ALGORITHM TO DETERMINE THE CALIBRATION PARAMETERS FOR A NDA METHOD
OF INVENTORY VERIFICATION IN A DIFFUSION ENRICHMENT CASCADE
Gevaldo Lisboa de Almeida, Carlos Feu Alvim
Agência Brasileiro-Argentina de Contabilidade e Controle de Materiais Nucleares - ABACC Av. Rio Branco, 123 - 5o. andar 20040-005 Rio de Janeiro-RJ Brazil 5521/2213464
[email protected] [email protected] Abstract
An algorithm was developed to determine the calibration parameters for a proposed Method of Inventory Verification in a Diffusion Enrichment Cascade. The method is based on the correlation between the count produced in a NaI(Tl) detector by the 185.7 keV gamma rays (U-235) and its mass in a diffuser. The algorithm embodies two computer programs: the first one, calculates the detector efficiencies for point sources distributed over the diffuser. The second program, fed with these efficiencies, performs an integration over 5 dimensions - 3 spatial and 2 for uranium mass and enrichment - producing a family of curves expressing the count rate at the detector against the mass of U-235 for each enrichment. The results show that the uranium mass and enrichment affect substantially the count rate, precluding the using of a simple calibration factor to transform that count rate into mass of U-235. To simplify the using of the algorithm by the inspectors, that family of curves was condensed in one single function, expressing the ratio count rate/enrichment versus mass of uranium, from which, the mass of U-235 can be deduced. A fair agreement with the Operator’s declared values was obtained by applying this algorithm to experimentally measured count rates.
1. Introduction
An algorithm has been developed to calculate the calibration parameters for a previously proposed method to assess the amount of U-235 in a Diffusion Enrichment Cascade. The method is based on the relationship between the mass of U-235 contained in a diffusor and the count rate
versus total mass of uranium in the diffusor. Therefore, once known the enrichment and the count rate, the mass of U-235 can be assessed by using a simple pocket calculator. This algorithm was applied to the data obtained by ABACC during a measurement campaign conducted in Pilcaniyeu, producing results in good agreement with those declared by the Facility’s Operator.
2. Previous Works
Some efforts [1,2,3,4] have been applied in the last years to assess uranium inventory and enrichment at gaseous diffusion enrichment facilities in USA. After ratification of the Brazil-Argentina-ABACC-IAEA Quadripartite Agreement, this matter caught also the attention of the parties, due to the Argentine plant in Pilcaniyeu.
On a series of measurements conducted at Oak Ridge, Portsmouth and Pilcaniyeu [5], the bias with regard to the declared mass of U-235 was 5% for the U.S. facilities and 10% for the Argentine one, where a refurbished diffusor was fed with a known quantity of UF6. By using this internal standard, a calibration constant was obtained by taking the ratio count rate due to the 185.7 keV photopeak, to the U-235 mass.
Bias of about 3% on the U-235 mass, were achieved [6], by using a prismatic collimator and seeing all the diffusor. The calibration constant was also determined by integration of the volumetric source constituted by the diffusor, using point and linear sources [7], including an iterative process to correct for the uranium self-attenuation, resulting in bias of 10% with regard to the values arising from the internal standard technique.
The detector response to a diffusor-like source has been experimentally assessed [8] by measuring its relative efficiency to point sources. By integrating their contribution to the count rate, and measuring a known source, the actual point sources efficiencies were inferred and used to calculate the count rate produced by other sources sizes. The bias ranged from -7.4 to 9.1%.
A deterministic calculation model to obtain a function count rate versus mass of U-235, directly, e.g., with no need for an iterative process has been developed [9,10]. It was then confirmed, as expected, that the calibration function is specific for each enrichment, i.e., the enrichment itself or the mass of uranium, has to be known, in order to assess the mass of U-235.
3.1. Determination of the intrinsic photopeak efficiencies for point sources
The count rate induced in the detector by a point source, is quantified by measuring the net area of the 185.7 keV line in the spectrum, which is directly related with the intrinsic photopeak efficiency detector-collimator set. This parameter, dependent upon the energy of the incident photon, size and shape of the detector-collimator, as they ultimately determine the probability of absorption is usually expressed as a product of the total intrinsic efficiency by the photofraction.
The total intrinsic efficiency, i.e., the ratio events produced in the detector to the actual number of photons reaching it, is affected by the distance traveled in the crystal. This distance depends upon the site and angle that the photon reaches the detector front surface, and thus, it’s necessary to integrate the contribution of all of them.
For this purpose, source and detector axis were aligned in a Cartesian system of coordinates having the source center as origin. A grid drawn to the top face of the collimator, split its surface into squares which are projected on the detector top surface - displaced by the focus distance - having as vertex the point source. The total intrinsic efficiency is then computed by using the following expression:
ε
o=
1
S
∫
Sε
(t) .ds(1)
where:
ε
(t) = Intrinsic total efficiency as function of the detector thickness seen by the photon. ds = Projected element of area at the top surface of the detector.S = Area of the detector base.
