NEUTRON INTERACTIONS

Neutron interactions within the formation or borehole form the basis of operating principals for a variety of openhole and cased hole tools. For this reason, it is important to understand elementary physics relating to the way neutrons and their gamma rays interact with key components in the formation or wellbore. The following lists a sampling of the breadth of approaches used in logging which take advantage of neutron interactions:

• The gamma ray log makes counts of natural gamma radiation to indicate the presence of shales.
• The neutron log exploits the slow-down of neutrons resulting from neutron scattering to estimate formation porosity.
• The density log uses attenuation of gamma rays caused by Compton scattering to estimate formation porosity.
• The natural gamma ray spectrometry log counts gamma rays and measures their energy levels to evaluate specific geochemical components of the formation, such as potassium, uranium, and thorium.
• The P_e log compares gamma ray counts between energy regions dominated by photoelectric effect and by Compton scattering to determine the photoelectric absorption index, which is used to ascertain formation lithology.
• The thermal decay time log uses the rate of thermal neutron absorption to estimate water saturation in cased holes.
• The cased hole gamma spectrometry tool measures the spectrum of capture gamma rays, given off after the process of thermal neutron absorption, to estimate the abundance of hydrogen, chlorine, silicon, calcium, iron, and sulfur for evaluating lithology behind casing.

COMPONENTS OF THE ATOM

Before we start our discussion of neutron interactions, we will describe key atomic components, in order of discovery date.

• Electron (discovered 1897) - carries a negative charge, and is the lightest stable elementary particle. Because of their charge, electrons are stopped by solid matter of a few centimeters thick.
• Alpha particle (discovered 1899) -a particle sometimes emitted by an unstable nucleus during decay. These particles have much less penetrating power than beta particles, and can be stopped by a sheet of paper.
• Beta particle (discovered 1899) -classed as either positive or negative. The negative beta, discovered in 1899, is an electron emitted from an unstable nucleus when one of its neutrons decays to a proton. The positively charged positron (discovered 1932) is emitted by an unstable nucleus when its proton decays to a neutron. Except for its positive charge, a positron is identical to an electron. When a positron and an electron meet, they annihilate and their masses convert to two gamma rays. Positrons can be stopped by solid matter a few centimeters thick.
• Photon -a quantity of energy emitted in the form of electromagnetic radiation, such as radio waves, light, x-rays, and gamma rays. The quantum of electromagnetic energy, generally regarded as a discrete particle having zero mass, no electric charge, and an indefinitely long lifetime.
• Gamma ray (discovered 1900) -a bundle of high frequency, electromagnetic energy that has no mass, and which travels at the speed of light. Gamma-rays penetrate farther than most particles.
• Proton (discovered 1910) - carries a charge equal to, but opposite that of an electron. It is about 2000 times more massive than the electron. The hydrogen nucleus consists of a single proton. Protons, because of their charge and large mass, are much less penetrating than beta particles.
• Nucleus (discovered 1911) -a dense, tightly bound packet of neutrons and protons. The number of protons, equal to the number of orbiting electrons in an electrically neutral atom, defines the element and is called its atomic number (Z). Adding the number of neutrons and protons gives the atomic weight (A). Most elements occur in different forms, called isotopes, where A varies and Z remains constant.
• Neutron (discovered 1932) -an electrically neutral particle with a mass approximately equal to that of the proton. The lack of a charge gives it good depth penetration.

NEUTRONS

Neutrons are electrically neutral subatomic particles. The mass of a neutron is almost identical to the mass of a hydrogen atom. Some logging tools use a neutron source contained within the tool to bombard a formation or cement bond or other such target with neutrons. As the neutrons bombard their target, they collide with atomic nuclei. These collisions cause the neutrons to slow down as they lose energy with each collision. The amount of energy that a neutron loses during a collision is largely dependant on the relative mass of the nucleus that the neutron hits. Energy loss is greatest when the neutron strikes a nucleus of equal mass -in particular, a hydrogen nucleus.

After a series of collisions, the neutron velocity decreases to a level sufficient to be captured by a nucleus. In some reactions, the collision will cause the nucleus to become unstable. The unstable nucleus will then give off gamma rays in order to return to a stable state. Depending on the type of neutron tool, either the gamma rays or the neutrons themselves will be counted by a detector in the logging tool. We will discuss this process in further detail below.

Radioactive Sources

Logging tools require the penetrating powers of gamma rays and neutrons to bombard their targets. A number of gamma ray or neutron sources have been developed for use in logging tools. These sources can be classified as either chemical sources or electrical generators.

