Types of radioactive radiation, the main processes of interaction of gamma quanta with matter. Interaction of gamma radiation with matter Interaction of gamma rays with matter photoelectric effect
There are 12 known types of interaction of y-quanta with matter. Of these, in the energy region of 0.05-5-1.5 MeV, characteristic of isotope sources used in geophysics, three are significant: the photoelectric effect, the Compton effect and the formation of pairs.
The total microscopic cross section for the interaction of quanta with matter is equal to the sum of the cross sections for the listed processes:
Photoelectric effect (photoelectric absorption) is the interaction of a quantum with an atom in which the quantum is absorbed, and its energy is partially spent on the separation of an electron, and partially transferred to the latter in the form of kinetic energy.
An atom that has lost an electron as a result of the photoelectric effect finds itself in an unstable state. Almost instantly, the vacated shell is filled by an electron from a more distant level. The excess energy, equal to the difference between the energies of these levels, is released in the form of quanta of characteristic X-ray radiation, which has a specific energy for a given element.
Compton effect called elastic scattering of y-quanta on electrons of atoms. As a result, the quanta change direction and transfer part of the energy to the electrons. When Eg>Ei, atomic electrons can be considered free and at rest. Their connection with the atom has virtually no effect on the patterns of scattering.
(Eg is the energy of gamma rays, Ei is the energy of the total electron, Z is the atomic number of the element).
Pairing effect consists in the formation of an electron and a positron by a quantum at an energy equal to the sum of the rest energies of these particles = 1.02 MeV.
A positron annihilates almost instantly as a result of a collision with a free electron of the substance. In this case, two g-quanta with an energy of 0.51 MeV are formed.
Sources of gamma rays and neutrons are the most important elements of downhole radioactive logging equipment. If the change in the flux density of the particles being studied over time is associated only with statistical fluctuations, the source is called stationary. If the change is caused not only by statistical fluctuations, the source is called non-stationary. Usually non-stationary sources work
in pulse mode.
Fluctuation- Random deviation of a physical quantity from its average value; cyclical fluctuations, instability.
Sources of g-quanta are metal ampoules containing, as a rule, (b-active drugs. As a result of b-decay, g-radiation arises. The radiation of b-particles is extinguished in the ampoule body or using special filters
trov. The type of drug that determines -g activity, radiation energy and other parameters of the source depends on the type of problem being solved (Table 3). Ampoule sources are stationary.
Radiation detectors are divided into gas-filled, scintillation and semiconductor. The principle of their operation is based on the registration of electrons and ions or light photons resulting from the interaction of radiation with matter.
Gas-filled detectors They are a glass or metal tube filled with an inert gas and having two electrodes. In the absence of ionizing radiation, no current flows between the electrodes. Gamma rays are absorbed in the gas to form electrons, neutrons to form alpha particles and protons. Charged particles ionize the gas, resulting in pulses of electric current.
Scintillation counters made from optically active substances - scintillators. When ionizing radiation interacts with an optically active substance, atoms and molecules are excited, from which they are released, emitting photons. When recording quanta, single crystals of sodium iodide NaJ or cesium iodide CsJ, activated with thallium T1 to increase the light output, are used as scintillators. To register thermal neutrons
Lithium iodide crystals activated with europium, enriched with the 6Li isotope, or crystals based on zinc sulfide activated with silver are used.
Semiconductor detectors are based on the generation of free charge carriers in a solid under the influence of ionizing radiation. The range of particles in a solid is approximately 103 times less than in a gas, and the probability of ionization
much higher.
Semiconductor detector (SCD) is a crystal of semiconductor silicon or germanium material with small p- and n-regions, characterized by a high concentration of impurities, and an extended impurity-free region L located between them. The width of region i can be increased to 8-12 mm by compensating impurities with lithium ions. Therefore, existing SPDs are usually silicon-lithium or germanium-lithium. When ionizing the i-region, the
there is a current pulse, the strength of which is proportional to the energy
ionizing particle.
SPD is used mainly for recording quanta. The relatively small working volume leads to the fact that the efficiency of the SPD is low - most quanta pass through it without being absorbed.
Question
physical foundations of yafmas - see above (beginning 31). Plus this!
Detectors- see above (31).
Elastic neutron scattering is a nuclear reaction in which the internal energy of the nucleus does not change and the sum of the kinetic energy of the system before and after the collision is conserved.
The slowdown continues until the neutrons are in thermal equilibrium with the medium, that is, until their energy becomes, on average, comparable to the energy of thermal motion of atoms and molecules. That is why such neutrons are called thermal.
Question
Density GGC
Density gamma-ray logging (GD-G) is used to determine the density of rocks and assess the quality of well casing. Accordingly, there are gamma-gamma density meters and gamma-gamma cement meters.
Physical basis of GGK-P can be understood by analyzing the phenomena that arise when a substance is irradiated with hard y-quanta. With the geometry implemented in downhole conditions, the sources and detectors are on one side of the object under study (Fig. 94). Therefore, only scattered scattered particles enter the detector through special collimation holes in a screen made of metal with a large Z (lead, tungsten).
quanta. Consequently, the type of interaction of gamma quanta with matter is regulated by the camton effect.
Compton effect called elastic scattering of y-quanta on electrons of atoms.
Ratio of Z value, number of protons to A-
rate of decrease in the number of identical nuclei over time = 0.5.
In turn, at Z/A=0.5, according to the relation mk is proportional to the bulk density of the substance d. Below are the explanations..
shares and is denoted mk
For campton effect:
The fulfillment of the condition Z/A = 0.5 means that the volume density of the medium is equal to its electron density 6e. The density of the solid phase of the bsp of most rocks, in particular sandstones and carbonates, is almost equal to its electronic density
news be tv. At the same time, for the liquid phase (water, oil and some other formation fluids) Z/A=0.5 due to the influence of hydrogen. Therefore, for the liquid phase, the density dв and electron density deв differ significantly. For example, for water:
For porous water-saturated rocks we can write:
If we subtract one from the other and use equality 1, we get:
Thus, the error due to the influence of hydrogen content is small, approximately constant and can be taken into account during interpretation.
Probes
There are single-probe (one source - one detector) and double-probe (one source - two detectors) density meters. The total length of the probe Lз (probe) is the distance between the centers of the source and detector, the length of the probe L is the distance
along the outer generatrix of the probe between the nearest edges of the collimation holes. The maximum length of the probe is limited by the source activity permissible from a safety point of view, the minimum by the screen dimensions. For most two-probe devices, the small probe has Lз = 15-25 cm (L = 10-18 cm), the large probe has Lз = 35-45 cm (L = 30-35 cm).
HGMs have a shallow depth, and therefore their readings have a large
the influence is exerted by the clay cake and caverns. For the same reason, they cannot be used to determine the parameters of rocks in cased wells.
Problems solved using gamma-gamma densitymetry:
identification of rocks with different densities in well sections; isolation and quantification of the content of minerals whose density differs from the density of the host rocks; determination of porosity coefficient.
