Boundary value problems for second order linear difference equations: application to the computation of the inverse of generalized Jacobi matrices

We have named generalized Jacobi matrices to those that are practically tridiagonal, except for the two final entries and the two first entries of its first andits last row respectively. This class of matrices encompasses both standard Jacobiand periodic Jacobi matrices that appear in many contexts in pure and appliedmathematics. Therefore, the study of the inverse of these matrices becomes ofspecific interest. However, explicit formulas for inverses are known only in a fewcases, in particular when the coefficients of the diagonal entries are subjected tosome restrictions.We will show that the inverse of generalized Jacobi matrices can be raisedin terms of the resolution of a boundary value problem associated with a secondorder linear difference equation. In fact, recent advances in the study of lineardifference equations, allow us to compute the solution of this kind of boundaryvalue problems. So, the conditions that ensure the uniqueness of the solution ofthe boundary value problem leads to the invertibility conditions for the matrix,whereas that solutions for suitable problems provide explicitly the entries of theinverse matrix.Peer ReviewedPostprint (author's final draft

Radiochemistry of iodine: Outcomes of the CAIMAN program

Iodine is a fission product of major importance because volatile species can be formed under severe nuclear reactor accident conditions and may potentially be released into the environment, leading to significant radiological consequences. The CAIMAN program was devoted to studying the radiochemistry of iodine in the reactor containment in the case of a severe accident occurring in a pressurized water reactor; this is a database of prime importance for the validation of codes, namely IODE, which is a module of the integral Accident Source Term Evaluation Code (ASTEC), jointly developed by the Institut de Radioprotection et de Sûreté Nucléaire and the Gesellschaft für Anlagen-und Reaktorsicherheit. These computations are generally used to predict the radiological consequences of such an accident. The experimental program, which ran from 1996 to 2002, concerned 18 experiments in a facility of intermediate scale (300 dm3), where labeled iodine, 131I, was used to perform gamma counting. The CAIMAN tests are here analyzed, and the main experimental observations and trends are described. For each experiment, IODE computations were performed and compared with experimental results in order to assess the possible weak points of the present modeling and to identify key parameters. Broadly speaking, the gaseous concentrations predicted are quite consistent with the experimental ones; the remaining gaps have been identified

Reaction Kinetics of a Fission-Product Mixture in a Steam-Hydrogen Carrier Gas in the PHEBUS Primary Circuit.

Abstract not availableJRC.F-Institute for Energy (Petten

Mass transfer modeling with and without evaporation for iodine chemistry in the case of a severe accident

Iodine is a fission product of major importance in a severe reactor accident because volatile species exist under reactor containment conditions. Radiolytic oxidation of iodide ions is an important source of volatile iodine species. The SISYPHE tests provide an experimental database of prime importance for the study of the mass transfer between the sump and the atmosphere of a containment building under natural convection and in an evaporating flow regime. This phenomenon greatly impacts the airborne iodine concentrations. The two main effects of evaporating conditions are to increase the kinetics of transfer from the liquid to the gaseous phase and to change the steady-state iodine concentrations. The well-known two-film model has been modified to extend to these types of conditions. The agreement between the experimental results and modeling is satisfactory. However, when applied to typical reactor conditions, the impact of this improved modeling on gaseous iodine concentration is not as strong as other phenomena; for example, uncertainties remain concerning organic iodide production mechanisms. Correlations enabling the calculation of individual mass transfer coefficients for the liquid and the gas phases are proposed. The values resulting from these correlations agree well with those obtained from the test interpretations

Modeling liquid-gas iodine mass transfer under evaporative conditions during severe accidents

During postulated severe accidents transfer of volatile iodine dissolved in containment water sumps to atmosphere can be fostered under pool evaporative conditions. Scarcity of representative data has resulted in semi-empirical models that relies on fitting parameters and still need of further validation. This paper presents a mechanistic model based on: the two-film model, the heat-mass transfer analogy and the surface renewal theory. Comparison to data from the SISYPHE program, performed at the French "Institut de Radioprotection et de Sûreté Nucléaire", has resulted in an accurate response, the error band being 9-25% for the aqueous steady state concentration. Likewise, the model performance has been compared to the model implemented in the ASTEC code. In addition to yield similar results, some advantages have been highlighted: the mechanistic nature, the estimates conservatism, and the thorough documentation of model grounds and assumptions. © 2009 Elsevier B.V. All rights reserved

