Induction probes four-coil

Figure 8.2.2 (a) Schematic of the four-coil probehead introduced in Reference [12]. The four individual solenoidal coils are represented by an inductance (L), series resistance (R), and inter-turn capacitance (Q. The entire circuit was impedance-matched to 50 it at a frequency of 300 MHz by using the variable capacitors Ct and Cm. (b) Photograph of the four-coil assembly. Reprinted from MacNamara, E., Hou. T., Fisher, G., Wilhams, S. and Raftery, D., Multiplex Sample NMR an approach to high-throughput NMR using a parallel coil probe , Anal. Chem. Acta, 397, 9-16, copyright (1999), with permission of Elsevier Science... 

Figure 4.46. Three- and four-coil induction probes. TABLE 4.15...

For this reason an expression for the apparent conductivity of the four-coil induction probe is ... 

Unlike the three-coil induction probe (Fig. 4.46a), simultaneous measuring of a and with the four-coil probe has two shortcomings ... 

This function is the geometric factor of the cylinder for a four-coil induction probe with internal focusing and parameters p and c, i.e. it is the integral radial response. Let us notice that normalization of geometric factor allows us to compare radial responses of various probes. 

Introducing a fifth compensating coil, coefficient K becomes equal to zero, and correspondingly the radial response somewhat improves at its initial part. From this consideration follows that with an increase of the length of two-coil induction probes, forming a differential four-coil probe, the cylinder radius, characterized by small values of geometric factor, increases, provided that the primary electromotive force is compensated. 

Coefficient K2 exceeds unity, and therefore the radial response approaches its asymptote slower than that of a two-coil probe, i.e. the four-coil induction probe possesses a greater depth of investigations with respect to a two-coil induction probe of the same length. 

Figure 7.5 presents the integral radial response of a four-coil probe with parameters p = 0.4 and c = 0.05. Unlike the radial response of a two-coil induction probe, in this case function G r/L) at the beginning has small but negative values, near r/L = 0.27 it changes sign and monotonically approaches unity. 

G is the differential response of a four-coil induction probe and defines the ratio of signals from a thin cylindrical shell to that from a uniform medium. 

Until now it has been assumed that at all points of a medium induced currents are shifted in phase by 90°, i.e. the skin effect is absent. Now we will investigate radial responses of the probe, making use of results of the exact solutions in a medium with two cylindrical interfaces when the four-coil induction probe is located on the borehole axis. 

Figure 7.39. Profiling curves of induction probes (la) three-coil probe = S °Ll (lb) three-coil probe = S, (2) two-coil probe (3) four-coil probe p = 0.4, c = 0.08.

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