Device and method for characterizing a depth of activity of a radionuclide in a solid medium

Abstract

The invention is a method for determining a depth at which a gamma-emitting radionuclide lies in a solid medium, the latter possibly being concrete or earth. The method is based on a measurement of a spectrum of the gamma radiation emitted by the radionuclide and emanating from a surface bounding the solid medium. Two energy bands are selected in the spectrum. On the basis of spectral values in each energy band, a calibration function allowing the depth to be estimated may be applied. The calibration function is established beforehand based on spectral models.

Description

[0001] Description

[0002] Title: DEVICE AND METHOD FOR CHARACTERIZING THE DEPTH OF THE ACTIVITY OF A RADIONUCLIDE IN A SOLID MEDIUM

[0003] TECHNICAL FIELD

[0004] The technical field of the invention is the characterization of a depth of the activity of a radionuclide in a solid medium, in particular a concrete wall.

[0005] PREVIOUS ART

[0006] During the operation of a nuclear facility, civil engineering structures may be contaminated by radionuclides. When structures are made of concrete, some radionuclides may migrate, particularly when they are in a liquid phase. As a result, the activity due to contamination is distributed inhomogeneously within a concrete structure. It is generally accepted that the activity is distributed according to a decreasing gradient with the thickness of the structure: the closer one is to the surface exposed to contamination, the higher the activity.

[0007] During dismantling operations, it is useful to estimate the residual activity levels in the concrete structures of a facility. This allows for scenarios of the work to be carried out, as well as to predict the quantity of nuclear waste that will be generated. It is understood that this presupposes an estimate of the depth of contamination migration through the concrete.

[0008] Currently, the main method for estimating such depth relies on sample collection followed by destructive laboratory analyses. However, taking samples, such as coring, can be tedious. Another limitation is the statistical representativeness of the samples collected.

[0009] The publication Potapov VN et al "Reliably Implemented Non-destructive Spectrometry Method for the Characterization of Volume Contamination of Objects at Nuclear Industry", IEEE 2019 IEEE Nuclear Science Symposium and Medical Imaging Conference, describes a non-destructive method for estimating the migration depth of contamination in contaminated soil or concrete. The method is based on the use of gamma spectrometry. Estimating the contamination depth, based on non-destructive measurements, is particularly interesting. Implementation is considerably simplified compared to taking samples. This makes it possible to multiply the number of measurements, and to achieve a more comprehensive knowledge of the radiological state of civil engineering.

[0010] The inventors found that the method previously described could be improved, particularly during the calibration phase or during implementation in the field. The invention presented below meets these needs for improvement.

[0011] STATEMENT OF THE INVENTION

[0012] A first subject of the invention is a method for estimating a depth along which a radionuclide extends in a solid medium, from a surface, the solid medium being delimited by the surface, the radionuclide emitting gamma radiation at at least one emission energy, the method comprising:

[0013] - a) arrangement of a spectrometric detector facing the surface of the solid medium, and measurement, by the spectrometric detector, of an energy spectrum of the gamma radiation, emitted by the radionuclide and emanating from the surface, the measured spectrum comprising a number of pulses detected by the detector for different energy values, the energy spectrum comprising a peak at the emission energy;

[0014] - b) taking into account a first and a second energy band, previously defined, the first energy band comprising energy values ​​lower than the second energy band, the second energy band comprising the peak at the emission energy;

[0015] - c) from the measured spectrum, determination of a first spectral value at the first energy band and of a second spectral value at the second energy band;

[0016] - d) application

[0017] - from a first calibration coefficient to the first spectral value to obtain a first calibrated spectral value;

[0018] - a second calibration coefficient to the second spectral value, to obtain a second calibrated spectral value; each calibration coefficient corresponding to a ratio, in each energy band, between a predetermined activity of the solid medium and an estimate of a spectral value corresponding to said predetermined activity;

[0019] - e) calculating a comparison indicator from a comparison of the first calibrated spectral value and the second calibrated spectral value resulting from d);

[0020] - f) applying a calibration function to the comparison indicator resulting from e), so as to estimate the depth to which the radionuclide extends in the solid medium, the calibration function being previously established, considering an activity of the radionuclide decreasing as a function of depth; the method being characterized in that during step d), the first calibration coefficient and the second calibration coefficient are determined, in each energy band, by a numerical modeling of a spectrum detected by the spectrometric detector, the solid medium being considered, during the modeling, as having said predetermined activity.

[0021] The first spectral value and the second spectral value are a number of pulses or a count rate in the first energy band and in the second energy band respectively.

[0022] The unit activity can be a uniform surface activity or a uniform mass activity in the analyzed medium or a predetermined activity distributed according to a predefined activity gradient.

[0023] The method may comprise, prior to step c):

[0024] - taking into account a spectrum representative of the solid medium;

[0025] - taking into account at least one predetermined energy band corresponding to an emission energy of a natural radionuclide, naturally present in the solid medium;

[0026] - from a spectral value of the representative spectrum in said predetermined energy band, estimation of an activity of the natural radionuclide in the solid medium;

[0027] - estimation of a contribution of the natural radionuclide in the spectrum measured during step a);

[0028] - correction of the spectrum measured during step a), so as to remove the contribution of the natural radionuclide, at least in the first energy band.

[0029] The representative spectrum of the solid medium can be

[0030] - the spectrum measured during step a);

[0031] - or a spectrum measured by a spectrometric detector different from the spectrometric detector used during step a);

[0032] - or a spectrum measured by the spectrometric detector implemented during step a).

