Pseudo-Analytical Modeling of Tilted-Coil Antennas in Anisotropic Geophysical Formations

Abstract

Abstract-In this paper we present an efficient mode-matching technique to analyze tilted-coil antennas in anisotropic geophysical formations. In this problem, a number of coil antennas with arbitrary relative tilt angle with respect to the symmetry axis are used to radiate electromagnetic fields in a cylindrically layered medium comprised of a metallic mandrel, a borehole, and a surrounding layered Earth formation. This configuration corresponds to that of directional well-logging tools used in oil and gas exploration. Our technique combines closed-form solutions for the Maxwell's Equations in uniaxially anisotropic and radiallystratified cylindrical coordinates with the generalized scattering matrix (GSM) at each axial discontinuity based on the modematching technique. The field from the transmitter tilted-coil source is represented by a set of modal coefficients which, after computation using GSM matrices, are used to compute the transimpedances. We present validation results which show that our technique can efficiently model directional well-logging tools used for oil and gas exploration.Index Terms-Anisotropic media, mode matching methods, stratified media, well logging tools. I. INTRODUCTIONLogging-while-drilling (LWD) and measurement-while-drilling (MWD) tools are frequently used to evaluate hydrocarbon reservoirs. The complex geophysical formations present in this type of problem can be successfully modeled using numerical techniques such as finite-differences (FD), finite elements (FE) and finite volumes (FV) [1]- [5]. However, these brute-force techniques suffer from relatively high cost in terms of both computer memory and CPU time. Bearing in mind that oil exploration usually employs LWD tools comprised of coil antennas wrapped around a metallic mandrel inside a borehole, as illustrated in Fig. 1, a series of practical scenarios can be properly approximate as a radially-stratified medium [6]. In this case, efficient algorithms based on pseudoanalytical methods [6]-[10] are good alternatives to model these geometries and provide efficient inversion algorithms designed to estimate the Earth formation properties given the tool responses.More complicated geometries including inhomogeneities in the Earth formation along both radial and axial directions can be accounted by using the numerical mode-matching (NMM), which may be seen In this work, we employ an axial mode-matching combining attractive features of the early described pseudo-analytical techniques, to obtain a flexible technique for analyzing directional welllogging tools in anisotropic formations which can be easily extended to model wells with curvature. II. PSEUDO-ANALYTICAL FORMULATIONThe geometry shown in Fig. 1 Journal of Microwaves, Optoelectronics and Electromagnetic Applications, Vol. 16,No. 1, March A. Electromagnetic Fields Along Radial StratificationsThe forward propagating axial fields can be written in a compact fashion asThe modal propagation constant in the z direction is , .In order to simplify the notation, we will tempor...

Pseudo-Analytical Modeling for Electromagnetic Well-Logging Tools in Complex Geophysical Formations

“…For sources with non-zero span along the axial direction (such as tilted-coil antennas that are described in Section 3.5.4), vertical mode expansion described in [6,8,27,46] (where both sources and radial discontinuities are matched over a constant radial plane) appears an appropriate way to model the problem. In [147][148][149] we demonstrate a way to compute the contribution of general and non-zero span sources using the axial mode-matching. To use this method; that is described in detail in Section 3.5.6; we need to consider the existence of general modal excitation coefficients, which may leads toĀ…”

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

“…With this motivation, the pseudo-analytic solution was developed. Compared with other numerical methods, such as finite element, Numerical mode matching and finite difference (Pardo et al 2008;Wang et al 2008;Wang, Torres-Verdín and Gianzero 2009;Nam, Pardo and Torres-Verdín 2010;Davydycheva 2010Davydycheva , 2011Dai and Liu 2015;Rosa, Bergmann and Teixeria 2015), the pseudo-analytic solution requires much less computational cost and has the higher computational accuracy. Besides, the solution can take the drilling collar and the fine sizes of the coil antennas into account so that the tool responses can be accurately simulated.…”

“…; Wang et al . ; Wang, Torres‐Verdín and Gianzero ; Nam, Pardo and Torres‐Verdín ; Davydycheva , ; Dai and Liu ; Rosa, Bergmann and Teixeria ), the pseudo‐analytic solution requires much less computational cost and has the higher computational accuracy. Besides, the solution can take the drilling collar and the fine sizes of the coil antennas into account so that the tool responses can be accurately simulated.…”

Study of the Electromagnetic Propagation in Stratified Anisotropic Media via Semi-Analytical Methods

“…Before computational advances, experiments that required large costs and approximate analytical techniques were the main methods to analyze the response of the EM logging tools [34,35]. With the advance of computational power, it was possible to model computationally these tools in more complex environments in a more efficient way.…”

“…34 Normalized amplitude of the azimuthal component of the electric field (E φ ) for decoupled TE and TM modes in an axially-stratified two-layers isotropic medium (Third Mode).…”