy, true dip, and dip azimuth by integrating processed relative dip and azimuth and borehole directional logging data. Finally, all of these data process enhancements have been validated with synthetic data and field log data.

Fast determination and characterization of formation resistivity anisotropy, dip, and fracture using multicomponent induction data

Multicomponent induction (MCI) logging measurements have been widely used in the past decade for determining formation resistivity anisotropy (horizontal and vertical resistivities: [Formula: see text] and [Formula: see text]), dip, and azimuth. Currently, almost all MCI processing and interpretation algorithms of determining [Formula: see text], [Formula: see text], dip, and azimuth are based on simplified transversely isotropic (TI) formation models. In most geologic environments, formations are layered or laminated, making the TI model a reasonable assumption. Subsurface formations usually contain different types of fractures (natural or drilling-induced), and exhibit azimuthal resistivity anisotropy in the bedding plane, which leads to formation biaxial anisotropy (BA) in the same bedding plane. (This type of media is usually called orthorhombic or orthotropic in mechanical engineering and geomechanics.) Therefore, MCI data processing based on TI models may not be valid in complex BA formations caused by fractures. MCI processing and interpretation methods based on BA formation models are needed for more accurate descriptions of complex anisotropic formations. Fractures significantly affect fluid flow in formations, and therefore the fracture characterization with MCI logging can provide some useful information for oil/gas development and production, especially in unconventional reservoirs. We have developed a fast and practical integrated method of borehole multiarray MCI data processing for effective determination of formation BA anisotropy (or triaxial resistivities: [Formula: see text], [Formula: see text], and [Formula: see text]), dip, and azimuth. The multiple MCI data sets were further applied to fracture evaluation, and they were tested with synthetic and field log data sets. The method has the following components: the inversion algorithm based on the multiple BA models, a fracture identification function for detection of the fracture, and the corresponding approach for estimation of the fracture relative azimuth and dip angle. The application results demonstrated that accurate triaxial formation anisotropy and dip can be obtained based on the BA models compared with the TI processed logs. Furthermore, fractures can be characterized by integrating measurements and processed log data, such as the recovered horizontal resistivities [Formula: see text] and [Formula: see text], vertical resistivity [Formula: see text], and formation dips based on the BA and TI models.

Three dimensional Born geometrical factor of multi-component induction logging in anisotropic media

Geometrical factor has been widely used in the design of induction tool and analysis of complex logging responses, as well as the high resolution processing of logging data. Works in this area are usually limited to two-dimensional isotropic medium and are only available to cases of coaxial transmitter and coaxial receiver coupling. For a more thorough understanding of multicomponent induction logging in the presence of transverse anisotropy, a knowledge of anisotropic geometrical factor is often necessary. In this paper, the two-dimensional and isotropic geometrical factors are extended to the anisotropic media using Born approximation, and the expressions of 3D Born geometrical factors for multicomponent induction logging are derived. Then the sensitivity and detectability of coaxial, coplanar and cross-coupling measurements are investigated. Numerical results show that with increasing coefficients of conductivity anisotropy, the spatial distribution of geometrical factors becomes increasingly complicated, and more sensitivity information can be detected by multicomponent induction tools. The multicomponent induction tool is sensitive to conductivity anisotropy at arbitrary dipping angles. In vertical wells, coplanar measurements are significantly affected by the conductivity anisotropy. Compared with coaxial and coplanar measurements, cross-coupling component offers superior sensitivity information to the conductivity anisotropy with the dipping angle being 40～ 60°. In horizontal wells, coaxial measurements are the most sensitive to the conductivity anisotropy. The extended 3D Born geometrical factor directly exhibits the anisotropy sensitivity in terms of spatial contribution, and has made up for the shortage of previous geometrical factors. The new geometrical factor will create favorable conditions for the development of new multicomponent induction tool and the interpretation of anisotropic formations.