Let's look briefly at each of them. Gamma-gamma densitymetry makes it possible to separate rocks whose densities differ by more than 0.03-0.05 g/cm3. It clearly identifies rock salts, anhydrites, and, in terrigenous and carbonate sections, oil and gas reservoirs characterized by low density.
Using gamma-gamma densitymetry, it is possible to determine the depth, thickness and structure of coal seams d = 1.2-1.8 g/cm3). It is also used to isolate minerals whose density differs from the density of the host rocks. First of all, this applies to manganese and chromite ores d = 3.7-4.5 g/cm3). The presence of a correlation between the ash content of coals and their density, the density of ferruginous quartzites and the iron content in them allows the use of GGK-P for
inventory counting.
The porosity coefficient is determined by the formula:
Derived from formula 2) (above).
Question
NEUTRON LOGING
The GIS method, based on irradiating rocks with a stationary flux of fast neutrons and recording thermal neutrons, suprathermal neutrons or g-quanta of radiation capture, is called neutron logging (NK).
NK modifications
There is suprathermal neutron-neutron logging (NNK-NT), thermal neutron-neutron logging (NNK-T), integrated neutron gamma ray logging (ING) and spectrometric neutron gamma ray logging (SNGL).
Downhole instruments neutron methods are approximately similar (Fig.).
In general, they contain: a shank / with an ampoule source of fast neutrons 2 (during transportation and storage, the shank with the source is placed in a protective container); excluding direct irradiation of the detector, a moderator screen 3 made of hydrogen-containing material and an absorber screen 4 made of lead; detector of 5 neutrons or 7 quanta; detector of 6 y-quanta of natural radiation; electronic circuit 7. Thus, the devices are designed for simultaneous NDT and GK.
The length of the detectors and the presence of screens in the downhole tool lead to
due to the fact that detector 4 is located behind the inversion point. Therefore, environments with large con-
concentration of moderators, such as porous oil formations, differ by
diagrams of neutron methods with reduced indicators, and the layers are dense, low-
spongy - increased. Probes of neutron methods, detectors in which are located
placed behind the inversion point are called beyond inversion.
The modification of the NC depends mainly on the type of detector and the filters surrounding it. In NNK-T measuring installations, helium and, less commonly, scintillium are used.
tion counters. The recorded count rate is determined mainly by the flux of thermal neutrons. In NNK-NT measuring installations, the counters are surrounded by cadmium filters that absorb thermal neutrons. Scintillation and, less commonly, gas-filled detectors are used in NGC equipment.
y-quanta, in the spectrometric equipment of the SNGK - high-quality proportional scintillation detectors. In some cases, semiconductor detectors (SSDs) are used, which provide significantly higher energy resolution. However, PPDs require cooling, which significantly complicates the design of devices and measurement technology.
An important parameter of the NK equipment is the length of the probe Lz - the distance from the middle of the source to the middle of the detector (for multi-probe devices - to the beginning of the detector).
Physical Basics
The readings of neutron methods depend on the moderating, absorbing and radiating properties of the rock. Let us consider the parameters that determine these properties.
Neutron moderation length Ls. It can be seen that the deceleration length is determined by the porosity coefficient of the rocks, i.e., it is related to their hydrogen content; the influence of lithology is significantly less. For
For most rock-forming minerals that do not contain water of crystallization, the differences in Ls values are insignificant. Moreover, they are caused not only by different retarding properties of the elements included in the minerals, but also by differences in densities.
IN rocks, the pores of which are saturated with water, oil and gas, the total hydrogen content is estimated by the hydrogen index (HI), which is equal to the ratio of the volumetric concentration of hydrogen in a given environment to its concentration in fresh water
water under normal conditions. this parameter is also called
equivalent humidity w. For fresh water the equivalent
humidity wв=1. For oils wн ~ wв=1.
For clean rocks that do not contain chemically bound water, saturated with water and oil with water:
i.e., the VI of such rocks is equal to their porosity. For gas wg Average lifetime of thermal neutrons t. As the content of elements with a high absorption cross section increases, t decreases. Abnormally low values t are characteristic of chlorides, low - for iron minerals, sulfates, potassium feldspars, potassium and iron-containing clay minerals. Thermal neutron diffusion coefficient D depends primarily on Thermal neutron diffusion length- Ld. Being a function of D and t, the value of Ld depends on both the retarding and absorbing properties of the medium. With an increase in the hydrogen content and the number of elements with a high absorption cross section, the value of Ld decreases. Rock emissivity n represents the average number of g-quanta produced during the radiative capture of one neutron. Migration options-the total length of migration of thermal neutrons Ln in the process of their slowing down and diffusion and the total length of migration of neutrons and gamma radiation of radiative capture Lnv are determined by the relations: The research radius of the NNM-NT is smaller than that of the NNM-T, and that of the NNM-T is smaller than that of the GPS. Neutron methods allow solving the following problems: lithological division of the section; determination of rock porosity; determination of the position of the gas-liquid contact. The NNM-T and GPS methods make it possible to determine the location of the oil-water contact with significant salinity of formation waters and a small area penetration, as well as in cased wells based on observations of deformation roving the penetration zone. The NNM-NT and NNM-T methods are used when searching coal seams (coal contains up to 12% hydrogen) and to isolate rocks with a high boron content. Question With pulsed neutron methods, rock is irradiated for a short time. high (duration Δτ = 1-200 μs) fluxes of fast neutrons, the following at intervals of time τ. Registration of the density of thermal neutrons or gamma radiation capture quanta are carried out after a certain period of time no delay τz. There are pulsed neutron gamma method (PNGM) and im- pulsed neutron-neutron method (PNNM). More widespread pulsed radiation mode is achieved by using small-sized wells gas accelerators, in which ions are accelerated to high speeds in a magnetic field high intensity field. By bombing a special target, they knock out strong neutrons having an energy of 14.1 MeV. Such high energy provides research depth is up to 60-70 cm, which is greater than when using stationary Narny sources. In addition, when the power supply is turned off, the pulsed source nick does not emit and is therefore safe. The benefits don't end there impulse methods. With INM, the processes of slowing down and diffusion occur as if sequentially in time and can be studied separately depending on the delay time registration. The intensity of the recorded radiation during deceleration (up to 10 2μs) characterizes the hydrogen content of rocks during diffusion (10(2) 10(4) µs) - concentration of absorbers. It is important that the lifetime of thermal neutrons in a well is less than in the rock, and in formations saturated with mineralized water, it is less than in oil-saturated formations. This allows, by applying the appropriate existing delays (more than 800 μs), obtain information independent of the influence well fluid and characterizing the type of filler. Determination of gender The study of oil-water contact by pulsed neutron methods is possible with salt concentrations are more than 30 g/l, while in stationary methods this value not less than 100 g/l. In principle, OSIs solve the same problems as stationary methods, however, the efficiency of the solution is higher. The disadvantages of OSI include the complexity equipment and low logging speed. Look 35 37. Nuclear magnetic logging in the natural field of the Earth (NML). Physical