Induction probes multi-coil

H. Doll also introduced the differential multi-coil probes, which became very efficient logging tools and defined the path of development and application of induction logging over almost forty years. The use of these differential measurements in induction logging provides a result in which the effect of the borehole fluid, and in many cases also the invasion zone, on measurements is greatly reduced. Such devices are described in detail in this monograph. 

It is important to emphasize that the analysis of calculations based on the exact solution and this theory allows us to establish the character of distribution of induced currents in a medium that is of great practical interest for the development and application of multi-coil focusing induction probes. 

There is another factor defining an upper limit of frequency. It is dictated by the fact that the efficiency of focusing multi-coil induction probes takes place provided that currents in the borehole have to be shifted in phase by 90°. 

A choice of frequency or frequencies for induction logging cannot be done by using the results of calculation of the field in a medium with only cylindrical interfaces. However, these data allow us to investigate radial characteristics of two-coil induction probes, as well as other types of probes, consisting of several coils. In particular, comparison of calculations basted on exact and approximate methods permits us to establish a range of frequencies and resistivities of a medium where it is reasonable to apply so-called focusing multi-coil 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. 

In this chapter we will consider vertical responses of two-coil induction probes located arbitrarily with respect to interfaces between a bed and a surrounding medium. Special attention will be paid to the influence of frequency, ratio of conductivities and geometric factors such as formation thickness probe length and probe position. It is appropriate to notice that analyses performed in this chapter are used for investigation of vertical responses of multi-coil induction probes. 

It is appropriate to notice that results of this investigation are directly used in developing the theory and interpretation of multi-coil induction probes. 

At the beginning we will consider multi-coil induction probes, proceeding from the theory of small parameters, when we can neglect the interaction between currents. In other words, currents in any part of the medium, regardless of how far from the probe it is located, create a signal which is only defined by the conductivity and the geometric factor of this part. 

For improving the vertical response of a two-coil induction probe it is necessary to decrease the relative contribution from the surrounding medium with respect to the signal caused by currents in the formation against which a two-coil induction probe is located. In other words, in this case the influence of more remote parts of the medium has to be reduced providing a significant signal from currents induced in that part of the medium which is located relatively close to the probe. Thus, improvement of radial and vertical responses of a two-coil induction probe is related to the development of multi-coil probes which have to satisfy opposite requirements. 

Arbitrarily, a multi-coil induction probe can be presented as a sum of two-coil induction probes. Currently, there are known symmetrical and non-symmetrical multi-coil induction probes, and their characteristics will be considered in detail in the next sections. As a rule in induction logging using one frequency the electromotive force, caused by the current in the transmitter coil or coils, is significantly greater than that generated by induced currents in the medium. For this reason an additional compensating coil to increase the accuracy of measurement is installed. Due to this the electromotive force caused by the primary field is practically equal to zero. It is also appropriate to notice that some differential probes do not require a compensation coil. 

It is obvious that the radial differential response of the multi-coil induction probe does not depend on the distribution of conductivity in the radial direction if within every cylindrical layer the resistivity remains constant. 

Direct and inverse integral responses are presented in Fig. 7.2. Applying the graphical method we can choose corresponding characteristics of multi-coil induction probes. 

From the point of the depth of investigation the direct integral response of a multi-coil induction probe has to satisfy two conditions ... 

The accuracy of determination of small values of the geometric factor at the initial part of the response is usually very low. It becomes specially noticeable in the case of a nonuniform medium, for example, when the borehole is much more conductive than the formation. For these conditions the focusing abilities of a probe, chosen by the graphical method, can be insufficient in order to eliminate the influence of the borehole or the invasion zone especially, if the latter is more conductive than the formation. For this reason focusing features of a multi-coil induction probe, chosen by the graphical method, manifests themselves as a rule only for relatively small ratios p jP -... 

Thus, the procedure of choosing parameters of multi-coil induction probes allowing us to eliminate the influence of k arbitrary parts of the medium is reduced to a solution of a system of k equations ... 