[0033] The method may comprise, prior to step d):

[0034] - determination of the density of the solid medium examined;

[0035] - depending on the density of the solid medium examined, selection of the first calibration coefficient from among first calibration coefficients respectively determined for different densities. The method may comprise, prior to step f):

[0036] - determination of the density of the solid medium examined;

[0037] - depending on the density of the solid medium examined, selection of the calibration function from calibration functions respectively determined for different densities.

[0038] According to one embodiment, the determination of the density of the solid medium examined comprises the following sub-steps:

[0039] - taking into account a spectrum representative of the solid medium;

[0040] - selection of at least two energy bands corresponding to emission energies of the same radionuclide, in particular natural, present naturally in the solid medium;

[0041] - estimation of activities of the natural radionuclide from a spectral value of the representative spectrum respectively in each selected energy band, each activity estimation being carried out taking into account a density of the solid medium;

[0042] - determination of the density minimizing a difference between the activities of the radionuclide estimated from the selected energy bands.

[0043] The representative spectrum of the solid medium can be:

[0044] - the spectrum measured during step a);

[0045] - or a spectrum measured by a spectrometric detector different from the spectrometric detector used during step a);

[0046] - or a spectrum measured by the spectrometric detector implemented during step a). The method may comprise:

[0047] - g) multiplication of the second calibrated spectral value, resulting from e), by a correction function so as to estimate an activity of the solid medium, the correction function being previously established for different values ​​of the comparison indicator.

[0048] The comparison indicator can be a ratio or a difference between the first calibrated spectral value and the second calibrated spectral value.

[0049] The solid medium can be concrete or earth or sand.

[0050] A second object of the invention is a device intended to estimate a depth along which a radionuclide extends in a solid medium, from a surface, the solid medium being delimited by the surface, the device comprising:

[0051] - a spectrometric detector, configured to measure a spectrum of gamma radiation emanating from the surface; a processing unit, programmed to implement steps b) to f), and possibly step g), of a method according to the first embodiment from the spectrum measured by the spectrometric detector.

[0052] The invention will be better understood by reading the description of the exemplary embodiments presented in the remainder of the description, in conjunction with the figures listed below.

[0053] FIGURES

[0054] Figure 1 shows a diagram of the main components of a device according to the invention.

[0055] Figure 2 shows the main steps of a method for implementing the invention.

[0056] Figure 3 illustrates two energy bands applied to a spectrum.

[0057] Figure 4A shows a spectrum of the natural activity of a concrete wall.

[0058] Figure 4B is an activity spectrum of a weakly contaminated concrete wall in 137 Cs.

[0059] Figure 5A shows an evolution of a first calibrated spectral quantity and a second calibrated spectral quantity (y-axis) as a function of the activity depth (x-axis).

[0060] Figure 5B represents a calibration function (curve 1) and a correction function (curve 2).

[0061] Figure 6A shows a measuring device whose detector is a cooled Germanium crystal.

[0062] Figure 6B shows models of a spectrum of a concrete wall with a density of 2.3 g.crrr 3 for the same total activity of 137 Cs and different depths of activity.

[0063] Figure 6C shows models of a spectrum of a baryta concrete wall with a density of 3.35 g.crrr 3 for the same total activity of137 Cs and different depths of activity.

[0064] Figure 6D shows models of a spectrum of a concrete wall with a density of 2.3 g.crrr 3 for the same total activity of 60 Co and different depths of activity.

[0065] Figure 6E shows models of a spectrum of a baryta concrete wall with a density of 3.35 g.crrr 3 for the same total activity of 60 Co and different depths of activity.

[0066] Figure 7A shows calibration functions established by taking into account two different densities (2.3 g.crrr 3 and 3.35 g.crrr 3 ) and an activity of 137 Cs.

[0067] Figure 7B shows calibration functions established by taking into account two different densities (2.3 g.crrr 3 and 3.35 g.crrr 3 ) and an activity of 60 Co.

[0068] Figure 7C shows correction functions established by taking into account two different densities (2.3 g.crrr 3 and 3.35 g.crrr 3 ) and an activity of 137 Cs. Figure 7D shows correction functions established by taking into account two different densities (2.3 g.cm -3 and 3.35 g.cm -3 ) and an activity of 60 Co.

[0069] PRESENTATION OF SPECIAL EMBODIMENTS

[0070] Figure 1 describes a device 1 suitable for an implementation of the invention. The device comprises a spectrometric detector 10, intended to be placed facing a surface S delimiting a solid medium M. The solid medium is a medium likely to have been contaminated by a radionuclide. It may in particular be a medium comprising concrete or earth or sand. An objective of the invention is to estimate a thickness Zo of the medium likely to contain a major part of the activity. By major part, we mean more than 80% or more than 90% of the activity of the radionuclide.

[0071] The spectrometric detector 10 is arranged at a distance D from the surface S of the medium M. It is a detector sensitive to X or gamma radiation. Thus, the implementation of the invention assumes that the radionuclide is an X or gamma emitter. Depending on the type of installation, the radionuclide may be, in a non-limiting manner, 137Cs (e.g. in fuel reprocessing facilities) or 60 Co (e.g. in nuclear reactors).