• Chemical Sources: Neutron sources, such as americium-beryllium (Am²⁴¹-Be⁹) and californium (Cf ²⁵²) emit neutrons with mean energies of 4.2 MeV and 2.35 MeV respectively. Other neutron chemical sources include isotopes of polonium-beryllium (Po²¹⁰-Be), radium-beryllium (Ra²²⁶Be), and plutonium-beryllium (Pu²³⁹Be).
  Gamma ray sources such as cesium (Cs¹³⁷) produce a steady flux of gamma rays, at 662 keV. Other gamma ray chemical sources include isotopes of iodine (I¹³¹), iridium (Ir¹⁹²), cobalt (Co⁶⁰), barium (Ba¹³⁷), radium (Ra²²⁶), and krypton (Kr⁸⁵).
• Electrical Generators: Neutron pulses can be generated downhole by using a neutron generator or accelerator. This device produces 14-MeV neutrons by accelerating deuterium ions into a tritium target.

Chemical sources consist of radioactive material encapsulated into pellets that must be inserted into the logging tool prior to running in the hole. These sources require special handling procedures and shielding when being transported or stored outside of the logging tool. The chemical sources generally emit a lower-energy product than the generator. Neutron generators are electromechanical devices that require high voltages of 125-130,000 Volts DC to produce neutrons. Because they first require electrical input, neutron generators are considered safer than chemical sources, which give off radiation continuously.

Neutron Energy Levels

Neutrons exhibit a broad range of kinetic energies from 0.025 eV to 50 MeV, and are classified by energy level either as Fast, Epithermal, or Thermal. The table below shows the range of energy levels that characterizes each neutron state. For the purposes of this discussion however, the oilfield tools that we are interested in work within the range listed under the "Typical Energy Level" column, depending on the type of source used by any particular tool.

Table 1: Neutron states and energy levels

At high neutron energies, inelastic interactions dominate. After a few collisions, the neutron energy is reduced below the threshold for inelastic events. As neutrons slow to thermal energy levels, capture interactions dominate. Some elements are more likely to capture neutrons than others, and so contribute more to the capture gamma ray spectrum. We will discuss this process below.

Bombardment, Excitation and Decay

Prior to bombardment, most atomic nuclei reside at their ground state, a condition of lowest internal energy. A neutron collision involving either inelastic neutron scattering or neutron absorption will cause the nucleus to become excited, wherein the internal energy of the nucleus is raised above its ground state to create an unstable nucleus in a process called activation. Almost immediately after the nucleus becomes excited, the nucleus will seek a return to its ground state by emitting its surplus energy in the form of gamma radiation. These gamma rays are known as prompt gamma rays, because they are emitted so quickly after the nucleus becomes excited.

The process of giving off particulate (proton, alpha or beta) radiation or electromagnetic (gamma) radiation can cause a nucleus to become unstable and transform to a nucleus of a different, more stable element. This other daughter product may initially be excited, but will become less excited through the process of gamma ray emission -possibly decaying to yet another element. The gamma rays given off by the daughter product are known as delayed gamma rays, because they are not observable until the initial, unstable isotope decays. This process of decay is measured in terms of half-lives, which may span from microseconds to more than a billion years, depending on the isotope.

Prompt gamma rays are produced through irradiation, while delayed gamma rays are the product of decay.

Three Basic Neutron Interactions

When a neutron bombards a target nucleus, one of the following three important interactions takes place. These interactions are controlled largely by the relative mass of the target nucleus and by the speed of the neutron. The interactions are listed below, from fastest to slowest.

• Inelastic Neutron Scattering - the neutron bounces off the target nucleus and excites the nucleus into giving off a gamma ray.
• Elastic Neutron Scattering - the neutron simply bounces off the nucleus without causing any excitation or destabilization of the target nucleus.
• Neutron Absorption (or neutron capture) -the neutron is absorbed by the target nucleus, which may cause gamma rays to be emitted, and sometimes leaves the resultant nucleus in an unstable ground state.

Inelastic Scattering

Inelastic scattering (Figure 1) results from an inelastic collision in which the total kinetic energy of the colliding particles changes as a result of the collision.

Inelastic scattering can occur when a neutron travels at kinetic energies above 1MeV. As the fast neutron collides with a nucleus, part of the kinetic energy from the neutron is transferred to the nucleus as excitation energy, giving the nucleus a higher internal energy state. Almost instantly, the excited nucleus will emit one or more gamma rays (called inelastic gamma rays) in order to de-excite back to its previous ground state. These prompt gamma rays are emitted at energies that are particularly characteristic of the nucleus of the irradiated element.

