**RSICC CODE PACKAGE CCC-745**

** **

**1. NAME AND TITLE**

**ERANOS 2.0:**
Modular Code and Data System for Fast Reactor Neutronics Analyses.

**RESTRICTIONS**: Users from NEADB member countries http://www.nea.fr/html/nea/mcdb.html
are advised to order ERANOS from the NEA Data Bank. Users from other OECD
member countries http://www.nea.fr/html/nea/flyeren.html
(specifically Canada and the United States) may order these codes
from RSICC. Users from non-OECD member countries are advised to contact the NEA
Data Bank; the NEADB will transmit the requests to CEA, who will deal directly
with these requests. For non-comercial use only

**2. CONTRIBUTORS**

DER/SPRC/LEPh, CEA-Cadarache, France, through the OECD Nuclear Energy Agency Data Bank, Issy-les-Moulineaux, France.

**3. CODING LANGUAGE AND
COMPUTER**

C and FORTRAN-77; Linux-based PC (C00745MNYWS00).

NEA Package ID: NEA-1683/01.

**4. NATURE OF PROBLEM
SOLVED**

The European Reactor ANalysis Optimized calculation System, ERANOS, has been developed and validated with the aim of providing a suitable basis for reliable neutronic calculations of current as well as advanced fast reactor cores. It consists of data libraries, deterministic codes and calculation procedures which have been developed within the European Collaboration on Fast Reactors over the past 20 years or so, in order to answer the needs of both industrial and R&D organisations. The whole system counts roughly 250 functions and 3000 subroutines totalling 450000 lines of FORTRAN-77 and ESOPE instructions.

ERANOS is written using the ALOS software which requires only standard FORTRAN compilers and includes advanced programming features. A modular structure was adopted for easier evolution and incorporation of new functionalities. Blocks of data (SETs) can be created or used by the modules themselves or by the user via the LU control language. Programming, and dynamic memory allocation, are performed by means of the ESOPE language. External temporary storage and permanent storage capabilities are provided by the GEMAT and ARCHIVE functions, respectively. ESOPE, LU, GEMAT and ARCHIVE are all part of the ALOS software. This modular structure allows different modules to be linked together in procedures corresponding to recommended calculation routes ranging from fast-running and moderately-accurate 'routine' procedures to slow-running but highly-accurate 'reference' procedures.

The main contents of the ERANOS-2.0 package are: nuclear data libraries (multigroup cross-sections from the JEF-2.2 evaluated nuclear data file, and other specific data files), a cell and lattice code (ECCO), reactor flux solvers (diffusion, Sn transport, nodal variational transport), a burn-up module, various processing modules (material and neutron balance, breeding gains,...), tools related to perturbation theory and sensitivity analysis, core follow-up modules (connected in the PROJERIX procedures), a fine burn-up analysis subset named MECCYCO (mass balances, activities, decay heat, dose rates). Coupled neutron/gamma calculations are also possible using specific libraries.

**Nuclear data libraries: **

The ECCO/ERANOS 2.0 code package contains four neutron cross section libraries derived from the JEF-2.2 nuclear data evaluated files. They are:

- 1968-group library (41 main nuclides)

- 33-group library (246 nuclides, including pseudo fission products)

- 175-group library (VITAMIN-J energy group scheme)

- 172-group library (XMAS energy group scheme, 246 nuclides, including pseudo-FP).

These libraries were obtained by processing the JEF-2.2 files with the NJOY and CALENDF codes. Probability tables are included for the main 37 resonant nuclides. The 172-group library (XMAS energy scheme) may be used for thermal spectrum calculations. The 175-group library (some cross-sections in P5, but no probability tables) is used for shielding calculations only.

Other nuclear data (fission yields and energies, decay constants, gamma production and interaction libraries, etc.) are provided in separate files.

**Cell/lattice calculations:**

The ECCO cell/lattice code in the ERANOS-2.0 package uses the subgroup method to treat resonance self-shielding effects. This method is particularly suitable for calculations involving complex heterogeneous structures. ECCO prepares self-shielded cross sections and matrices by combining a slowing-down treatment in many groups (1968 groups) with the subgroup method within each fine group. The subgroup method takes into account the resonance structure of cross-sections by means of probability tables and by assuming that the neutron source is uniform in lethargy within a given fine group. Flux calculations in heterogeneous geometry are performed by means of the collision probability method.

