Neutron-Photon Energy Deposition in CANDU Reactor Fuel Channels: a Comparison of Modelling Techniques Using ANISN and MCNP Computer Codes

AECL EACL

CA9700305

CA9700305 AECL-11160, COG-94-387

Neutron-Photon Energy Deposition in CANDU Reactor Fuel Channels: A Comparison of Modelling Techniques Using ANISN and MCNP Computer Codes

Depot d energie des photons et des neutrons dans les canaux de combustible des reacteurs CANDU: Comparaison des techniques de modelisation a l'aide des programmes de calcul MCNP et ANISN

Z. Bilanovic, D.R. McCracken

December 1994 decembre 8 8s 1 9 AECL

NEUTRON-PHOTON ENERGY DEPOSITION IN CANDU REACTOR FUEL CHANNELS: A COMPARISON OF MODELLING TECHNIQUES USING ANISN AND MCNP COMPUTER CODES

Z. Bilanovic and D.R. McCracken

System Chemistry and Corrosion Branch Chalk River Laboratories Chalk River, Ontario, CANADA KOJ 1J0

1994 December AECL-11160 COG-94-387 EACL

DEP6 t D ’ENERGIE des photons et des neutrons DANS LES CANAUX DE COMBUSTIBLE DES r6a CTEURS CANDU : COMPARAISON DES TECHNIQUES DE MODELISATION A L’AIDE DES PROGRAMMES DE CALCUL MCNP ET ANISN

par

Z. Bilanovic et D.R. McCracken

RESUME

II est necessaire de determiner les profits de depot d'energie des neutrons, des photons et des electrons dans les canaux de combustible du coeur du reacteur afm d'evaluer les effets de la corrosion radio-induite, la radiolyse du caloporteur et la degradation des proprietes physiques des materiaux et des composants du reacteur. Actuellement, on doit utiliser plusieurs programmes de calcul differents pour y parvenir. La demiere version du programme MCNP en est la plus recente, la plus evoluee et la plus polyvalente, et elle pourrait bien s'averer capable de remplacer tous les autres programmes. Les divers programmes avancent des hypotheses differentes et presentent des restrictions differentes quant a la maniere de modeliser la geometric et la physique du coeur. Le present rapport donne les resultats des modeles MCNP et ANISN de depot d'energie des photons et des neutrons. Ces resultats valident 1'utilisation du programme MCNP pour la moderation geometrique simplifiee du depot d'energie des neutrons et des photons dans le cas de la geometric complexe des canaux de combustible des reacteurs CANDU. Des programmes faisant appel a la methode des ordonnees discretes, tel que le programme ANISN, constituaient les programmes de reference utilises dans les travaux anterieurs.

Ce rapport presente egalement les resultats des calculs effectues a l'aide de divers modeles et ils concordent tres bien en ce qui conceme le depot d'energie des neutrons rapides. Dans le cas du depot d'energie des photons, on a du toutefois apporter quelques modifications aux methodes de modelisation. Les problemes poses par le recours a des frontieres reflectrices ont ete resolus soit par la prise en compte dans le modele des huit canaux de combustible en peripherie, soit par le recours a une source limite a la surface limite du probleme. Une fois que ces modifications ont ete incorporees, des resultats concordants ont ete obtenus entre les differents programmes de calcul.

Dans le passe, des representations annulaires simples du coeur ont ete employees, en raison de la difficulty de realiser une modelisation detaillee avec les codes plus anciens. On a demontre que la modelisation a l'aide du programme MCNP, faisant appel a une geometric plus precise et plus detaillee, donne des resultats tres differents et bien meilleurs.

Chimie et corrosion des systemes Laboratoires de Chalk River Chalk River (Ontario) Canada KOJ 1J0 1994 Decembre AECL-11160 COG-94-387 AECL

NEUTRON-PHOTON ENERGY DEPOSITION IN CANDU REACTOR FUEL CHANNELS: A COMPARISON OF MODELLING TECHNIQUES USING ANISN AND MCNP COMPUTER CODES

Z. Bilanovic and D.R. McCracken

ABSTRACT

In order to assess irradiation-induced corrosion effects, coolant radiolysis and the degradation of the physical properties of reactor materials and components, it is necessary to determine the neutron, photon, and electron energy deposition profiles in the fuel channels of the reactor core. At present, several different computer codes must be used to do this. The most recent, advanced and versatile of these is the latest version of MCNP, which may be capable of replacing all the others. Different codes have different assumptions and different restrictions on the way they can model the core physics and geometry. This report presents the results of ANISN and MCNP models of neutron and photon energy deposition. The results validate the use of MCNP for simplified geometrical modelling of energy deposition by neutrons and photons in the complex geometry of the CANDU reactor fuel channel. Discrete ordinates codes such as ANISN were the benchmark codes used in previous work. The results of calculations using various models are presented, and they show very good agreement for fast-neutron energy deposition. In the case of photon energy deposition, however, some modifications to the modelling procedures had to be incorporated. Problems with the use of reflective boundaries were solved by either including the eight surrounding fuel channels in the model, or using a boundary source at the bounding surface of the problem. Once these modifications were incorporated, consistent results between the computer codes were achieved. Historically, simple annular representations of the core were used, because of the difficulty of doing detailed modelling with older codes. It is demonstrated that modelling by MCNP, using more accurate and more detailed geometry, gives significantly different and improved results.

System Chemistry and Corrosion Branch Chalk River Laboratories Chalk River, Ontario, CANADA, KOJ 1 JO 1994 December AECL-11160 COG-94-387 TABLE OF CONTENTS Page

1. INTRODUCTION ...... 1

2. THE ANISN COMPUTER CODE...... 2 2.1 General Introduction ...... 2 2.2 CANDU Lattice Cell Calculations...... 3

3. THE MONTE CARLO NEUTRON AND PHOTON TRANSPORT CODE. MCNP...... 5 3.1 General Introduction ...... 5 3.2 MCNP - ANISN: Comparative Study ...... 5 3.3 MCNP 18- Element Annular Geometry ...... 7 3.4 Study of MCNP 37-Element Geometry...... 8

4. CONCLUSIONS ...... 8

5. DIRECTION OF FUTURE WORK...... 9

6. ACKNOWLEDGEMENTS...... 10

7. REFERENCES ...... 10

LIST OF TABLES

Table 1: Energy structure of the 39-group coupled neutron-gamma cross-section library ...... 12 Table 2: Materials found in the 39-group cross section library...... 13 Table 3: Dimensions and regions used in the ANISN 37-element lattice site...... 14 Table 4A: Compositions of materials for the fuel regions, used in ANISN calculations. The data are based on WIMS calculations for a 37-element lattice at a bumup of approximately 3300 MW.d/MgU ...... 15 Table 4B: Composition of materials used in ANISN calculations for the fuel channel region. The data are based on WIMS calculations for a 37 -element lattice at a bumup of approximately 3300 MW.d/MgU ...... 15 Table 5: Neutron fission spectmm for the centre pin based on a fission rate of 7.03xl012 fissions/cm3.s...... 16 Table 6 A: Energy deposition in the outer coolant region for ANISN calculations using annular geometry. Neutrons were generated by SOURCE. Photons were generated internally by ANISN...... 17 Table 6B: Energy deposition in the outer coolant region for ANISN calculations using annular geometry. Neutrons were generated by SOURCE. Photons were generated internally by ANISN...... 17 - 11 -

