Effects of Mandrel, Borehole, and Invasion for Tilt-Coil Antennas

Abstract

Summary Several recently published studies discuss the concept of inductive resistivity-logging devices with oblique transmitting and/or receiving coils. Both wireline induction and logging-while-drilling (LWD) propagation resistivity-tool concepts have been considered. Directional resistivity measurements and improved anisotropy measurements are among the benefits promised by this type of device. Analyses based on point-magnetic dipole antennas were used to illustrate these potential benefits. The effects of a metallic mandrel, borehole, and invasion were not considered because of the absence of a suitable forward model. This paper characterizes mandrel, borehole, and invasion effects for a variety of candidate tilt-coil devices with antenna array parameters similar to those of the previous studies. The characterization is based on calculations from a new forward model that includes tilted transmitting and receiving coils of finite diameter embedded in a concentric cylindrical structure. Important details of the forward model used in the calculations are also provided. Introduction Conventional propagation resistivity devices are routinely used for geosteering applications. Because data from these devices have essentially no azimuthal sensitivity, the LWD engineer is greatly aided by a priori information regarding the proximity of the target bed relative to other geologic features such as shales and water-bearing zones. Suitable a priori information is often available from offset logs. In cases in which offset logs are not fully useful because of changing depositional environments or different tectonic settings, azimuthally sensitive resistivity data would improve the quality of the geosteering effort. One way to achieve azimuthal sensitivity to benefit geo-steering (and to use it for imaging) is to construct a tool similar to a conventional propagation resistivity device, but with the transmitters and/or receivers tilted with respect to the axis of the drill collar. In fact, directional resistivity tools(DRTs) have been proposed in the literature for this pur-pose.1–3 To the knowledge of the authors, DRTs have only been analyzed with point-dipolemodels, which ignore both the drill collar and the finite size of the antennas. For apparent lack of a suitable forward model, mandrel, borehole, and invasion effects have not been considered in the literature. A model has been developed that accounts for tilted transmitters and receivers embedded in arbitrary layers of a concentric cylindrical structure. Many important details of this model are discussed in Appendix A. The term mandrel effect is used here to denote the difference between values calculated with a point-dipole model and the model that accounts for the mandrel encompassed by the antennas. Mandrel effects on DRT measurements will be grouped into three categories:Absolute effects where the mandrel primarily attenuates the signals because of a reduction in the magnetic moment of the antennas.Residual effects that remain after an air-hang calibration is applied to the data.Perturbations to the azimuthal sensitivity of the measurement caused by the finite size of the antennas and the drill collar. Algorithms that transform raw tool measurements to resistivity values can be based on computationally simple point-dipole solutions without significantly degrading the accuracy of the results if mandrel effects associated with categories 1 and 2 can be suppressed. For conventional LWD propagation resistivity measurements, mandrel effects of type 1 are addressed by air-hang calibration. Algorithms that suppress type 2 mandrel effects are discussed in the literature.4 Type 3 mandrel effects are not discussed here.

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

“…129 3. 47 Voltage amplitude ratio and phase difference for the triaxial LWD tool depicted in case 1 (see Fig. 3.46) as a function of the invasion thickness d. The results from our (A-NMM-based) algorithm and from the R-NMM [9] are indicated by solid lines and small circles, respectively.…”

“…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].…”

Numerical Mode-Matching Method for Tilted-Coil Antennas in Cylindrically Layered Anisotropic Media With Multiple Horizontal Beds

“…, where θ T and φ T are the axial and azimuthal tilt angles of the TCA source, ρ T is the radius of the projection of the coil onto the transversal plane, and z T is the vertical location of the center of the coil [13], [14]. Note that ∇ · J = 0 [13] and even though the magnitude of the current density J above varies with φ, the flux of J over any (infinitesimal) cross section of the coil antenna (and hence the total current flowing along it) is constant and equal to I T .…”

“…Note that ∇ · J = 0 [13] and even though the magnitude of the current density J above varies with φ, the flux of J over any (infinitesimal) cross section of the coil antenna (and hence the total current flowing along it) is constant and equal to I T . Equation (2) can be rewritten as…”