In the reference calculation scheme, ECCO treats the heterogeneous geometry in fine groups (1968) for the most important nuclides while broad group libraries (33 or 172 groups) are used for the less important nuclides. These calculations are very accurate as the fine group plus sub-group scheme have been set up to represent accurately the reaction thresholds and the resonances in any situation, narrow or wide. One usually distinguishes wide and narrow resonances depending on their width compared to the neutron energy loss by scattering, which is smallest for scattering by heavy nuclides. Translated into lethargy gain, the value for U238 is almost constant and is equal to 0.008. This compares well with the fine group width of 1/120 = 0.0083 and explains the fact that 3/4 of the neutrons having a collision in a given fine group escape from that group. Wide resonances are treated explicitly, the resonances in that case having a width larger than the fine group width. On the other hand, narrow resonances are represented by probability tables, and hence use of the subgroup method can be applied in a very accurate way.

Self-shielded cross sections and matrices are condensed and smeared to provide effective cross sections and matrices in the user required broad group scheme. The neutron balance is preserved in ECCO after condensation and smearing. The effective cross-sections and matrices produced by ECCO are subsequently used in full-core ERANOS calculations.

Many types of geometries are available within the ECCO code: 1D (plane or cylindrical: exact collision probabilities), 2D (rectangular lattice of cylindrical and/or square pins within a square tube, hexagonal lattice of cylindrical pins within an hexagonal wrapper: approximate collision probabilities by Roth and double step methods), 3-D (slab with the sides of the boxes and the tube described explicitly: approximate collision probabilities).

The user can chain several calculation steps so as to produce design (less accurate, faster) or reference (more accurate, slower) calculations, or even to use specific capabilities, according to the needs of a given study.

**Flux solvers:**

Three main classes of flux solvers are available. In each case, external sources, up-scattering and adjoint calculations can be addressed. Anisotropic scattering is available for transport calculations.

Finite difference diffusion solvers can be used in any geometry: 1D (plane, cylindrical, spherical), 2D (RZ, R-theta, rectangular lattice XY, hexagonal lattice), and 3D (rectangular lattice XYZ, hexagonal-Z). An efficient solution of the diffusion equation is obtained by using either the successive line over-relaxation method (SLOR), the alternating direction implicit method (ADI) or the strongly implicit method (SIM).

Finite difference Sn transport calculations are performed by the BISTRO code, using a highly efficient convergence algorithm. It can be used in 1D geometry (plane, cylindrical, spherical) and some 2D geometries (RZ, XY). Different algorithms (step, diamond and "theta-weighted") and a negative flux fix-up capability exist. The inner iterations are accelerated by the DSA method using the source correction scheme.

In this package distributed by OECD and RSICC, the version of the variational nodal method developed for the VARIANT code has been used in ERANOS-2.0 as the TGV/VARIANT module. This method is based on the second-order form of the even-parity transport equation. A solution is searched in form of expansions for the even and odd parity fluxes in pre-computed angular and spatial basis functions with unknown coefficients. These basis functions are orthogonal polynomials for the spatial variables and spherical harmonics for the angular variables. Scattering anisotropy can be taken in to account as Pn moments up to the order N of the Legendre expansion of the flux. Both Cartesian (XY or XYZ) and hexagonal (Hex or Hex-Z) geometries are available with TGV/VARIANT. A 'simplified transport' option exists, in which the angular developments both within the nodes and at the node boundaries are truncated by neglecting high-order cross terms. This option is rather accurate in practice (large reactors), and less time and memory consuming.

**Burn-up calculations:**

Calculation of isotopic concentration evolution is possible in the ERANOS system for actinides as well as fission and activation products. The Bateman equations governing the time dependence of concentrations are solved with various techniques related to the type of nuclide (actinide, fission product or activation product). Burn-up can be performed at the full core scale, with suitable 'burnable zones' subdividing the fuel and fertile regions, or in elementary cells/lattices.

