Antonio Carlos Marques Alvim

On the Fractional Neutron Point Kinetics Equations

This work proposes a fractional derivative model for some anomalous neutron diffusion phenomena in nuclear reactors. The model is solved in terms of the neutron flux density and current. The fractional diffusion model displayed may be applied to large variations neutron cross-section that normally prevent the use of the classic model of the neutron diffusion equation. In this chapter we present a new method and approach for solving the fractional neutron kinetics equations and several precursor groups using the decomposition method.

Radionuclide Transport in Fractured Rock: Numerical Assessment for High Level Waste Repository

Deep and stable geological formations with low permeability have been considered for high level waste definitive repository. A common problem is the modeling of radionuclide migration in a fractured medium. Initially, we considered a system consisting of a rock matrix with a single planar fracture in water saturated porous rock. Transport in the fracture is assumed to obey an advection-diffusion equation, while molecular diffusion is considered the dominant mechanism of transport in porous matrix. The partial differential equations describing the movement of radionuclides were discretized by finite difference methods, namely, fully explicit, fully implicit, and Crank-Nicolson schemes. The convective term was discretized by the following numerical schemes: backward differences, centered differences, and forward differences. The model was validated using an analytical solution found in the literature. Finally, we carried out a simulation with relevant spent fuel nuclide data with a system consisting of a horizontal fracture and a vertical fracture for assessing the performance of a hypothetical repository inserted into the host rock. We have analysed the bentonite expanded performance at the beginning of fracture, the quantified radionuclide released from a borehole, and an estimated effective dose to an adult, obtained from ingestion of well water during one year.

ON A CLOSED FORM SOLUTION OF THE POINT KINETICS EQUATIONS WITH REACTIVITY FEEDBACK OF TEMPERATURE

An analytical solution of the point kinetics equations to calculate time-dependent reactivity by the decomposition method has recently appeared in the literature. In this paper, we consider the neutron point kinetics equations together with temperature feedback effects. To this end, point kinetics is perturbed by a temperature equation that depends on the neutron density, obtaining a second-order non-linear ordinary differential equation. This equation is then solved by the decomposition method by expanding the neutron density in a series and expressing the non-linear terms by Adomian polynomials. Upon substituting these expansions into the non-linear ordinary equation, we construct a recursive set of linear problems that can be solved and resulting in an exact analytical representation for the solution. We also report numerical simulations and comparison against literature results.

Transverse net leakage into the second-order Nodal expansion method

Abstract A new formulation of the second-order version of the Nodal Expansion Method (NEM) is presented, based on the inclusion of a high-order transverse leakage source term into the Galerkin-weighted one-dimensional equations. This is done in a way that enhances the coupling between average group fluxes and incoming partial currents in the nodal balance equation. The equations for outgoing partial currents then take into account the transverse leakage contributions from the node of interest and the neighboring ones, in a manner similar to the standard fourth-order nodal expansion method. This formulation establishes a more physically coherent neutron balance inside an arbitrary node and preserves the iterative structure of the various versions of the NEM family, i.e., equations for outgoing currents and average fluxes in the inner iterations and fission source in the outer iterations. To illustrate the efficiency and accuracy of this second-order approach, numerical results for a typical 2-D, two-group benchmark model problem are presented.

Depletion Calculation for a Nodal Reactor Physics Code

This paper deals with an alternative numerical method for calculating depletion and production chains of the main isotopes found in a pressurized water reactor. It is based on the use of the exponentiation procedure coupled to orthogonal polynomial expansion to compute the transition matrix associated with the solution of the differential equations describing isotope concentrations in the nuclear reactor. Actually, the method was implemented in an automated nuclear reactor core design system that uses a quick and accurate 3D nodal method, the Nodal Expansion Method (NEM), aiming at solving the diffusion equation describing the spatial neutron distribution in the reactor. This computational system, besides solving the diffusion equation, also solves the depletion equations governing the gradual changes in material compositions of the core due to fuel depletion. The depletion calculation is the most time-consuming aspect of the nuclear reactor design code, and has to be done in a very precise way in order to obtain a correct evaluation of the economic performance of the nuclear reactor. In this sense, the proposed method was applied to estimate the critical boron concentration at the end of the cycle. Results were compared to measured values and confirm the effectiveness of the method for practical purposes.Copyright

Sensitivity analysis on the accident rate of a plant equipped with a single protective channel by generalized perturbation methods

Abstract In this paper we discuss the application of the GPT methodology to a reliability engineering problem which is of great practical interest: that of the analysis on the influence of the demand rate of the accident rate of a process plant equipped with a single protective channel. This problem has been solved in the literature by traditional methods; that is, for each demand rate value the system of differential equations which governs the system behavior (derived from a Markovian reliability model) is solved, and the resulting points are employed to generate the desired curve. This sensitivity analysis has been performed in this paper by means of a GPT approach in order to show how it could simplify the calculations. Sensitivity studies were performed on the repair efficiency and the demand rate, then on the repair rate and repair efficiency and, finally, on the demand rate and repair rate. GPT results of third order approximations were well in agreement with direct calculations. The relevance of the GPT approach is discussed in the context of redundant protective channels.