An Efficient Algorithm of Both Fréchet Derivative and Inversion of MCIL Data in a Deviated Well in a Horizontally Layered TI Formation Based on TLM Modeling

In this paper, we set up an efficient Frechet derivative algorithm of inversion of multicomponent induction logging (MCIL) data in horizontal layered transversely isotropic (TI) formations based on transmission line method (TLM) in order to simultaneously reconstruct the model vector including both horizontal and vertical conductivities, horizontal interfaces, borehole dipping angle, and tool azimuth in deviated well from the MCIL data. First, MCIL responses in the TI model are efficiently determined by both the spectrum EM fields obtained by TLM and the semianalytical computation of Sommerfeld integrals based on the cubic spline interpolation. Then, the Born approximations are executed to derive the MCIL Frechet derivatives as the sixfold integrals of the products of two spectrum EM fields in infinite domains. By using the integral characters of the 2-D Dirac function, the sixfold integrals of Frechet derivatives are further simplified into twofold integrals: One is the Sommerfeld integral in the radial spectrum domain, and the other is the definite integral in the vertical spatial domain. They are efficiently computed by the semianalytical approach similar to the MCIL simulation. Therefore, we obtain the linear equations between changes in the MCIL responses and small perturbations in the model vector. After that, we iteratively modify all of the model parameters to realize the best fit between the input data and the synthetic data of the inverted model by the normalization of the Frechet derivative and singular value decomposition technique. Finally, we apply numerical results to investigate the characteristics of the Frechet derivatives and to validate the inversion method and its antinoise ability.

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.

Definitive Petrophysical Evaluation of Thin Hydrocarbon Reservoir Sequences

SummaryThe petrophysical evaluation of thinly-bedded sand/shale sequences is strongly dependent on the way in which layered and dispersed shales are taken into account. There are two underpinning issues: the recognition of thin bed geometries and the estimation of shale content from lithology logs. The first of these is managed through a scenario approach, whereby different downhole scenarios are set out according to specified ranges of bed thickness. Each range has its own interpretation protocol. The second issue relates to the inherent overestimation of clay-mineral volume fraction by shale indicators and its impact on the petrophysical evaluation of thinly-bedded sand porosity. This shortcoming is managed by applying a validated scaling factor to log-derived estimates of shale volume fraction so that these become workable estimates of clay-mineral fraction for the porosity evaluation of sand layers. Both these problems become more acute for thinner beds. These two key issues are addressed conjunctively through interpretive workflows, each of which relates to a discrete range of bed thickness and uses fit-for-purpose petrophysical data sets. In particular, the multicomponent induction log is adopted as a pivotal technology for the evaluation of sand resistivity within thinly-bedded sand/shale sequences. The objective is to achieve a sound petrophysical interpretation for each downhole situation. Therefore, groundtruthing through core data is advocated where this allows the shale problem to be managed better. The outcome is a systematic approach to thin-bed evaluation, based on prescribed data inputs that optimize project effectiveness. The benefits are illustrated through case histories that demonstrate a securable upside in projected hydrocarbon volumes.

Efficient and Reliable Simulation of Multicomponent Induction Logging Response in Horizontally Stratified Inhomogeneous TI Formations by Numerical Mode Matching Method

An efficient and reliable numerical mode matching (NMM) method is developed to simulate the responses of multicomponent induction logging (MCIL) in the horizontally layered inhomogeneous transversally isotropic (TI) formations with the borehole and the invasion zone. The computation of MCIL responses is entirely transformed into three axially symmetrical problems on the Fourier harmonic components of the electromagnetic (EM) fields. The two extra singular differential operators about the horizontal EM components are introduced to describe the influence of the accumulation charge at the cylindrical interfaces on the EM fields excited by the horizontal magnetic dipoles. The first and second kinds of homogeneous boundary conditions of the different harmonic components of horizontal electrical fields near the borehole axis are derived to ensure that the EM problems become well posed in the cylindrical coordinate system. Then, the NMM is applied to solve the three axisymmetric problems with the extra singular differential operators. The numerical results demonstrate that the proposed method can accurately and efficiently simulate the MCIL responses in the horizontally layered TI formations with the large contrast resistivity.

Adaptive Regularization Iterative Inversion of Array Multicomponent Induction Well Logging Datum in a Horizontally Stratified Inhomogeneous TI Formation

An adaptive regularization iterative inversion of array multicomponent induction well logging datum is established to simultaneously reconstruct the horizontal and vertical conductivities of both invasion zone and origin formation, invasion radius, and the interface depth of each bed in the horizontally stratified inhomogeneous transversally isotropic (TI) formation. Applying numerical mode matching method, we can obtain a much compact semianalytic expression of the electromagnetic tensor Green's functions by magnetic current source in the inhomogeneous TI formation. Then, using the perturbation principles, an efficient computation of Fréchet derivatives of the multicomponent induction logging response is set up with respect to all the model parameters. After that, the combination of Morozev's discrepancy principle with Cholesky's decomposition is applied to adaptively select regularization factor during inversion so that stabilization of inversion solution is assured as well as realization of best fit of the input data with the modeling logs. Finally, the numerical tests validate the algorithm.