**Result-processing modules.**

Besides the modules related to basic data preparation (creation of medium, geometry, and burn-up chain SETs, modelling of operating conditions, etc.), a variety of modules computes and/or extracts specific information from the code output (fluxes, concentrations, etc.). Here is a non-exhaustive sample of such modules:

- Traverse extraction and processing

- Mass and atom balances by region

- Neutron balance by region, reaction and energy group

- Integrated reaction rate processing

- Equivalence coefficients and Breeding gain

- Beta effective

- Linear and bilinear integrals (with respect to the forward and possibly adjoint fluxes)

**Perturbation theory and sensitivity analysis.**

The reactor physicist is often interested in the breakdown of the variation (or of the first order derivative) of integral parameters such as the multiplication factor, reaction rates and more generally ratios of bilinear integrals, nuclide concentrations, reactivity coefficients, etc., with respect to input data such as multigroup cross-sections, decay constants, or initial concentrations. This can be readily obtained through the use of adjoint (standard or generalized) flux calculations and the computation of suitable bilinear integrals. Several modules of ERANOS are available for a modular processing of such problems: calculation of perturbation integrals, of cross-section variations, sensitivity analysis, perturbation analysis.

As a matter of fact, sensitivity analyses, and first-order or exact perturbation analyses can be performed for the multiplication factor (standard perturbation theory, SPT), ratios of linear or bilinear integrals (generalized perturbation theory, GPT), and reactivity effects (equivalent generalized perturbation theory, EGPT). If a dispersion (variance/covariance) matrix is provided, a specific module can be used to perform uncertainty and representativeness calculations.

**Core follow-up:**

Specific ERANOS modules and appropriate complex subroutines written in the LU user's language (the PROJERIX package) are available to perform a detailed core follow-up. Each individual sub-assembly can be followed through its entire life (moves during shuffles and batch reloadings, time spent in internal storage, etc.).

**Fine burn-up**:

For sub-assemblies burnt in significant flux gradients (e.g. fertile sub-assemblies) a detailed burn-up capability is available through specific ERANOS modules.

**Other topics**:

Several other features are available:

- Coupled neutron/gamma Sn transport calculations (with specific libraries)

- Detailed treatment of damage and kerma (with specific libraries)

- Detailed burn-up with computation of decay (alpha, beta, gamma and neutron particles) activities, energies, energy spectra of emitted particles, dose rates (for simple geometries), decay heat (the MECCYCO package, with specific libraries).

**5. METHOD OF SOLUTION**

Methods used in ERANOS modules have been mentioned briefly above. The user can feed and connect these modules in a variety of ways to produce specific analytic sequences. Conditional chaining (IF, FOR, WHILE instructions) is possible with the user's language. This allows a great deal of flexibility in the use of the code system.

**6. RESTRICTIONS OR
LIMITATIONS**

None noted.

**7. TYPICAL RUNNING TIME**

Not noted.

**8. COMPUTER HARDWARE
REQUIREMENTS**

ERANOS 2.0 sources and installation procedures are provided for SUN, IBM_RISC, and for PC under linux architectures.

To install the whole ERANOS package, 1600 Mb are required for installing the cross-section libraries JECCOLIB2, 700 Mb for installing the code, and 60 Mb for the code documentation (html and PDF files).

At least 128 Megabytes of Random Access Memory (RAM) are needed to compile the code and run the test cases.

**9. COMPUTER SOFTWARE
REQUIREMENTS**

This program is distributed by the NEA Data Bank and by RSICC as received from the authors. At the CEA, the installation was tested with the following characteristics on a linux system and may fail on other systems:

- REDHAT 7.0

- Kernel 2.2.19

- Gcc 2.96

- Lib_c 2.2-5

The programming language is ESOPE, an extension of FORTRAN 77 specific to CEA, and treated by a built-in pre-compiler. The main objective of this extension is to make the management of the data used by the various subroutines easier. The data structuration is made by using new entities called SEGMENTs. A segment is a collection of simple variables and/or arrays, addressed by a POINTER. Segments can be connected with each other by pointers in such a way as to produce tree-like or graph-like structures. The basic data structures exchanged by the ERANOS modules are SETs (for Structured ERANOS Tree), which are arborescent structures made of connected segments, and related to basic logical entities (e.g. geometry, concentrations, fluxes, etc.). All these structures are manipulated by a memory manager called GEMAT (creation, destruction, updating, swaps between RAM and disk, etc.).