foundations. Magnetic properties of rocks. Nuclear magnetization vector. Longitudinal and transverse relaxation. PHYSICAL BASICS Nuclear magnetic logging (NML) is based on the study of the nuclear magnetic properties of hydrogen in fluids filling rock pores. The nuclei of hydrogen atoms, like other elements (fluorine, aluminum, carbon-13, etc.), have their own mechanical moment P (spin) and a magnetic moment μ, the axes of which coincide. Spin (twisting) characterizes the intrinsic mechanical angular momentum of elementary particles. It can only take integer or half-integer values (0; 0.5; 1; 1.5), expressed in units of h/2π, where h is Planck’s constant (6.6261·10-34 J·Hz-1). The spins of the electron, positron, proton and neutron are 0.5. This means that they take the value 0.5 h/2π. When such nuclei are placed in a constant external magnetic field H, their magnetic moments μ tend to be oriented in the direction of the vector of this field, which leads to the occurrence of nuclear magnetization. When removing the external magnetic field the acquired nuclear magnetization is destroyed due to the random thermal movement of atoms and molecules of the substance. Since this occurs in the Earth's magnetic field, the nuclei are oriented along this field, precessing (performing damped rotations) around it like a top in a gravity field with the so-called Larmor frequency where Hz is the strength of the Earth’s magnetic field (Hz≈40 A/m); γgyr= μ/P - gyromagnetic ratio (the ratio of the magnetic moment μ of precessing nuclei to their mechanical moment P). The highest value of γgyr is characteristic of hydrogen. This causes the strongest expression of the effect of nuclear magnetism in hydrogen. In all other rock-forming elements this effect is too small to be measured in a borehole. The main task of NMR is to register the effects of free precession of protons of hydrogen nuclei in the Earth's magnetic field. For this purpose, a downhole tool is lowered into the well, including an elongated rectangular coil, a switch that alternately connects the coil leads either to a direct current source with a power of 2-3 A, or to the output of the amplifier. When the coil is connected to a current source, a polarizing constant magnetic field is created in the environment. When the coil is connected to an amplifier, the EMF induced in it by the precession of hydrogen nuclei is amplified and transmitted via cable to the surface to ground-based equipment, where it is recorded (Fig. 79). When a polarization current Ip is passed through a polarizing coil for a time tp (Fig. 80, II, a), a constant magnetic field of intensity Hp is formed in the medium under study. The vector of this field makes a certain angle with the vector of the Earth's field strength Hz and significantly (about two orders of magnitude) exceeds it in magnitude. The nuclear magnetization vector M that arises during the time tp is oriented along the resulting vector Hav, which is the sum of two intensity vectors Нп and Нз (Fig. 80, I, b). where M0 is the nuclear magnetization vector at tп→∞; practically tп is taken equal to (3-5)T1 After turning off the polarizing current (stepwise reduction to the value of the residual current Ires and complete turn-off after a time tres), only the Earth’s magnetic field acts in the medium, and the nuclear magnetization vector processes around the Hz vector with a circular frequency ω (VI.1), gradually returning to its original size (Fig. 80, I, c). The nuclear magnetization vector M with respect to Hz can be decomposed into two components: longitudinal Mll, coinciding with the direction of the Hz vector, and transverse M⊥, perpendicular to Hz. Under the influence of the vector M⊥, an electric sinusoidal signal (EMF variable) is induced in the coil - a free precession signal (FSP), corresponding to the Et amplitude of the FSP (in V) at time t (in s), elapsed from the beginning of precession, decaying according to the exponential law with transverse relaxation time constant T2 (Fig. 80, II, c): The transverse relaxation time T2 characterizes the rate of signal attenuation (T2 is usually taken to be the time during which the initial amplitude E0 decreases by approximately 2.7 times, E0 is the initial amplitude of the SSP, proportional to the nuclear magnetization vector M). To prevent the influence of transient processes caused by turning off the residual current, the moment of connecting the coil to the amplifier is shifted by the dead time τ (see Fig. 80, II, d). The EMF induced in the probe coil is amplified and transmitted via a cable to the day surface, where the recording device records the EMF amplitude Ut at time t. The amplitude Ut is the envelope of the free precession signal: Ut = U0exp(-t/T2), where U0 is the initial amplitude of the free precession signal. Since the free precession signal decreases exponentially, it is enough to have two values of its amplitude U1 and U2 or U1 and U3, separated by certain time intervals t1, t2 and t3 (35, 50 and 70 ms) after the start of precession, so that by extrapolation restore the signal amplitude U0, which is used to determine the free fluid index: NMR equipment allows you to simultaneously automatically register two or three Nuclear magnetic logging in the natural field of the Earth (NML). Probe, method for determining the free fluid index (FFI), factors influencing the readings of the method, depth and areas of application of NMR. Interpretation of NMR diagrams Interpretation of NMR diagrams involves determining the values of the free precession signal and the longitudinal relaxation time T1. The transverse relaxation time T2, being distorted by the inhomogeneity of the Earth's field, is not used to study well sections. Based on the interpretation of NMR diagrams, it is possible to solve the main problems: identifying reservoirs and assessing their reservoir properties; assessment of the nature of reservoir saturation and the prospects for obtaining oil, gas or water from the reservoir. Isolation of collectors The reservoir properties of rocks are studied using U0. The magnitude of the measured free precession signal is influenced only by those hydrogen nuclei that are part of molecules capable of moving in the pore space of the reservoir. Studies have shown that bound water and solid hydrocarbons (bitumen, brine, asphaltenes), containing low-mobility protons, are not marked by a free precession signal on NMR diagrams. This is due to the fact that, due to the presence of dead time τ (see Fig. 80), only those ERPs that are characterized by a time T2>30 ms are recorded in NMR. The value of U0 is calibrated in units called the free fluid index (FFI) and characterizing the volume of pores (in %) occupied by the liquid participating in the formation of FSF. The free fluid index is conventionally considered to correspond to the effective porosity coefficient where kwo is the coefficient of residual water saturation. The free fluid index is defined as the ratio of the initial SSP amplitude recorded on a rock sample whose pores are filled with fresh water to the initial SSP amplitude measured on distilled water occupying the same volume as the rock sample. Accordingly, the ISF varies from 0 to 100%. To establish the scale of NMR curves in ISF units, the equipment is standardized. The nature of the dependence of ISF on the free water content is not affected by lithological, structural and other features of the rock. Consequently, in formations that represent an alternation of reservoir and non-reservoir layers, only reservoir layers contribute to the ISF value, and the remaining differences, which do not contain free fluid, do not create a free precession signal. Therefore, the effective porosity kp.eff, determined for a heterogeneous formation or layer pack, makes it possible to determine the total capacity of the object under consideration. Accordingly, the product of kp.eff by the capacity of the object H gives the total effective capacity of all the reservoir layers contained in it. In reservoirs with fracture porosity included in the general pore system, the transition from ISF to kp.eff is carried out in the same way as for granular reservoirs. For reservoirs characterized by the presence of isolated cavities not associated with common system pores, the comparison of kp.eff and ISF is incorrect, since the total volume of isolated cavities is not included in the effective porosity, but is included in the ISF. In