A THERP/ATHEANA Analysis of the Latent Operator Error in Leaving EFW Valves Closed in the TMI-2 Accident

This paper aims at performing a human reliability analysis using THERP (Technique for Human Error Prediction) and ATHEANA (Technique for Human Error Analysis) to develop a qualitative and quantitative analysis of the latent operator error in leaving EFW (emergency feed-water) valves closed in the TMI-2 accident. The accident analysis has revealed a series of unsafe actions that resulted in permanent loss of the unit. The integration between THERP and ATHEANA is developed in a way such as to allow a better understanding of the influence of operational context on human errors. This integration provides also, as a result, an intermediate method with the following features: (1) it allows the analysis of the action arising from the plant operational context upon the operator (as in ATHEANA), (2) it determines, as a consequence from the prior analysis, the aspects that most influence the context, and (3) it allows the change of these aspects into factors that adjust human error probabilities (as in THERP). This integration provides a more realistic and comprehensive modeling of accident sequences by considering preaccidental and postaccidental contexts, which, in turn, can contribute to more realistic PSA (Probabilistic Safety Assessment) evaluations and decision making.

On probability models for the unavailability analysis of safety systems under aging phenomena

This paper presents and discusses three probability models for approaching aging of a component. NRC and IAEA views of aging phenomena are reviewed and discussed. Repair is approached in the first model by stochastic point processes, and a statistical dynamical model is employed to allow for Bayesian forecasting. A discussion on repairable systems terminology is presented because much controversy may be found concerning this feature. A queueing model is then presented for a component considering its age as a supplementary variable. Presented also are numerical and exact solutions (for some cases). Aging is modeled by Weibull and lognormal distributions for failure times. Repair is approached by exponential distributions. The device of stages is applied to the same problem, and results are obtained for a Weibull failure time distribution. Typical means and variances for the times to failure are considered, and combinations of stages are checked. Alternative solutions by failure rates discretization are generated to check the validity of the developed models. An important issue concerning these models is discussed, that of appropriate failure data for each of them.

Simplification of State Transition Diagrams in Average Unavailability Analysis by Using Generalized Perturbation Theory

Safety analysis studies in nuclear engineering, more specifically system reliability, usually handle a great number of components, so that computational difficulties may arise. To face the problem of many component systems a method for simplifying the state transition diagram in Markovian reliability analyses has been proposed, using the edges which can be cut, since these latter have a smaller influence on system failure probability. In order to extend the application of GPT (Generalized Perturbation Theory), this work uses GPT formalism to reduce the number of states in a transition diagram, not considering the state probability as the integral quantity of interest, but the mean system unavailability instead. Therefore, after simplifying the original diagram, the mean unavailability for the new system was calculated and the results were very close to those of the original diagram integral quantity (giving a relative error of about 2%), showing that the proposed simplification is quite reasonable and simple to apply.

Failure Probability Evaluation of a Near-Surface Radioactive Waste Repository Due to Water Infiltration

This paper aims to determine, for the period of institutional control (300 yr), the probability of occurrence of the net release scenario of radioactive waste from a near-surface repository. The radioactive waste focused on in this work is that of low and medium activity generated by a pressurized water reactor plant. The repository is divided into eight modules, each of which consists of six barriers (top cover, upper layer, packages, base, walls, and geosphere). The repository is a system where the modules work in series and the module barriers work in active parallel. The module failure probability for radioactive elements is obtained from a Markov model because of shared loads assumed for the different barriers. Lack of field failure data led to the necessity of performing sensitivity analyses to assess the failure rate impact on module and barrier failure probabilities. Module failure probabilities have been found to be lower for those radioactive elements with higher retardation coefficients. The geosphere mean time to failure is the most important parameter for calculating module failure probabilities for each radioactive element. The repository module has presented higher failure probabilities for iodine, technetium, and strontium. For iodine, the estimated probability is 16% for 300 yr and 96% for 1000 yr. The basis for performance evaluation of the deposition system is the understanding of its gradual evolution. There are many uncertainty sources in this modeling, and efforts in this direction are strongly recommended.