[0072] When a gamma photon interacts in the detector 10, the latter generates a pulse whose amplitude depends, preferably linearly, on the energy released by the photon during its interaction in the detector. The detector 10 is connected to an electronic spectrometry circuit 12. During a measurement period, which may last a few seconds to a few minutes or tens of minutes, the pulses generated by the detector 10 are counted and classified according to their amplitude, so as to form an amplitude spectrum. By using an energy calibration function, establishing a relationship between the amplitude of the pulse and the energy released in the detector, an energy spectrum is obtained. Generally, the energy spectrum is discretized into different energy channels k, the number K of channels generally being between several hundred and several thousand.

[0073] Thus, the device 1 makes it possible to form an energy spectrum of the photons emitted by the medium M. When a gamma-emitting radionuclide is present in or on the wall, in a detectable quantity, it produces, in the measured spectrum, a spectral signature comprising one or more peaks whose energy is known. The energy of each peak corresponds to the energy of the photons emitted by the radionuclide. The emission energies of the main radionuclides are known and available in nuclear databases. In the example shown in Figure 1, the detector is a scintillator detector, of the NaI type, coupled to a scintillation photon / charge carrier converter. Other types of detectors can be used, for example a LaBrs scintillator detector. Advantageously, a semiconductor detector, for example Ge, can be used, which makes it possible to obtain spectra whose energy resolution is more favorable.The use of a Germanium detector is described below, in connection with Figures 6A to 6E.

[0074] In Figure 1, we also schematized a gradient of the activity ct(z) as a function of the depth z.

[0075] The measured spectrum may include a background noise component, which corresponds to the radiological background to which the detector 10 is exposed. The background noise may have several components.

[0076] A first component is the natural background noise, due to the natural radioactivity of the medium under examination. This is particularly the case when the medium is made of concrete or earth. The natural background noise comes from radioactive isotopes, gamma emitters, naturally present in the medium M. A commonly encountered natural gamma emitter is 40 K, knowing that other gamma emitters, resulting from the decay chains of 238 U or of 232Th can be encountered. Taking into account natural background noise constitutes an interesting aspect of the invention, described later.

[0077] A second component is the background noise induced by the vicinity of the controlled wall. In order to reduce the contribution of the “neighborhood” background noise, the detector is usually surrounded by a shield 14. The shield forms a collimator delimiting an opening angle so as to limit the field of observation of the detector 10. However, the shield does not act in an all-or-nothing manner and certain photons, emitted in the vicinity of the detector, can pass through the shield and be detected by the detector. This is particularly the case when the neighborhood background noise is more intense than the signal emitted by the medium M, in the field of observation of the detector. The shield 14 may comprise a removable cap 14', configured to close the field of observation of the detector 10. In this case, the neighborhood background noise is taken into account by carrying out two successive measurements with and without a cap.The measurement taken with the earplug is then considered representative of the background noise in the vicinity. It can therefore be subtracted from the measurement taken without the earplug.

[0078] The device 1 comprises a processing unit 20, intended to carry out processing of each spectrum resulting from the spectrometry circuit 12. The processing unit 20 may for example comprise a microprocessor. The processing unit is programmed to implement certain steps of the method described below, in connection with FIG. 2.

[0079] Figure 2 shows the main steps in implementing the process, which are now described.

[0080] 100 arrangement of device 1 facing the medium to be analyzed. In this example, the solid medium is a concrete wall. acquisition of a neighborhood background noise spectrum. This step is optional.

[0081] During this step, as previously described, the cap 14' closes the observation field of the detector. A spectrum representative of the background noise in the vicinity is acquired.

[0082] 120 acquisition of a measurement spectrum. During this step, a spectrum of the gamma radiation detected by the detector 10 is acquired, the collimator being open. Depending on the activity of the wall and the sensitivity of the detector 10, the acquisition time can be between a few tens of seconds and a few tens of minutes.

[0083] 130 taking into account the neighborhood background noise. This step is implemented when a background noise spectrum is available, resulting from step 110. During this step, the neighborhood background noise spectrum is subtracted from the measurement spectrum, so as to obtain a corrected spectrum. Preferably, the acquisition times of the measurement spectrum (step 120) and the neighborhood background noise spectrum (step 110) are identical. Otherwise, the spectra are readjusted so as to correspond to the same acquisition time.

[0084] Following step 120 or possibly step 130, an energy spectrum of the gamma radiation emanating from the surface is available. In the remainder of the description, this spectrum is referred to as the spectrum of interest. It is either the spectrum resulting from step 120 or the corrected spectrum resulting from step 130.

[0085] 140 Energy Band Selection

[0086] During this step, two different energy bands are selected in the spectrum of interest. Part of the invention is based on a different evolution of the content of the spectrum of interest in two different energy bands, depending on the depth of contamination. Each energy band was determined during a preliminary calibration phase 70, described below.

[0087] A first EE energy band extends on either side of a spectral region corresponding to the Compton front. The width of the first EE energy band depends on the energy resolution of the detector, the maximum energy of the EE energy band being able to correspond to the minimum energy of the AE2 energy band. It generally extends over a few hundred keV. A particularity of the first energy band is that the spectral value changes little with the depth of the contamination. By spectral value, we mean the number of detected pulses, whose energy belongs to the first energy band. The number of detected pulses is usually referred to as the "count number".

[0088] Figure 3 shows a spectrum obtained by a 1 inch by 1 inch Nal scintillator detector, simulated using a particle transport calculation code (MCNP code). The detector is placed facing a concrete wall delimited by a surface S, and having an activity of 137 Cs whose gradient, depending on the depth z, is modeled by a decreasing exponential function. In Figure 3, the first energy band EE extends between 290 keV and 600 keV.

