Induction probes three-coil

Let us notice that this behavior of the geometric factor of the borehole defines a radial characteristics of the simplest focusing induction probe consisting of three coils. 

These last three equations allow us to investigate the radial responses of a two-coil induction probe in detail, in other words, to evaluate the influence of the borehole, the invasion zone and the formation as a function of the induction probe length, L, for various geo-electric parameters. 

In the far zone the influence of the borehole and the invasion zone does not depend on the length of the induction probe. Such a behavior of the field presents a certain practical interest, inasmuch as it allows us to increase the depth of investigation significantly, measuring the ratio of amphtudes and differences of phases by three-coil induction probes. 

In Chapter 7 we will consider in detail multi-coil induction probes which essentially allow a decrease on influence on induced currents in the borehole as well as in the invasion zone. At that time questions related to magnetic permeability will not be investigated more. For this reason let us here briefly demonstrate that multi-coil probes can be applied in order to reduce the influence of induced currents in a conductive and magnetic medium of the borehole (Fig. 4.46). As the first example we will consider a three-coil induction probe consisting of one generator and two measuring coils (Fig. 4.46a). The distance between the later is significantly less than that between the transmitter and receiver coils. Moments of receiver coils are chosen in such a way that the electromotive force in a free space, is equal to zero. 

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

In accord with eq. 4.263, a coefficient of the three-coil probe is a function of parameter s, in particular, of magnetic permeability of the borehole. For this reason in order to calculate the apparent conductivity, aa, it is necessary to define parameter s. It can be done by measuring the inphase component of the field, since within a wide range of frequencies and conductivities this component practically depends on parameter s only. Values of the inphase component of the magnetic field expressed in units of the primary field in a free space for a two-coil induction probe with various lengths, are given in Table 4.16. 

We assume that, for most cases which are of great practical interest in induction logging, data presented in this table coincide with the magnetic field of a direct current. Therefore, by measuring the inphase component with a three-coil induction probe or with a probe of two coils, parameter s and, respectively, coefficient of the probe are defined. This enables us to calculate, the apparent conductivity by making use of quadrature component data. 

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

Development of interpretation of soundings based on use of two- or three-coil induction probes with different lengths. 

Now let us consider the influence of parameters of a three-layered medium (an invasion zone is present) on the apparent conductivity measured by probes 6F1M, 4F1 and 4F1.1. Values of <7a/o 3 for various parameters of a three-layered medium along with data for a two-coil induction probe are given in Tables 7.12-7.22. The borehole resistivity is assumed to be 0.5 ohm-m. The behavior of (Ta/c s depends to a certain extent on the sign of geometric factor of Gi(r) for r = oi and r = 02. 

Assuming that for three-coil induction probe Pmin = 0.13 and Pmax = 0.8 we obtain Ap = 40, i.e. it has a relatively broad range of measured resistivities. Of course, in practice this range is essentially wider. 

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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