Three-coil differential probe

Now we will investigate the simplest differential system, namely the three-coil probe which consists of two transmitter and one receiver coil or one transmitter and two receiver coils. The distance between the pair of transmitter or receiver coils is significantly smaller than that to the remote coil. Let us suppose that the probe is located on the borehole axis, and it consists of one receiver coil with moment Ni, and two transmitter coils with moments Mi, and Mq. The latter are characterized by opposite direction of turns. Then, for electromotive force induced in the receiver by currents in the borehole and in the formation at the range of small parameters we have  

Suppose that the electromotive force of the primary field is compensated, i.e. we have Mi/L = M2lL. Then we obtain  

Let us assume that the lengths of both two-coil probes are much greater than the borehole radius, i.e. ai 1 and 2 3 1. Then, maJring use of the asymptotic expression for function Gi  

Thus due to the compensation of the electromotive force of the primary field the value of the geometric factor G turns out to be much smaller than the values of the geometric factor for two-coil probes, Gi(ai) and Gi(q 2). 

Radial responses of three-coil probes characterizing focusing features of these systems are presented in Figs. 7.33-7.35. 

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This behavior of the radial response of a three-coil differential probe is of great practical interest for solution of various problems, in particular for the determination of a relatively high resistive formation when the borehole is filled by a strongly mineralized solution (s = (T2/(Ji < 0.001). Inasmuch as for obtaining reliable measured signals created by currents in a slightly conductive medium it is necessary to apply relatively high frequencies, when the skin effect in the mineralized solution of the borehole can be noticeable, it is appropriate to use results of calculations by exact formulae. 

In conclusion, it is appropriate to notice that three-coil differential probes due to their simplicity can be used for lateral soundings. Examples of sounding curves, calculated for the range of small parameters, are given in Figs. 7.41-7.44. They demonstrate that such soundings can be performed with relatively short probes. 

The depth of investigation can be significantly increased in applying a three-coil differential probe. In this case the minimal length of a two-coil probe forming a differential array should correspond to the ascending branches of curves For illustration, values... 

We will consider several differential probes and will start with a symmetrical four-coil probe with additional internal coils. This type of probe is defined by three parameters, namely the distance between basic coils, L, the ratio of the length of focusing probe RTr to that of the basic probe, which is denoted by p, and the ratio of moments of focusing coils to the moment of basic ones (parameter c). 

Equations 10.49 and 10.51 present the magnetic field as a sum of terms, each of which depends on the conductivity of the borehole or that of the formation only. This fact allows us to apply differential probes described in previous chapters, which significantly decrease the effect of the borehole. The simplest differential probe, investigated in detail above is three-coil probe providing compensation of the primary field (Fig. 10.15). 

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