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atw Vol. 64 (2019) | Issue 3 ı March DECOMMISSIONING AND WASTE MANAGEMENT 164 | | Fig. 6. Left part: Modeled activity distribution with the form of a cylindrical 30°sector (red). The dots indicate the locations for which a localized point source was assumed in simulated measurements of SGS and ASGS. Right part: The field of view of the collimation geometry shown in comparison between Segmented Gamma Scanning (SGS) and Advanced Sectorial Gamma Scanning (ASGS). content in activity with the peak count rate for an individual gamma line determined from the gamma spectrum obtained during the measurement. Each single partial volume contributes additively to the count rate such that the total peak count rate for a given measurement position P i is expressed by the sum over all partial peak efficiencies weighted with the activity of the partial volume P i = ∑ k ε ik · A k . With a source model consisting of 6 layers and 12 sectors, for example, this results in 72 summands for each measurement position. The number of measurement positions is determined by the scan mode, where the default mode is a scan of 12 angular sectors and 6 segments leading to in total 72 equations for all count rates obtained from the spectra that were recorded for each position. In its basic form, the reconstruction is based on a linear system of equations which is fully determined and can be solved for all partial activities A k , k = {1,..,m} using the P i , i = {1,..,n} obtained | | Fig. 7. Ratio of true to assumed efficiency in Segmented Gamma Scanning for a non-uniform activity distribution localized in a cylindrical sector for individual sectors (left) and after averaging over a rotation scan (right). during the measurement and the m × n calculated partial efficiencies. If the model is chosen with additional radial subdivisions, the number of volume partitions and the number of activities A k which need to be determined increases, whereas the number of equations remains the same. In this case, the system of equations is undetermined and special solvers are needed. Mathematically, the problem becomes an optimization (minimization) problem for which several mathe matical algorithms exist. The use of non-negative least-squares solver determines the A k with the additional constraint that A k >0 for all k. The solution of this method therefore automatically fulfills the positivity condition for the activity because negative values would mean an unphysical result. The total activity of the radionuclide is obtained from the sum of partial activities obtained from solving the linear equations. The underdetermined set of equations has some additional degrees of freedom and the lack of information can lead to spurious results for the reconstructed activity distribution and the total activity. If more than one gamma line is emitted by the isotope of interest, however, the additional information can be used in the set of equations which provides a stable solution for the sum activity even for a large number of radial subdivisions of the source model. Performance assessment of ASGS The performance of the reconstruction method is compared using simulated measurements for the standard method SGS and the novel method ASGS. The test object has the material composition of a waste drum with a homogenously filled cement matrix, i.e. the same material composition of the benchmark case used for the ECIAD efficiency calculation. Reconstruction of a localized activity distribution A test case was defined, where a hotspot activity is located at the drum bottom where an activity of 78 MBq Eu-152 is located within a shape of a 30° sector of a cylinder with 14 cm radius (Figure 6). The activity is uniformly distributed within the cylindrical sub-volume. For SGS a typical setup with a cylindrical collimator with 20 cm length and a hole diameter of 4 cm was simulated ( Figure 6 – uppper right) using the validated 40 % n-type detector model. The resulting segment that is scanned during every single rotation scan has the corresponding height of 4 cm and therefore in total 10 segments are scanned to cover the entire height of the test object. In SGS a simplified evaluation is performed on the basis that the matrix and the activity distribution is homogenous. In this case, the activity can be derived from a single expression A reco = P r/ e hom , where A reco is the reconstructed activity, P r is the peak rate and e hom is the assumed efficiency for the homogeneous activity distribution within the volume. Even if the activity is not equally distributed within the matrix an average peak rate is determined from the sum spectrum obtained during the rotation scan and the evaluation is performed using the efficiency determined for homogeneous distribution. The error expressed as the ratio of the reconstructed to the true activity is related to the ratio of the true efficiency e true to the assumed efficiency for a homogeneous activity distribution e hom and therefore is determined by A reco/A true = e true/e hom . The true efficiency e true is calculated in a simulation for the assumed activity distribution with the entire activity located uniformly within a single sector-shaped volume. A strong deviation between e true and e hom is observed where the true efficiency is strongly underestimated when the actual activity is not within the field of view during the scan, whereas a strong overestimation occurs when the activity is within the view of the detector (Figure 7). In SGS, the individual segments are evaluated which is performed on the sum of the registered events recorded during rotation, divided by the total Decommissioning and Waste Management Advanced Sectorial Gamma Scanning for the Radiological Characterization of Radioactive Waste Packages ı M. Dürr, M. Fritzsche, K. Krycki, B. Hansmann, T. Hansmann, A. Havenith, D. Pasler and T. Hartmann
