Modelling of release of particulate material from transport containers

Abstract

The Nuclear Decommissioning Authority (NDA) is developing a family of Standard Waste Transport Containers (SWTCs) for the transport of unshielded intermediate level radioactive waste packages. The SWTCs are shielded transport containers designed to carry different types of waste packages. The combination of the SWTC and the waste package is required to meet the regulatory requirements for Type B packages. One such requirement relates to the containment of the radioactive contents, with the IAEA Transport Regulations specifying release limits for normal and accident conditions of transport. In the impact tests representing accident conditions of transport, the waste package will experience significant damage and radioactive material will be released into the SWTC cavity. It is therefore necessary to determine how much of this material will be released from the cavity to the external environment past the SWTC seals. Typical assessments use the approach of assuming that the material will be evenly distributed within the cavity volume and then determining the rate at which gas will be released from the cavity, with the volume of radioactive material released with the gas based on the concentration of the material within the cavity gas. This is a pessimistic approach as various deposition processes would reduce the concentration of gas-borne particulate material and hence reduce their release rate from the SWTC. This paper assesses these physical processes that control the release rate and develops a conservative methodology for calculating the particulate releases from the SWTC lid and valve seals under normal and accident conditions of transport, in particular:

a) the flows within the SWTC cavity, especially those near the cavity walls;

b) the aerodynamic forces necessary to detach small particles from the cavity surface and suspend them into the cavity volume;

c) the adhesive forces holding contaminant particles on the surface of a waste package;

d) the breakup of waste material upon impact that will determines the volume fraction and size distribution of fine particulate released into the cavity.

Three mechanisms are specifically modelled, namely Brownian agglomeration, Brownian diffusion and gravitational settling, since they are the dominant processes that lead to deposition within the cavity and the easiest to calculate with much less uncertainty than the other deposition processes. Calculations of releases under normal conditions of transport concentrate on estimating the detachment of any waste package surface contamination by inertial and aerodynamic forces and show that very little of any contamination removed from the waste package surface would be released from the SWTC. Under accident conditions of transport, results are presented for the fraction released from the SWTC to the environment as a function of the volume fraction of the waste package contents released as fine particulate matter into the SWTC cavity. These show that for typical release fractions of 10^-6 to 10^-8 for the release of radioactive material from waste packages into the SWTC cavity, the release fraction of the waste package inventory from the SWTC of typically 10^-9 to 10^-10. Hence, the effective decontamination factor provided by the SWTC is 10² to 10³. Whilst this analysis has been carried out specifically for the SWTC carrying waste packages, it is applicable to other arrangements and its use would reduce the high degree of pessimism used in typical containment assessments, whilst still giving conservative results.     

Pulse height distributions from deterministic radiation transport simulations

In this paper, we demonstrate that deterministic transport simulations can be used to calculate the pulse height distribution for photons interacting in detector geometries. Typically, Monte Carlo transport methods are used for this application. Utilizing the collided components of the scalar flux calculated from the standard Source Iteration procedure used in many deterministic transport codes, we have generated photon pulse height distributions that compare favorably with those from MCNP5. Several test problems in 1-D slab geometry form the basis of our comparison with MCNP5, but the algorithm is easily extensible to 3-D geometries.     

The status of the general radiation transport code MCBEND

MCBEND is an established Monte Carlo code in the fields of shielding, dosimetry and general radiation transport. The development of the code is continuing within a partnership between Serco Assurance and BNFL and this paper reviews the current status of the code and describes some recent developments, including a point energy adjoint facility and automatic generation of a splitting mesh for variance reduction.     

Modelling radiation effects using the ab-initio based tungsten and vanadium potentials

The Embedded Atom Model (EAM) Derlet-Nguyen-Manh-Dudarev tungsten and vanadium potentials were modified to correctly reproduce the experimentally obtained defect threshold energies. This was done by letting the interactions at short distances be dictated by the universal screened Coulomb potential. Both the repulsive part and the electron density function of the potentials were modified. The potentials were then used in collision cascade simulations and the resulting defects were compared with the corresponding defects in iron. Based on this comparison, factors affecting the outcome of a cascade were identified.     