[0089] The first energy band EE is formed by interactions having two origins: interactions corresponding to Compton scattering, in the detector, of gamma photons not or weakly attenuated by the concrete wall: these interactions form a first component of the spectrum in the first energy band at E1. In Figure 1, such interactions are represented by solid arrows. interactions corresponding to absorption, in the detector, by photoelectric effect, of gamma photons having scattered, according to scattering angles between 0° and 90° by the concrete wall: these interactions form a second component of the spectrum in the first energy band EE. In Figure 1, such an interaction is represented by a dotted arrow.

[0090] In the presence of a low contamination depth, the first component is predominant. In the presence of a high contamination depth, the second component becomes predominant. Thus, the spectral content in the first EE energy band is considered to be weakly dependent, for example at ± 20%, on the contamination depth.

[0091] The first energy band EE can be defined beforehand and optimized by modeling spectra detected by the detector by considering different activity gradients in the wall and, for the same activity gradient, different contamination depths. This aspect is described below in connection with Figures 6A to 6E. A second energy band AE2 comprises an emission energy of the radionuclide. It is known that, subject to a sufficient branching rate, each emission energy of a radionuclide results in the appearance, on the spectrum, of a peak, called the total energy peak. The second energy band AE2 corresponds to all or part of the total energy peak. Depending on the energy resolution of the detector, the second energy band AE2 is more or less wide. Preferably, the second energy band AE2 is centered on the emission energy of the radionuclide.Unlike the first energy band, the spectral content in the second energy band varies strongly depending on the contamination depth. This is due to the photoelectric absorption, in the solid medium M, of the photons emitted at the emission energy.

[0092] In the example shown in Figure 3, the second energy band AE2 extends on either side of the emission energy of 137 Cs, or 662 keV. In this example, the second energy band AE2 extends between 577 keV and 747 keV.

[0093] Preferably, the first energy band and the second energy band do not overlap, or only slightly. The first energy band may extend between a first minimum bound and a first maximum bound. The second energy band may extend between a second minimum bound and a second maximum bound. The second minimum bound is greater than or equal to the first maximum bound.

[0094] Following step 140, we have a first number of pulses N in the first energy band and a second number of pulses N2 in the second energy band AE2. The numbers of pulses are generally expressed per unit of time, in which case they are count rates: number of pulses detected per second.

[0095] In the remainder of the description, the term spectral value designates a number of pulses, or a number of pulses per unit of time, in an energy band of the spectrum. Following step 140, a first spectral value N is available ± and a second spectral value N2

[0096] 150 taking into account natural activity. This step is optional but is advantageous in particular for low levels of contamination of the M environment.

[0097] The method is intended for use on materials such as concrete or earth. This type of material is likely to contain natural radionuclides, some of which are gamma emitters. The presence of these can lead to a measurement error. Indeed, the quantity of natural radionuclides can have an influence on the first spectral value N ± . In order to improve the measurement accuracy, the contribution of natural gamma-emitting isotopes, particularly in the first energy band must be quantified and removed.

[0098] Similarly, the presence of natural radionuclides can have an influence on the second N2 spectral value. Thus, it is preferable that the contribution of natural gamma-emitting isotopes, in the second AE2 energy band, be quantified and removed.

[0099] The main natural emitters can easily be identified by their photoelectric emission peaks. These are descendants of the 232 Th, of the 238 U. This is also the 40 K.

[0100] Taking into account natural radioactivity corresponds to sub-steps 151 to 154. These steps are carried out by taking into account a representative spectrum Sp' of the volume examined. The representative spectrum may be the spectrum Sp acquired during step 120 or a different spectrum, for example acquired with the same detector and a longer acquisition time, so as to obtain a more precise quantification of the natural activity. The representative spectrum is carried out on the wall examined or on a wall considered to be representative of the wall examined. The representative spectrum may also be acquired by a different detector.

[0101] 151 Identification, in the representative Sp' spectrum, of emission peaks corresponding to descendants of 232 Th and of 238 U or of 40 K.

[0102] The following table lists naturally occurring radionuclides (first column) and their gamma-emitting descendants (second column), along with their emission energies (third column - keV) and branching rates (fourth column - %). This list is not exhaustive. Only the highest energy lines are considered.

[0103]

[0104] Table 1

[0105] Figure 4A represents a spectrum, measured by a Germanium spectrometric detector, on a clean concrete wall. The spectrum is representative of natural radioactivity. Peaks corresponding to the energies mentioned in Table 1 are observed. The duration of spectrum acquisition was 12 hours. Such a spectrum can be considered representative of all or part of the walls of the same installation. It allows an estimation of an average activity of the main natural radionuclides composing the concrete, as described below. The contribution of the activity of each radionuclide can be taken into account to correct spectra measured on the walls of the installation, in particular in the first AEi energy band.

[0106] Sub-step 152: Estimation of a mass activity of 232 Th, of 238 U and of 40 K.

[0107] The specific activity of 232 Th and 238U is estimated from averaged mass activities calculated from spectral peaks detected at each emission energy. It is assumed that the radioactive descendants of 232 Th and of 238 U are in radioactive equilibrium with their respective parents.

[0108] From each emission peak, a mass activity A( of a natural radionuclide RN( is obtained by applying the expression: where N Et) is the counting rate at the emission energy Et of the radionuclide RN( considered and FT(i, Et, d) is a transfer function, obtained by modeling, corresponding to a number of counts detected per unit of time for a predetermined activity of the wall considered, for example a unit activity of 1 Bq. g 1The transfer function is considered by taking into account a hypothesis of homogeneous distribution in the wall, which is relevant with regard to natural radioactivity. The transfer function FT(i, Ei, d) depends on the density d of the concrete. The latter can be determined a priori, or be the subject of an experimental determination as described below. Preferably, the modeling of the detector has been previously verified in the laboratory, using standard irradiating sources.

