Jan Leen Kloosterman

Comparison and Extension of Dancoff Factors for Pebble-Bed Reactors

Abstract A method is developed for the computation of infinite-medium Dancoff factors for spherical kernels with a stochastic packing as used in high-temperature reactors. The method is used to compute Dancoff factors that are then compared to those obtained by four preexisting methods from the literature. The older methods assume either infinitesimally small kernels with a random distribution, or finite kernels with some assumptions. In the new method, the infinite-medium Dancoff factor is calculated rigorously by numerically integrating the Dancoff factor of two adjacent finite-size kernels over their surfaces and relative positions. It turns out that for practical pebble-bed fuel designs, as currently envisioned, all four methods give results accurate (i.e., compatible with one another) within 2%, but that larger deviations are observed for extreme cases (either at high or low dilution). A Monte Carlo program, named INTRAPEB, was written to calculate the average value and the space dependency of the Dancoff factor of one single fuel pebble, as well as the angular distribution of neutrons escaping the pebble. For the Dancoff factor, the analytical results from literature agree very well with the new computational approach. However, for a cubic packing of particles, as is usually modeled in MCNP calculations, a larger Dancoff factor is found for the pebble. The angular distribution of neutrons escaping from the moderator zone of a pebble is much more forwardly peaked than the cosine angular distribution assumed in the derivation of the analytical methods. If the previously developed analytical methods need improvement, this could be achieved by using a more forwardly peaked neutron distribution. A second program, named PEBDAN, was written to calculate the average value and the space dependency of the interpebble Dancoff factor (the probability that a neutron escaping from the fuel zone of a pebble crosses a fuel particle in another pebble) and the pebble-pebble Dancoff factor (the probability that a neutron escaping from the fuel zone of a pebble crosses the fuel zone of another pebble). In this program, the coordinates of the pebbles in a randomly packed bed are determined, after which the Dancoff factors are calculated using a Monte Carlo ray-tracing method. The packing distribution obtained in this code reproduces the principal features of experimental data; however, the predicted radial porosity profile of the packed bed displays less-pronounced oscillations (i.e., lower peaks) and a slightly larger average porosity value. Because of the larger first-flight escape probability of neutrons, the Dancoff factors drop several tens of percent along the inner and outer reflector of the core.

Validation of the DALTON-THERMIX Code System with Transient Analyses of the HTR-10 and Application to the PBMR

Abstract The DALTON-THERMIX code system has been developed for safety analysis and core optimization of pebble-bed reactors. The code system consists of the new three-dimensional diffusion code DALTON, which is coupled to the existing thermal-hydraulic code THERMIX. These codes are linked to a database procedure for the generation of neutron cross sections using SCALE-5. The behavior of pebble-bed reactors during a loss of forced cooling (LOFC) transient is of particular interest since the absence of forced cooling could lead to a significant increase of the temperature of the coated particle fuel. Therefore, the reactor power may be constrained during normal operation to limit the temperature. For validation purposes, calculation results of normal operation, an LOFC transient, and a control rod withdrawal transient without SCRAM have been compared with experimental data obtained in the High Temperature Reactor–10 (HTR-10). The code system has been applied to the 400-MW(thermal) pebble bed modular reactor (PBMR) design, including the analysis of three different LOFC transients. Theses results are verified by a comparison with the results of the existing TINTE code system. It was found that the code system is capable of modeling both small (HTR-10) and large (PBMR) pebble-bed reactors and therefore provides a flexible tool for safety analysis and core optimization of future reactor designs. The analyses of the LOFC transients show that the peak fuel temperature is only slightly elevated (less than +100°C) as compared to its nominal value in the HTR-10 but reaches a maximum value of 1648°C during the depressurized LOFC case of the PBMR benchmark, which is significantly higher than the peak fuel temperature (976°C) during normal operation.

Stress Analysis of Coated Particle Fuel in Graphite of High-Temperature Reactors

Abstract The PArticle STress Analysis (PASTA) code was written to evaluate stresses in coated particle fuel embedded in graphite of high-temperature reactors (HTRs). Existing models for predicting stresses in coated particle fuels were extended with a treatment of stresses induced by dimensional change of the matrix graphite and stresses caused by neighboring particles. PASTA was applied to two practical cases in order to evaluate the significance of this model extension. Thermal hydraulics, neutronics, and fuel depletion calculation tools were used to calculate the fuel conditions in these cases. Stresses in the first fuel loading of the High-Temperature Engineering Test Reactor (HTTR) and in the fuel of a 400-MW(thermal) pebble bed reactor were analyzed. It is found that the presence of the matrix material plays a significant role in the determination of the stresses that apply to a single isolated TRISO particle as well as in the transmittal of the stresses between particles in actual pebble designs.