Table 7A: Photon source strength (photons/s) and spatial distribution as calculated by GAMSRC...... 18 Table 7B: Photon source strength (photons/s) and spatial distribution as calculated by GAMSRC...... 19 Table 8A: Energy deposition in the outer coolant region for ANISN calculations using annular geometiy. The photon source was generated by GAMSRC...... 20 Table 8B: Energy deposition in the outer coolant region for ANISN calculations using annular geometiy. The source was generated by GAMSRC...... 20 Table 9A: Ratio of ANISN to MCNP results in percent, for neutron energy deposition...... 21 Table 9B: Ratio of ANISN to MCNP results in percent, for photon energy deposition...... 21 Table 10: Dimensions and regions used for the eight outer channels in the "square cylinder" approximation of Figure 9...... 22 Table 11: Photon source flux at the outer boundary of the problem, in the moderator, half a lattice pitch between the central channel and the surrounding fuel. The data are for a bundle operating at 611 kW...... 23 Table 12: Properties and attributes of different codes used for calculations of energy deposition...... 24

LIST OF FIGURES

Figure 1: Annular representation of a CANDU fuel channel...... 25 Figure 2: Neutron fission spectrum for the centre pin based on a central-pin fission rate of 7.0368E12 fissions/cm3.s ...... 26 Figure 3: ANISN calculation of the neutron energy deposition in the outer coolant region between the fuel and pressure tube ...... 27 Figure 4: ANISN calculation of the gamma energy deposition in the outer coolant region...... 28 Figure 5: Photon energy and spatial distribution for a 611 kW bundle power as calculated by GAMSRC...... 29 Figure 6: ANISN calculation of the gamma energy deposition in the annular geometry outer coolant region: source particles generated by GAMSRC ...... 30 Figure 7: A comparison of neutron energy deposition in the outer coolant region for ANISN and MCNP with annular geometry ...... 31 Figure 8: A comparison of gamma energy deposition in the outer coolant region for ANISN and MCNP with annular geometiy ...... 32 - Ill -

Figure 9: A schematic representation of the transition from a square lattice to a "smeared" lattice geometry...... 33 Figure 10: MCNP calculations of neutron energy deposition for the reflective, non-reflective and 9-channel geometry cases...... 34 Figure 11: MCNP calculations of gamma energy deposition for the reflective, non-reflective and 9-channel geometry cases...... 35 Figure 12: MCNP calculations of gamma energy deposition for the reflective, non-reflective, 9-channel geometry and boundary source calculations...... 36 Figure 13: 18-element/annular representation of the CANDU reactor fuel channel...... 37 Figure 14: A comparison of neutron energy deposition for MCNP calculations with 18-element annular geometry and annular ANISN results ...... 38 Figure 15: A comparison of gamma energy deposition for MCNP calculations with 18-element/annular geometry and annular ANISN geometry...... 39 Figure 16: MCNP calculations of gamma energy deposition for the reflective, non-reflective, 9-channel geometry and boundary source calculations for the 18-element/annular geometry ...... 40 Figure 17: A 37-element representation of a CANDU fuel channel ...... 41 Figure 18: A comparison of neutron energy deposition between calculations done by MCNP using 37-element geometry and ANISN using annular geometry ...... 42 Figure 19: A comparison of gamma energy deposition calculations between MCNP using 18-element annular geometry and ANISN using annular geometry ...... 43 Figure 20: MCNP calculation of gamma energy deposition for the reflective, non- reflective, 9-channel geometry and boundary source calculations for the 37-element geometry ...... 44 1. INTRODUCTION

In order to assess irradiation-induced corrosion effects, coolant radiolysis and the degradation of the physical properties of reactor materials and components in the Primary Heat Transport System (PHTS) of nuclear reactors, it is necessary to determine the neutron, photon, and electron energy deposition profiles in the fuel channels of the reactor core. At present, several different computer codes must be used to do this; e.g., ANISN, DOT, MORSE, GAMSRC, SANDYL, and MCNP. The most recent, advanced and versatile of these is a new version of MCNP, which may be capable of replacing all the others. We are currently examining this prospect. Different codes have different assumptions and different restrictions on the way they can model the core physics and geometry. This report presents comparative results of ANISN and MCNP geometrical models of neutron and photon energy deposition; discrete ordinates codes such as ANISN were the benchmark codes used in previous work. The physics of MCNP is very accurate for neutrons and photons, but being a Monte Carlo code, it is subject to statistical uncertainty. In principle, it can calculate energy deposition for very complex geometries, but this can require inordinate amounts of computing time. The advantage of ANISN is that, being a deterministic code, it is faster and provides better accuracy, but it is veiy limited in the geometry that it can work with. In this work we test the use of MCNP with a simplified geometry, similar to that used in ANISN calculations with reflective boundaries, before going on to use MCNP on more complex problems.

Previous work (1) on the modelling of CANDU* reactor channels involved performing calculations using an essentially one-dimensional geometrical model with the discrete ordinates code ANISN (2), to solve the multi-group Boltzmann transport equation and determine the neutron and gamma fluxes in a CANDU core. ANISN has been used extensively in previous studies of neutron and photon energy deposition in CANDU reactor fuel channels (3, 4), and historically was the benchmark code for such work. More recently, the Monte Carlo transport code, SANDYL (1, 5), has been used in studies (6, 7) of photon- electron, energy deposition calculations with essentially two-dimensional geometry. A third computer code, the Monte Carlo Neutron Photon Transport Code (MCNP 4.2) (8), obtained from the Radiation Shielding Information Centre (RSIC) at the Oak Ridge National Laboratory, has been recently released with an option for doing electron transport. All of these computer codes have their own inherent strengths and weaknesses. Some of the important ones are discussed and demonstrated in this report.

Both ANISN and SANDYL calculations were used with symmetry in one dimension. The computer code ANISN, being a one-dimensional, coupled neutron-photon transport code, is obviously limited in the geometry that it can use, as well as limited in the particles that it can study: electrons are excluded. SANDYL is a three-dimensional Monte Carlo transport code that can calculate only photon-electron transport: neutrons are excluded. MCNP has the advantage of being a true three-dimensional code, and of being able to calculate neutron, photon and electron transport with up to 100 different source distributions. It is because of these capabilities that the use of MCNP is being investigated. It has the potential to do very

‘CANDU: CANada Deuterium Uranium; registered trademark. - 2 - detailed work on energy deposition profiles in the complex geometry of the CANDU reactor fuel channel, and to calculate radiation-induced damage in components. MCNP results using a simplified fuel channel model are compared with ANISN results in this report. MCNP has often been used for comparisons and for measuring the accuracy of emerging Monte Carlo transport codes, and also particle transport codes already in use. The widespread acceptance of MCNP and its impressive pedigree are other reasons it was chosen for this comparative study. The main features of MCNP will be discussed in this report. The intent is to extract comparable results using various computer codes which are based upon different methodologies. For such a comparison, two aspects must be considered. The first is to ascertain the adequacy of each particular computer code for performing the task at hand. The second is to determine the accuracy of the geometric models that are used to model the CANDU fuel channel in these codes. These models are constrained by the limitations of the codes, so that different assumptions must be made in formulating the different models for each code. Results obtained from MCNP are compared with those from ANISN. Although the SANDYL code itself has not been used in preparing this report, the radiation sources and geometry, used in other studies with SANDYL, have been incorporated into the present MCNP calculations, to provide a comparable, coherent and consistent set of results. The gamma calculations in this report do not account for electron migration, which should be done to get accurate coupled photon-electron results. The work reported here compares results for MCNP modelling and ANISN modelling of neutron and photon interactions, assuming that energy deposition occurs at the site of interaction. The accuracy of photon- electron modelling will be reported in another document.