[0109] Average activity A m of each parent radionuclide is estimated by taking an average of the mass activities A( of each radionuclide RN( descendants of said parent radionuclide: where Ai corresponds to the mass activities of the descendant radionuclides of each parent radionuclide and o Aj 2 is the variance assigned to A t .

[0110] In the case of 40K, the specific activity is obtained by applying expression (1) to the emission peak at 1460 keV.

[0111] Substep 153: Simulation of the contribution of 232 Th, of 238 U and of 40 K.

[0112] From the mass activities estimated in sub-step 152, the contribution of natural activity in the spectrum, and more particularly in the first energy band AE lt is estimated. According to one possibility, a contribution of each natural radionuclide has been previously simulated for a unitary homogeneous activity, for example 1 Bq. g 1 , taking into account the measurement configuration: wall thickness, position of the detector relative to the wall. The contribution of the natural activity is then obtained by weighting each unit contribution of each natural radionuclide by the mass activity of said radionuclide, resulting from sub-step 152. We thus obtain a natural contribution Nl nat in the first energy band.

[0113] Sub-step 154

[0114] During this step, the contribution of natural activity is subtracted from the first spectral value: the N value ± is replaced by N ± — N l nat . Similarly, the value N2 can be replaced by / V2- N 2 nat

[0115] Figure 4B shows a spectrum of a weakly contaminated concrete wall in 137 Cs. We observe the emission peak of 137 Cs, at energy 661.6 keV. Figure 4B shows the first energy band AE 17 which was defined between 300 keV and 659 keV. The second energy band AE2 corresponds to the emission peak of 137 Cs, taking into account the spectral resolution of the detector. In this example, it extends between 659.5 keV and 663.1 keV.

[0116] 160 Obtaining calibrated spectral values

[0117] During this step, the first spectral value N and the second spectral value N2 are multiplied respectively by a first calibration coefficient and by a second calibration coefficient.

[0118] Each calibration coefficient is determined during a preliminary calibration step 50. During this step, a first reference value N is determined 10 and a second reference value N 20 .

[0119] Each reference value corresponds to an estimate of a spectral value (count or count rate) which would be detected by the detector, in the same measurement configuration (same collimator, same position and orientation relative to the surface S), considering a reference activity A o of the wall. For example, the reference activity A ois a purely surface activity, homogeneous, of predetermined value. It can for example be a uniform surface activity equal to 1 Bq. cm -2 , which corresponds to a so-called unit surface activity. Alternatively, the reference activity is a mass activity of 1 Bq. g 1 taken into account on a predetermined wall thickness, for example 1 cm. The reference activity can also be a mass activity of 1 Bq.g 1 which is considered distributed according to a predetermined gradient, up to an arbitrary depth.

[0120] The first calibration coefficient a and the second calibration coefficient P are such that: a x 10 — 710(3) and ft X ^20 = -^o (4)

[0121] Preferably, the determination of each calibration coefficient is carried out by numerical modeling, implementing a particle transport code, for example the previously mentioned MCNP code. The determination of the first calibration coefficient and the second calibration coefficient using a numerical model, based on a reference activity, makes it possible to obtain precise values ​​of each coefficient, which improves the accuracy of the measurement.

[0122] During step 140, the first spectral value N multiplied by the first calibration coefficient a, and the second spectral value N2 multiplied by the second calibration coefficient p. We thus obtain a first calibrated value G = ax N = (5) and a

[0123] W 10 second calibrated value A = / 3 x N2= (6). 20

[0124] When the reference activity is a unit surface activity, G and A can be considered as equivalent surface activities estimated on the basis of A^ and N2, assuming no depth of contamination.

[0125] Figure 5A shows the evolution of the first calibrated quantity G and the second calibrated value A as a function of the contamination depth Z (x-axis). It can be seen that the quantity G is relatively stable, and varies within a margin of ± 10% up to a depth of approximately 15 cm.

[0126] 180 Calculation of a ratio of the first calibrated value to the second calibrated value.

[0127] During this step, we calculate a ratio of the first calibrated value G to the second calibrated value A. We thus obtain a ratio - . This ratio corresponds to a comparison indicator.

[0128] 190 Taking into account a calibration function.

[0129] During this step, the ratio - resulting from step 180 is used as an argument of a calibration function f, previously defined, in order to estimate a contamination depth Z o in the examined wall.

[0130] Thus, Z0= fg) (7) The calibration function is defined during a preliminary step 70, during which an analytical form of an activity gradient in the wall is taken into account, for example a decreasing exponential form, and the spectral values ​​N are estimated ± and N2 for different contamination depths Z o . Note that the term contamination depth refers to a depth containing x% of the activity, with preferably x > 75%. In this example, x = 90%. For example, we consider that the activity gradient of the radionuclide, in concrete, follows a decreasing law P(z) of analytical form:

[0131] So, ct(z) = Act tot P z) (9) where: z corresponds to a depth, along the Z axis, perpendicular to the surface S delimiting the solid medium M;

[0132] Act z) is a surface activity at depth z;

[0133] Act tot is the total activity.

