Depth of investigation

Azimuthal resistivity (depth of investigation Gamma ray 12in. orless) detector... 

Mud filtrate invasion is normally restricted to within a few inches into the formation, after which the build up of mudcake prevents further filtrate loss. If resistivity tools with different depths of investigation (in the invaded and non-invaded zones) are used to... 

As was shown in Chapter 2, near the source the quadrature component of the current is practically defined by the primary vortex electric field. Correspondingly, if the area, where such behavior takes place, is greater than the depth of investigation of the given probe, Doll s theory describes the field behavior with a sufficient accuracy. 

Again the inphase component of the magnetic field in the borehole is not practically subjected to the influence of induced currents in the borehole and in the invasion zone, and it coincides with the inphase component in a uniform medium with the formation conductivity, (73. In this approximation induced currents in the borehole and in the invasion zone contribute to the quadrature component of the field. This consideration clearly shows that the inphase component of the magnetic field has a different sensitivity to geoelectric parameters of a medium than the quadrature component, and therefore they are characterized by different depths of investigation. It is clear that the analysis of the current distribution in a uniform medium, performed in Chapter 2, is in complete agreement with these results. 

It is obvious that with an increase of the probe length the depth of investigation also increases, that is, the probe becomes more sensitive to removed parts of a medium. For this reason the skin effect display is more noticeable for longer probes regardless of the character of the resistivity distribution within the borehole and the invasion zone. 

Calculations demonstrate that the influence of frequency and conductivity of a formation on the magnitude of the ratio Q S/So is practically the same as in the previous case. At the range of small values of parameter (T2/xa the relative contribution of currents induced in the bed constitutes about 80% while for a value of 02lMXi = 0.64 the contribution of the formation is equal to 70% but the ratio Q S/So essentially increases. For this reason with an increase of the frequency the depth of investigation of a two-layered medium by a two-coil induction probe does not change until the signal from the formation is greater or at least comparable with that caused by induced currents in the borehole. Also the natural limitation of a further increase of frequency is related with a nonunique interpretation, inasmuch as the spectrum of the quadrature component has a maximum. 

From eq. 4.126 it follows that the leading terms of the quadrature and inphase components are related with parameters of a geoelectric section in a completely different manner and therefore, in general, have a different depth of investigation. This question will be considered later in detail. 

As follows from eqs. 4.126 the second term of the quadrature component and the leading term of the inphase component of the magnetic field, H, do not depend on the probe length, nor on the geoelectrical parameters of the borehole and the invasion zone. Therefore, regardless of the separation of the coils measuring these quantities we can essentially increase the depth of investigation on the induction probe. 

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. 

The depth of investigation of the probe becomes greater with an increase of the probe length. 

As was pointed out before, this fact demonstrates the greater depth of investigation in the radial direction when the inphase component is measured. 

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

Choice of optimal parameters of a differential probe which provides a certain depth of investigation or a sensitivity to specific parts of a medium as well as a maximal signal from these parts of the medium. 

For this reason we can say that a necessary condition for the application of differential probes is the absence of interaction between currents in those parts of a medium the influence of which should be significantly reduced. In other words, those parts of the medium have to correspond to Doll s area where the current density is defined by the primary magnetic flux and the conductivity at a given point. It is natural that in choosing parameters of probes in order to increase the depth of investigation in the radial direction, it is important to eliminate the influence of parts of the medium located relatively close to the source. As calculations show, this condition usually takes place even for sufficiently high frequencies. 

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. 

Also, a choice of a frequency is defined by focusing features of the probe. For example, for multi-coil probes having a greater depth of investigation in a relatively conductive medium the frequency should be smaller. In particular, it was established that for probe... 

Due to the use of these probes induction logging in most cases has the greatest depth of investigation among other logging tools. 

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. 

As is well known with the help of multi-coil differential probes we can reduce significantly the influence of the borehole and, often, the invasion zone, if the conductivity and the radius of the latter are not large enough. In other words, the depth of investigation of such probes in the radial direction essentially depends on the geoelectric parameters of the medium. Also, in calculating coil moments and their position for these probes it is assumed that the resistivity of the medium is only a function of the distance from the borehole axis, i.e. it changes only in the radial direction. 

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. 

In principle, as was pointed out above, measuring the inphase component at one frequency corresponding to the low-frequency spectrum provides the same depth of investigation. At the same time, it is reasonable to notice that inasmuch as first terms of series for the inphase component decrease slower than those of series for the quadrature one, in measuring the inphase component it is necessary to use lower frequencies in order to provide the same depth of investigation. 

In the case when the radius of the invasion zone is eight times greater than the borehole radius (02 = 8ai) the upper boundary frequency becomes essentially smaller. Correspondingly, the vertical response of the probe deteriorates. At the same time with a decrease of frequency the depth of investigation in the radial direction increases, and it becomes possible to determine the formation resistivity with the small probe even when the radius of the invasion zone exceeds by more than ten times the borehole radius. 

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. 

However, the theory and numerous experiences show that for a given length of the basic probe, L, the depth of investigation in the radial direction does not exceed (0.5 0.6)L, and with an increase of the conductivity of the borehole and the invasion zone it becomes less. 

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