2. THE ANISN COMPUTER CODE 2.1 General Introduction The computer code ANISN (obtained from the RSIC) solves multi-group-transport-theory, eigenvalue, adjoint, time-dependent, fixed-source and criticality calculations in one dimensional slab, cylindrical or spherical geometry (2). The code may be used for neutron only, gamma only, or coupled neutron-gamma problems. Provision has been made for diffusion-theory or infinite homogeneous media calculations. The method of solution uses an iterative approach to solving multi-group finite-difference discrete-ordinates equations with anisotropic scattering. Source particles (neutrons or gammas) can be dealt with in two ways: the spatial distribution of the source particles can be supplied as an input to the code; or the code itself can calculate the source particle distribution by finding the criticality of a fissile assembly. ANISN provides two ways of dealing with boundary conditions: 1. the vacuum, or no-reflection boundary, condition, where any particle crossing the outer boundary is treated as being lost from the problem; and - 3 -

2. the reflection boundary condition, where any particle crossing the outer boundary is converted to an incoming particle at that boundary, with an angular distribution that is equivalent to the exiting particles (black reflection condition), or that is isotropic (white reflection condition). For the calculations involving the CANDU lattice cell, ANISN uses a coupled 39-group cross section library distilled from Evaluated Nuclear Data Tables (ENDF/B - II and ENDF/B - ID) cross-section libraries (energy groups and details of materials are listed in Tables 1 and 2).

2.2 CANDU Lattice Cell Calculations

In the ANISN analysis of the CANDU reactor fuel channel, nineteen regions are used to represent the standard 37-element lattice cell in cylindrical geometry (3,4). ANISN is a restricted two-dimensional code: it can only track transport in radially symmetrical geometry, and only the central fuel pin and sheath can be represented using actual dimensions. The 6-element inner, 12-element intermediate and 18-element outer fuel rings are represented by three annuli, with areas equal to the cross-sectional area of fuel that they each represent. The annuli are defined by the radius of the pitch circle of each of the corresponding three fuel rings, with an equal thickness of fuel on each side of this radius. Each of the fuel annuli are bounded by an inner and outer annulus of zircaloy representing the fuel sheaths, with cross-sectional areas and thicknesses equal to that of the zircaloy in the appropriate ring of fuel sheaths. The pressure tube, gas annulus and the calandria tube are represented using actual dimensions and geometry. Details of the lattice cell representation are shown in Figure 1; Table 3 lists the dimensions used in the problem and the material composition of the lattice cell region. Tables 4A and 4B list the atom densities for the materials in the ANISN input based upon WIMS (9) calculations for a 37-element lattice at a bumup of approximately 3300 MW.d/MgU. The fission products are represented by xenon at a concentration that simulates the absorption rate of thermal neutrons by the fission products (3, 4). The neutron spatial and energy distribution was calculated using the program SOURCE (description to be published by C. Boss), in which the WIMS bumup calculations for a 611 kW bundle power were again used as input. SOURCE generates an independent neutron source spectrum from the fission rate and fuel data. The fixed fission sources in the four rings have relative strengths of 1.00, 1.043, 1.156, and 1.422, respectively. Relative fission-source data were used to provide results in terms of energy deposition per source particle, thereby simplifying future calculations for different reactor powers and reactor channels. Figure 2 shows a histogram of the neutron source for the different neutron energy groups, while Table 5 lists the data, which are based on a central-pin fission rate of 7.0368x1012 fissions/cm3.s.

Figure 3 shows the results for the energy deposition profile across the ANISN-defined coolant region between the outer fuel sheath annulus and the pressure tube (region 15 from Table 3) for neutrons with no reflection, black reflection (particles are reflected back along their flight path) or white reflection (isotopic scattering) at the boundary. There is not a large difference in energy deposition between the reflective boundary case and the non-reflective boundary case. This is because the energy deposition is due to fast neutrons, and in the reflective - 4 - boundary cases those returning through the moderator have been efficiently thermalized (the CANDU reactor is over-moderated). Consequently, the contribution of neutrons coming from other fuel channels (i.e., reflected neutrons in the model) to the overall energy deposition profile in the central channel is small. However in the case of gamma rays, as shown in Figure 4, there is a highly pronounced difference between the reflection and non-reflection calculations. This same type of behaviour has been observed previously (Table A-3 in reference 1), when allowing ANISN to generate the photons with no reflection at the boundary. Gamma rays are not as efficiently attenuated as fast neutrons or electrons by the moderator, so there is a much larger contribution from other channels than there is for neutrons. The results presented in both of these figures are based upon a neutron source distribution as calculated by the ANISN adjunct program, SOURCE. Table 6 summarizes the results shown in Figures 3 and 4, giving the energy deposition in both MeV/g.s and mW/g. The reflective boundary conditions simulate the effects of neighbouring fuel channels, and are therefore applicable only for modelling fuel channels away from the edge of the core; i.e., with a homogeneous flux from surrounding channels. For fuel channels near the edges of a reactor core, detailed two- or three-dimensional models are necessary. Alternatively, a one-dimensional code such as ANISN would have to adequately account for the albedo. ANISN has the ability to handle coupled neutron-gamma transport. However, in some instances this coupled prompt gamma approach is inadequate, since it requires accurate determination of the low energy and thermal neutrons. To determine a more accurate photon energy deposition profile, an independent photon source routine, GAMSRC (description to be published by C. Boss), is used to generate the source input, including delayed gammas and those from equilibrium concentrations of fission products. This is then input to ANISN. GAMSRC calculates a twelve-energy-group photon source for all of the ANISN regions (except for the annulus gas). These photon sources, as calculated by GAMSRC, are shown in Figure 5 and listed in Table 7. The results of using them for the photon energy deposition in the outer coolant region are shown in Figure 6. Tables 8A and 8B list the data in MeV/g.s and mW/g. For the case of no reflection, the energy deposited in the coolant is predicted to be greater when the source particle input is generated by GAMSRC (which includes prompt, delayed and fission-product gamma rays) than when the fission source is only prompt gammas as calculated internally by ANISN, SANDYL and MCNP. Since GAMSRC accounts more fully for the gamma rays, and does not depend on finding an accurate solution for the thermal neutrons, the GAMSRC/ANISN results are considered to be more accurate than the purely ANISN results.

In the cases considered so far, the dependence of the energy deposition profile on the type of outer-boundary reflection is significant, particularly for gamma rays. The results for calculations with no reflective boundary are the least realistic, because they assume an isolated channel completely free from the influence of neighbouring channels. This is obviously contrary to the real situation in a reactor core. The black reflective boundary condition, in which particles crossing the boundary are reflected back in the direction from which they came, yields the highest energy deposition rates. Photons are trapped inside the boundary. The white reflective boundary condition, in which particles are reflected back isotropically, perhaps more closely approximates reality among the three reflection options, but it still does not depict the real situation. This will be discussed in more detail later. - 5 -