[0134] In this example, the Z depth o corresponds to the depth up to which it is estimated that 90% of the radionuclide's activity is contained. Thus,

[0135] 7 7 f0° Act(z)dz = f0° Act tot P(z)dz = 0.9 Act tot (10)

[0136] The definition of the calibration function f consists of taking into account, for the same analytical form of the contamination gradient, and for the same total activity, different depths of contamination Z o . For each contamination depth Z otaken into account, we simulate a spectrum resulting from the detector, from which we estimate the spectral values ​​^(ZQ) and N2(Z0). We use the calibration coefficients a and / 3, obtained following step 50, so as to estimate, for each depth Z o , calibrated values ​​G(Z0) and (Z0) .

[0137] The calibration function f corresponds to the evolution of the quantity as a function of Z o . It (Z0) is obtained by numerical modeling, using a calculation code modeling the transport of photons in matter, and taking into account the geometry of the measurement: modeling of the detector, of the possible collimator, of the concrete wall, and of the position of the detector in relation to the concrete wall. The models can be carried out with the calculation code

[0138] MCNP.

[0139] Figure 5B (curve 1 - left y-axis) shows an example of a calibration function f obtained by considering a decreasing activity gradient following an exponential function as explained in (8). In Figure 5B, the x-axis corresponds to the quantity G / A and the left y-axis corresponds to the activity depth Z o as defined in expression (10).

[0140] The models used to simulate the detected spectrum are also based on an assumption regarding the density of the concrete. Different models can be carried out, taking into account different values ​​of the density d of the material forming the solid medium. This makes it possible to obtain a calibration function for each considered value of the density.

[0141] Step 200: Estimation of total activity.

[0142] During this optional but preferable step, the total activity is estimated from the first calibrated value G. As a first approximation, the total activity Act tot can be estimated using G directly. However, it is better to apply a correction function K corr to the function G. The correction function K corr is established in advance, based on models.

[0143] Thus, as a first approximation, the total activity Act tot can be estimated by the first calibrated value G: Act tot "G

[0144] A more accurate way to estimate activity is to use the K function corr with

[0145] The K function corr is determined beforehand, during a step 80, on the basis of models, taking into account several activity gradients.

[0146] Steps 50, 70 and 80 form device calibration steps, allowing the definition of the first calibration coefficient a, and the second calibration coefficient / 3 (step 50), the calibration function f (step 70) and the correction function K corr (step 80). Conveniently, steps 50, 70 and 80 can be carried out simultaneously, based on the same models.

[0147] Figure 5B (curve 2 - right y-axis) shows an example of a correction function obtained by considering a decreasing activity gradient following an exponential function as described in (8). In Figure 5B, the right y-axis corresponds to the value of the correction function K corr . We observe that the function K corr varies within a narrow range of variation, between 0.9 and 1.2.

[0148] As described in step 190, the modeling is performed taking into account an assumption regarding the density of the concrete. Different modeling can be performed, taking into account different values ​​of the density of the concrete. This makes it possible to obtain a correction function for each considered value of the density of the concrete.

[0149] Density estimation

[0150] The method may include a step 170 of estimating the density of the material forming the volume examined. The density of the material forming the wall, whether concrete or earth, is generally not known precisely. However, this density may vary, for example when the concrete is standard concrete (density = 2.35) or baryta concrete (density = 3.35). In order to improve the accuracy of the measurement, the method may include an estimation of the density of the material forming the medium examined. To do this, the natural activity of the material is taken advantage of and different emission peaks of the same natural radionuclide are selected, for example 214 Bi covering a wide energy range to exploit the contrast linked to the more or less significant attenuation of the emission lines in the medium depending on their energy

[0151] The specific activity of the selected natural radionuclide is estimated, based on different emission peaks, based on expression (1). The transfer function FT (i, d) depends on the density of the concrete. Based on several energy peaks E t , we determine the mass activities A^Ei) of the natural radionuclide i, and this by using different transfer functions FT (i, E^ d) established by taking into account different values ​​of the density of the concrete. We then determine the density d for which the different mass activities of the same radionuclide are closest.

[0152] It is considered that when the density taken into account in the transfer function is higher than the actual density of the material under examination, the mass activities determined from the lowest emission energy peaks are higher than the mass activities determined from the highest emission energy peaks. Conversely, when the density taken into account in the transfer function is lower than the actual density, the mass activities determined from the lowest emission energy peaks are lower than the mass activities determined from the highest emission energy peaks.

[0153] Estimating the density of the material forming the medium under examination is beneficial because it allows a selection of the calibration function and the correction function when different calibration functions and / or different correction functions based on different density values ​​have been previously established.

[0154] Density estimation is also applicable to any other material that may contain natural radioactivity, for example concrete or earth.

[0155] As with natural activity, density estimation is based on a spectrum considered representative of the wall or walls of an installation. The representative spectrum can be measured on a wall considered representative of the installation. The density determined from the representative spectrum is then used to process different spectra acquired on the same wall, or even on several walls of the same installation. This solution makes it possible to obtain a representative spectrum over a long acquisition period, so as to estimate the density more accurately. Alternatively, the density is estimated from each measured spectrum.This assumes, however, that the acquisition time is long enough for the density to be estimated precisely and that the presence of low artificial radioactivity or of the same order of magnitude as natural radioactivity so that the characteristic lines of natural radioactivity can be identified.

[0156] Modeling

[0157] The inventors modeled different measurement configurations. Figure 6A illustrates a modeling configuration. Each modeling assumes a description of the geometry of: the detector; the shielding and the collimator arranged around the detector; the material examined: thickness, density, activity gradient as a function of depth; position of the detector relative to the material examined, in particular the distance of the detector relative to the surface delimiting the material examined.

