Pulsed Neutron Logging

V. M. Zaporozhets, S. A. Kantor

(Presented at the Second Interuniversity Conference on Electron Accelerators)

An electron accelerator can be used as a pulsed neutron generator, which makes it possible to implement a number of new methods of neutron logging [7].

Let us consider two of the most promising of these methods.

Neutron gamma logging by recording gamma radiation arising from inelastic scattering of fast neutrons by the nuclei of atoms in rocks

Scattering of fast neutrons by atomic nuclei may occur as a result of their elastic and inelastic collisions with nuclei. In inelastic collisions, part of the neutron’s kinetic energy is transferred to the nucleus as excitation energy. After the neutron has been emitted by the compound nucleus, a final nucleus is formed in an excited state, from which a transition is possible with the emission of one or several gamma quanta. The transition process may be regarded as practically instantaneous.

There are data [1] showing that the energy spectrum arising in the inelastic scattering of gamma radiation differs for different elements and therefore can be used for their identification.

Figure 1 shows the differential spectra of gamma radiation arising from inelastic scattering of neutrons with an energy of 14 MeV by the nuclei of atoms of the principal rock-forming elements. Noteworthy is the presence in the spectrum of carbon gamma radiation of a clearly expressed line at approximately 5 MeV, and the absence of clearly expressed lines in the spectra of other rock-forming elements, except oxygen, which gives harder radiation of about 6.5 MeV.

Carbon is a constituent of oil; therefore, detecting the presence of carbon is equivalent to detecting the presence of oil, when the oil-bearing formations are devoid of calcareous cement and impurities of organic origin.

Of great interest is the development of a method for studying rocks penetrated by a borehole, based on irradiating them with a flux of fast neutrons and recording the gamma radiation arising from inelastic collisions of neutrons with atomic nuclei.

To make this possible, a measurement technique is needed that ensures the recording of gamma radiation from inelastic collisions

Fig. 1. Differential spectra of gamma radiation from inelastic collisions of neutrons with an energy of 14 MeV with nuclei of atoms of the principal rock-forming elements.
1 — background, 2 — carbon (graphite), 3 — oxygen, 4 — iron, 5 — magnesium, 6 — aluminum, 7 — calcium, 8 — silicon

separately from the gamma radiation arising when slowing neutrons are captured by the nuclei of atoms in rocks. This procedure can be carried out using a pulsed neutron generator. In this case the measurement process is as follows.

After a certain time \(t_1\) following the start of generation of a neutron pulse, the input of the gamma spectrometer is opened for a time \(t_2\), and the spectrum of gamma radiation from inelastic collisions is recorded until the intensity of the interfering gamma radiation from the capture of thermal neutrons becomes significant. Then neutron generation is stopped, a certain time \(t_3\) is allowed to elapse until all neutrons have been absorbed, a neutron pulse is generated again, and so on. Let us consider the time characteristics of this process.

To provide the best measurement conditions, it is desirable that generation of the neutron pulse cease simultaneously with the closing of the gamma-spectrometer input, or immediately after it, and that the intervals between pulses not be excessively long. For the same reasons it is desirable that the time interval \(t_1\) between the beginning of generation of the neutron pulse and the opening of the gamma-spectrometer input not exceed the time required for the fast neutrons emitted first to undergo inelastic collisions.

This time is very short. Consider, for example, the practically most interesting case, in which the initial energy of the generated neutrons is equal to 14 MeV. The velocity \(v\) of these neutrons is approximately \(5.4 \cdot 10^9\ \mathrm{cm/sec}\), and the mean free path \(\lambda\) in rocks does not exceed \(10\ \mathrm{cm}\).

In this case

\[ t_1 = \lambda/v < 2 \cdot 10^{-8}\ \mathrm{sec}. \]

We do not consider substantially lower neutron energies, since the probability of their inelastic scattering on the nuclei of atoms of rock-forming elements, accompanied by the emission of \(\gamma\)-quanta, is small.

Since the gamma radiation from inelastic collisions arises and disappears almost simultaneously with the switching on and switching off of the neutron generator, we arrive at the conclusion that the gamma spectrometer

should be switched on practically simultaneously with the start of pulse generation ($t_1 \simeq 0$).

In estimating the optimal value of $t_2$, we shall proceed from the time required for the first fast neutrons to slow down to the thermal state and to be captured by the nuclei of atoms of the rocks, with emission of gamma quanta. The slowing-down time in water of a fast neutron to thermal energy is equal to $10^{-5}$ sec [3]. In rocks the hydrogen content is always less than in water, and the slowing-down time will exceed this value. Thus, for at least $10$ μsec after the start of neutron generation, one should not expect the appearance of any appreciable intensity of capture gamma radiation; therefore the duration $t_2$ of the generator pulse may be equal to, or somewhat exceed, this value. Subsequently it will be necessary to determine more accurately the optimum value of the time interval $t_2$ by calculation and experiment, taking into account the probability of inelastic scattering of neutrons not in the first, but in their subsequent collisions with the nuclei of atoms of the rocks.