3. THE MONTE CARLO NEUTRON AND PHOTON TRANSPORT CODE. MCNP

3.1 General Introduction

MCNP is a computer code developed at Los Alamos National Laboratory to solve neutron and photon transport problems (8). MCNP is a general-purpose, continuous-energy, generalized-geometry, time-dependent, neutron-photon, Monte Carlo transport code. It treats an arbitrary three-dimensional configuration of materials as geometric cells bounded by first- and second-degree surfaces. The cells are defined by the intersections, unions, and complements of the regions bounded by the surfaces. The code can be used for neutron transport exclusively, neutron-photon transport, or photon transport exclusively. The latest version of MCNP has just been released, and this additionally incorporates electron transport. MCNP has been designed to use up to 40 different isotopes with discrete cross-section data. A representative set of neutron and photon cross-section libraries is provided with the code. For neutrons, all reactions in the evaluation of a particular cross-section are accounted for. For photons, the code takes into account coherent and incoherent scattering, the possibility of fluorescent emission following photoelectric absorption, and absorption in pair production with local emission of annihilation radiation. An advantage of particular relevance is that angular distributions for elastic and inelastic events are prescribed, so that these distributions can be sampled continuously. 3.2 MCNP - ANISN: Comparative Study In order to place confidence in the results, and the interpretation of results obtained by MCNP, this code has been compared with others in current use. As the first step in confidence building, the model and calculational method used for ANISN calculations were reproduced using MCNP. Data sets using exactly the same geometiy (as shown in Figure 1), material composition, and neutron and photon source distributions as ANISN were constructed in the format for input into MCNP. ANISN calculates energy deposition in a 1 cm length of an infinite cylinder. MCNP uses a 1 cm cell with axial reflection. MCNP uses black reflection. Figures 7 and 8 show the results of a comparison between MCNP and ANISN for neutron and gamma energy deposition in the outer coolant region. The two codes used identical geometiy and source particle specifications. Figure 7 shows that MCNP tends to predict slightly higher neutron energy deposition rates. Several factors may account for this difference. ANISN discretizes the energy for cross sections and particle transport into 27 neutron and 12 gamma groups when performing calculations, whereas MCNP relies upon extensive continuous cross-section data files, with particle transport also being continuous in energy. This may be of importance, since neutron energy deposition is predominantly in a region where only few groups are considered by ANISN. In the gamma-ray energy deposition calculations, the difference between the two codes is virtually negligible, but MCNP still predicts a slightly higher energy deposition rate for the reflection case. The use of reflective surfaces in both ANISN and MCNP traps all of the photons within the region of interest until there is complete absorption. This can artificially inflate the energy deposited in the coolant, unless the dimensions of the problem are greater than the half-thickness value for absorption of energetic gamma-rays. To illustrate the - 6 - closeness of the data, particularly for photons, Tables 9A and 9B list the ratios of ANISN to MCNP results, in percent, for neutron and gamma ray energy deposition in different meshes of the outer coolant. As mentioned previously, no electron transport takes place. Two approaches were taken to improve the inaccurate use of reflective surfaces in MCNP. The first approach was to model the eight channels surrounding the central channel of interest. As the CANDU channels are in a square lattice, annular approximations are not strictly accurate. Since MCNP is not restricted to annular geometry, we could define a better model than the one-dimensional annular model of ANISN. The surrounding channels were modelled as a box surrounding the central channel. As done previously, the cross-sectional areas of materials were preserved. A representation of the geometry is shown in Figure 9. Table 10 lists the dimensions and composition of the additional materials used in the simulation. The individual material compositions are unchanged from those of the central channel annuli. Source particle distributions were multiplied by the appropriate factors (based upon geometrical considerations) assuming that the eight surrounding channels were at the same bundle power (611 kW) as the central channel. The difference between the reflective and non-reflective case for neutron energy deposition is small, so the further refinement introduced by the use of 9-channel geometry was not expected to make a large impact. This is confirmed by the results for neutron energy deposition shown in Figure 10: the change in going to 9-channel geometry is minimal. The gamma energy deposition case is shown in Figure 11. In this case, there is a significant difference for the 9-channel model. The results lie intermediately between the reflective and non-reflective cases, being closer to the latter. Comparison with ANISN calculations in Figure 6 shows very good agreement for reflective MCNP and non-reflective MCNP calculations (Figure 11) with black reflective and non-reflective ANISN (Figure 6). We believe that the 9-channel MCNP calculation is best, since it most realistically mimics reality.

The second approach was to calculate the particle flux distribution crossing the outer bounding surface of the problem (halfway across the moderator between the central fuel and the surrounding fuel) with no reflection, and then to use this flux as a boundary source in a subsequent calculation. This assumes a homogeneously symmetric core. As shown in previous analyses, significant change was expected for the gamma rays, but not for the neutrons. Accordingly, this new type of calculation was not done for neutrons: further refinement is not necessary for them. Source data are shown in Table 11 for the twelve gamma groups. Figure 12 shows the gamma-ray energy deposition calculated by MCNP for reflective, non-reflective, 9-channel and boundary source calculations. Similarl to the 9-channel simulation, the energy deposition profile determined by using a boundary source lies between the reflective and non-reflective case, being closer to the latter.

The preceding analyses and results indicate good agreement between ANISN and MCNP for both neutron and gamma-ray energy deposition. In addition, the analyses show that reflective boundary conditions, particulary for gamma calculations, tend to over-predict the amount of energy deposited in the coolant. The reason, as stated previously, is that reflective boundaries trap all of the photons in the region of interest until they reach their energy cutoff limit; that is, all of the gamma energy is absorbed. Unless a sufficiently large volume of the lattice is modelled, this technique will always overpredict the true situation. The MCNP user's manual has - 7 - a warning regarding the use of reflective surfaces, specifically for the reasons mentioned above. Unlike the case for neutrons, significant attenuation of gamma rays does not occur within one cell of the lattice. At equilibrium, the half-thickness for neutron absorption is less than one lattice pitch, so that one unit cell with reflection can fairly accurately model their situation. The two different approaches described above to simulate the effects on gamma-ray deposition of a larger lattice show excellent agreement, and give good confidence in the results. 3.3 MCNP 18-Element Annular Geometry In previous studies, the computer code SANDYL has been used to determine photon and electron energy deposition in the coolant region. SANDYL is also a Monte Carlo transport code, but there are some advantages in using MCNP. First, MCNP is a true three-dimensional code, whereas SANDYL is fundamentally a two-dimensional code. Second, the cross-section data files within MCNP are far more extensive and complete. The source particle handling capabilities in MCNP are much more versatile than in SANDYL. MCNP can handle up to 100 source regions and distributions, while SANDYL is capable of dealing with only ten source regions and one source distribution. This gives MCNP the advantage of requiring far fewer calculations, which drastically reduces the computer time and post-computation analysis. It also allows more accurate modelling. Finally, MCNP is capable of simultaneous neutron, photon, and electron transport calculations. This again greatly reduces the time spent modelling and matching methods and results from different computer codes. In a recent study using SANDYL, a parametric study of energy deposition by photons and electrons in the CANDU fuel channel was done using a model which mixed annular and multi pin geometry (6). Using the ability of SANDYL to model two-dimensional problems, the geometry of the fuel channel was simulated by explicitly modelling the 18 outer fuel pins as shown in Figure 13. It was demonstrated that very accurate models of the fuel channel were needed to get accurate results for gamma-electron energy deposition. This is because fuel channel dimensions are greater than the path length of a significant number of the electrons. As a complement to this work, and in preparation for future electron calculations with MCNP, this same geometry has been incorporated into an MCNP input file, using the same gamma source distribution as SANDYL. Remember that the gamma calculations in this report do not account for electron migration, which should be done to get accurate coupled photon-electron results. Neutron and photon results for MCNP and ANISN are illustrated in Figures 14 and 15. In these figures, the coolant region is smaller in the MCNP model, between the outermost part of the fuel radius and the pressure tube, because the 18 outer fuel elements are represented more accurately. Figure 14 shows that the neutron energy deposition profile as calculated by MCNP overlaps that predicted by the annular ANISN model, and is higher closer to the fuel. The effect is small: the new geometry does not make a great difference to the neutrons whose path- length is greater than the channel dimensions (c.f. Figure 10). Figure 15 shows the results for gamma energy deposition. With this geometry, the MCNP results are very close to, but slightly higher than, the ANISN results. This may be due to photons from the intermediate fuel annulus passing through the gaps between the 18 outer fuel elements. This is discussed in detail in reference 6. Figure 16 shows the results of calculations for which the eight surrounding channels were smeared into a series of "square cylinders" around the central channel; it also - 8 - shows results obtained using a boundary source, as discussed previously for Figures 11 and 12. Both sets of results are very close to each other; in fact, they really do not differ greatly from the annular calculations shown in Figure 12. They lie between the reflection and non-reflection results, being closest to the latter.