Common elements that emit gamma rays resulting from inelastic scatter are: carbon, oxygen, silicon, and calcium. The energy spectrum of gamma rays is primarily used to measure the relative concentrations of oxygen (due to water) and carbon (due to hydrocarbons) in the formation fluids. These concentrations are useful in determining fluid saturations.

Elastic Scattering

Elastic scattering (Figure 2 ) is sometimes classified as a slowing down interaction.

Elastic scattering can take place regardless of kinetic energy. With each collision, the neutron loses kinetic energy to the nucleus, but the nucleus remains in its ground state. Just how much energy will be lost depends on:

• the mass of the target nucleus relative to that of the neutron, and
• the angle of collision between the neutron and the nucleus:
• head-on collisions cause the neutron to lose the maximum amount of energy;
• glancing collisions cause the neutron to lose very little energy.

In well logging, the elastic collisions between fast neutrons and nuclei of hydrogen atoms serve as the predominant interaction through which fast neutrons lose energy before reaching epithermal or thermal energy levels. More energy will be lost when the neutron collides elastically with the nucleus of a hydrogen atom, since the hydrogen nucleus (a proton) has a mass equal to that of the neutron. The rate at which a formation slows down neutrons is an indicator of the abundance of hydrogen, which is found primarily in formation fluids, and hence is indicative of porosity. This principle is employed in all neutron porosity logging tools.

Neutron Capture

Neutron capture (Figure 3) is possible for neutrons of any energy, however it is most often seen as a slow process that typically occurs after fast interactions have taken place.

In the most common model, neutrons from the tool are slowed within a few microseconds by elastic and inelastic scattering to thermal energies -about 0.025 eV. Once the neutrons are thermalized, they are subject to absorption by the target nuclei. This absorption, called thermal-neutron capture, may create a new stable isotope or an unstable isotope with an excited nucleus.

The excited nucleus immediately emits prompt gamma rays (called gamma rays of capture). These capture gamma rays have unique energies that are characteristic of the newly formed nucleus. Chlorine, calcium, silicon, hydrogen, and iron are examples of elements that produce gamma rays from thermal capture.

The gamma spectrometry tool uses the energy spectrum from prompt gamma rays to identify elements for determining formation lithology. The thermal-neutron decay time tool measures the rate of thermal-neutron absorption in the formation to indicate the presence of chlorine. Downhole, chlorine is the most efficient, abundant thermal-neutron absorber. Chlorine is present mainly in saline formation water. Therefore, rapid absorption indicates abundant saline water; slow absorption indicates fresh water or hydrocarbons.

Absorption is possible for neutrons of any energy. The nucleus that absorbs a fast neutron (typically at kinetic energies higher than 1 MeV), will immediately eject a proton or other nuclear particle and become an excited, unstable nucleus of a new element in the process of activation. This process will create daughter products, with the ensuing emission of delayed gamma rays. The aluminum activation clay tool is used to detect delayed gamma rays produced from fast neutron interactions.

Gamma Rays

Gamma rays are photons without mass or charge that are emitted as nuclei change from an excited state to a lower energy state through transmutations and radioactive disintegration. The number and energies of emitted gamma rays are distinctive for each element, and can be used to identify which elements have emitted various gamma rays. (For example, the potassium isotope (K⁴⁰) emits gamma rays of a single energy at 1.46 MeV.) The count of distinct gamma rays is proportional to the abundance of the element that emitted them. Gamma rays interact with matter through either Compton scattering, or pair production, or photoelectric absorption. Some of these interactions are roughly analogous to the neutron interactions discussed previously.

When gamma rays pass through a formation, they lose energy as they undergo a number of Compton scattering collisions with atoms of the formation material. After the gamma ray has lost enough energy, an atom of the formation will absorb the gamma ray through photoelectric effect. Thus gamma rays will gradually be absorbed and their energies will be reduced as they pass through the formation.

Compton Scattering

Compton scattering of gamma rays (Figure 4) is similar to the inelastic scattering of neutrons described previously.

Compton scattering occurs when a gamma ray with energy in the range of 2 keV to 2 MeV (2000 keV) collides with an electron orbiting around an atom. This collision knocks the electron out of its orbit, and causes the gamma ray to lose a portion of its energy. As a result, the frequency of the gamma ray is reduced, and the gamma ray changes direction according to its energy loss.

The probability of Compton scattering is proportional to a material’s electron density, which in turn, is related to bulk density. This important relationship is exploited in density logging by bombarding the formation with gamma rays from a Cs¹³⁷ source and measuring the gamma ray flux away from the source.

