Modification of the Reactivity Equivalent Physical Transformation Method for HTGR Fuel Element Analysis

The so called “double-heterogeneity”, characterizing High Temperature Gas cooled Reactors (HTGR) block type fuel elements, presents a challenge for existing deterministic lattice codes that were originally developed for LWR applications. A large number of TRISO particles randomly dispersed in the fuel compact introduces an additional complexity into the modeling. The Monte Carlo (MC) based codes, which are capable of simulating complex geometries of HTGR fuel elements, are mainly used for the reference calculations. The use of MC codes as production tools for a few-group cross section generation for 3D nodal codes is still very limited due to the high computational costs.
Recently a new few-group cross section generation methodology for a full core analysis of HTGRs was proposed. This methodology is based on homogenization approach called Reactivity equivalent Physical Transformation (RPT). The RPT methodology combines high spatial resolution of MC codes with superior computational speed of deterministic lattice codes. At the first stage, a MC code is used to simulate an HTGR fuel element with explicitly described TRISO particles at the beginning of life (BOL) and at the nominal operational conditions. At the second stage the TRISO particles are homogenized with the fuel compact graphite to get rid of double-heterogeneity problem. It is well known that a simple volume-weighted homogenization of TRISO particles in the graphite matrix results in the underestimation of the self-shielding effect. However, according to the RPT approach, TRISO particles are homogenized in a smaller central volume rather than in entire fuel compact. The volume of the smeared region is adjusted in such way that k-inf of homogenized geometry matches that of the reference heterogeneous one obtained from MC reference calculations. Since the radius of the smeared zone was determined at the beginning of life (BOL) it is kept constant and is used for depletion and branch-off calculations by lattice codes.
The main disadvantage of the RPT approach is the fact that TRISO particles are smeared together with the compact graphite and constitute one homogeneous material. Keeping in mind that the fuel and graphite temperatures may significantly vary during the reactor operation, these temperatures should be decoupled during a few-group cross section generation. However in the majority of lattice codes temperatures are assigned to the regions (e.c. HELIOS code) or to the homogeneous materials (e.c. CASMO code) rather than to particular nuclides like in the MC codes. In order to overcome this disadvantage the RPT methodology has been modified in a way that only TRISO particles are smeared in the central compact region while all compact graphite is concentrated in the remained outer compact region. This modification allows assigning different temperatures to the fuel and as well as to the compact matrix graphite.
The main objective of this study is to verify the modified RPT methodology. A set of depletion calculations of a prismatic block-type HTGR fuel lattice of fuel and coolant channels was performed. Two models of prismatic fuel assembly are considered: 1) 3D model with explicitly described TRISO particles; 2) 2D model, in which TRISO particles are homogenized using the modified RPT approach. 3D calculations are performed with MCNP based depletion code BGCore. 2D calculations are carried out with BGCore code and deterministic lattice code HELIOS 1.9. The comparison between 3D and 2D results is reported. Conclusions regarding validity of modified RPT approach are drawn.