The time during which the capture of slowed-down neutrons occurs with emission of gamma quanta is characterized by the mean lifetime of a thermal neutron in the rock, which for most rocks lies within the range from several tens to several hundreds of microseconds. The time $t_3$ between pulses of neutron radiation should desirably be chosen so large that, when the subsequent pulse is generated, there is no gamma radiation caused by the preceding pulse. This condition will be fulfilled if $t_3$ is not less than $500 \div 1000$ μsec, i.e., if the pulse repetition frequency does not exceed $1000 \div 2000$ pulses/sec.

With the indicated operating regime of the pulsed neutron generator, one may hope to record gamma radiation from inelastic collisions separately from the gamma radiation arising upon capture of thermal neutrons. If these conditions are departed from, the effectiveness of detecting gamma radiation from inelastic collisions will decrease. It may be estimated from the following considerations.

As is known [4], the cross section for inelastic scattering of fast neutrons amounts to about one half of the total cross section. If the first collision of a fast neutron is elastic, it will lose only an insignificant fraction (of the order of 0.1%) of its energy and, with high probability, may undergo an inelastic collision at the next collision. Therefore it may be assumed that almost every fast neutron will participate in inelastic scattering. On the other hand, the loss of energy by a fast neutron in inelastic scattering is so considerable that the probability of the occurrence of gamma radiation in subsequent inelastic collisions with the nuclei of atoms of rock-forming elements is practically excluded for it. Hence it follows that each emitted neutron undergoes one inelastic collision, causing intense gamma radiation.

Since every neutron will ultimately be captured with emission of gamma radiation, the ratio of the intensities of the radiation from inelastic collisions and from capture will depend on the ratio of the number and energy of the gamma quanta emitted in these processes.

According to a preliminary estimate, for rock-forming elements the average number of gamma quanta emitted upon capture of a thermal neutron is close to 2, and upon inelastic scattering of a fast neutron—to 1. Therefore the number of gamma quanta emitted upon capture may be twice as great as their number due to inelastic scatter-

From this it is clear that the use of a pulsed technique can substantially increase the resolving power of the method.

As the duration of the neutron-radiation pulse is increased, the gain in sensitivity will decrease; as it is shortened, it will increase, but the accuracy of the measurements for a given duration will decrease. Depending on the research problem, the optimum ratio of efficiency and accuracy will have to be established experimentally. Thus, for example, if the time during which capture radiation occurs, measured from the start of generation of the neutron pulse, is equal to \(T\), and the duration of generation of the pulse and of registration of gamma radiation is \(t_2\), then, roughly speaking, the weakening of the effect of capture radiation is equal to \(t_2/T\). Since \(T \gg 100\ \mu\text{sec}\), taking \(t_2 = 20\ \mu\text{sec}\), which is quite feasible, we reduce the effect of capture gamma radiation by a factor of 5.

Examination of the spectra shown in Fig. 1 leads to the conclusion that, for the most common rocks, the spectra will be characterized by the presence of clearly expressed energy lines. By contrast, for gamma radiation from the capture of thermal neutrons, a spectrum closer to a continuous one will be characteristic. Therefore, by using a slot discriminator, one can achieve a substantial increase in the efficiency of registering gamma radiation from inelastic collisions when using pulsed techniques. It may even prove possible to carry out continuous registration of changes in the intensity of gamma radiation from inelastic collisions while moving a borehole instrument in the well.

It should be noted that, in addition to the pulsed mode of operation, a neutron generator has, over ordinary sources, the important advantage of generating high-energy neutrons. In this case the probability of inelastic scattering of neutrons with emission of a gamma quantum increases significantly; the efficiency of the neutron gamma-logging method under consideration should increase substantially.

Neutron–neutron logging by the method of investigating a nonstationary field of thermal neutrons

The method is based on the following considerations.

The space-time distribution of neutrons in a homogeneous medium surrounding a pulsed source of thermal neutrons is described by the nonstationary diffusion equation

\[ D \Delta n - n/\tau + Q \delta(\vec r)\delta(t) = \partial n/\partial t, \tag{1} \]

where
\(n\) is the neutron density;
\(D\) is the diffusion coefficient;
\(\tau\) is the mean lifetime of thermal neutrons;
\(Q\) is the number of neutrons emitted by the source during the pulse;
\(\delta(x)\) is the Dirac delta function of \(x\).

The solution of this equation, decreasing as \(r = (\vec r) \to \infty\) and \(t \to \infty\), has the form:

\[ n(r,t) = \frac{Q}{(4\pi Dt)^{3/2}} e^{-t/\tau - \frac{r^2}{4Dt}}. \tag{2} \]

It follows from relation (2) that the time dependence of the neutron density at a point located at a distance \(r\) from the source,

will have the form shown in Fig. 2. The neutron density at a point located at a distance \(r\) from the source reaches a maximum at the time \(t_m\)

\[ t_m=\frac{3}{4}\tau\left(\sqrt{1+\frac{4}{9}\frac{r^2}{L^2}}-1\right), \tag{3} \]

where \(L=\sqrt{D\tau}\) is the diffusion length of thermal neutrons.