this case, it is necessary to exclude the volume of isolated cavities that are taken into account according to the ISF curve, but do not affect kp.eff. Homogeneous hydrogen-containing formations, the thickness of which is equal to or greater than the length of the probe, are marked on the NMR curves by symmetrical maxima located in the middle part of the formation; the boundaries of the layers are drawn along the middle of the inclined lines (Fig. 82). If the thickness of the formation is less than the length of the probe, the ISF decreases compared to the true values and the maximum expands; Determining the boundaries of thin layers using NMR curves is difficult. Their average values are taken as significant (characteristic) values (ISF)k. Determination of the nature of rock saturation This determination is made using the longitudinal relaxation time T1. To measure T1, the device is installed at a given depth in intervals characterized by the ISF curve as reservoirs containing free liquid. The longitudinal relaxation time T1 can be determined using Utп without taking into account a number of factors that influence the amplitude of the SSP - well diameter, mud cake thickness and spatial orientation of the well. T1 measurement is performed at the depth of the studied formation in two ways: in a strong field - T1c. p and in a weak field - T1sl.p. To determine T1c. n a series of measurements of the amplitudes Utп (in V) is carried out for different times tп (in s) and the polarizing magnetic field Нп (in A/m). One of the measurements is performed with a sufficiently long time tп→∞, ensuring the equilibrium state of the nuclear magnetization vector М∞с.п (in A/m) (see Fig. 81, II, a and b). This vector corresponds to the amplitude U∞с.п and Т1с. n can be calculated: Longitudinal relaxation time in a weak field T1s. n is determined by the duration of action of the residual polarizing field Nost. To do this, measure the amplitudes of the SSP at a fixed polarization time tп, but at a sequentially changing action time tref and, accordingly, the residual current Iref (see Fig. 80, II, c, d). In practice, to determine T1 from measurement results, the direct dependences of the amplitudes Utп and Utоst on the times tп and tоrt are not used. The T1 values are found graphically. To do this, the values of the so-called longitudinal relaxation functions Fc are calculated from the measurement results. p(tp) and Fcl.p(tost), which in a strong and weak field, respectively, have the form: where U(tп) is the amplitude of the SSP at the polarization time tп; where U(tres) is the amplitude of the SSP during the duration of the residual current; U(trest→∞) is the amplitude of the SSP at trest→∞, not directly measured, but calculated by the formula U(trest→∞)=U0 (Irest/Ip). Calculated values of the Fc function. p(tp) or Fcl.p(trest) correspond to real measurements of tp and tost and are used to graphically determine T1. For this purpose, the calculated functions are plotted on a form with a semi-logarithmic scale (Fig. 83). In a homogeneous water-saturated medium, the pores of which have the same sizes, the longitudinal relaxation function, even in the presence of bound water, is one-component. On a semi-logarithmic scale, such a dependence has the form of a straight line with constants T1 and function values of about 0.37 (Fig. 83, a). In the presence of a mixture of fluids with different Т1, the dependence is depicted in the form of a curve that can be decomposed into several straight lines. Using these straight lines, T1 of each component is found (Fig. 83, b). The tangent of the angle of the resulting straight lines is equal to time T1. As can be seen from the example shown in Fig. 83, straight lines representing functions Fc. p(tp) or Fcl.p(tost), are transferred parallel to themselves so that they intersect the ordinate axis at a point equal to one. Time T1, corresponding to ordinate 0.37, is counted (in ms) on the abscissa axis. For an approximate estimate of T1, it is sufficient to carry out measurements at two values of polarization time. For accurate determinations, up to 15 measurements are made for the values of tp or trest. In highly permeable formations, the longest relaxation times (more than 1 s) are observed in water-saturated formations or oil-saturated formations containing light oil. However, the dispersion of these values is large: the T1 value, in addition to the nature of reservoir saturation, is also influenced by factors such as the specific surface of the reservoir, its hydrophilicity or hydrophobicity, type of porosity, clay content, and fluid viscosity. When the oil and water saturation of the formation differs, it is taken into account that the highly viscous (resinous) components of oil when low temperatures are characterized by rapidly decaying free precession signals and are marked by low readings on NMR diagrams. According to the experience of studying productive horizons with injected fresh water, the T1 time of the penetration zone for aquifer reservoirs lies in the range of 200-600 ms, and for oil and gas reservoirs - 700-1000 ms. In addition, oil and gas bearing formations, due to the presence of residual oil or gas in the penetration zone, are characterized by two components in the longitudinal relaxation characteristic. Nuclear magnetic logging is designed to identify layers containing mobile fluid, determine their porosity and the nature of saturation. Integrating NMR results with data from other well logging studies makes it possible to expand and clarify the possibilities for quantitative assessment of reservoir porosity, their effective thickness, saturation and commercial oil content. The NMR method is also used to separate oil-bearing and bituminous rocks. The limitations of the NMR method are associated with the impossibility of measuring SSP in a medium (clay solution, rock) with increased magnetic susceptibility, in rocks with low effective porosity (1.5-2%), including in fractured reservoirs, if part of the fractures are filled with clay solution . This method is not applicable for very viscous oils - more than 600 mPa s, or if there is free fluid in the washing liquid - water or oil, which creates additional SSP. The disadvantages of the method are: the duration of measurements (the speed of movement of the NMR device is limited by the polarization time tп>3Т1 and should not exceed 250 m/h); small depth of investigation (about 0.2 m), as a result of which the influence of the penetration zone on NMR readings is great. Nuclear magnetic logging is applicable when studying sections of wells that are not cased with a casing. Related information. Interactiong
Question 36
A schematic representation of the processes occurring during NMR studies and the resulting nuclear magnetization vectors is given in Fig. 80. In the absence of an external artificial magnetic field, the magnetic moments of hydrogen nuclei μ are oriented in the direction of the Earth’s magnetic field Hz, precessing around it (Fig. 80, I, a).
The nuclear magnetization vector M is not established immediately after turning on the current In, but during the time T1 of longitudinal relaxation (establishment of equilibrium), which characterizes the rate of increase of nuclear magnetization in the direction of the applied polarization field (Fig. 80, II, b):
logging curves of changes with depth in the amplitudes of the free precession signal U1, U2 and U3 at fixed times t1, t2 and t3 and constant values of tp and trest. From these data, the value of U0, reduced to the moment the residual polarizing current is turned off, is estimated (or directly recorded when using a calculating device). Curves U1, U2, U3, U0, recorded as a function of depth, are called NMR curves (Fig. 81).
To obtain true values (ISF) and from (ISF)k data, corrections are introduced for the influence of the well, mud cake, spatial orientation of the well, etc. For this purpose, corresponding palettes and nomograms have been constructed.
Main interaction processes g- quanta with matter are the photoelectric effect, Compton scattering and pair formation. The probability of a particular interaction g- quanta with matter is characterized by the interaction cross section for a given process. Typically the interaction cross section g- quanta is expressed in barns per atom ( s) or in Thomson units per electron s m, the relationship between which is:
Where Z- serial number of the element.