A view of strategies for transmutation of actinides

Developments in the field of recycling and transmutation of actinides are discussed. Three general strategies are discriminated: (i) an evolutionary strategy based on gradual implementation of partitioning and transmutation techniques in the fuel cycle; (ii) a radical strategy based on implementation of partitioning and transmutation in the fuel cycle, once all steps of this technology are proven; (iii) plutonium incineration, based on the conversion, with existing reactor types, of separated plutonium into a spent fuel form that is suited for direct storage.

Development of a Three-Dimensional Time-Dependent Calculation Scheme for Molten Salt Reactors and Validation of the Measurement Data of the Molten Salt Reactor Experiment

Abstract This paper presents the development, validation, and results of a three-dimensional, time-dependent, coupled-neutronics–thermal-hydraulic calculational scheme for channel-type molten salt reactors (MSRs). The reactor physics part is based on diffusion theory, extended by a term representing the flow of the fuel through the core. The calculation of the temperature field is done by modeling all fuel channels, which are coupled to each other by a three-dimensional heat conduction equation. For the purpose of validation, the results of the MSR Experiment (MSRE) natural-circulation experiment and the thermal feedback coefficients of the reactor have been calculated and compared. With the aid of a code system developed to implement this scheme, calculations were carried out for the normal operating state of the MSRE and some debris-induced channel-blocking-incident transients. In the case of the MSRE, it is shown that the severity of such an incident strongly depends on the degree of channel blocking and that high-temperature gradients in the moderator can connect thermally the adjacent fuel channels. Results are included for an unblocking transient (i.e., the debris suddenly exits the core, and the fuel flow reverts to the normal operating pattern), and it was demonstrated that during the unblocking large power peaks can be induced.

Experimental results from noise measurements in a source driven subcritical fast reactor

Both pulse counting techniques and continuous current measurements have been applied in the MASURCA subcritical fast reactor driven by the GENEPI pulsed neutron source in order to get the prompt neutron decay constant. The data from the pulse counting experiments were analysed using auto- and cross-correlation techniques, which are similar to one- and twodetector Rossi-a measurements, and Feynman-a techniques. The data from the continuous current measurements were analysed by calculating the Cross Power Spectral Density. We have found a good agreement between the values extracted from the auto- and crosscorrelation techniques and from the cross-covariance and CPSD. The application of the time domain techniques becomes easier when there is no overlapping of the neutron chains originating from different source pulses. The application of the Feynman-a method shows some problems for pulsed systems, because of the dominance of the periodic terms in the variance-to-mean ratio, which leaves very little information to fit the prompt neutron decay constant. However, good agreement exists between our results and predictions from literature. Of the methods studied, CPSD is shown to be the best of the noise techniques to get the reactor decay time constant. It is applicable for a wide range of source frequencies and it converges rapidly comparing with subcritical systems driven by a radioactive source. In general, we conclude that the noise analysis techniques applied here are applicable to pulsed source driven systems.

On the average chord length in reactor physics

Abstract By elaborating on the meaning of the average chord length in reactor physics, it is shown that the average chord length for a convex body in an isotropic flux is given by the bodys volume divided by its average projection area. The relation is known in literature (Weinberg, A.M., Wigner, E.P., 1958. The Physical Theory of Neutron Chain Reactors./The University of Chicago Press, Chicago), but in view of a recent technical note on the average chord length by Sjostrand [Ann Nucl Eng 29 (2002) 1607] it seems useful to explain the background of the simplicity of the average chord length for a convex body in an isotropic flux. For another angular flux distribution the average chord length cannot be expressed in such an elegant way, and has to be calculated for each body (and orientation) separately.