Study of RuO4 decomposition in dry and moist air

During a hypothetical severe nuclear accident on a pressurized water reactor (PWR), it is of primary importance to assess potential radionuclide release into the environment, and thus to better understand the volatile ruthenium tetroxide stability, in the containment building, due to its high radiotoxicity. The stability of RuO4 (g) in dry and moist air, under conditions representative of a PWR containment building, is investigated. RuO4 decomposition occurs in bulk gas phase, without any specific affinity with surfaces. The kinetic rate law of RuO4 reduction is found to be dependent on the presence of steam. The humidity seems to play a catalytic role, as well as the presence of ruthenium dioxide deposits. The temperature is also a key parameter. In the presence of steam, the half-life times of RuO4 are found to be respectively of 5 h and 9 h at 90°C and 40°C. A chemical reaction scheme consistent with the experimental observations is proposed. © by Oldenbourg Wissenschaftsverlag

Oxidation of ruthenium oxide deposits by ozone

During a hypothetical severe accident on a nuclear Pressurized Water Reactor (PWR), the formation of highly radiotoxic RuO4(g) may occur in the reactor containment building, resulting from the interactions of ruthenium oxide deposits with the oxidising medium induced by air radiolysis. Consequently, there is a risk that the gaseous ruthenium tetroxide could be dispersed into the environment through containment leakages; therefore data concerning the behaviour of ruthenium oxide deposits is of primary importance for safety studies. An experiment has been designed to study the interactions of ruthenium oxide deposits with ozone, formed by air radiolysis. Experimental results have shown that the oxidation reaction leading to the formation of RuO4(g) occurred to a large extent. An oxidation kinetic rate law has been determined, in dry and moist air, for ruthenium deposited onto painted substrates, representative of the inner surfaces of PWR's. This law, combined with tetroxide stability data [1], will allow a first evaluation of ruthenium revolatilisation phenomenon, possibly occurring in the containment during a severe accident. © by Oldenbourg Wissenschaftsverlag

Microhydration of caesium compounds Cs, CsOH, CsI and Cs2I 2 complexes with one to three H2O molecules of nuclear safety interest

International audienceStructure and thermodynamic properties (standard enthalpies of formation and Gibbs free energies) of hydrated caesium species of nuclear safety interest, Cs, CsOH, CsI and its dimer Cs2I2, with one up to three water molecules, are calculated to assess their possible existence in severe accident occurring to a pressurized water reactor. The calculations were performed using the coupled cluster theory including single, double and non-iterative triple substitutions (CCSD(T)) in conjunction with the basis sets (ANO-RCC) developed for scalar relativistic calculations. The second-order spin-free Douglas-Kroll-Hess Hamiltonian was used to account for the scalar relativistic effects. Thermodynamic properties obtained by these correlated ab initio calculations (entropies and thermal capacities at constant pressure as a function of temperature) are used in nuclear accident simulations using ASTEC/SOPHAEROS software. Interaction energies, standard enthalpies and Gibbs free energies of successive water molecules addition determine the ordering of the complexes. CsOH forms the most hydrated stable complexes followed by CsI, Cs2I2, and Cs. CsOH still exists in steamatmosphere even at quite high temperature, up to around 1100 K. © Springer-Verlag 2014

Modeling of iodine radiochemistry in the ASTEC severe accident code: Description and application to FPT-2 PHEBUS test

In the case of a hypothetical severe accident in a nuclear power plant, iodine is one of the fission products of major importance. It may be present in various gaseous forms that could be released to the environment, impacting population health. In such a case, the amount released (the so-called "source term") has to be estimated in order to help the safety authorities protect the population from radiological consequences. This estimation is one of the main objectives of the Accident Source Term Evaluation Code (ASTEC) that is developed jointly by the French Institut de Radioprotection et de Sûreté Nucléaire (IRSN) and the German institute Gesellschaft für Anlagen- und Reaktorsicherheit. ASTEC is composed of various modules able to model the nuclear reactor behavior during an accident. One of these modules, named IODE, predicts iodine behavior in the reactor containment. It is able to model the kinetics of about 35 chemical reactions and mass transfer processes. IODE is validated against separate effect tests, semi-integral experiments, and integral experiments. This paper presents the experimental phenomena that would take place in reactor containment in the case of a severe accident. Then, IODE is used to model the experimental gaseous concentration of organic and inorganic iodine in the PHEBUS FPT-2 test carried out by IRSN. The comparison of experimental data and the modeling show a general good agreement for inorganic iodine even if some differences are evidenced. For organic iodides the modeling is not satisfying. These differences might be explained by the deficiencies of some models and by some assumptions that still have to be validated by dedicated experiments