atw Vol. 64 (2019) | Issue 3 ı March measurement time for the individual segment. This results in an average over the angular profile for each segment, where the ratio of true to assumed efficiency at a gamma energy of 1408 keV is reduced to maximally 3.3 and therefore the activity of this segment would be overestimated by this factor. At this gamma energy, the summation over all 10 segments results in a ratio of 0.95, which means that SGS reaches the true value of the activity. This, however, is pure coincidence and depends on the gamma energy of the line used for evaluation and the density of the matrix: at the gamma energies of 122, 344, 779, 964, 1112 keV the ratio of reconstructed to true activity for SGS amounts 0.09, 0.32, 0.66, 0.75, 0.82, respectively. To evaluate the ASGS method, a MCNP model of the 78 MBq Eu-152 activity distribution and the waste drum was implemented, where full gamma spectra for the 40 % n-type detector were simulated for every measurement position (Figure 8). A full sectorial scan for three segments and 12 sectors per layer was simulated with in total 36 measurement positions, where the measurement time for each position is 120 seconds. For the ASGS geometry, the collimator design is such that it covers a larger area of the drum surface in the vertical direction and therefore less vertical scan positions are needed (see Figure 6 bottom-right). The spectra were analyzed using a gamma spectrum analysis software and the peak area was evaluated for six Eu-152 gamma lines at 122, 344, 779, 964, 1112, and 1408 keV. The peak efficiencies were calculated for different source partition models using the ECIAD tool which were used as an input for the reconstruction using the non-negative least squares reconstruction algorithm. Using the analysis of two of the in total six gamma lines of Eu-152, the reconstruction algorithm can assign the activity to the correct location in the partitioned model and the total activity is reconstructed to 77.1 MBq (using the 1112 and 1408 keV lines), which is an underestimation of 1.3 % of the true activity. The result for the reconstructed activity did not vary strongly with the choice of gamma lines used and the deviation ranges from -1.3 % to +4.7 % of the true activity. The reconstruction algorithm leads to a solution, where a small part of the activity is assigned to the neighboring layers of the source partitions, however, this is only a minor effect | | Fig. 8. Simulated spectra for sectorial scanning of the simulated test case containing a localized Eu-152 activity distribution. and is attributed to the noise in the gamma spectrum. This showcase demonstrates, that the partitioned source model can reconstruct a non-uniform activity distribution. Uncertainties, decision threshold and detection limit For gamma scanning the largest uncertainty contribution stems from the unknown location of the uncertainty which is attributed as ‘model uncertainty’. These errors are evaluated by assuming worst-case scenarios for a non-homogeneous activity distribution and are treated as Type B uncertainties according to the GUM and DIN ISO 11929. For the cement waste matrix used in the previously mentioned test case, single point sources located in various positions of the waste drum were simulated and evaluated with SGS and the ASGS reconstruction method. In ASGS a finer radial subdivision was chosen with 6 radially subdivided partitions for each 30° sector. Hereby, an improved spatial resolution can be reached to reconstruct a localized activity distribution. With ASGS the reconstruction method localizes the point source and therefore this information reduces the ‘model uncertainty’ relative to SGS. For ASGS the reconstruction is made for the evaluation of several combinations of two gamma lines of Eu-152. Even though the linear system of equations is underdetermined the reconstruction algorithm was able to solve the minimization problem. A comparison of the ratio for A reco/A true is shown for four different point source locations (indicated as green dots in Figure 6) representing locations where the radiation from the source experiences maximal and minimal self-attenuation within the active matrix (Table 1 – Ratios of true to reconstructed activities for simulated point source activities located at four different positions within the waste drum for SGS and ASGS.). In SGS this ratio strongly depends on the gamma line chosen for evaluation and for the worst case for the gamma line at 122 keV the activity is underestimated up to a factor of 50 and overestimated by a factor of 4. In ASGS multiple lines are used in the analysis, where the reconstruction of the simulated measurement of point source activity was performed using two lines, three lines, and six lines. For the line energy combinations shown in Table 1 the largest spread is observed when the 122 and 1408 keV lines is chosen for the reconstruction with an underestimation by a factor of approximately 1.2 and an overestimation by a factor of approximately 1.8. This spread represents also the worst case in ASGS for all line combinations of the six strongest Eu-152 lines. Therefore, ASGS reconstruction reduces the bandwidth of errors which is potentially caused by the unknown activity distribution and therefore this lack of information leads to lower model uncertainties and correspondingly much lower conservative estimates than in SGS. The ASGS system relies on the spatial reconstruction of the activity and therefore uses the spatial information of the gamma count rate recorded at the different measurement positions of the waste drum. The decision threshold determines the minimum amount of the radionuclide DECOMMISSIONING AND WASTE MANAGEMENT 165 Decommissioning and Waste Management Advanced Sectorial Gamma Scanning for the Radiological Characterization of Radioactive Waste Packages ı M. Dürr, M. Fritzsche, K. Krycki, B. Hansmann, T. Hansmann, A. Havenith, D. Pasler and T. Hartmann
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