Multi-component induction logging response in large dielectric formation

Wireline induction logs operating at a frequency of some tens of kHz are used to detect the resistivity of hydrocarbon reservoir. The dielectric constant of typical formation is usually smaller than that of pure water and its effect is negligible for induction log. However some peculiar rocks including organic matter named source rock have large dielectric permittivities caused by polarization, which can lead the traditional induction logging to have an nusual log response. Multi-component induction logging is new log method and has been developed in nearly ten years, which can provide more information about formation than traditional axial instrument and has large potential applications. In this paper, we study the effect of large dielectric constant on multi-component induction logging response and extract the information about resistivity and dielectric permittivity through the different combinations, there by realizing the formation parameters reconstruction and intuitive recognition for the hydrocarbon source rock.

Study on the Response of a Multicomponent Induction Logging Tool in Deviated and Layered Anisotropic Formations by Using Numerical Mode Matching Method

AbstractIn this paper, we advance an efficient algorithm to compute the responses of multicomponent induction logging (MCIL) tool in deviated and layered anisotropic formations through a numerical mode matching method (NMM). First, the three mutually orthogonal magnetic dipoles located at the borehole axis are represented as the sum of three harmonic components about the dipole angle θ so that the electromagnetic (EM) fields produced by the dipoles can be transformed into three axisymmetric problems. And new boundary conditions satisfied by every EM harmonic component at borehole axis are given to assure the EM field near the borehole axis can still be calculated. Then NMM is used to solve the three axisymmetric problems and obtain a semianalytic expression of a dyadic Green function by magnetic current source in the formation. Furthermore, the formula to compute the MCIL response is given. The numerical tests are carried out to validate the algorithm and investigate the characteristics of MCIL response in several different cases.

A weak-anisotropy approximation to multicomponent induction responses in cross-bedded formations

The multicomponent induction logging response to a cross-bedded formation has been modeled under a weak-anisotropy approximation. With the approximation, a cross-bedded formation can be modeled as a transversely isotropic (TI) medium. The validity of the approximation has been tested for the main (coplanar and coaxial) components of the induction response. The conditions for the weak-anisotropy approximation to be valid depend on the component of the response. For the coplanar components, the approximation is valid for an anisotropy ratio up to 2 if the relative dipping angle between the cross-bedded formation and the borehole axis is below [Formula: see text]. For the coaxial component, the approximation reduces to a previously established result that the apparent resistivity for such a component is the geometric average of the resistivities, parallel and perpendicular to the bedding planes of an anisotropic formation, respectively, if the borehole is ignored. Hence, the approximation holds for the coaxial component regardless of the anisotropy ratio.

Numerical analysis of near‐borehole and anisotropeic layer effects on the response of multicomponent induction logging tools

We present finite‐difference simulation results that lend new insight into the behavior of multicomponent induction logging tools when in the presence of anisotropic layers, boreholes, and invasion zones. We use four independent models to investigate multicomponent tool properties as well as typical magnetic field responses. In addition, model variations with respect to formation dip angle, layer geometry, and conductivity provide data about the effects of geological variation on the multicomponent responses. Simulations suggest a coaxial tool configuration senses a depth of twice the source–receiver offset, although this depth is reduced to the source–receiver offset with coplanar configurations. Numerical responses in the presence of transversely isotropic layers provide evidence that anisotropy can have a measurable effect on both coaxial and coplanar magnetic fields; these effects increase as layer dip increases. Sensitivity analyses substantiate these numerical results. An investigation of tool responses to varying borehole and invasion zone conductivities and diameters demonstrates that the coplanar tool orientation is much more sensitive to near‐borehole variations than the coaxial configuration. A frequency‐differencing technique is presented to mitigate unwanted borehole‐induced bias in multicomponent data; however, drawbacks include decreased signal strength and possible geological signal destruction.