Photoelectric effect. With the photoelectric effect, the energy g- the quantum is transferred to one of the bound electrons of the atom, which flies out of the atom with kinetic energy equal to the difference in the energies of the incident g- quantum and ionization energy of the shell of the atom on which the electron was located. The photoelectric effect is the process of complete absorption g- quanta. Photoelectric effect cross section s f increases with increasing atomic number as Zn
(4
Compton scattering. If energy g- the quantum is significantly greater than the binding energy of the electron in the atom, the electron in the process of interaction with g- a quantum can be considered free. The Compton effect is a scattering process g- quanta on free electrons, as a result of which both the direction of movement and the energy of the incident particles change g- quanta. Compton scattering occurs on free electrons, as a result of which the main characteristics of the phenomenon can be determined for a single electron, and the cross section for an atom will result from an increase in the cross section of a single electron by Z once. Total Compton interaction cross section s c proportional to the atomic number of the element and decreases relatively slowly with increasing energy g- quanta. The average relative loss of photon energy during Compton scattering is often introduced into consideration: q cp =((E -E ’)/E ) cp, Where E- energy of the incident photon; E'- energy of the scattered photon. Using this value, the cross section is determined
which is called the energy absorption cross section or true absorption cross section g- quantum due to the Compton effect. In Thomson units this cross section can be calculated using the formula:
Where E expressed in units of energy of an electron at rest.
For energy values g- quanta E g =0.5 MeV, Compton cross section s c inversely E g, i.e. the probability of Compton scattering decreases more slowly than the probability of the photoelectric effect. Therefore, the Compton effect is the predominant interaction process in a wide energy range. Even for heavy elements such as lead, the Compton cross section accounts for the bulk of the total absorption cross section in the range from 0.5 to 5 MeV. Therefore, in practice, quite often the interaction g- quanta with matter can be considered Compton scattering.
Pair formation. In the electric field of nuclei at energy g- a quantum exceeding twice the rest energy of the electron ( 2m e c 2 =1.0022MeV, Where m e- electron rest mass; With- the speed of light in vacuum), the process of formation of an electron-positron pair can occur, in which all the energy of the incident g- the quantum is transferred to the formed particles and the nucleus, in the field of which the pair was formed. The process leads to complete absorption g- quantum. Its energy threshold is 1.022 MeV, after which the cross section for pair production slowly increases. At energies g- quanta exceeding 4 MeV, the cross section of the process becomes approximately proportional lnE g . It is also proportional to the element's ordinal number. The process of formation of each pair is accompanied by a secondary g- radiation in the form of two photons with the same energy, equal E g = m e c 2 =0.511 MeV due to the annihilation of a slowed down positron and electron. Annihilation radiation is absorbed at the site of its formation.
Thus, the total interaction g- quanta with matter are characterized by a total cross section, which represents the sum of the cross sections of the photoelectric effect, Compton scattering and pair formation s n:
(5.13),
and energy absorption is the total energy absorption cross section:
Fig.5.1. Dependence of the total interaction cross section and its individual components on the energy of g-quanta for oxygen (a) and lead (b): 1 – Compton scattering; 2 - photoelectric effect; 3 - full section; 4 – formation of pairs.
Figure 5.1 shows the dependence of the total cross section and its individual components on energy for oxygen and lead. When calculating interaction g- quanta with matter usually use macroscopic interaction characteristics g- radiation in the form of the product of the microscopic cross section and the concentration of atoms: the mass interaction coefficient, which includes the concentration of atoms per gram of substance, and the linear interaction coefficient, which includes the concentration of atoms per unit volume of the substance (1 cm 3). Mass attenuation coefficient g- radiation, cm 2 /g:
Where M- atomic mass; s- section, barn. Because Z/M approximately equal to 0.5 for all elements except hydrogen, mass attenuation coefficient g- radiation has approximately the same value for all elements in the energy region where the predominant process is the Compton effect.
Linear attenuation coefficient g- radiation, 1/cm:
Where r- density of the medium, g/cm 3 .
The energy absorption coefficients are determined similarlyg- radiation W a And m a. Values of linear and mass interaction coefficientsg- quanta with various materials are given in.The interaction of gamma rays with matter can be accompanied by the photoelectric effect, Compton scattering and the formation of electron-positron pairs. The type of effect depends on the energy of the gamma quantum: = һυ- , where һ is Planck’s constant; υ - radiation frequency; E-ionization energy of the corresponding atomic shell (binding energy of an electron knocked out of an atom).
The photoelectric effect occurs at relatively low energies and occurs on the inner electrons of the atom, mainly on the K-shell electrons. In this case, all the energy of the gamma quantum is transferred to the orbital electron and it is knocked out of the orbit.
The ejected electron is called a photoelectron. It is he who can cause the ionization of other atoms. As a result of its detachment, a free level appears in the atom, which is filled with one of the outer electrons. In this case, either secondary soft characteristic radiation (fluorescent radiation) is emitted, or energy is transferred to one of the electrons, which leaves the atom. Fluorescent emission is observed in materials with high atomic number. The probability of a photoelectric effect increases with increasing atomic number of the material and decreases with increasing photon energy.
Compton scattering is the process of interaction of photon radiation with matter in which the photon, as a result of an elastic collision with an orbital electron, loses part of its energy and changes the direction of its initial motion, and a recoil electron (Compton e) is knocked out of the atom. In this case, the frequency, and therefore the energy, of the scattered gamma quantum will be less.
The energy of the Compton electron is equal to: E = һυ- һ
where һυ is the energy of the primary photon; һ is the energy of the scattered photon.
This process is most typical for photons, the energy of which significantly exceeds the binding energy of electrons in the atom, so scattering occurs only on external (valence) electrons.
Interaction of beta radiation with matter
The passage of beta particles through matter is accompanied by elastic and inelastic collisions with nuclei and electrons of the braking medium.
Elastic scattering of beta particles on nuclei is more likely and occurs at relatively low electron energies. Elastic scattering of beta particles on electrons is Z times (Z-value of the nuclear charge) less likely than on nuclei. A shift of the nuclei of atoms in a crystal lattice is also theoretically possible.
When the energy of beta particles is higher than the binding energy of the electron with the nucleus (up to - 1 MeV), the main mechanism of energy loss is inelastic scattering by bound electrons, leading to ionization and excitation of atoms.
At high electron energies, the main mechanism of energy loss is radiative braking, in which bremsstrahlung occurs.
Thus, the processes of interaction of beta particles with the medium are characterized by radiation braking and a relatively large loss of energy or a significant change in the direction of their movement in an elementary act. As a result of this interaction, the intensity of the beta particle beam decreases almost exponentially with increasing thickness of the absorbing layer x.
The path of beta particles in matter usually represents a broken line, and the path of beta particles of the same energies has a significant scatter. This is due to the fact that the mass of beta particles is extremely small, so the probability of elastic scattering by nuclei is greater than that of heavy particles. So, beta particles do not have an exact penetration depth, since they have a continuous energy spectrum. To roughly estimate the depth of travel of beta particles, approximate formulas are used. One of them: Rav/Rair=ρair/ρav
where Rav is the path length in the medium; Rair - air travel length; ρair and ρav - density of air and medium, respectively; E is the energy of beta particles.