The role of the Boltzmann transport equation in radiation damage calculations

The purpose of this article is to discuss in some detail the uses of the Boltzmann equation in assessing displacement damage due to fast atoms in solids. We derive the appropriate equations for describing atomic motion in solids directly from the non-linear Boltzmann equation for mixtures. The basic assumption is that binary collisions are valid and that the solid can be regarded as amorphous or as a random lattice of atoms. Moreover, we assume that the density of fast atoms (i.e. those with energy greater than about 25 eV) is so small that they do not interact with each other. With these assumptions a set of linear, coupled Boltzmann transport equations are derived which describe the projectile and recoil atom distributions in space, time and velocity. Additionally, we show how electronic interactions may be accounted for in an accurate and analytically useful manner.The Boltzmann equations thus derived are in the so-called forward form, that is the final co-ordinates are the ones operated upon rather than the initial ones. We consider the corresponding adjoint equations and from the mathematical properties of the operators prove a reciprocity relation between the solutions of the forward equations and the adjoint ones. This enables either equation, forward or backward (adjoint), to be used to calculate the distribution function, a fact which is extremely useful in simplifying calculations for certain types of problem. It also demonstrates the inter-relationships between the works of various groups.The essentials of the scattering cross-sections are discussed and it is seen that two distinct problems arise: scattering in the C.M. system, which is determined by the interparticle force law, and scattering in the L-system which is governed only by the laws of conservation of energy and momentum. In both cases we discuss analytical simplifications which lead to useful approximations for solving the transport equation in closed form.One of the basic problems of radiation damage theory is that of sputtering and we spend some time explaining how binding forces at a vacuum-solid interface affect the solution of the transport equation.Several infinite medium problems are solved using backward and forward equations, thus we calculate the collision density of recoiling atoms due to a high energy source and also the time dependent behaviour of the energy spectrum following a pulse of fast atoms. The energy deposition and total number of moving particles at time t is calculated for various scattering models. The importance of electronic stopping in calculating the amount of energy eventually ending up in atomic motion is assessed via a time dependent forward equation. Its connection with the work of Lindhard is pointed out.We discuss displacement damage and show how the number of displacements per primary particle may be calculated via the collision density approach or through the backward equation with suitably modified energy transfer terms. The ideas of energy partitioning are discussed and methods for assessing its accuracy outlined.The spatial distribution of radiation damage receives considerable effort and we look at the various methods of dealing with the anisotropy of scattering, from Legendre polynomial expansions to the straight-ahead, or path-length, approximation. Analytical solutions are given for a variety of simple problems and in particular the vexed question of ion implantation in heterogeneous layered structures is discussed and various solutions proposed. For infinite, homogeneous media we discuss the method of moments using forward and backward equations and conclude that in many situations the forward form has much to commend it although in some situations the backward equation is not without merit. They are indeed complementary techniques.Sigmund's method for calculating the sputtering yield and efficiency is described via the backward equation and the approximations introduced by his “infinite medium boundary condition” are examined. We propose a more accurate theory which includes the half space nature of the system but which, because of this, leads to difficult mathematical problems. Certain simplified problems are solved and ideas for future progress are put forward.The concept of channelling is discussed and methods for including it directly into the Boltzmann equation are outlined. Essentially, these suggest the introduction of an angularly dependent cross-section which accounts in a phenomenological manner for the anisotropy of the microstructure of the solid.A final section is devoted to a stochastic formulation of the particle distribution function through a probability density. An equation is obtained for this density by probability balance and is then simplified by the introduction of a generating function. Successive differentiations of the generating function enable equations for the average value to be obtained, i.e. the conventional Boltzmann equation, and also higher order correlation functions which give a measure of the fluctuations in the number of particles in a cascade. Equations for vacancies and interstitials and their correlations are discussed in this respect.Finally, it should be noted that this paper shows a very personal and possibly biased view of radiation damage calculation. Indeed, it is not intended to discuss radiation damage as such, but rather to outline the difficulties and particularly to show how the Boltzmann equation has beeb and can be used in its forward and backward forms to understand atomic displacement problems.     