Pair Production

In this process, a gamma ray collides with a nucleus and is then converted into a pair of electrically charged particles, being an electron and a positron. (We have previously stated that a positron is identical to the electron, except that the electron is negatively charged, whereas the positron is positively charged.) If the gamma ray has enough energy, it will also knock an electron out of the atom’s outermost shell, as seen in Figure 5 .

The energy threshold for pair production can be predicted through Einstein’s equation relating mass and energy. A gamma ray has more than twice the rest mass energy of an electron (about 0.51 MeV per electron). Since the electron and positron together have a mass equivalent of 1.02 MeV, a gamma ray must have at least 1.02MeV to cause pair production.

Immediately after pair production takes place, the positron and electron disappear in the process of annihilation, which produces a release of energy approximately equal to the sum of their masses, such that two 0.51 MeV gamma rays are created.

This process is used in the detection of gamma rays in ionization chambers and Geiger-Mueller counters.

Photoelectric Absorption

Photoelectric absorption (Figure 6 ) commonly takes place among low-energy gamma rays, when energies are below about 100keV. When a low-energy gamma ray collides with an atom, the atom will be able to absorb the gamma ray completely.

Inside the atom, the subsequent addition of energy from the gamma ray will cause one of the orbital electrons from the atom’s nucleus to be ejected. Part of the gamma ray’s energy will be used to overcome the energy that binds the electron to the atom; while the rest of the energy will provide velocity to the recoiling electron.

Though photoelectric absorption tends to affect low-energy gamma rays below 100 keV, it can also take place when gamma rays of higher energies collide with atoms of higher atomic numbers.

The process of photoelectric absorption produces electrons that react with phosphors within a logging tool’s scintillation detectors. The measure of photoelectric absorption cross section (Pe), which depends on the number of protons in the atoms of the formation, is used by some density tools to indicate lithology.

CAPTURE CROSS SECTIONS

Capture cross sections can be loosely defined as a measure of probability that a neutron or gamma ray will be captured by an atom. The capture cross section is usually expressed in terms of the effective area that a given target presents to the incoming neutron or gamma ray. In logging, we distinguish between capture cross sections as they relate to neutrons versus gamma rays. Neutron capture cross sections are measured in barns, sigma units or capture units. Gamma ray capture cross sections are measured in terms of Pe.

The nuclear capture cross section for neutrons is the effective area within which a neutron must pass in order to be captured by the nucleus of an atom. The nuclear capture cross section is a probabilistic value which is measured in terms of barns (a barn equals 10^-24 cm²). This probabilistic value depends on both the nature and energy of the particle as well as the nature of the capturing nucleus.

The macroscopic capture cross section for neutrons is referred to as sigma (S). Sigma is defined as the effective cross-sectional area per unit volume of material for capture of neutrons. The macroscopic capture section of a formation depends on the number of atoms and their nuclear capture cross sections. Thus, the macroscopic capture cross section is the sum of the various weighted capture cross sections. The unit of measure for S is cm²/cm³ or reciprocal cm (cm^-1), and may be measured in "capture units" or "sigma units." A capture unit = 10^-3 cm^-1. The rate of absorption of thermal neutrons with of velocity (v) is expressed as vS.

For gamma rays, the capture cross section is measured in terms of photoelectric absorption cross section (Pe), which is related to the atomic number (Z -the number of neutrons in an element) of the formation. Pe can be expressed in terms of barns per atom. Pe can also be expressed in terms of U, which is measured in units of barns per cubic centimeter.

Certain elements or formation constituents are especially important for their implication regarding formation producibility. Below are capture cross section values for key elements or constituents found in the formation. Values are given in capture units.

Gamma Ray Spectrometry

A nucleus can only be excited to a certain energy level above its ground state, and each element has a characteristic set of gamma rays that will be emitted for any given neutron interaction. These gamma rays are characterized by unique, well-defined energies of excitation. For each type of neutron interaction, therefore, it is possible to identify each element by its gamma ray signature, or spectrum, as shown in Figure 7 .

Since neutron energies from a logging tool’s neutron source are already known, it is possible to determine the type of neutron interaction that has taken place. Hence, the presence of an element can be established by the presence of a set of gamma rays of characteristic energy. The concentration of that element is related to gamma ray count rate.

The following common elements contribute gamma rays as a result of inelastic scatter or thermal capture: hydrogen, carbon, oxygen, chlorine, silicon, calcium, iron, and sulfur. These elements are indicative of the following minerals or fluids:

The gamma ray spectra can be used to estimate abundances of these elements, which in turn, are used to indicate hydrocarbon saturation, lithology, porosity, salinity and shaliness of the formation.