Gamma radiation is characterized by intensity, which is understood as the product of energyγ -quanta by their number falling every second on a unit of surface normal to the flow of gamma quanta.
As for any type of electromagnetic radiation, the intensity of γ-radiation from a point source decreases in inverse proportion to the square of the distance from the radiation source (if it is not additionally absorbed in the medium). This is determined by the purely geometric properties of the radiation flux, i.e. its divergence with distance from a point source of radiation. In reality, such a weakening will be observed in an absolute vacuum.
Gamma radiation is a highly penetrating radiation. But when passing through any substance, it will be absorbed by this substance. This absorption can occur due to the interaction of γ-radiation with atoms, electrons and nuclei of matter, manifested in the form of the following effects:
· photoelectric effect– consisting of the γ-quantum knocking out electrons from the internal electron shells of atoms (most often from TO-shell), which leads to its ionization and the appearance of a free electron. This effect predominates at γ-quanta energies below 0.5 MeV;
· Compton effect, which consists in the fact that a γ-quantum excites an electron in the outer shell of an atom, transferring part of its energy to it, as a result of which its energy decreases and its direction changes (Compton scattering);
· pair formation – if a γ-quantum flies directly near the nucleus and its energy exceeds 1.022 MeV, then an electron-positron pair can be formed;
· photonuclear reactions, in which gamma rays, absorbed by the nucleus, excite it, transferring their energy to it, and if this energy is greater than the binding energy of a neutron, proton or alpha particle, then these particles can leave the nucleus. On fissile nuclei (235 U, 239 Pu, etc.), if the energy of the gamma quantum is greater than the nuclear fission threshold, fission will occur.
As a result of all these interactions, when gamma radiation passes through an absorber, its intensity decreases according to the law:
Where I 0 , I– intensity of γ-radiation before and after passing through the absorber;
μ – linear attenuation coefficient;
d– absorber thickness.
In Fig. Figure 3.1 shows a simple design of an attenuation experiment. When gamma radiation with intensity I 0 falls on an absorber of thickness d, intensity I radiation passing through the absorber is described by exponential expression (3.1).
Rice. 3.1. Basic law of gamma radiation attenuation
Transmitted radiation intensity I is a function of gamma radiation energy, composition and thickness of the absorber. Attitude I/I 0 is called the gamma radiation transmittance. Figure 3.2 shows the exponential attenuation for three different gamma ray energies. The figure shows that the transmittance increases with increasing gamma radiation energy and decreases with increasing absorber thickness. The coefficient μ in equation (3.1) is called the linear attenuation coefficient.
Linear attenuation coefficientμ depends on the energy of γ quanta and the properties of the absorbing material. It has a dimension of m -1 and is numerically equal to the fraction of monoenergetic gamma quanta leaving a parallel beam per unit radiation path in the substance. The linear attenuation coefficient depends on the density and serial number of the substance, as well as on the energy of gamma rays. For example, lead has a high density and high atomic number and transmits a much smaller fraction of incident gamma radiation than aluminum or steel of the same thickness.
Rice. 3.2. Dependence of the transmittance of gamma quanta on the thickness of the lead absorber
The values of the linear attenuation coefficient of gamma radiation from the 60 Co source for various materials are presented in Table 3.1, and their dependence on the energy of γ quanta is in Table 3.2.
The thickness of the absorber layer required to reduce the radiation intensity by half is called half-thickness d 1/2.
From the absorption law (3.1) it follows that the half-thickness is equal to
Table 3.1
Linear attenuation coefficient μ of γ-radiation materials Co-60
Table 3.2
Dependence of the linear attenuation coefficient μ of materials
on the energy of γ quanta
| E, MeV | μ, cm -1 | |||||
| Lead | Water | Aluminum | Iron | Graphite | Air | |
| 0,10 | 0,171 | 0,455 | 2,91 | 0,342 | 2.00·10 -4 | |
| 0,15 | 22,8 | 0,151 | 0,371 | 1,55 | 0,304 | 1.76·10 -4 |
| 0,20 | 11,1 | 0,137 | 0,328 | 1,15 | 0,277 | 1.59·10 -4 |
| 0,30 | 4,43 | 0,119 | 0,280 | 0,865 | 0,241 | 1.38·10 -4 |
| 0,40 | 2,62 | 0,106 | 0,249 | 0,740 | 0,214 | 1.23·10 -4 |
| 0,50 | 1,80 | 0,0966 | 0,227 | 0,661 | 0,196 | 1.12·10 -4 |
| 0,80 | 0,999 | 0,0786 | 0,184 | 0,526 | 0,159 | 9.13·10 -5 |
| 1,0 | 0,798 | 0,0279 | 0,165 | 0,471 | 0,143 | 8.21·10 -5 |
| 1,5 | 0,591 | 0,0575 | 0,135 | 0,382 | 0,117 | 6.68·10 -5 |
| 2,0 | 0,518 | 0,0493 | 0,116 | 0,334 | 0,0999 | 5.74·10 -5 |
| 3,0 | 0,475 | 0,0396 | 0,0950 | 0,284 | 0,0801 | 4.63·10 -5 |
| 4,0 | 0,472 | 0,0340 | 0,0834 | 0,260 | 0,0684 | 3.98·10 -5 |
| 5,0 | 0,480 | 0,0302 | 0,0761 | 0,247 | 0,0603 | 3.54·10 -5 |
| 8,0 | 0,519 | 0,0242 | 0,0651 | 0,233 | 0,0482 | 2.87·10 -5 |
| 0,552 | 0,0220 | 0,0619 | 0,233 | 0,0439 | 2.62·10 -5 | |
| 0,628 | 0,0193 | 0,0584 | 0,241 | 0,0380 | 2.31·10 -5 | |
| 0,694 | 0,0180 | 0,0578 | 0,250 | 0,0351 | 2.19·10 -5 | |
| 0,792 | 0,0170 | 0,0584 | 0,269 | 0,0329 | 2.08·10 -5 | |
| 0,863 | 0,0166 | 0,0603 | 0,285 | 0,0320 | 2.06·10 -5 | |
| 0,915 | 0,0166 | 0,0616 | 0,299 | 0,0320 | 2.08·10 -5 |
Linear attenuation coefficient is the simplest attenuation coefficient that can be measured experimentally, but is not usually given in lookup tables due to its dependence on the density of the absorbing material. For example, water, ice and steam have different linear extinction coefficients for the same energy, even though they are composed of the same substance.
Gamma rays interact mainly with atomic electrons, therefore, the attenuation coefficient must be proportional to the electron density P, which is proportional to the volumetric density of the absorbing material. For any given substance, the ratio of the electron density to the volume density of that substance is the constant Z/A, independent of the volume density. The Z/A ratio is almost constant for all elements except the heaviest elements and hydrogen:
P=Zρ / A, (3.3)
Where P- electron density;
Z- atomic number;
ρ - mass density;
A- mass number.