Monte Carlo methods for radiation transport analysis on vector computers

The development of advanced computers with special capabilities for vectorized or parallel calculations demands the development of new calculational methods. The very nature of the Monte Carlo process precludes direct conversion of old (scalar) codes to the new machines. Instead, major changes in global algorithms and careful selection of compatible physics treatments are required. Recent results for Monte Carlo in multigroup shielding applications and in continuous-energy reactor lattice analysis have demonstrated that Monte Carlo methods can be successfully vectorized. The significant effort required for stylized coding and major algorithmic changes is worthwhile, and significant gains in computational efficiency are realized. Speedups of at least twenty to forty times faster than CDC-7600 scalar calculations have been achieved on the CYBER-205 without sacrificing the accuracy of standard Monte Carlo methods. Speedups of this magnitude provide reductions in statistical uncertainties for a given amount of computing time, permit more detailed and realistic problems to be analyzed, and make the Monte Carlo method more accessible to nuclear analysts. Following overviews of the Monte Carlo method for particle transport analysis and of vector computer hardware and software characteristics, both general and specific aspects of the vectorization of Monte Carlo are discussed. Finally, numerical results obtained from vectorized Monte Carlo codes run on the CYBER-205 are presented.     

A finite transform approach to the solution of radiation transport equation

Starting from the integral form of transport equation and defining a new transform G(x,μ,μ_m), the integration over space is carried out analytically resulting in an integral equation for F in μ. Use of Legendre polynomial for the solution of this equation is explored. The method is applicable to practical problems of radiation transport in multiregion, energy dependent systems with arbitrary degree of anisotropy. Its simplification for idealised systems and comparison with earlier work are indicated.     

Modelling of carbon transport in fusion devices: evidence of enhanced re-erosion of in-situ re-deposited carbon

The paper presents new Monte-Carlo transport simulations of methane ¹³CH₄ injected through a hole in a testlimiter and exposed to the edge plasma of TEXTOR. The results show that the spatial distribution of ¹³C re-deposited locally on the testlimiter surface can be modelled if the parameter S for the sticking of returning hydrocarbons ¹³CH_y is set to zero or almost zero. This is interpreted as a negligible effective sticking of the returning hydrocarbon radicals due to the instantaneous re-erosion caused by the hydrogen carried with the CH_y radicals (`self re-erosion'). However, the calculated local deposition efficiency of ¹³C, remains too high compared with the observed value. Therefore, in addition an enhanced yield for chemical erosion caused by the background hydrogen for the fresh re-deposits has to be assumed. Similar assumptions can reproduce also the high amount of carbon deposition found on the inner louvers in the MkIIa divertor configuration of JET and on the plasma-shadowed areas of the MkIIGB divertor.     

Modeling of radiation heat transport in complex ladder-like structures placed in rectangular enclosures

Complex ladder-like structures recently have been considered as the target design for accelerator applications. The decay heat, during a postulated beyond design-basis loss-of-coolant accident in the target where all normal and emergency cooling fails, is removed mainly by radiation heat transfer. Modeling of the radiation transport in complex ladder-like structures has several challenges and limitations when the standard net-radiation model is used. This paper proposes a simplified lumped, or ‘hot-rung’ model, that considers the worst elements and utilizes the standard net-radiation method. The net-radiation model would under-predict structure temperatures if surfaces were subject to non-uniform radiosity. The proposed model was assessed to suggest corrections to account for the non-uniform radiosity. The non-uniform radiosity effect causes the proposed hot-rung model to under-predict the center-rung temperatures by ≈4–74°C when all parametrics, including temperatures up to 1500°C, were considered. These temperatures are small. The proposed model predicted that an important effect of decreasing the emissivity was smoothing of non-isothermal effects. The radiosity effects are more pronounced when there are strong temperature gradients. Uniform rung temperatures tend to decrease the radiosity effects. We concluded that a relatively simple model that is conservative with respect to radiosity effects could be developed.     