ERANOS modules can be chained by means of the LU user's language. LU capabilities include the manipulation of variables/arrays of different types, the use of logical, arithmetical and character operators/functions, and of a variety of special functions. Conditional structures of various types can be used (e.g. IF, FOR; WHILE), and LU subroutines, called LU procedures, can be written, stored and used. A specific data manager, called ARCHIVE, is used for data structures such as SETs and procedures. A database manager is available, connected to the LU language, producing and managing structures (various operators available). The execution of LU scripts is made by a built-in interpreter.

**10. REFERENCES**

Documentation is distributed on CD #2. Click on files HTML_ERANOS_2.0/index.html and install.html for the documentation index and links to the various references. Click on TUTORIAL/turorialERANOS.htm for a brief overview and tutorial. Note that the code documentation is primarily written in French with some pages in English. The libraries documentation is provided in English. The following references are included in package distribution:

ECCO:

----

- G. Rimpault:

Physics Documentation of ERANOS - The ECCO Cell Code

ERANOS : Manuel des Methodes - Le Code de Cellule ECCO

(Rapport Technique RT/SPRC/LEPh 97-001)

- G. Rimpault:

Approximate Buckling Dependent Diffusion Coefficients for the ECCO Cell Code

Coefficients de Diffusion Approches Dependant du Laplacien pour le Code de

Cellule ECCO (Note Technique NT/SPRC/LEPh 99/212)

- G. Rimpault, P. Smith:

Developpements Algorithmiques dans le Code ECCO pour le Traitement des Effets

de Fuites Anisotropes dans les Situations Vidangees de Sodium (Note Technique

NT/SPRC/LEPh 97-229)

- Generalisation du Calcul des Probabilites de Collision dans ECCO (Note

Technique NT/SPRC/LEPh/00/214)

- Integration d'un Module de Calcul de Probabilites de Collision en R-Z dans

ECCO, (Note Technique NT/SPRC/LEPh/00/215)

BISTRO:

------

- C. Gho, G. Palmiotti:

BISTRO : Bidimensionnel Sn Transport Optimise - Un Programme Bidimensionnel de

Transport Sn aux Differences Finies, Note No.1 Definition Des Algorithmes Pour

La Geometrie X-Y (Note Technique NT/SPRC/LEPh 84/270)

- C. Gho, G. Palmiotti:

Algorithmes pour la Geometrie R-Z et Optimisation de la Solution 'Diffusion'

pour L'Acceleration

Module de Passage Maille-Point

Solution de L'Equation de la Diffusion

BISTRO - Note No. 2 (Note Technique NT/SPRC/LEPh 85-202)

- C. Gho, G. Palmiotti, J-M. Rieunier:

Comparaison des Resultats et Temps de Calcul entre BISTRO er DOT

BISTRO - Note No. 3 (Note Technique NT/SPRC/LEPh 85-204)

- C. Gho, G. Palmiotti:

Definition des Algorithmes Necessaires au Calcul de Configurations a Spectre

Thermique (Traitement du Groupe Thermique, Upscattering) et du Transport des

Rayons gamma (Formalisme SN Pn) BISTRO - Note No. 4 (Note Technique

NT/SPRC/LEPh 86/238)

NODAL:

-----

- J.M. Ruggieri:

ERANOS - Manuel des Methodes - Reconstruction Fine d'un Flux Nodal (Note

Technique NT/SPRC/LEPh 99-217)

- A. Rineiski:

KIN3D : Module de cinetique spatiale et de perturbations pour TGV2.

A space-time kinetics and perturbation theory module for TGV2.

(Note Technique NT/SPRC/LEPh 97-203)

- G. Palmiotti, C.B. Carrico, E.E. Lewis:

Variational Nodal Method for the Solution of the Diffusion and Transport

Equation in Two and Three Dimensional Geometries (Note Technique NT/SPRC/LEPh

91-208)

DEGAGEMENT D'ENERGIE (ENERGY RELEASE):

-------------------------------------

- Anton Luethi:

Les Fichiers de Degagement d'Energie d'ERANOS (Note Technique NT/SPRC/LEPh

97-231)

- G. Rimpault, D. Calamand, P. Peerani:

Physics Documentation of ERANOS

Energy Release and Displacement Damage Dose Calculations

Documentation Physique d'ERANOS

Calculs de Dommage aux structures et de Degagement d'Energie

(Note Technique NT/SPRC/LEPh 93-236)