If we divide the linear attenuation coefficient by the density of the substance ρ, we get mass attenuation coefficient, independent of the density of the substance:
The mass attenuation coefficient is measured in cm 2 /g (in the SI system - m 2 /kg) and depends only on the serial number of the substance and the energy of gamma rays. Judging by the unit of measurement of this coefficient, it can be considered as the effective cross section for the interaction of electrons per unit mass of the absorber. The mass attenuation coefficient can be written in terms of the reaction cross section σ (cm 2):
Where N 0 - Avogadro's number (6.02 10 23);
A- mass number of the absorbing element.
Interaction cross section σ i by their definition are similar to reaction cross sections, i.e. determines the probability of leakage i-th process during the interaction of a gamma quantum with an atom. It is related to the linear attenuation coefficients μ i formula
Where N– number of atoms of a substance in 1 cm3;
i– a short designation for the photoelectric effect (ph), the Compton effect (k) and the effect of the formation of electron-positron pairs (p).
Cross sections are expressed in barns per atom.
Using the mass attenuation coefficient, equation (3.1) can be represented as follows:
, (3.7) where x = ρ d.
The mass attenuation coefficient does not depend on density, but depends on the photon energy and the atomic number of the absorber. Figures 3.3 and 3.4 show the dependence on photon energy in the range from 0.01 to 100 MeV for groups of elements from carbon to lead. This coefficient is more often given in tables than the linear attenuation coefficient, since it quantifies the probability of interaction of gamma rays with a particular element.
Rice. 3.3. Dependence of the total mass absorption coefficient on photon energy for various materials (energy range from 0.01 to 1 MeV)
The reference book contains tables of the dependences of the linear and mass attenuation coefficients and the free path of gamma quanta on their energy in the range from 0.01 to 10 MeV for various substances.
The interaction of gamma radiation with a complex substance is characterized by effective ordinal number Z eff of this substance. It is equal to the ordinal number of such a conventional simple substance, the mass attenuation coefficient of which at any energy of gamma rays coincides with the mass attenuation coefficient of the given complex substance. It is calculated from the ratio:
Where Р 1, Р 2, …, Р n– weight percentage of constituent substances in a complex substance;
μ 1 /ρ 1 , μ 2 /ρ 2 , …, μ n/ρ n– mass attenuation coefficients of constituent substances in a complex substance.
Taking into account the above three main effects of interaction of gamma radiation with matter, the total linear attenuation coefficient will consist of three components determined by the photoelectric effect, the Compton effect and the pair generation effect:
Each of them depends in different ways on the serial number of the substance and the energy of gamma rays.
At photoelectric effect The gamma quantum is absorbed by the atom, and an electron escapes from the atom (Figure 3.5).
Rice. 3.5. Photoelectric absorption process diagram
Part of the gamma quantum energy, equal to the binding energy ε e, is spent on detaching an electron from the atom, and the rest is converted into the kinetic energy of this electron Her:
The first feature of the photoelectric effect is that it occurs only when the energy of the gamma quantum is greater than the binding energy of the electron in the corresponding shell of the atom. If the energy of a gamma quantum is less than the binding energy of an electron in TO-shell, but larger than in L-shell, then the photoelectric effect can occur on all shells of the atom, except TO-shells, etc.
The second feature is the increase in photoelectric absorption of gamma rays with increasing binding energy of electrons in the atom. The photoelectric effect is practically not observed on weakly bound electrons, and free electrons do not absorb gamma rays at all. The linear attenuation coefficient of the photoelectric effect is proportional to the ratio Z 4/E γ 3 .
This proportionality is only approximate, since the exponent Z varies in the range from 4.0 to 4.8. As the energy of the gamma quantum decreases, the probability of photoelectric absorption increases rapidly (see Fig. 3.6). Photoelectric absorption is the predominant interaction process for low-energy gamma rays, X-rays and bremsstrahlung.
The photoelectric effect is mainly observed on K- And L-shells of heavy atoms at gamma quanta energies up to 10 MeV. The coefficient μf sharply decreases with increasing energy of gamma rays and at an energy of about 10 MeV approaches zero, i.e. photoelectrons do not appear. In Fig. Figure 3.6 shows the photoelectric mass attenuation coefficient for lead. The probability of interaction increases rapidly with decreasing energy, but then decreases sharply at gamma-quantum energies just below the K-electron binding energy. This jump is called K- edge. Below this energy, the gamma quantum does not have enough energy to knock out K-electron. Below K-edge the probability of interaction increases again until the energy becomes lower than the binding energies L-electrons. Such jumps are called L I - , L II - , L III - - edges.
Rice. 3.6. Photoelectric mass attenuation coefficient for lead
Scattering of γ quanta occurs on weakly bound electrons of atoms, called Compton effect . With this interaction, elastic collisions of γ-quanta with an equivalent mass occur m γ = E/c 2 with electrons mass m e. Such a collision is shown schematically in Figure 3.7. In each such collision, the γ quantum transfers part of its energy to the electron, giving it kinetic energy. Therefore, such electrons are called recoil electrons. The kinetic energy of the recoil electron will be equal to
Where v and is the frequency of the γ-quantum before and after the collision;
h– Planck’s constant.
Rice. 3.7. Scheme of interaction of a gamma quantum with matter
with Compton effect
After the collision, the recoil electron and the γ-quantum fly apart at angles θ and φ relative to the initial direction of motion of the γ-quantum. Taking into account the laws of conservation of energy and momentum (momentum), the wavelength of the γ-quantum will change:
In tangential collisions, the γ-quantum is deflected by small angles (φ ~ 0) and its wavelength changes insignificantly. It will be maximum in frontal collisions (φ ~ 180 0), reaching the value
Energy of scattered gamma quantum and recoil electron E e are related to the initial energy of the gamma quantum, with the angles φ and θ by the relations:
Since the interaction of a γ-quantum with any electron is independent, the value μ To proportional to electron density N e, which, in turn, is proportional to the ordinal number Z substances. Dependence of μk on the energy of the γ-quantum h v and Z, obtained by physicists Klein, Nishina and Tamm, has the form:
Where N– the number of atoms in 1 cm 3 of a substance.
The Compton effect occurs mainly on weakly bound electrons in the outer shells of atoms. With increasing energy, the fraction of scattered γ quanta decreases. But the decrease in the linear scattering coefficient μ to happens slower than μ f. Therefore, in the energy field Eγ > 0.5 MeV the Compton effect dominates over the photoelectric effect.
In gamma ray spectrometry the quantity used is dμ k /dE e, called differential Compton scattering coefficientγ -quanta. Its physical meaning is that it determines the number of recoil electrons per unit volume of matter, formed by the flow of gamma quanta Ф with energy Eγ, the energy of which lies in the range from zero to maximum value Her Max. The Klein-Nishina-Tamm theory allows us to obtain an analytical expression for the quantity dμ To / dE e = Nd, Where N– the number of atoms per unit volume of a substance. To illustrate this dependence, we present graphical distributions of recoil electrons for three fixed energies of gamma rays (Fig. 3.8). In the case of high γ-quanta energies (more than 2 MeV), the energy distribution of recoil electrons is almost constant. Deviation from a constant value (increase in the distribution density of recoil electrons) begins as their energy approaches the energy of the γ-quantum, forming the so-called Compton peak. In this case, the energy of recoil electrons in the Compton peak is somewhat lower than the energy of the gamma quanta that generated them (as can be seen from the figure).