ε
o = Total intrinsic efficiency for a specific point source. The function ε(t) was constructed after published data [11, 21]. Regarding the photofraction,the published data refer to sources placed on the detector axis. For the geometry here considered, where the detector frontal face is backwards displaced from the collimator face by a focus distance,
Fig. 1 - Effect of the relative aspect ratio on the photofraction. Diameter & height are displayed.
Fig. 2 - Photofraction as function of the detector volume. Continuous line is a Boltzman fitting.
3.2. Integration of the Volumetric Source
The diffusor is treated as a volumetric source constituted by a self-absorbing medium, the membrane containing UF6 in both forms solid and gaseous.It’s assumed that the membrane and UF6 is an homogeneous medium, with an effective linear attenuation coefficient, equal to the sum of their individual ones. The contribution of the membrane is fix, but that of UF6 depends upon its apparent density, i.e., the ratio of its mass to the active volume of the diffusor. Multiplying this apparent density, by UF6 mass attenuation coefficient, its correspondent linear one is obtained. Surrounding the membrane the diffusor cask adds an extra attenuation to the photons on its travel to the detector.
4. Results
Feeding the integration program with the point source efficiencies, the related diffusor data and a variable mass of U under a given enrichment, one achieves a vector expressing the ratio count rate to enrichment versus mass of uranium, which is valid for calculated mass dominion, and for any enrichment. Fitting a hyperbole y = a . x / (b+x) to this vector, one get the calibration function, shown on Fig. 3, which can require only a simple slight attenuation correction to contemplate eventual differences - when existent - between the nominal and actual hull wall thickness.
In practice, having the coefficients a and b, the measured count rate C and the enrichment ε of the uranium in the diffusor, the mass m of U-235 is deduced by using the expression shown on Table I, where a comparison with the Operator’s data is presented as well. Measurements 1 and 2 embody 20 diffusors, while the measurement No. 3 only 10 of them.
0 1k 2k 3k 4k 5k 6k 7k 0 2k 4k 6k 8k b = 6728 a = 15618 y = a*x/(b+x) Calculated points Hyperbolic Fit CPM / Enrichment
Mass of Uranium (grams)
m = b.ε.C / (a.ε-C)
a, b = Curve coefficients C = Count rate CPM ε = U enrichment m = Mass of U-235
Measurement No U-235 (g) Operator U-235 (g) This work Difference % 1 530.2 515.6 - 2.75 2 616 605.1 - 1.77 3 231 200.4 - 13.3
7. Conclusions
The count rate produced at the detector as function of the Uranium or U-235 mass, doesn’t follow a linear behavior, due to the self-attenuation of the material, being furthermore dependent upon the enrichment. Once this parameter is known, it’s possible however, by measuring the count rate produced at the detector, to concatenate them with the coefficients of a calibration function represented by a hyperbole, to obtain directly the aimed U-235 mass, with no necessity for further iterative process. Such a task can be accomplished on the field by the safeguards inspector by using a simple pocket calculator, as it involves solely a couple of arithmetical operations.
Another important feature of the method, is that, it’s indeed a sampling process, where the detector sees only a fraction of the source. Therefore, the total active volume of the diffusor has to be known, in order to determine the total mass of U-235.
References
1. Whitaker J.M. et al., Nondestructive assay measurements of gaseous diffusion process equipment. Vol 18, INMM, 605, (1989).
2. Hagenauer, R..C., Nondestructive uranium enrichment determination in process holdup deposits., Vol 20, INMM, 74, (1991).
3. Hagenauer, R..C., Mayer R..L., Methods for nondestructive assay holdup measurements in shutdown uranium enrichment facilities. 4th. International Conference on Facility Operations- Safeguards Interface, (1991).
4. Mayer, R.L., et al., Nondestructive assay measurements in support of HEU suspension at Portsmouth Gaseous Diffusion Plant.Vol 22, INMM, 717, (1993).
5. Cooley J.N. et al, Development of an NDA approach for verifying the Process Inventory of a Gaseous Diffusion Enrichment Cascade.,IAEA Symposium, SM-333/121, (1994).
6. Beninson D. et al, A method for Non-destructive Measurement of the Uranium Hold-up in a Gaseous Diffusion Enrichment Plant., 17th Annual Symposium ESARDA, 1995.
7. Beninson, D. et al., Calibration of an NDA Measurement System for the Determination of the Uranium Hold-up in a Gaseous Diffusion Enrichment Plant, 17th Ann.Symp. ESARDA, (1995).