[0158] In the example of Figure 6A, the detector used is a detector based on a Germanium crystal cooled by a liquid nitrogen tank.

[0159] Figure 6B represents simulated spectra taking into account the same activity of 137 Cs purely surface (curve a) or extending, according to a decreasing gradient, over 100 mm (curve b), 200 mm (curve c) and 300 mm (curve d). The activity gradient taken into account was an exponential gradient. In Figure 6B, a concrete with a density of 2.3 g.crrr was taken into account 3. This type of simulation allows the limits of the first energy band EE to be defined. In this example, the upper limit of the first energy band corresponds to the lower limit of the second energy band AE2- The lower limit of the first energy band EE corresponds to an energy at which the spectrum obtained by simulating a surface activity (curve a) crosses the spectrum obtained by simulating an activity in depth, for example curve b. In this example, the spectrum of the lower limit of the first energy band EE is 290 keV. Feedback has shown that the lower limit of the first energy band can vary between 290 keV and 400 keV, or even more, depending on the radioelements considered and the measurement conditions.

[0160] Figure 6C represents simulated spectra taking into account the same activity of 137Cs purely surface (curve a) or extending, according to a decreasing gradient, over 100 mm (curve b), 200 mm (curve c) and 300 mm (curve d). The activity gradient taken into account was an exponential gradient. In Figure 6C, a concrete with a density of 3.35 g. cm was taken into account. -3 , which corresponds to a baryta concrete. We observe that by taking the same assumptions regarding the activity gradient, the spectra of Figure 6C are different from those of Figure 6B. This comes from the difference in the densities considered. By taking into account the same criterion for the determination of the lower limit of the first energy band AE 17 this lower limit is here equal to 310 keV.

[0161] Figures 6D and 6E correspond to simulated spectra taking into account an activity of 60 Co considering respectively standard concrete (d = 2.3 g. cm -3 ) and baryta concrete (d = 3.35 g. cm -3). In each of these figures, spectra are represented taking into account purely surface activity (curve a) or extending, according to a decreasing gradient, over 100 mm (curve b), 200 mm (curve c) and 300 mm (curve d). The lower limit of the first energy band is respectively 340 keV (figure 6D) and 360 keV (figure 6E).

[0162] The simulations as described in connection with Figures 6B to 6E make it possible to establish a calibration function, by varying the contamination depth Z o between 0 and 300 mm.

[0163] The calibration function was established taking into account, for an activity of 137 Cs: for ordinary concrete (d = 2.3 g. cm -3 ), a = 4.507 Bq. cm -2 and P = 6.716 Bq. cm -2 ; for baryta concrete (d = 3.35 g. cm -3 ): a = 4.535 Bq. cm -2 and P = 6.716 Bq. cm -2 ; and for an activity of 60Co: for ordinary concrete (d = 2.3 g. cm -3 ), a = 1.157 Bq. cm -2 and P = 4.013 Bq. cm -2 ; for baryta concrete (d = 3.35 g. cm -3 ): a = 1.161 Bq. cm -2 and P = 4.013 Bq. cm -2 . a varies with density because the boundaries of the first energy band at E1 vary with density, as described in connection with Figures 6B to 6E.

[0164] Figures 7A and 7B show calibration functions established respectively by taking into account ordinary concrete (curve a) and baryta concrete (curve b), for activities of 137 Cs and 60 Co respectively. In each of these figures, the x-axis corresponds to the GG ratio

[0165] - and the y-axis corresponds to the Z depth o . For the same value of -, the difference between the two depths Z oestimated by taking into account the calibration functions, corresponding to each density, shows the impact of a lack of knowledge of the density on the estimation of the depth Z o .

[0166] Figures 7C and 7D show correction functions established respectively by taking into account ordinary concrete (curve a) and baryta concrete (curve b), for an activity of 137 Cs and 60 Co respectively. In each of these figures, the x-axis corresponds to the ratio

[0167] - and the y-axis corresponds to the value of the correction function.

[0168] Figures 6B to 6E and 7A to 7D illustrate the importance of the measurement modeling phase, so as to establish, as precisely as possible, the calibration function and the correction function. The models are based on hypotheses, concerning the density of the concrete or the shape of the activity gradient as a function of depth. As previously described, the hypotheses relating to the density can be confirmed by a density estimation phase (see step 170). With regard to the activity gradient, it is difficult to estimate it precisely, because this assumes an analysis of samples. The inventors consider that an exponential gradient, as described in connection with expression (8), is appropriate. More generally, when the real activity gradient deviates from the activity gradient taken into account in the models, the measurement uncertainty increases.It is however considered that subject to taking into account a decreasing activity gradient, the process makes it possible to obtain a sufficient order of magnitude of the depth Z. o .

[0169] Furthermore, given the attenuation of gamma radiation by concrete, the method is considered suitable for determining activity depths between 0 cm and 20 cm or 30 cm. Beyond this, the effect of attenuation is too great: the amount of gamma radiation emitted at depths greater than 20 cm or 30 cm is too low. The range of validity of the method is limited by the vertical asymptote of the function of

[0170] GG calibration (-). It is observed that the more the slope of the function (-). increases, the higher the measurement uncertainty. The "limit" depth depends on the material observed, in particular its density, as well as the acquisition time of each spectrum. It is preferable that the latter be a few minutes, and preferably less than 10 min or 15 minutes if we wish to remain compatible with an industrial measurement rate. The limit depth also depends on the emission energy of the radionuclide whose depth we are seeking to evaluate in the medium examined. The limit depth is higher for 60 Co (emission energies of 1173 keV and 1332 keV) than for 137 Cs (emission energy 662 keV).