3.4 Study of MCNP 37-Element Geometry

The natural extension of the preceding analysis is to accurately model the complete CANDU channel; that is, to explicitly model all 37 fuel elements. This is beyond the capabilities of the current SANDYL code. Although we do not expect to see significant differences in neutron or gamma-ray energy deposition in the outer coolant, we do expect the 37-element model to make significant differences in electron deposition in all regions of the coolant. This will be reported in a future MCNP study of electron deposition. Figure 17 depicts the geometry of the 37-element model used in the subsequent MCNP calculations in this report.

As in the previous analyses, single channel geometry was employed to obtain the energy deposition profile across the outer coolant. Figure 18 shows the results of the neutron energy deposition calculations, while Figure 19 shows the results of the gamma energy deposition calculations. The data are virtually identical to those obtained for the 18-element annular geometry case (c.f. Figures 18 and 14, and Figures 19 and 15). Figure 20 shows the results for the 9-channel geometry calculations and the boundary source calculations. The energy deposition profile is consistent with the previous geometries.

4. CONCLUSIONS

This study has demonstrated the feasibility (and accuracy compared to other codes) of using the computer code MCNP to calculate neutron and photon transport, and energy deposition, in very complex geometries. Attributes of the different codes are summarised in Table 12. It is possible using MCNP to model the CANDU fuel channel accurately and in detail. While we have demonstrated that such detail is not necessary for neutrons and photons, it has been clearly demonstrated in other work using SANDYL that accurate detailing of the fuel channel geometry is necessary to get accurate results for electron deposition. The necessary geometry cannot, however, be detailed by the current SANDYL code. The next step is to use the detailed 37-element model described here in an electron calculation with MCNP.

Very good agreement has been reached between the discrete ordinates computer code ANISN's calculations and the Monte Carlo code MCNP’s calculations, for neutron energy deposition both in terms of magnitude and profile. This agreement survives the transitions from a one dimensional annular geometry to a geometry where the 18 outer elements are modeled explicitly, and finally to a completely realistic 37-element representation of the fuel channel. Results of a study of gamma energy deposition, not surprisingly, found that use of the reflective boundary condition with MCNP caused overprediction of energy deposition. This is because the use of reflective surfaces causes the trapping of photons until they are all absorbed, and does not adequately simulate the source from surrounding fuel channels. - 9 -

It was found that a necessary modification to the gamma calculations was to explicitly include the eight surrounding channels and materials of the core lattice. This was done by representing them by a series of square cylinders extending outwards one and a half lattice pitches from the channel of interest towards the surrounding 16 channels. As a check on the results from the above, a different calculational method was used. A two-step calculation involved determination of the outer boundary particle flux in a single-channel model, and incorporation of that flux as a boundary source in a subsequent calculation. This gave results almost identical to the 9-channel model. Both these models obviate the need for reflective surfaces, and produce results in harmony with the physics of the reactor core. The conclusion is that both the 9-channel geometry and the boundary source methods accurately determine the energy deposition profile in a fuel channel for neutrons and gamma rays.

5. DIRECTION OF FUTURE WORK The next step in the determination of energy deposition in fuel channels is to perform calculations to determine the electron energy deposition profile in all the coolant regions. A comparative study will be performed between MCNP and SANDYL. Upon completion of this task, current MCNP input data sets will be expanded to include determination of energy deposition profiles in other materials and components in the core. Simulations of the 28-element fuel bundle will be performed so that operating plants like Pickering can be included in the calculations. Complete energy deposition calculations will be done for Pickering, Bruce, CANDU-6 and CANDU-3 power reactors. Two sets of calculations are envisaged. The first is the current model, where the fuel bundle is centred in the channel, and the second will be a model with the fuel bundle resting on the bottom of the pressure tube, as in the real world. Two- and three-dimensional calculations of both the channel inlet and outlet ends will need to be considered. It is also necessary to include the impact of two-phase flow in fuel channels containing boiling coolant. The subroutine GAMSRC, used to generate the spatial and energy distribution of the gamma source for input into the ANISN and MCNP codes, is to be updated to include a wider selection of fission products as well as non-elastic scattering events. Further improvements are the inclusion of tin and niobium, elements found in the calandria tube, the fuel sheath, and pressure tube: Zircaloy-2 and Zircaloy-4 contain 1.20-1.70 weight % tin, and the pressure tube contains 2.4-2.S weight % niobium. The importance of other impurities found in the cladding, calandria tube and pressure tube, such as silicon and manganese, will also be assessed for inclusion in the data sets. The inclusion of 241Pu is required for more accurate calculations at high bumups. These modifications will provide a tmer representation of the materials, and the consequent neutron, gamma, and electron interactions. Where applicable, modifications of the materials' libraries will be based upon WIMS calculations of material compositions for various reactor powers and bumups. - 10 -

6. ACKNOWLEDGEMENTS

Thanks are due to Charles Boss of AECL CANDU and Esam Hussein of the University of New Brunswick for numerous helpful discussions. This work was funded by CANDU Owners Group Technical Committee 15.

7. REFERENCES

1. Boss, C.R., and McCracken, D.R., "Neutron and Photon Energy Deposition in Water- Cooled Reactors and Consequences for Coolant Chemistry", AECL, Report, AECL-10190, 1991 May.

2. ANISN, Multigroup One-Dimensional Discrete Ordinates Transport Code System with Anisotropic Scattering, Users Manual, Radiation and Shielding Information Center (RSIC), K-1693, Oak Ridge National Laboratory, Oak Ridge, Tennessee, 1967.

3. Boss, C.R., "Nuclear Energy Deposition in the 37 Element Lattice Cell of a CANDU Reactor", Atomic Energy of Canada Limited, Engineering Company, Report TDAI-168, 1979 May.

4. Boss, C.R., "A Two Dimensional Discrete Ordinates Analysis of the Darlington NGS 'A' End Shield", Atomic Energy of Canada Limited, Engineering Company, Report TDAI-247, 1982 July.

5. Colbert, H.M., "SANDYL-A Computer Program for Calculating Combined Photon-Electron Transport in Complex Systems", Sandia Laboratories Report SLL-74-0012, 1974 May. 6. Abdelbaky, M.E.A., Hussein, E.M.A., McCracken, D.R., "Photon-Electron Transport in CANDU Reactor Channels", presented at the CNS Conference in Montreal, 1994 June, AECL Report AECL-11093, 1994. 7. McCracken, D.R., Abdelbaky, M.E.A. and Hussein, E.M.A., "Photon and Electron Energy Deposition in CANDU Reactor Fuel Channels: A Study Using SANDYL and EGS4", AECL Report, AECL-11178, COG-94-461, 1994. 8. Monte Carlo Neutron and Photon Transport Code, Users Manual CCC-200, Radiation and Shielding Information Center (RSIC), Oak Ridge National Laboratory, Oak Ridge, Tennessee, 1992. 9. Askew, J.R., Foyes, F.J. and Kemshell, P.B., "A General Description of the Lattice Code WIMS", J. of the B.N.E.S., 4(4), 564, 1966. -11 -

Table 1: Energy structure of the 39-group coupled neutron-gamma cross section library.

Grouo: Unner Energy Limit Grouo: Gammas Uooer Energy Limit 1 14.92 MeV 28 10.0 MeV 2 12.21 MeV 29 7.0 MeV

3 11.05 MeV 30 5.0 MeV

4 6.07 MeV 31 4.0 MeV

5 3.68 MeV 32 3.0 MeV

6 2.23 MeV 33 2.0 MeV

7 1.35 MeV 34 1.5 MeV

8 821.0 keV 35 1.0 MeV

9 498.0 keV 36 0.622 MeV

10 302.0 keV 37 0.4 MeV

11 183.0 keV 38 0.2 MeV

12 76.4 keV 39 0.12 MeV

13 40.9 keV (0.01 MeV lower

14 24.8 keV limit)

15 15.0 keV

16 5.53 keV

17 2.03 keV

18 749.0 eV

19 275.0 eV

20 101.0 eV

21 47.9 eV

22 22.6 eV

23 10.7 eV

24 3.93 eV

25 1.45 eV

26 0.683 eV

27 0.414 eV - 12 -

Table 2: Materials found in the 39-group cross section library.