蒙特卡罗法内照射剂量计算中不同物理模型的比较

在核医学内照射剂量计算中，Monte Carlo方法是一种十分重要的方法。但其计算结果的准确性直接取决于所使用的物理模型。分析了光子与物质作用过程的三种模型，比较了它们各自的特点，使用条件和对计算结果的影响，以便于科研工作中正确的选用。     

High resolution time integration for SN radiation transport

First-order, second-order, and high resolution time discretization schemes are implemented and studied for the discrete ordinates (S_N) equations. The high resolution method employs a rate of convergence better than first-order, but also suppresses artificial oscillations introduced by second-order schemes in hyperbolic partial differential equations. The high resolution method achieves these properties by nonlinearly adapting the time stencil to use a first-order method in regions where oscillations could be created. We employ a quasi-linear solution scheme to solve the nonlinear equations that arise from the high resolution method. All three methods were compared for accuracy and convergence rates. For non-absorbing problems, both second-order and high resolution converged to the same solution as the first-order with better convergence rates. High resolution is more accurate than first-order and matches or exceeds the second-order method.     

A review of corrosion product transport and radiation field buildup in boiling water reactors

Cobalt-60 is the major radiation source in the boiling water reactor (BWR) for personnel exposure during shutdown maintenance. The Co-60 activity is produced by neutron activation of cobalt with other corrosion products deposit on fuel surfaces, and is released into the coolant and deposited on primary system piping walls in the system. The transport phenomena of corrosion products in the primary system and radiation field buildup are reviewed separately in three different areas: the behavior of corrosion products in the BWR coolant, including the chemistry of corrosion products and formation of mixed metal oxides; the transport of corrosion products on fuel cladding surfaces, and the mechanisms of deposition and release are discussed; and the transport of Co-60 and radiation field buildup on out-of-core surfaces under various chemistry conditions, including normal water chemistry, hydrogen water chemistry and with chemical additives. It is concluded that with understanding the mechanisms of transport, the radiation field buildup in most operating BWRs has been considerably reduced in recent years. The major factors are reduction of cobalt source reduction, control of Co-60 release from fuel surfaces with zinc addition and improvement in water quality to minimize the corrosion product input and the material corrosion.     

A new high speed solution for the evaluation of Monte Carlo radiation transport computations

Advancements in parallel and cluster computing have made many complex Monte Carlo simulations possible in the past several years. Unfortunately, cluster computers are large, expensive, and still not fast enough to make the Monte Carlo technique useful for calculations requiring a near real-time evaluation period. For Monte Carlo simulations, a small computational unit called a Field Programmable Gate Array (FPGA) is capable of bringing the power of a large cluster computer into any personal computer (PC). Because an FPGA is capable of executing Monte Carlo simulations with a high degree of parallelism, a simulation run on a large FPGA can be executed at a much higher rate than an equivalent simulation on a modern single-processor desktop PC. In this paper, a simple radiation transport problem involving moderate energy photons incident on a three-dimensional target is discussed. By comparing the evaluation speed of this transport problem on a large FPGA to the evaluation speed of the same transport problem using standard computing techniques, it is shown that it is possible to accelerate Monte Carlo computations significantly using FPGAs. In fact, we have found that our simple photon transport test case can be evaluated in excess of 650 times faster on a large FPGA than on a 3.2 GHz Pentium-4 desktop PC running MCNP5.     

