Daniela Renjel Encinas
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Besides the GR logs, neutron logging is another radioactivity logging method. The interaction between formation and neutron is the physical foundation for neutron logging, and its behavior depends on the energy when the neutron emitted from the source. The interaction, after the neutron entering into the formation, has four variable types with changing of the energy of neutron. These are fast inelastic scattering, fast neutron activating, fast elastic scattering, and thermal neutron diffusion and capture.
There are several types of fast neutron interaction, broadly classified as follows:
4.2.1 Fast Neutron Scattering
4.2.1.1 Inelastic Scattering
Some of the incident neutron energy imparted to the target nucleus excites it to a higher bound-state. The excited state lasts less than a microsecond, and the ensuing prompt return to ground-state results in the emission of radiation. Excitation half-life is 3.8 10−l4s, and a gamma ray of energy 4.44 meV is produced. In fact, this is the only emission peak observed from12C. Reaction: an important example is the neutron-induced alpha emission from16O, which results in the production of a13C isotope and the annihilation of the neutron. The13C nucleus may be already at ground-state, or it may be excited, in which case a gamma ray is promptly emitted at 3.09, 3.68 or 3.86 meV.
4.2.1.2 Activation of Atom
The target nucleus is transformed to an unstable intermediate isotope which decays with a relatively long half-life to thefinal nucleus. If this is in an excited state, a prompt emission of gamma radiation accompanies the return to ground-state.
The common elements currently detected by inelastic spectrometry include:
carbon C; oxygen O; silicon Si; calcium Ca; iron Fe; sulfur S; (chlorine C1, an almost negligible yield).
4.2.1.3 Slowing-Down Phase
Following the fast neutron phase, the neutrons are rapidly slowed down by elastic collisions with nuclei. The energy lost at each encounter depends on the angle of incidence with, and the mass of, the target nucleus. Slowing-down length (Ls) is introduced to depict this procession, which is defined that length before the fast
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neutron ultimately reaching thermal neutron with energy decreased from 2 to 0.025 meV. The mechanics of elastic collisions predict that the maximum energy will be lost when the target nucleus has a mass equal to that of the incident neutron.
The decayed energy (△E) can be calculated by the following equation:
DE ¼ 2A
ðA þ 1Þ2En0 ð4:9Þ
where
△E the average energy loss of fast neutron;
A number of target nucleus En0 initial energy of fast neutron
The time of elastic scattering of fast neutron mainly depends on the number of target nucleus. The more nucleuses with little number are there in the mass, the shorter time of the elastic scattering time. As seen in the Table4.1, hydrogen has the smallest nuclear number, hence it most strongly slow down the fast neutron. So the scattering time and slowing-down length depend on the content of hydrogen.
Thus it is that neutron slowdown is most strongly affected by hydrogen atoms (H), the single proton of the nucleus having very nearly the mass of a neutron. The average energy lost in collisions involving12C. For instance, is only 14 %, while for16O is 11 %.
The probability of a collision occurring with a particular element depends, obviously, on the number of its atoms present in a given volume of formation, i.e., the atomic concentration per cm. However, another parameter must be considered:
the elastic interaction cross section. This is a characteristic of each type of atom. It has the dimensions of area and can be considered as the effective surface area presented by the nucleus to the oncoming neutron.
Since, at moderate porosities, hydrogen is relatively highly abundant, and its atoms are at least a factor of 10 more effective at slowing-down neutrons than the other common elements, it follows that the slowing-down phase is very dependent on the concentration of hydrogen or the hydrogen index (Hx). Hxis the ratio of the amount of Hydrogen atoms with that of same volume of water.
