Triaxial Induction Logging Tool Research Articles

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.

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.

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.

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.

Application of OpenMP to Wireline Triaxial Induction Logging in 1D Layered Anisotropic Medium

Efficient and accurate forward modeling of logging tool responses is essential for data inversion in the log data interpretation in both real time and postprocessing. With the aggressive advancement of various high-performance computing techniques and computer hardware technology, it is possible to significantly improve the efficiency of the forward modeling. In this paper, we apply OpenMP to parallelize the simulation of triaxial induction logging tools in 1D multilayered anisotropic formation. The parallel process is explained in detail and numerical examples are presented to demonstrate the effect of the parallel programming. Comparison of the original code and the parallel code shows that the latter is much faster without loss of accuracy, which is very promising for future real-time inversion.

1-D INVERSION OF TRIAXIAL INDUCTION LOGGING IN LAYERED ANISOTROPIC FORMATION

In this paper, we present a one-dimensional (1-D) inversion algorithm for triaxial induction logging tools in multi-layered transverse isotropic (TI) formation. A non-linear least-square model based on Gauss-Newton algorithm is used in the inversion. Cholesky factorization is implemented to improve the stability and the reliability of the inversion. Zero-D inversion is conducted at the center of each layer to provide a reasonable initial guess for the best e-ciency of the inversion procedure. Cross components are used to provide su-cient information for determining the boundaries in the initial guess. It will be illustrated that using all the nine components of the conductivity/resistivity yield more reliable inversion results and even faster convergence than using only the diagonal components. The resultant algorithm can be used to obtain various geophysical parameters such as layer boundaries, horizontal and vertical resistivity, dipping angle and rotation angle etc. from triaxial logging data automatically without any priori information. Several synthetic examples are presented to demonstrate the capability and reliability of the inversion algorithm.