Analysis of Directional Logging Tools in Anisotropic and Multieccentric Cylindrically-Layered Earth Formations

Abstract

Abstract-We develop a pseudoanalytical method for the analysis of directional resistivity well-logging tools consisting of multiple tilted-coil antennas in cylindrically-layered Earth formations which have anisotropic conductivities and where each layer may be eccentric to the others (multieccentric formations). The cylindrically-layered, anisotropic, and multieccentric scenarios considered here are often encountered in deviated/horizontal drilling for hydrocarbon exploration, where the logging tool may be eccentric to the borehole due to mechanical vibrations and/or gravitational pull, and where eccentric invaded zones (of mud filtrate into the formation) may also arise because of gravitational pull on the mud filtrate.

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

“…In the radial direction, each region is modeled as a bounded, radially-stratified waveguide. Field solutions for Maxwell's equations in uniaxially anisotropic multilayered cylindrical structures are well-known, and to avoid repetition, we adopt here a notation similar to that in [6,8,15,47,48,50] by assuming a time-harmonic dependence in the form exp(−iωt). It should be observed that the notation adopted here despite being very similar to that in [48] and [15], differs slightly in a few places.…”

“…Over the years, various techniques have been used to properly model logging-while-drilling (LWD) tools used in hydrocarbon exploration [8,14,15,26,47,48]. The complex geophysical formations that are prevalent in this type of problem can be handled using brute-force numerical techniques such as finitedifferences (FDs), finite-elements (FEs) and finite-volumes (FVs) [6,7,[17][18][19][20].…”

“…This geometry can be well approximated as a cylindrically stratified medium [10,14]. In this case, pseudo-analytical methods [10,14,29,[47][48][49][50] are a good alternative to brute-force methods as the former provide more efficient algorithms and a more practical forward engine for integration into inversion algorithms designed to estimate the Earth formation properties given the tool response [26,48,49].…”

“…Tilted-coil antennas (TCAs) are routinely utilized in well-logging tools [18,[47][48][49] to provide directional response (azimuthal sensitivity). Welllogging tools employing TCAs are also often called triaxial tools.…”

A Numerical Mode-Matching Method Based on Multiple-Knot Cubic B-Splines Applied to the Analysis of Well-Logging Tools

“…However, it is still impractical to employ brute-force methods in inversion efforts where a large number of forwards simulation is required for a parameter space sweep. On the other hand, methods that combine both numerical and analytical steps [8][9][10][11][12][13], such as the numerical mode-matching (NMM) [14][15][16][17], are able to model complex geophysical formations while requiring only a modest amount of computational resources compared to brute-force methods.…”