[0171] The invention can be used to monitor the structures of nuclear installations, to support maintenance or dismantling operations. It can also be deployed to carry out radiological monitoring on contaminated land.

Claims

CLAIMS Method for estimating a depth (Z o ) according to which a radionuclide extends in a solid medium (M), from a surface (S), the solid medium being delimited by the surface, the radionuclide emitting gamma radiation at least one emission energy, the process comprising: - a) disposition of a spectrometric detector (10) facing the surface (S) of the solid medium, and measurement, by the spectrometric detector of an energy spectrum of the gamma radiation, emitted by the radionuclide and emanating from the surface, the measured spectrum comprising a number of pulses detected for different energy values, the energy spectrum comprising a peak at the emission energy; - b) taking into account a first and a second energy band, previously defined, the first energy band (AE^) comprising energy values ​​lower than the second energy band (AE2), the second energy band comprising the peak at the emission energy; - c) from the measured spectrum, determination of a first spectral value (N^) at the first energy band and a second spectral value (N2) at the second energy band; - the process being characterized in that the first spectral value is considered independent of the depth to which the radionuclide extends, and in that it comprises: - d) application - from a first calibration coefficient (a) to the first spectral value to obtain a first calibrated spectral value; - a second calibration coefficient ( / 3) to the second spectral value, to obtain a second calibrated spectral value; each calibration coefficient corresponding to a ratio, in each energy band, between a predetermined activity ( o ) of the solid medium and an estimate of a spectral value (N w , N 20 ) corresponding to said predetermined activity; - e) calculation of a comparison indicator (-) from a comparison of the first calibrated spectral value (G) and the second calibrated spectral value ( ) resulting from d); - f) application of a calibration function ( ) to the comparison indicator (-) resulting from e), so as to estimate the depth (Z o ) according to which the radionuclide extends in the solid medium, the calibration function being previously established, considering a radionuclide activity decreasing as a function of depth; the process being characterized in that during step d), the first calibration coefficient and the second calibration coefficient are determined, in each band, by a numerical modeling of a spectrum detected by the spectrometric detector, the solid medium being considered, during the modeling, as having said predetermined activity.

2. A method according to claim 1, wherein the first spectral value and the second spectral value are a number of pulses or a counting rate respectively in the first energy band and in the second energy band.

3. A method according to any one of the preceding claims, wherein the predetermined activity is a uniform surface activity or a uniform mass activity in the analyzed medium or a predetermined activity distributed according to a predefined activity gradient.

4. A method according to any one of the preceding claims, comprising, prior to step c): - taking into account a spectrum representative of the solid medium; - taking into account at least one predetermined energy band corresponding to an emission energy of a natural radionuclide, naturally present in the solid medium; - from a spectral value of the representative spectrum in said predetermined energy band, estimation of an activity of the natural radionuclide in the solid medium; - estimation of a contribution of the natural radionuclide in the spectrum measured during step a); - correction of the spectrum measured during step a), so as to remove the contribution of the natural radionuclide, at least in the first energy band.

5. A method according to claim 4, wherein the representative spectrum of the solid medium is: - the spectrum measured during step a); - or a spectrum measured by a spectrometric detector different from the spectrometric detector implemented in step a); - or a spectrum measured by the spectrometric detector implemented in step a). A method according to any one of the preceding claims comprising, prior to step d): - determination of the density of the solid medium examined; - depending on the density of the solid medium examined, selection of the first calibration coefficient from among first calibration coefficients respectively determined for different densities. A method according to any one of the preceding claims, comprising, prior to step f): - determination of the density of the solid medium examined; - depending on the density of the solid medium examined, selection of the calibration function from among calibration functions respectively determined for different densities. A method according to any one of claims 6 or 7, wherein the determination of the density of the solid medium examined comprises the following substeps: - taking into account a spectrum representative of the solid medium; - selection of at least two energy bands corresponding to emission energies of the same natural radionuclide, naturally present in the solid medium; - estimation of activities of the natural radionuclide from a spectral value of the representative spectrum respectively in each selected energy band, each activity estimation being carried out taking into account a density of the solid medium; - Determination of the density minimizing the discrepancy between the radionuclide activities estimated from the selected energy bands. A method according to claim 8, wherein the spectrum representative of the solid medium is: - the spectrum measured during step a); - or a spectrum measured by a spectrometric detector different from the spectrometric detector implemented in step a); - or a spectrum measured by the spectrometric detector implemented in step a). A method according to any one of the preceding claims, comprising: - g) multiplication of the second calibrated spectral value (G), resulting from e), by a correction function (K corr ) in order to estimate the activity of the solid medium, the correction function being previously established for different values ​​of the comparison indicator i (- G \).

11. A method according to any one of the preceding claims, wherein the solid medium is concrete or earth.

12. A method according to any one of the preceding claims, wherein the first spectral band extends over several hundred keV.

13. A device (1) for estimating a depth (Z o ) according to which a radionuclide extends in a solid medium, from a surface (S), the solid medium being delimited by the surface, the device comprising: - a spectrometric detector (10), configured to measure a spectrum of gamma radiation emanating from the surface; - a processing unit (20), programmed to implement steps b) to f) of a process according to any one of the preceding claims from the spectrum measured by the spectrometric detector.

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