Plutonium recycling in pressurized water reactors : Influence of the moderator-to-fuel ratio

The reactor physics trends that can be observed when the moderator-to-fuel (MF) ratio of a mixed-oxide (MOX) fuel lattice increases from two (the standard value) to four are investigated. The influence of the MF ratio on the moderator void coefficient, the fuel temperature coefficient, the moderator temperature coefficient, the boron reactivity worth, the critical boron concentration, the mean neutron generation time, and the effective delayed neutron fraction has been investigated. Increasing the MF ratio to values larger than three gives a moderator void coefficient sufficiently large to recycle the plutonium at least four times. Also, the values of other parameters like the boron reactivity worth, the fuel temperature coefficient, the moderator temperature coefficient, and the mean neutron generation time improve with increasing MF ratio. The effective delayed neutron fraction is almost independent of the MF ratio. According to a point-kinetics model, the response of a MOX-fueled reactor with an MF ratio of four to a moderator temperature decrease is similar to that of a UO2-fueled reactor with an MF ratio of two. Scenario studies show that recycling plutonium four times in pressurized water reactors reduces the plutonium production by a factor of three compared with a reference once-through scenario, but the americium and curium production triples. If the plutonium remaining after recycling four times is disposed of, the radiotoxicity reduces by only a factor of two. This factor increases to a maximum of five if the plutonium can be eliminated in special burner reactors. Recycling of americium and curium is needed to reduce the radiotoxicity of the spent fuel to lower values. In general, the plutonium mass reduction increases and the minor actinide production decreases with increasing MF ratio of the MOX fuel. Enlarging the MF ratio can be achieved by increasing the rod pitch or by reducing the fuel pin diameter. In both cases, the economic penalty is about the same and is quite large.

Design of a Rotating Facility for Extracorporal Treatment of an Explanted Liver with Disseminated Metastases by Boron Neutron Capture Therapy with an Epithermal Neutron Beam

Abstract Nievaart, V. A., Moss, R. L., Kloosterman, J. L., van der Hagen, T. H. J. J., van Dam, H., Wittig, A., Malago, M. and Sauerwein, W. Design of a Rotating Facility for Extracorporal Treatment of an Explanted Liver with Disseminated Metastases by Boron Neutron Capture Therapy with an Epithermal Neutron Beam. Radiat. Res. 166, 81–88 (2006). In 2001, at the TRIGA reactor of the University of Pavia (Italy), a patient suffering from diffuse liver metastases from an adenocarcinoma of the sigmoid was successfully treated by boron neutron capture therapy (BNCT). The procedure involved boron infusion prior to hepatectomy, irradiation of the explanted liver at the thermal column of the reactor, and subsequent reimplantation. A complete response was observed. This encouraging outcome stimulated the Essen/Petten BNCT group to investigate whether such an extracorporal irradiation could be performed at the BNCT irradiation facility at the HFR Petten (The Netherlands), which has very different irradiation characteristics than the Pavia facility. A computational study has been carried out. A rotating PMMA container with a liver, surrounded by PMMA and graphite, is simulated using the Monte Carlo code MCNP. Due to the rotation and neutron moderation of the PMMA container, the initial epithermal neutron beam provides a nearly homogeneous thermal neutron field in the liver. The main conditions for treatment as reported from the Pavia experiment, i.e. a thermal neutron fluence of 4 × 1012 ± 20% cm−2, can be closely met at the HFR in an acceptable time, which, depending on the defined conditions, is between 140 and 180 min.

Application of boron and gadolinium burnable poison particles in UO2 and PUO2 fuels in HTRs

Abstract Burnup calculations have been performed on a standard HTR fuel pebble (fuel zone with radius of 2.5 cm surrounded with a 0.5 cm thick graphite layer) and burnable poison particles (BPPs) containing B 4 C made of pure 10 B or containing Gd 2 O 3 made of natural Gd. Two types of fuel were considered: UO 2 fuel made of 8% enriched uranium and PuO 2 fuel made of plutonium from LWR spent fuel. The radius of the BPP and the number of particles per fuel pebble were varied to find the flattest reactivity-to-time curve. For the UO 2 fuel, the reactivity swing is lowest (around 2%) for BPPs made of B 4 C with radius of 75 μm. In this case around 1070 BPPs per fuel pebble are needed. For the PuO 2 fuel to get a reactivity swing below 4%, the optimal radius of the BPP is the same, but the number of particles per fuel pebble should be around 1600. The optimal radius of the Gd 2 O 3 particles in the UO 2 fuel is about 10 times that of the B 4 C particles. The reactivity swing is around 3% when each fuel pebble contains only 9 BPPs with radius of 840 μm. The results of the Gd particles illustrate nicely the usage of black burnable poison particles introduced by Van Dam [Ann. Nuclear Energy 27 (2000) 733].