Neutrons continue to be slowed down until their mean kinetic energies are equal to the vibration energies of the atoms in thermal equilibrium. Thermal energy is 0.025 eV at 25 °C, corresponding to a mean velocity of 2200 m/s. There are only 18 collisions required for hydrogen to slow a neutron down from 2 meV to thermal
Table 4.1 Slowing-down length and diffusion length for clean sandstone
Porosity (%) Slowing-down length (Ls, cm) Diffusion length (Ld, cm)
3 17.8 13.1
11 13.7 8.5
23 11.5 6.6
34 10.5 4.2
4.2 Interaction Between Formation and Neutron 133
energy, while other common elements require several hundred. The entire slowing-down phase requires of the order of 10–100 ms, depending on conditions.
4.2.2 Thermal Neutron Interaction
The important chlorine capture interaction is:
35Clþ n !36Clþ c Its half-life is of the order of 10−20 s.
The neutron is absorbed, or captured, and the excited nucleus decays to ground-state with the emission of a gamma ray, in this case at 7.42 or 7.77 meV among others. Not all elements produce gamma rays, and some are outside the range of detection of the logging equipment. Common elements currently measured by capture spectrometry include: chlorine C1; hydrogen H; silicon Si; calcium Ca;
iron Fe; and sulfur S.
Capture events generally occur at highest probability when neutrons reach thermal energy, and the term“thermal neutron capture” is used commonly for this class of interaction. The mean free path of 14-MeV neutrons down to thermal energy is, not surprisingly, larger than that of the fast neutron phase.
4.2.2.1 Diffusion
A cloud of thermal neutrons forms around the source. It is unevenly distributed in space because of the inhomogeneous nature of the borehole and formation.
Collisions between the vibrating neutrons and nuclei continue and there is a general spreading or diffusion of the cloud outwards into the formation, where the con-centration of thermal neutrons is low. Some diffusion of neutrons back towards the borehole may also occur.
4.2.2.2 Capture
Occasionally, during this diffusion phase, a nucleus will capture a neutron, resulting in its total absorption. The nucleus becomes momentarily excited and on returning to its ground-state, emits one or several gamma rays, or some other radiation.
A number of common elements are compared in Table4.2. In much the same way as for elastic interactions, each element has its thermal capture cross section (c in the Table). Note that, for capture, hydrogen is only moderately important, while chlorine ranks as the most effective of the common elements. Gadolinium, boron, and lithium occur infrequently as trace elements in formation water, and boron is often found in shales. Its proportion is related to the type of clay mineral and the
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salinity of the depositional environment (Fertl 1973). The significance of their presence can be appreciated from Table4.2.
4.2.2.3 Measurement Principles
Neutrons of energies between 4 and 6 meV are emitted continuously from a chemical source. The neutrons travel initially at some 10,000 km/s and have a high penetrating power. They interact both inelastically and elastically with atomic nuclei in the formation and the borehole surrounding the source. The life of these neutrons can be divided into four phases: fast, slowing down, diffusion, and capture.
Spatial Distribution of Thermal Neutrons and Capture Gamma Rays
Consider a point source of neutrons surrounded by an infinite homogeneous medium. High-energy neutrons are continuously emitted in all directions. The lifetime of these neutrons (from emission to capture) averages less than a millisecond in general.
A balance is rapidly established between the influx of “fresh” neutrons from the source and the absorption of thermal neutrons by capture, resulting in a spherical cloud of thermal neutrons whose spatial extent is primarily a function of the hydrogen concentration.
The thermal neutron density is constant over the surface of any sphere centered about the source, and decreases with distance from the source according to Fig.4.14. Note that near to the source (the “short spacing’’ region) the thermal neutron density increases with hydrogen concentration, while farther out (the“long spacing” region) the opposite occurs. In the intermediate “cross-over’’ region there is almost no dependence on hydrogen concentration.
Since the number of gamma rays being emitted by capture is proportional to the number of thermal neutrons being captured, the preceding comments apply, with the difference that the gamma rays are able to penetrate further into the formation.
Table 4.2 Capture cross section and scattering cross section common elements Element
4.2 Interaction Between Formation and Neutron 135
Fig. 4.14 Thermal neutron density with distance from a point source
Fig. 4.15 Schematic of the one detector density tool
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