Deuterium Boron-10 Boron-11 Carbon Oxygen Aluminum Silicon Chromium Manganese Iron Nickel Zirconium Xenon Gadolinium Lead Uranium-235 Uranium-238 Plutonium-239 Table 3: Dimensions and regions used in the ANISN 37-element lattice site.

Region Description Inner Radius (mm) Outer Radius (mm) Material for ANISN

1 Central Fuel Pin 0.0 6.075 Fuel 1

2 Fuel Sheath 6.075 6.540 Zircaloy 4

3 Coolant 6.540 10.594 Coolant

4 Fuel Sheath 10.594 11.185 Zircaloy 4

5 Inner Fuel Annulus 11.185 18.165 Fuel 2

6 Fuel Sheath 18.615 19.206 Zircaloy 4

7 Coolant 19.206 24.287 Coolant

8 Fuel Sheath 24.287 24.899 Zircaloy 4

9 Intermediate Fuel Annulus 24.889 32.601 Fuel 3

10 Fuel Sheath 32.601 33.213 Zircaloy 4

11 Coolant 33.213 38.855 Coolant

12 Fuel Sheath 38.855 39.464 Zircaloy 4

13 Outer Fuel Annulus 39.464 47.136 Fuel 4

14 Fuel Sheath 47.136 47.745 Zircaloy 4

15 Coolant 47.745 51.689 Coolant

16 Pressure Tube 51.689 56.210 Zr-2.5Nb

17 Gas Annulus 56.210 64.478 Carbon Dioxide

18 Calandria Tube 64.478 66.002 Zircaloy 2

19 Moderator 66.002 161.22 Moderator - 14 -

Table 4A: Compositions of materials for the fuel regions, used in ANISN calculations. The data are based on WIMS calculations for a 37-element lattice at a bumup of approximately 3300 MW.d/MgU.

Atom concentration (xlO24) in materials (atoms/cm3) Elements or Isotopes Fuel 1 Fuel 2 Fuel 3 Fuel 4 Oxygen-16 4.62E-02 4.62E-02 4.62E-02 4.62E-02 Xenon (pseudo fission product) 2.03E-09 2.92E-09 2.91E-09 2.97E-09 Uranium-235 1.13E-04 1.11E-04 1.04E-04 9.24E-05 Uranium-238 2.28E-02 2.28E-02 2.28E-02 2.28E-02 Plutonium-239 3.52E-05 3.60E-05 3.79E-05 4.39E-05

Table 4B: Composition of materials used in ANISN calculations for the fuel channel region. The data are based on WIMS calculations for a 37-element lattice at a bumup of approximately 3300 MW.d/MgU.

Atom concentrations (xlO24) in materials (atoms/cm3)

Elements Zircaloy 4 Coolant Zr-2.5Nb Carbon Zircaloy 2 Moderator Dioxide Hydrogen 1.34E-04 1.08E-04 Deuterium 4.8350E-02 6.50E-02 Boron-10 2.14E-07 1.53E-07 2.22E-07 Boron-11 8.52E-07 6.14E-07 8.88E-07 Carbon 2.83E-05 Oxygen-16 2.42E-02 5.66E-05 3.25E-02 Chromium 7.93E-05 8.20E-05 Iron 1.07E-04 1.11E-04 Nickel 3.83E-05 3.96E-05 Zirconium 4.09E-02 4.33E-02 4.23E-02 - 15 -

Table 5: Neutron fission spectrum for the centre pin based on a fission rate of 7.03x1012 fissions/cm3.s.

Neutron Group Upper Energy Limit (MeV) Neutrons (cm"3.s) 1 14.92 1.18xl09 2 12.21 2.08xl09 3 11.05 1.64x10“ 4 6.07 7.68x10“ 5 3.68 1.48xl012 6 2.23 1.62xl012 7 1.35 1.26xl012 8 0.821 8.05x10“ 9 0.498 4.54x10“ 10 0.302 2.39x10“ 11 0.183 1.79x10“ 12 0.0674 2.86xl010 13 0.0409 1.37xl0m 14 0.0248 6.53xl09 15 - 27 0.01 - 4.14xl0"7 0.00 - 16 -

Table 6A: Energy deposition in the outer coolant region for ANISN calculations using annular geometry. Neutrons were generated by SOURCE. Photons were generated internally by ANISN.

Energy deposition [MeV/g.s] x 1012 Radiation Mesh 1 Mesh 2 Mesh 3 Mesh 4 Mesh 5 Boundary Condition Neutron 6.97 6.77 6.61 6.49 6.40 No Reflection Photon 0.50 0.49 0.49 0.48 0.48 No Reflection Neutron 7.31 7.11 6.97 6.85 6.77 Black Reflection Photon 4.64 4.58 4.54 4.52 4.50 Black Reflection Neutron 7.20 7.00 6.85 6.74 6.65 White Reflection Photon 4.31 4.25 4.21 4.18 4.16 White Reflection

Fuel Sheath Boundary Pressure Tube Boundary

Table 6B: Energy deposition in the outer coolant region for ANISN calculations using annular geometry. Neutrons were generated by SOURCE. Photons were generated internally by ANISN.

Energy Deposition [mW/g] Radiation Mesh 1 Mesh 2 Mesh 3 Mesh 4 Mesh 5 Boundary Condition Neutron 1162 1084 1059 1040 1026 No Reflection Photon 80.68 78.99 77.86 77.13 76.74 No Reflection Neutron 1171 1140 1116 1098 1084 Black Reflection Photon 744 734 728 723 721 Black Reflection Neutron 1154 1122 1098 1080 1066 White Reflection Photon 691 681 674 670 667 White Reflection Fuel Sheath Boundary Pressure Tube Boundary Table 7A: Photon source strength (photons/s) and spatial distribution as calculated by GAMSRC.

Photon Centre Pin Centre Coolant Inner Inner Fuel Inner Coolant Intermediate Intermediate Intermediate Energy Sheath Sheath Sheath Sheath Fuel Sheath Group

1 1.56xl010 2.01X10 09 - 4.57X1009 9.79x10'°7.94X1009 - 1.18x10'” 2.20x10" 1.58x10'°

2 2.72x10" 6.14x10'° 7.17X1009 1.40x10" 1.71xl012 2.43x10" 2.57x10'° 3.60x10" 3.85xl012 4.82x10"

3 1.17xl012 3.52x10'° - 8.02x10'° 7.38xl012 1.39x10" - 2.07x10" 1.66xl013 2.76x10"

4 3.00xl012 5.74x10'° 2.38x10°" 1.31x10" 1.89xl0'3 2.27x10" 8.52x10°" 3.37x10" 4.26xl0'3 4.51x10"

5 9.91xl012 9.36x10'° 3.47x10°" 2.13x10" 6.21xl013 3.70x10" 1.24x10” 5.49x10" 1.39xl014 7.34x10"

6 1.45xl013 5.46x10'° 1.77x10°" 1.24x10" 9.06xl0'3 2.16x10" 6.33x10°" 3.20x10" 2.02xl014 4.29x10"

7 2.68xl013 1.01x10" 3.26x10°" 2.29x10" 1.68xl014 3.98x10" 1.17x10” 5.90x10" 3.73xl014 7.89x10" 17

8 3.59xl013 8.30x10'° 1.07x1009 1.89x10" 2.25xl014 3.28x10" 3.85x10” 4.87x10" 5.03xl0'4 6.51x10" -

9 3.63xl013 4.62x10'° - 1.05x10" 2.27x1 O'4 1.83x10" - 2.71x10" 5.08xl014 3.62x10"

10 4.29xl013 4.02x10'° 1.66x1009 9.15x10'° 2.68xl014 1.59x10" 5.96x10” 2.36x10" 5.98xl014 3.15x10"

11 5.83xl012 3.14X10 09 1.64x10°" 7.15X1009 3.65xl013 1.24x10'° 5.88x10°" 1.84x10'° 8.17xl013 2.46x10'°

12 4.37xl012 - - - 2.74xl0'3 - - - 6.14xl0'3 - - indicates insignificant source strengths - 18 -

Table 7B: Photon source strength (photons/s) and spatial distribution as calculated by GAMSRC.