Radiation processed polychloroprene-co-ethylene-propene diene terpolymer blends: Effect of radiation vulcanization on solvent transport kinetics

Blends of polychloroprene rubber (PCR) and ethylene propylene diene terpolymer rubber (EPDM) of different compositions were made and exposed to different gamma radiation doses. The radiation sensitivity and radiation vulcanization efficiency of blends was estimated by gel-content analysis, Charlesby-Pinner parameter determination and crosslinking density measurements. Gamma radiation induced crosslinking was most efficient for EPDM (p₀/q₀ ∼ 0.08), whereas it was the lowest for blends containing 40% PCR (p₀/q₀ ∼ 0.34). The vulcanized blends were characterized for solvent diffusion characteristics by following the swelling dynamics. Blends with higher PCR content showed anomalous swelling. The sorption and permeability of the solvent were not strictly in accordance with each other and the extent of variation in two parameters was found to be a function of blend composition. The ΔG values for solvent diffusion were in the range −2.97 to −9.58 kJ/mol and indicated thermodynamically favorable sorption for all blends. These results were corroborated by dynamic swelling, experimental as well as simulated profiles and have been explained on the basis of correlation between crosslinking density, diffusion kinetics, thermodynamic parameters and polymer-polymer interaction parameter.     

An approximate method for solving radiation and neutron transport problems in spatially stochastic media

A new approach has been developed to deal with stochastic transport problems in three-dimensional media. This is done by assuming, a priori, a functional form for the stochastic flux in terms of the members of a random set function. For the case of a two-phase medium, two coupled integro-differential equations are obtained for the deterministic functions that arise and expressions are given for the mean and variance of the angular flux. There is a close relationship between these equations and those of the Levermore–Pomraning (LP) theory, but they offer an opportunity to deal with more general forms of stochastic processes. It is also shown that the coupling coefficient between the phase equations is directly proportional to the gradient of the autocorrelation function evaluated at the origin; a feature which has been noted in other fields in which random media occur. By making plausible assumptions about the functional form of the autocorrelation function, different forms of the transport equations can be obtained, according to the structure of the medium. For the one-dimensional case, we may show an exact correspondence with the LP equations. Discussions are given regarding the application of the method to three-dimensional problems for which we expect it to be a good approximation for the mean. We also note that the equations are applicable to realistic problems, such as grains embedded in a background matrix, and not restricted to slabs. Investigations into the variance have also been made and a simple approximation scheme developed which gives reasonable agreement with the simulation results of Adams et al. [Adams, M.L., Larsen, E.W., Pomraning, G.C., 1989. Benchmark results for particle transport in a binary Markov statistical medium. Journal of Quantitative Spectroscopy & Radiative Transfer, 42, 253].     

Identification of the unknown shielding parameters with gammaray spectrum using a derivative-free inverse radiation transport model

Identifying the unknown geometric and material information of a multi-shield object by analyzing the radiation signature measurements is always an important problem in national and global security. In order to identify the unknown shielding layer thicknesses of a source/shield system with gamma-ray spectra, we have developed a derivative-free inverse radiation transport model based on a differential evolution algorithm with global and local neighbourhoods(IRT-DEGL). In the present paper, the IRT-DEGL model is further extended for estimating the unknown thicknesses with random initial guesses and material mass densities of multi-shielding layers as well as their combinations. Using the detected gamma-ray spectra,the illustration of inverse studies is implemented and the main influence factors for inverse results are also analyzed.     

EJUSTCO: Monte Carlo radiation transport code hybrid with ANN model for gamma-ray shielding simulation

Gamma ray shielding is essential to ensure the safety of personnel and equipment in facilities and environments where radiation exists. The Monte Carlo technique is vital for analyzing the gamma-ray shielding capabilities of materials. In this study, a simple Monte Carlo code, EJUSTCO, is developed to cd simulate gamma radiation transport in shielding materials for academic purposes. The code considers the photoelectric effect, Compton (incoherent) scattering, pair production, and photon annihil...