tomography has been recently used at the Paul Scherrer Institute (PSI) to characterize spent fuel [1]. The ratio of the 137Cs, 134Cs and 154Eu fission products.
CHARACTERIZATION AND QUALIFICATION OF A MEASUREMENT STATION FOR NEUTRON ASSAY OF BURNT FUEL Rodolfo Dietler, Mathieu Hursin, Kelly Jordan, Gregory Perret Paul Scherrer Institut, 5232 Villigen, Switzerland
The characterization of spent fuel is of interest to the nuclear industry for in- and outcore applications such as core design, spent fuel storage and transportation. The usual approach relies on the measurement of the gamma-ray emission of burnt fuel. The measurement of the neutron intrinsic source, together with the knowledge of the cooling time and initial enrichment of the fuel, could be another approach to measure the burnup of spent fuel.
1 Motivation and Objectives From an experimental point of view, there are several approaches to determine the burnup, the neutron and gamma-ray intrinsic sources, or the full isotopic composition of burnt fuel. Most of the actual methods rely on gamma measurements to determine the burnup of a given fuel sample. A non-destructive technique based on emission tomography has been recently used at the Paul Scherrer Institute (PSI) to characterize spent fuel [1]. The ratio of the 137Cs, 134Cs and 154Eu fission products were measured and used as burnup monitors. As regards neutron-based measurement, a widespread method involves the socalled fork detector. It allows doing in-pool measurements of the neutron intrinsic source of complete burnt fuel assemblies using fission and/or ionization chambers positioned on both sides of the assemblies. Unfortunately, this approach does not allow the characterization of central fuel rods due to shielding effects of the surrounding fuel [2], nor does it allows the determination of axial variation of the neutron emission. There are two main motivations for the development of a burnup measurement method based on intrinsic neutron emission that would allow determining its axial profile. On one hand, it would allow optimizing the criticality safety estimations for storage and transport purposes. On the other hand, it would be an alternative to the widely used gamma emission measurements for validation purposes. The relation between neutron emission and burnup is complex because of its dependence on various parameters such as initial enrichment, irradiation history, etc. As a first step, the study presented here focuses only on the determination of the intrinsic neutron emission of a burnt fuel sample and its spatial distribution. The derivation of burnup will be addressed later on. The goal of the presented work is to design a passive neutron measurement station to obtain the axial neutron emission distribution of a burnt fuel rod, and to assess its performance to reconstruct the axial neutron source profile. The measurement station characterization comprises the
determination of the collimator size, the applied reconstruction algorithm, the number of measurement points, and the counting time per measurement point assuming a 20 minutes total measurement time. The study is performed using MCNPX-2.4 [3].
2 The Reference Design & Geometrical Description The design of the measurement station has been adapted to the requirements of the hot cells of the hot laboratory at PSI, in which the measurements will be carried out in the future. A picture of the measurement station and its main components is shown in Figure 1. A 3He neutron detector has been chosen because of its wide use, high neutron detection efficiency, low gamma sensitivity, and its low maintenance [4]. It is surrounded by a layer of polypropylene (CH2) to slow down the high-energy neutrons generated by spontaneous fissions in the burnt fuel samples. The background radiations in the hot cell consist of photons and neutrons. A thin layer of cadmium is used to capture the background neutrons. A second shell of CH2 around the cadmium layer is used to moderate the background neutrons to enhance their absorption in the cadmium. To shield against the gamma rays emitted by the measured fuel rod, the background gamma-rays, and those produced by the neutron absorption in cadmium, a 10 cm thick layer of lead is inserted between the cadmium and the inner block of moderator. A hole in the three outer layers of material serves as a collimator, preferentially allowing the neutrons coming from the measured rod section in front of the hole to reach the detector.
Figure 1: Cross sectional cut of the first model (left) and its location in the Hotcell
The entire 4m of the measured fuel rod is modeled. The cladding is assumed to be made of pure zirconium and to have a 0.5 mm thickness. The isotopic specifications for the fuel composition come from real burnt fuel samples [5]. The effective neutron sources for UO2 spent fuel are mostly spontaneous fissions of 244Cm, 242Cm and 252 Cf and (α,n) reaction on oxygen [6]. For the typical light water reactor discharge burnup (50 GWd/t) and cooling time (10 years), spontaneous fission of 244Cm is responsible for more than 99% of the neutrons emitted in spent fuel. In our MCNPX2.4 model, the source term energy distribution is assumed to be that of 244Cm spontaneous fission and is distributed homogeneously in the radial section of the pin.
3 Signal Reconstruction and Processing Only poor collimation can be achieved with neutrons compared to gamma rays, causing an output signal degradation as seen in Figure 2, hence the idea of using signal post-processing to improve the output. A consequence of this is the smoothening of the input signal and the loss of information concerning smaller depressions or peaks, for example the ones caused by the presence of grid spacers along the fuel rod. Figure 2 illustrates this effect.
Figure 2: Detector response vs. standard input signal, data from a 2.5 cm collimator radius simulation, without any statistical deviation (viz. infinite measurement time).