Photon Coolant Outer Outer Fuel Outer Coolant Pressure Calandria Moderator Energy Sheath Sheath Tube Tube Group

1 - 2.24x10'° 4.16x10" 2.72x10'° - 3.21x10" 1.29x10" -

2 6.38xl012 6.85x10" 7.34xl012 8.31x10" 9.34x10" 9.82x10° 3.96x10° 9.38x10°

3 - 3.93x10" 3.18x10° 4.77x10" - 5.63xl012 2.27x10° -

4 2.11x10" 6.42x10" 8.21x10° 7.77x10" 3.10x10'° 9.19xl0'2 3.70x10° 3.11x10"

5 3.09x10" 1.05xl012 2.65xl014 1.27xl012 4.52x10'° 1.50x10° 6.03x10° 4.54x10"

6 1.57x10" 6.10x10" 3.79xl014 7.39x10" 2.30x10'° 8.74xl0'2 3.52x10° 2.31x10"

7 2.91x10" 1.12xl012 6.97xl014 1.36xl0'2 4.25x10'° 1.61x10° 6.48x10° 4.27x10"

8 9.54x10" 9.27x10" 9.44xl0‘4 1.12xl012 1.40x10" 1.33x10° 5.35x10° 1.40x10°

9 - 5.16x10" 9.56xl014 6.25x10" - 7.39xl0‘2 2.98x10° -

10 1.48x1012 4.49x10" 1.13x10° 5.44x10" 2.17x10" 6.43xl0'2 2.59x10° 2.17x10°

11 1.46x10" 3.51x10'° 1.54xl0'4 4.25x10'° 2.13x10'° 5.02x10" 2.02x10" 2.14x10"

12 - - 1.15xl014 - - - - -

- indicates insignificant source strength - 19 -

Table 8A: Energy deposition in the outer coolant region for ANISN calculations using annular geometry. The photon source was generated by GAMSRC. The units are MeV/g.s x 1012. The same data, but in mW/g, are listed in Table 8B.

Energy Deposition [MeV/g.s] x 1012 Radiation Mesh 1 Mesh 2 Mesh 3 Mesh 4 Mesh 5 Boundary Condition Photon 3.67 3.52 3.41 3.32 3.24 No Reflection Photon 4.57 4.44 4.33 4.24 4.16 Black Reflection Photon 4.27 4.13 4.03 3.94 3.86 White Reflection Fuel Sheath Boundary Pressure Tube Boundary

Table 8B: Energy deposition in the outer coolant region for ANISN calculations using annular geometry. The source was generated by GAMSRC. The units are mW/g. The same data, but in MeV/g.s, are listed in Table 8A.

Energy Deposition [mW/g] Radiation Mesh 1 Mesh 2 Mesh 3 Mesh 4 Mesh 5 Boundary Condition Photon 588 565 547 532 520 No Reflection Photon 733 712 694 680 667 Black Reflection Photon 684 663 646 631 619 White Reflection Fuel Sheath Boundary Pressure Tube Boundary - 20 -

Table 9A: Ratio of ANISN to MCNP results in percent, for neutron energy deposition. (See Figure 7.)

Coolant Mesh Point No Reflection Reflection 4.77 94.3 94.0 4.85 94.8 94.2 4.93 94.9 94.4 5.01 95.3 94.8 5.09 95.7 95.1

Table 9B: Ratio of ANISN to MCNP results in percent, for photon energy deposition. (See Figure 8.)

Coolant Mesh Point No Reflection Reflection 4.77 99.1 98.3 4.85 99.2 98.7 4.93 99.7 98.8 5.01 99.4 99.0 5.09 99.8 98.9 - 21 -

Table 10: Dimensions and regions used for the eight outer channels in the "square cylinder" approximation of Figure 9.

Region Description Inner Length (mm) Outer Length (mm) Material 20 Moderator 161.22 307.33 Heavy Water 21 Calandria Tube 307.33 307.35 Zircaloy 2 22 Annulus Gas 307.35 308.04 Carbon Dioxide 23 Pressure Tube 308.04 308.15 Zr-2.5Nb 24 Coolant 308.15 314.71 Coolant 25 Fuel Sheath 314.71 315.79 Zircaloy 4 26 Fuel 315.79 329.09 Fuel 4 27 Fuel Sheath 329.09 330.13 Zircaloy 4 28 Coolant 330.13 336.26 Coolant 29 Pressure Tube 336.26 336.35 Zr-2.5Nb 30 Annulus Gas 336.35 336.99 Carbon Dioxide 31 Calandria Tube 336.99 337.00 Zircaloy 2 32 Moderator 337.00 376.90 Moderator - 22 -

Table 11: Photon source flux at the outer boundary of the problem, in the moderator, half a lattice pitch between the central channel and the surrounding fuel. The data are for a bundle operating at 611 kW.

Gamma Group Energy (MeV) Flux at the Boundary (photons/s) upper limit 10.0 5.24xlOn 7.0 2.46xl013 5.0 1.90xl013 4.0 4.44x1013 3.0 1.27xl014 2.0 l.SlxlO14 1.5 2.65xl014 1.0 3.25xl014 0.622 3.12xl014 0.4 3.90xl014 0.2 2.03xl014 0.12 2.24x1014 - 23 -

Table 12: Properties and attributes of different codes used for calculations of energy deposition.

CODE ANISN SANDYL MCNP

Method of solution Discrete Ordinates Monte Carlo Monte Carlo

Spatial Dimensions 2 3 3

Symetric in 2nd Symetric in 3rd True 3D code dimension dimension

Particle Transport* neutron photon neutron photon electron photon neutron-photon photon-electron electron neutron-photon photon-electron neutron-photon- electron

Cross-Section 27-group neutron 64-group electron continuous Groups 12-group photon

Model Employed Annular 18-element/annular Annular 18-element/annular 37-element

* All photon calculations are for prompt fission gammas only: the program GAMSRC must be used to generate delayed fission gammas and fissio- product gammas. - 24 -

of a CANDU fuel channel. Figure 1: Annular representation Figure Neutron Population in 1012 /cm3 .s 1

. 2: 8

— ^ Neutron 7.0368E12

fission fissions/cm

spectrum 3 .s.

Neutron for

the -

centre

Energy -

Group based

central-pin

fission

rate

- 26 -

—Black Reflection - -A - White Reflection

2 4————j------1------!------1------1------h—------1 4.75 4.8 4.85 4.9 4.95 5 5.05 5.1 Distance From Channel Centre in cm.

Figure 3: ANISN calculation of the neutron energy deposition in the outer coolant region between the fuel and pressure tube. - 27 -

—a—No Reflection 7 — ♦- Black Reflection

- -a - White Reflection

▲ - - * A A A 4

0 4 4.8 4.85 4.9 4.95 5 5.05 5.1 Distance From Channel Centre in cm.

calculation of the gamma energy deposition in the outer coolant region. Figure

Photon GAMSRC. Photons/second 1.20E+15 8.00E+14 I.00E+I5 6.00E+14 4.00E+14 2.00E+14 0.00E+00

energy Photon

and

Energy

spatial Group 6

distribution g 9

10 - 11

for -

Centre a

Centre 611 Coolant

Pin Inner

kW Sheath Inner Inner

Sheath Coolant

Fuel bundle

Intermediate

Sheath Intermediate

Intermediate

Coolant

Outer

Outer power „ oMath

Sheath „

Sheath

Fuel PressureTubePressure

Fuel

Sheath —

andm%be

calculated

- 29 -

—■— No Reflection — ♦— Black Reflection 6 - -A - White Reflection

00 >

5 •ou o uo. Q >, uEP ttic 4 - A - - A

2 -I------1------1------1------1------1------1------1 4.75 4.8 4.85 4.9 4.95 5 5.05 5.1

Distance From Channel Centre in cm.