EVOLUTION/CONDITIONS FONCTIONNEMENT (BURNUP):

--------------------------------------------

- S. Czernecki, J.M. Rieunier:

ERANOS : Manuel des Methodes - Les Conditions de Fonctionnement (Note Technique

NT/SPRC/LEPh 99/213)

- D. Honde, J.M. Rieunier, G. Rimpault:

Procedures de Calcul d'Evolution Cellule (ECCO) dans ERANOS (Note Technique

NT/SPRC/LEPh 98-226)

- J. Y. Doriath, J.M. Rieunier, G. Rimpault:

ERANOS - Manuel des Methodes - Les Calculs d'Evolution (Note Technique

NT/SPRC/LEPh 96-204)

- D. Niddam:

Integration de MECCYCO dans ERANOS (projet MCOERA) (Note Technique NT/SPRC/LEPh 99-214)

SCHEMAS (SCHEMES):

-----------------

- S. Czernecki, F. Varaine:

ERANOS 1.2 : Notice d'utilisation des procedures PROJERIX (Note Technique

NT/SPRC/LEPh 97-437)

- G. Rimpault, P. Smith, R. Jacqmin, F. Malvagi, J.M. Rieunier, D. Honde, G.

Buzzi, P.J. Finck:

Schema de Calcul de Reference du Formulaire ERANOS et Orientations pour le

Schema de Calcul de Projet (Note Technique NT/SPRC/LEPh 96-220)

- S. Czernecki, F. Varaine:

ERANOS 1.2 : Note de presentation du nouveau schema de calcul de projet

'neutronique coeur' (Note Technique NT/SPRC/LEPh 97-438)

- F. Mellier:

ERANOS 1.2 - Procedures SIRENE pour le post-traitement des etudes projet Notice

de presentation et d'utilisation (Note Technique NT/SPRC/LEPh 97-436)

- F. Varaine, S. Czernecki:

ERANOS 1.2 : Notice d'Utilisation du Schema de Calcul de Projet 'Neutronique

Coeur' (Note Technique NT/SPRC/LEPh 97-440)

PERTURBATIONS/SENSIBILITE (PERTURBATIONS/SENSITIVITY):

-----------------------------------------------------

- D. Honde, P. Palmiotti, J.M. Rieunier, G. Rimpault:

ERANOS : Manuel des Methodes - Les Calculs de Perturbations et les Analyses de

Sensibilite (Note Technique NT/SPRC/LEPh 96-205)

- S. Czernecki, D. Nidda:

Extension des algorithmes de sensibilite d'ERANOS (Projet EAS) (Note Technique

NT/SPRC/LEPh 99-226)

MISCELLANEOUS:

------------------------

- G. Rimpault, D. Honde, J-M. Rieunier:

ERANOS : Manuel des Methodes, Transferts Internes de Donnees Nucleaires (Note

Technique NT/SPRC/LEPh 93-252)

- D. Plisson-Rieunier:

Descriptif Livraison ERANOS 2.0 (Note Technique NT/SPRC/LEPh/01/215)

- ERANOS 2.0 Installation Manual (Note Technique NT/SPRC/LEPh/01/217)

- E. Fort, W. Assal, G. Rimpault, R. Soule, P. Smith, J. Rowlands:

Principes Theoriques et Methodologies de la Validation de JEF2.2, Application a

La Realisation d'ERALIB1, Bibliotheque de Donnees Neutroniques pour le Calcul

des Systemes a Spectre Rapide (Rapport Technique RT/SPRC/LEPh 97-002)

- P. Smith, G. Rimpault:

Qualification du Formulaire ERANOS pour le Calcul de la Perte de Reactivite de

SUPER-PHENIX (Note Technique NT/SPRC/LEPh 98-239)

**11. CONTENTS OF CODE
PACKAGE**

ERANOS is distributed on 3 CDs which include source code, binary data libraries, Makefiles, scripts, test cases and documentation (manuals and technical documents in HTML and PDF formats).

**12. DATE OF ABSTRACT**

June 2008.

**KEYWORDS:** BURNUP;
CELL CALCULATION; DIFFUSION THEORY; DISCRETE ORDINATES; FUEL MANAGEMENT; PERTURBATION
THEORY; REACTOR PHYSICS; SENSITIVITY ANALYSIS; SPHERICAL HARMONICS