3.1
Mathematical description of neutron emission profile
In order to deal with the information loss due to the poor collimation of the neutrons, a mathematical description of the problem is developed. According to basic signal treatment theory [7], it is possible to represent the measured signal h by a spatial convolution of the source distribution f with the measurement station detector transfer function g, as illustrated in the following equation: (1) where n denotes the sampling point along the rod length. The transfer function g - or system response - is generally defined as the output of a steady-state system to a delta-dirac δ(t) input function in an ideal, noise-free environment. The transfer function has been obtained in the present study using MCNPX-2.4. A spatial discretization of the neutron source in the fuel rod is introduced. Each fuel rod segment acts as a step function source. The number of simulated segments influences the precision of the spatial reconstruction of the transfer function. It impacts also the MCNPX computing time. It has been found that a resolution of 1 cm is sufficient to obtain a sufficiently accurate transfer function. A reference raw detector response profile h (red curve in Fig. 2) is then predicted by simply evaluating Equation (1) using a theoretical neutron emission profile f (blue curve in Fig. 2) and the transfer function g determined by MCNPX-2.4. The
theoretical neutron emission profile is deduced from standard gamma-ray profiles using the transformation proposed in [8]. The reference raw detector response profile h is used in the next section to assess the performance of the deconvolution algorithms. 3.2
Deconvolution of the raw output emission signal
Using Equation (1), knowing g and performing a deconvolution treatment on h, it is possible to obtain a better estimation of the true source profile f. There are many approaches to solve the deconvolution problem, mainly solutions used in the field of image deblurring in case of point-spread function (PSF) interference generated by optical apparatus. For this approach we investigated three different reconstruction algorithms implemented as Matlab routines.
3.3
The Richardson-Lucy deconvolution is an iterative algorithm introduced by W. H. Richardson [9] and L. Lucy [10] in the seventies for astronomical image deblurring. The concept is based on Bayes’ theorem, which states the conditional probability of dependence between two events. An evolution of the approach above is the Blind deconvolution [11] using Maximum Likelihood algorithms by applying additional acceleration between iterations. The third method, the Tikhonov regularization [12], was introduced in 1977 as an estimation algorithm based on matrix calculations. Figure-of-Merit
In order to optimize the neutron measurement station, a figure-of-merit (FOM) is introduced as a quantifier for errors between the true and the reconstructed neutron source axial profile. The goal is to reconstruct the best possible representation of the actual axial neutron activity of the fuel rod by minimizing the FOM for each measurement along the rod. A general formula for the FOM is expressed as: (2) where Mk and Sk denote the reconstructed and the true neutron source at position k, and δkj is the Kronecker-Delta function. Two phenomena are considered to quantify the accuracy of the reconstruction process. The first one is the presence of depressions due to the grid spacers. The second one is the occurrence of oscillations by the reconstruction algorithms (see Figure 2 for illustration).
4 Characterization of the Measurement Station In order to find the best possible measurement station design, its parameters are chosen by minimizing the FOM after having fixed a maximal measurement time for the entire rod. Four interdependent parameters tend to influence the FOM value: the collimator radius, the reconstruction algorithm, the spatial sampling rate – i.e. the distance between single measurement points along the fuel rod, and the measurement time per point required to reach a sufficient statistical accuracy.
Table 1 gives an example of figure-of-merit values obtained with two fixed parameters, the collimator radius (2.5 cm) and the reconstruction algorithm (Tikhonov regularization). The best solution for a given total measurement time can be found along the diagonal – where the number of points times the duration of measurement per point is constant.
Table 1: Figure-of-merit for the 2.5 cm collimator case (rows: counts per step, columns: step width), reconstructed by Tikhonov regularization, relative error s = 1%
All analyses have been carried out considering the additional effects of the strong neutron and gamma ray background fields inside the hot cell. Their effects have proven to be negligible. On one hand, the strong neutron background source is efficiently shielded by the layers of CH2 and cadmium and can be excluded from the reconstructed signal by mathematical means. On the other hand, simple attenuation calculations have proven that the gamma ray shielding is sufficient to protect the detector from unwanted pileup signals and prevent radiation damages to the quenching gas [13].
5 Conclusions This paper presented a numerical study for the implementation of a measurement station at the hot laboratory of PSI. The measurement methodology is based on passive neutron detection and aims at reconstructing the axial profile of the neutron emission of a spent fuel rod using deconvolution algorithm. The implementation of an evaluation framework for the measurement station design and the selection of its optimal parameters – collimator diameter, reconstruction algorithm, number of axial measurements, etc. – using an empirical figure-of-merit (FOM) are the main results of this paper. The figure-of-merit (FOM), in conjunction with the transfer function of the measurement station, allows finding the optimal parameters without the need for additional MCNPX simulations. In this study, the highest possible background radiation present in the hot cell containing the measurement station has also been taken into account and shown as either negligible (γ-rays) or possible to handle by mathematical means (neutrons). In this condition, we have demonstrated that the designed measurement station allows determining the axial profile of the neutron emission rate for a full-length 4 m spent fuel rod (~50 GWd/t, 10 years cooling time) in about 20 minutes with a satisfactory precision (counting uncertainty of about 1% per measurement point). The final goal of the measurement station is the ability to reconstruct the axial burnup profile of single burnt fuel rods. Future work will have to address the reconstruction of the actual burnup profile. Its relationship to the intrinsic neutron source needs to be investigated. It is influenced by many factors such as cooling time and initial enrichment. One way to fully characterize this relationship is a measurement
campaign with spent fuel samples whose isotopic compositions and burnups are known from destructive analysis.
Acknowledgements The authors would like to thanks the different partners of the LWR-PROTEUS Phase II project for providing realistic data to conduct the design and performance assessment of this measurement station. The LWR-PROTEUS Phase II project has been conducted jointly by PSI and the Swiss Nuclear utilities with specific contribution from Alpiq AG. The authors would also like to express their sincere gratitude to Professor Chawla for his guidance.
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