Figure 6: ANISN calculation of the gamma energy deposition in the annular geometry outer coolant region: source particles generated by GAMSRC. - 30 -

CA J& 6 -

TN”t e<

*«4) "So «a e >» DO 4>fc. —s— ANISN: No Reflection e 4 6=3 4 ANISN:Black Reflection —□— MCNP No Reflection

3 — o- MCNP Reflection

2 1 —■—I------1------!------1------1------1 ■ I 4.75 4.8 4.85 4.9 4.95 5 5.05 5.1 Distance From Channel Centre in cm.

Figure 7: A comparison of neutron energy deposition in the outer coolant region for ANISN and MCNP with annular geometry. - 31 -

vi 6 do

—a—ANISN: No Reflection — ■♦ — ANISN: Black Reflection 1 5 ANISN: White Reflection —o— MCNP N o Reflection *5o a> — •o— MCNP Reflection Q UDC a ... ^ -~=S ==--. eV 65 4

3 -

2 -1------1------1------1------1 4.7 4.8 4.9 5 5.1 Distance From Channel Centre in cm.

Figure 8: A comparison of gamma energy deposition in the outer coolant region for ANISN and MCNP with annular geometry. - 32 -

Figure 9: A schematic representation of the transition from a square lattice to a "smeared" lattice geometry. - 33 -

8 o-

~ o — o — o

„0|D"2 6

2 H------1------1------!------1------1------1------1 4.75 4.8 4.85 4.9 4.95 5 5.05 5.1 Distance From Channel Centre in cm.

Figure 10: MCNP calculations of neutron energy deposition for the reflective, non-reflective and 9-channel geometry cases. - 34 -

8 Gamma deposition

——D— MCNP No Reflection

— O— MCNP Reflection — O - MCNP 9-Channels

2 4---- 1 —I------1------1------h —I------1 4.75 4.8 4.85 4.9 4.95 5 5.05 5.1

Distance From Channel Centre in cm.

Figure 11: MCNP calculations of gamma energy deposition for the reflective, non-reflective and 9-channel geometiy cases. - 35 -

—D—MCNP No Reflection

— o— MCNP Reflection

— o MCNP 9-Channels

— x — MCNP Boundary S» 6 - -2? Source

3 -

2 -1------1------i------1------1------1------1------1 4.75 4.8 4.85 4.9 4.95 5 5.05 5.1 Distance From Channel Centre in cm.

Figure 12: MCNP calculations of gamma energy deposition for the reflective, non-reflective, 9- channel geometry and boundary source calculations. - 36 -

Central Fuel

Figure 13: 18-element/annular representation of the CANDU reactor fuel channel. - 37 -

te 6 -Sf O) "™H—ANISN: No Reflection

ANISN: Black Reflection - - A - ANISN: White Reflection —c— MCNP No Reflection ea> H 4 — o- MCNP Reflection

2 -|------1------1------1------1------1------1------1------1 4.75 4.8 4.85 4.9 4.95 5 5.05 5.1 5.15 Distance From Channel Centre in cm.

Figure 14: A comparison of neutron energy deposition for MCNP calculations with 18-element annular geometry and annular ANISN results. For the same annular geometiy, ANISN and MCNP agreed within 6% (see Table 9A and Figure 7). - 38 -

8 Gamma deposition: 18-element/annular geometry

7 -ANISN: No Reflection

& 5 0— — o ♦ 65 6Q 4 - -A - - - -A

2 ^------1------1------1------1------1------1------1------1 4.75 4.8 4.85 4.9 4.95 5 5.05 5.1 5.15 Distance From Channel Centre in cm. Figure 15: A comparison of gamma energy deposition for MCNP calculations with 18-element/annular geometry and annular ANISN geometry. For the same annular geometry, MCNP and ANISN gave virtually identical results (see Table 9B and Figure 8). - 39 -

—d — MCNP No Reflection

7 -o- MCNP Reflection

— o MCNP 9-Channels

— x — MCNP Boundary Source

”S 5

8= : i ------X------— . * D--- — —------D——------——------□

2 -I------1------1------1------1------1------1------1 4.98 5 5.02 5.04 5.06 5.08 5.1 5.12 Distance From Channel Centre in cm. Figure 16: MCNP calculations of gamma energy deposition for the reflective, non-reflective, 9- channel geometry and boundary source calculations for the 18-element/annular geometry. - 40 -

H! fuel !§§ Zircaloy gj coolant □ gas □ moderator

Figure 17: A 37 -element representation of a CANDU fuel channel. - 41 -

Neutron deposition: 37-element MCNP

7 -

U 6

o> § r*

1 5 - *5 o «a O —B— ANISN No Reflection DO —ANISN Reflection L. c4) , —□—MCNP No Reflection Eti 4 —o— MCNP Reflection

3 -

2 A------1------1------1------1------1------—H------1------1 4.75 4.8 4.85 4.9 4.95 5 5.05 5.1 5.15 Distance From Channel Centre in cm.

Figure 18: A comparison of neutron energy deposition between calculations done by MCNP using 37-element geometry and ANISN using annular geometry. - 42 -

Gamma deposition: 37-element MCNP

7 -

-S—ANISN: No Reflection ■ ♦— ANISN: Black Reflection 6 - - A - ANISN: White Reflection V3 CUD -D-—MCNP No Reflection > ■ O— MCNP Reflection

5 -

4>g, Q >-> uee — o- ea) ~ o M ♦

2 ------1------1------1------1------1------1--- —---- H------1 4.75 4.8 4.85 4.9 4.95 5 5.05 5.1 5.15

Distance From Channel Centre in cm.

Figure 19: A comparison of gamma energy deposition calculations between MCNP using 37-element geometry and ANISN using annular geometry. - 43 -

Gamma deposition: different models using MCNP

——Q— MCNP No Reflection — O— MCNP Reflection — O - MCNP 9-Channels — X — MCNP Boundary Source

6 -- w til >e

■oe wo a>a Q gi>. a> mc 4 --

=8 —a------—------a— ------

2 -I------1------1------1------1------1------1------1 4.98 5 5.02 5.04 5.06 5.08 5.1 5.12 Distance From Channel Centre in cm.

Figure 20: MCNP calculation of gamma energy deposition for the reflective, non-reflective, 9-channel geometry and boundary source calculations for the 37 -element geometry. Cat. No. /No de cat.: CC2-11160E ISBN 0-660-16266-0 ISSN 0067-0367 To identify individual documents in the series, we have assigned an AECL- number to each. Please refer to the AECL- number when requesting additional copies of this document from: Scientific Document Distribution Office (SDDO) AECL Chalk River, Ontario Canada K0J 1J0 Fax:(613)584-1745 Tel.: (613) 584-3311 ext 4623 Price: B Pour identifier les rapports individuels faisant partie de cette serie, nous avons affects un numSro AECL- & chacun d ’eux. Veuillez indiquer le numSro AECL- lorsque vous demandez d ’autres exemplaires de ce rapport au: Service de Distribution des Documents Officiels EACL Chalk River (Ontario) Canada K0J 1J0 Fax: (613) 584-1745 TSL: (613) 584-3311 poste 4623 Prix: B