However, absence of the skin effect in the area, the influence of which it is necessary to reduce, is not sufficient for the efficiency of multi-coil induction probes. Let us present a signal measured by the probe as a sum of two signals, namely, one which is caused by currents in the area where there is not practically interaction between currents and a... 

As was mentioned above every multi-coil induction probe can be considered as a sum of two-coil probes namely the basic induction probe and additional coil probes which provide improvement of the radial response. Electromotive forces induced in these probes can have the opposite sign to that in the basic probe as well as the same sign. However, the probes where the electromotive force has opposite sign play the most essential role and correspondingly, only they will be taken into consideration here. 

As is known, parameters of the multi-coil induction probe are chosen with the assumption that the invasion zone has an infinite extension along the borehole axis. In real conditions penetration of borehole filtrate into a formation and surrounding medium occurs in a different manner due to the difference of their physical properties. For this reason it is appropriate to consider focusing features of multi-coil induction probes when the invasion zone has limited dimension along the borehole axis. 

As was shown before, the better the focusing of a multi-coil induction probe the narrower the range of measured resistivities, and correspondingly the same effect is observed for other differential probes. We will characterize the range of measured resistivities by the... 

If we assume that Pmin — 0.07 and Pmax = 1-4 (P = L/h) then for a two-coil induction probe Ap 400. For multi-coil induction probes Ap depends on parameters of the probe. For example, we have ... 

The Influence of Eccentricity on Focusing Features of Multi-coil Induction Probes... 

In Chapter 4 we investigated an influence of displacement, tq, from the borehole axis on the radial responses of a two-coil induction probe. These results allow us to consider the dependence of radial responses of multi-coil probes on the value of displacement Tq. 

If we suppose that all two-coil induction probes forming a multi-coil system are sufficiently long and that we can use the asymptotic expression for geometric factor GJ, then instead of eq. 7.51 we have ... 

Considering the field of the magnetic dipole as well as induced currents in a uniform conducting medium it was established that with an increase of frequency the role of those parts of the medium which arc relatively close to the probe increases. For this reason the vertical response of a two-coil induction probe significantly improves, but simultaneously the influence of currents induced in the formation, with respect to those in the borehole and in the invasion zone, becomes lesser. Unlike of a two-coil induction probe the influence of the medium directly surrounding the multi-coil probe is very small, and an increase of frequency up to a certain limit does not practically change its radial response. 

Besides, improvement of the vertical response of a multi-coil induction probe due to measurements at higher frequencies allows us to apply induction logging in a more resistive medium, inasmuch as the ratio between the quadrature component of the electromotive force and that of the primary field increases. 

Therefore, the coefficient of the multi-coil induction probe can be presented in the form ... 

The use of differential multi-coil probes is the most conventional approach in application of induction logging. 

Any multi-coil induction probe, regardless of the amount of transmitter and receiver coils, by no means performs focusing of the field as it takes place, for example, in optics. In effect, every induction probe, except a two-coil one, is a differential system measuring such a difference of signals in receivers that the influence of induced currents in the borehole and in the invasion zone is significantly reduced. 

In such cases when the depth of investigation of the multi-coil probe is not sufficient in the radial direction, and correspondingly the apparent conductivity differs from the formation conductivity, in order to perform interpretation it is necessary to have additional information derived from either other induction probes or applying different logging methods. It is obvious that similar types of problems arise when the influence of the surrounding medium becomes essential. 

In fact, the integral response, as well as the differential one, defining a signal in receiver coils due to induced currents in an arbitrary cylindrical layer with a constant resistivity, present the basic element of these calculations. However, the presence of caverns, deviation from radial distribution of resistivity because of nonuniform penetration of a borehole filtrate into a formation, its finite thickness are factors which can influence the focusing features of multi-coil induction probes. In order to eliminate the influence of these factors and to increase the depth of investigation, regardless of the geoelectric section, we will consider in this chapter another approach, based on the use of a two-coil probe and a simultaneous measurement at two or more frequencies if the quadrature component is measured. 

As is well known, an increase of the depth of investigation in induction logging is usually realized with the help of multi-coil differential probes that in many cases permit us to eliminate the influence of currents in the borehole and in the invasion zone. 

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