Rice. 3.8. Energy distribution of recoil electrons
for γ-quanta of various energies
Since the energy of recoil electrons cannot be higher than the initial energy of γ quanta, after the Compton peak the distribution abruptly ends to zero. As the energy of γ quanta decreases (less than 1.5 MeV), the uniformity of the distribution below the Compton peak is also disrupted. Figure 3.9 shows the dependence of the energy of the Compton edge on the energy of gamma rays. It follows from it that with increasing energy of gamma quanta, the difference in the energies of the photopeak and the Compton edge initially grows rapidly, but, starting from energies of 100-200 keV, this difference tends to a constant value.
Pairing effect occurs when a γ-quantum passes near the nucleus if its energy exceeds the threshold value of 1.022 MeV. Outside the field of the nucleus, a γ-quantum cannot form an electron-positron pair, because in this case the law of conservation of momentum will be violated. Although an energy of 1.022 MeV is enough to generate a pair, then the momentum of the generated particles should be equal to zero, while the γ-quantum has a momentum different from zero and equal to E γ /c. However, in the nuclear field this effect becomes possible, since in this case the energy and momentum of the γ-quantum are distributed between the electron, positron and nucleus without violating the conservation laws. Moreover, since the mass of the nucleus is thousands of times greater than the mass of the electron and positron, it receives an insignificant part of the γ-quantum energy, which is almost completely distributed between the electron and positron. The effect of the creation of an electron-positron pair is shown schematically in Figure 3.10.
Rice. 3.9. Dependence of the energy of the Compton edge on the energy of the gamma quantum
Rice. 3.11. Dependence of linear attenuation coefficients of gamma radiation on the energy of γ-quanta for lead
All three interaction processes described above contribute to the total mass attenuation coefficient. The relative contribution of the three interaction processes depends on the energy of the gamma quantum and the atomic number of the absorber. In Fig. Figure 3.12 shows a set of mass attenuation curves covering a wide range of energies and atomic numbers. The extinction coefficient for all elements, with the exception of hydrogen, has a sharp rise in the low energy region, which indicates that photoelectric absorption is the dominant interaction process in this region. The location of this rise is highly dependent on the atomic number. Above the rise in the low energy region, the value of the mass attenuation coefficient gradually decreases, defining the region in which Compton scattering is the predominant interaction.
Rice. 3.12. Mass attenuation coefficients of some elements
(the energies of gamma rays usually used in
identification of isotopes of uranium and plutonium by gamma radiation)
The mass extinction coefficients for all elements with atomic number less than 25 (iron) are virtually identical in the energy range from 200 to 2000 keV. In the range from 1 to 2 MeV, the extinction curves converge for all elements. The shape of the hydrogen mass attenuation curve shows that the interaction of gamma rays with energies greater than 10 keV occurs almost exclusively through Compton scattering. At energies above 2 MeV for elements with high atomic number Z The process of interaction to form pairs becomes important, and the mass attenuation coefficient begins to increase again.
There are three main processes of interaction between -quanta and matter. These are: the phenomenon of the photoelectric effect, the Compton effect and the process of formation of electron-positron pairs.
Photo effect.
The phenomenon is that a -quantum interacting with matter transfers all its energy to an electron, which in turn can take part in other processes. The energy balance of the photoelectric effect is described by Einstein's formula
h = A + E k,
where A is the work function of the atom, and E k is the kinetic energy of the electron.
Compton effect.
The effect manifests itself in the scattering of a -quantum by an electron. In this case, the scattered quantum has a longer wavelength than the primary -quantum. The change in the radiation wavelength during this process is determined by the relation
Where 
.
The value 0 is called Compton electron wavelength. Angle is the angle of scattering. The difference in the energies of the incident and scattered -quanta turns into the kinetic energy of the recoil electron. Thus, in the Compton phenomenon, the energy of -quanta is partially spent on knocking out electrons (recoil electrons) and the appearance of light quanta, which in turn lead to the photoelectric effect and the Compton effect. The number of electrons of a substance participating in Compton scattering decreases with increasing energy of γ-quanta (Fig. 2).
Pair formation.
The process of formation of electron-positron pairs begins with -quanta energies of 1.0210 6 eV (Fig. 2). This value is twice the rest energy of an electron or positron. The interaction occurs at one point near the nucleus or electron, but not in a vacuum, which is due to the need for simultaneous fulfillment of the laws of conservation of energy and momentum.
For -radiation arising during radioactive decay, the third mechanism considered is ineffective, since the energy of -quanta during radioactive decay does not exceed 3 MeV.
From all that has been said, it follows that the complete absorption of gamma quanta in a substance, leading to the release of electrons, depends on their energy and the ordinal number of the substance.
Rice. 2. Lead absorption spectrum, divided into three parts:
1 – photoelectric effect, 2 – Compton effect, 3 – pair production
Absorption of gamma rays.
Experience has proven that the higher the density of bodies, the more they attenuate γ-radiation. One of the least permeable metals for γ-radiation is lead, the most permeable metal (more than glass) is aluminum (Fig. 3).
The absorption of γ-rays, like any other electromagnetic radiation, depends on the thickness of the layer of the substance absorbing them. For each type of radiation, depending on the photon energy, the nature of absorption changes, as is the case for high-energy gamma rays absorbed to form electron-positron pairs. Experimental data have shown that the intensity of a parallel beam of gamma rays passing through a layer of matter of thickness x is sufficiently described by the Bouguer-Lambert law
, (6)
where - absorption coefficient gamma rays, depending on the wavelength and type of substance.
Taking into account all three types of interaction of gamma rays with matter that we talked about, the absorption coefficient can be represented as
,
Where 
- absorption coefficients for the photoelectric effect, the Compton effect and the process of creation of an electron-positron pair, respectively (Fig. 3).
Table 1
a) attenuation coefficient of -radiation for aluminum.
|
|
|
|
|
|
where are the coefficients 
are given to a layer thickness of 1 cm.
b) attenuation coefficient of -radiation for lead.
|
|
|
|
|
|
Values of absorption coefficients ,
as well as coefficients 
for different substances, depending on the energy of the incident radiation quantum, are usually given in the form of tables and graphs in reference literature,
In Fig. 3 shows the dependences of the coefficients 
from the energy of quanta when -radiation falls on lead and aluminum. More precisely, these dependencies are presented in the form of numbers in Table 1.
Rice. 3. Dependence of absorption coefficients on the energy of -quanta:
a - for lead; b - for aluminum.
The Bouguer-Lambert law (6) makes it possible to experimentally determine μ - absorption coefficients. As follows from (6) for the thicknesses of the absorbed layer x 1 and x 2
.
(7)
Subtracting equation one in (7) from the second equation, we obtain
,
(8)
.
(9)
Thus, if we plot the dependence of lnI on the thickness of the absorbing layer based on experimental data, then the slope of this linear graph will be numerically equal to the absorption coefficient - .
Rice. 4. Block diagram of the experimental setup