The decrease of the neutron density with time for \(t \gg t_m\) is proportional to the quantity \(\exp(1-t/\tau)/t^{3/2}\). It follows from this that, having obtained the dependence \(n(r,t)\big|_{r=r_1}\) by direct measurement, one can determine, from the position of the maximum on the curve and from its decay, the parameters \(r\) and \(L\), which characterize the ability of rocks to slow down neutrons and are connected with their elemental composition.

If the source emits fast neutrons of one energy and the medium contains no hydrogen, the neutron distribution may be considered in the following simplified way. In this case the age approximation is applicable, and it may be assumed that the fast neutrons diffuse in the medium, continuously changing their energy and simultaneously slowing down to thermal energy over the time \(t_3\)

\[ t_3 \simeq \frac{2\lambda}{\xi v}, \tag{4} \]

where \(\lambda\) is the mean free path of a neutron;
\(\xi\) is the average logarithmic loss of energy by a neutron in one collision with an atomic nucleus.

Fig. 2. Dependence on time \(t\) of the density \(n\) of thermal neutrons at distances \(r_1\) (curve 1) and \(r_2\) (curve 2) from a source of thermal neutrons \((r_1<r_2)\). \(t_1\) and \(t_2\) are the times at which the maximum density of thermal neutrons is reached.

Only starting from this moment does the indicator begin to register neutrons; therefore the dependence shown in Fig. 3 will be observed. As can be seen, this case may be interpreted as analogous to that shown in Fig. 2, with the difference that the indicator is, as it were, switched on after a time interval \(t_3\) following the generation of the pulse.

Having obtained such a dependence, we will apparently be able, with sufficiently fast apparatus, to determine three parameters: \(\tau\), \(L\), and \(t_3\).

Fig. 3. Dependence on time \(t\) of the density \(n\) of thermal neutrons at distances \(r_1\) (curve 1) and \(r_2\) (curve 2) from a source of fast neutrons \((r_1<r_2)\). \(t_3\) is the time during which the neutrons slow down.

The amplitude of the curves in Fig. 1 in the case of a homogeneous medium is a single-valued function only of \(\tau\), \(L\), and \(Q\), and therefore provides no additional data on the properties of the medium beyond those obtained by analyzing the shapes of the curves. However, in the case of a real inhomogeneous medium (for example, a bed penetrated by a borehole), the amplitude

these curves will also depend on the geometry of the medium and may be used in interpretation.

The formulas obtained make it possible to estimate the times over which the processes proceed in the study of the nonstationary field of thermal neutrons. As an example, let us consider the distribution of neutrons in loose sand saturated with fresh water (porosity 40%). In this case \(L \simeq 5\ \text{cm}\), \(\tau \simeq 4 \cdot 10^{-4}\ \text{sec}\) [6]. It follows from formula (3) that, with an indicator located at a distance of \(25\ \text{cm}\) or \(50\ \text{cm}\), \(t_m\) will be, respectively, \(\sim 2 \cdot 10^{-3}\ \text{sec}\) and \(\sim 4 \cdot 10^{-3}\ \text{sec}\). The decline of the curve will occur over a time of the order of \(4\tau\) after \(t_m\). Thus, the duration of the thermal-neutron pulse recorded by the indicator will be \(\sim (t_m + 4\tau)\) and, in the example considered, is equal to \(3.6 \cdot 10^{-3}\ \text{sec}\) for \(r = 25\ \text{cm}\) and \(5.6 \cdot 10^{-3}\ \text{sec}\) for \(r = 50\ \text{cm}\).

The result obtained is important for the design of pulsed neutron-logging equipment. In particular, it follows from the calculation given that the intervals between neutron pulses should be of the order of \(10^{-2}\ \text{sec}\), so that practically all neutrons from the preceding pulse have time to be captured in the vicinity of the indicator.

The duration of the neutron pulse must be much less than \(\tau\); otherwise the decline of the curve will be distorted and it will be difficult to determine the value of \(\tau\) from it. As a rough guide, the pulse duration should be no more than several tens of microseconds.

As can be seen, the use of a neutron generator makes it possible, by implementing a method for studying the nonstationary field of thermal neutrons, to study the character of rocks in substantially greater depth, since with this method it is in principle possible to obtain separately the neutron parameters of rocks, which are closely associated with the features of their elemental composition and, in particular, with the presence in them of elements that strongly absorb neutrons (for example, chlorine).

References

1. Caldwell R. L. Nuclear physics in petroleum exploration research. World Petroleum, 27, No. 4, 59—63, 1956.

2. Baner P. E. Neutron capture gamma-ray spectra of earth formations. Petroleum Transactions, 210, 97—101, 1957.

3. Glasstone S. and Edlund M. Fundamentals of Nuclear Reactor Theory, GIIL, 1954.

4. Vlasov N. A. Neutrons, Gostekhteorizdat, Moscow, 1955.

5. Pert J. E.; Bame S. J. Phys. Rev., 99, No. 5, 1955.

6. Kantor S. A. Fundamentals of the theory of neutron logging. Applied Geophysics, No. 13, Gostoptekhizdat, Moscow, 1955.

7. Zaporozhets V. M., Sulin V. V. The use of charged-particle accelerators for solving problems of field geophysics (present collection).