RERTR Publications:
Analysis Methods for Thermal Research and Test Reactors

ANL/RERTR/TM-29

COMPUTING CONTROL ROD WORTHS
IN THERMAL RESEARCH REACTORS

M. M. Bretscher
RERTR Program

Argonne National Laboratory
Argonne, IL 60439-4841 USA

February 1997

ABSTRACT

Simple diffusion theory cannot be used to evaluate control rod worths in thermal reactors because of steep flux gradients that occur within the absorber material. However, reliable control rod worths can be calculated within the framework of diffusion theory if the control material is characterized by a set of mesh-dependent effective diffusion parameters or if group-dependent current-to-flux ratios are specified on the absorber surface.

For thin slab absorbers the effective diffusion parameters are functions of a pair of blackness coefficients. Methods for calculating these blackness coefficients in the P₁, P₃ and P₅ approximations, with and without scattering, are discussed, and equations for the corresponding mesh-dependent effective diffusion parameters are derived.

For control elements whose geometry does not permit a thin slab treatment, other methods are needed for determining the effective diffusion parameters. One such method, based on reaction rate ratios, is presented.

An alternate method for calculating control rod worths isolates the absorber from the diffusion-theory calculation by specifying group-dependent current-to-flux ratios on the absorber surface. Neutron transport calculations are used to determine these current-to-flux ratio internal boundary conditions subject to limits set by radius-dependent black absorber rods.

These methods are illustrated for a number of absorber materials and geometries. Computed control rod worths are compared with detailed Monte Carlo calculations and, where possible, with experimental measurements. In general, control rod worths based on these diffusion-theory methods are found to be consistent with those from Monte Carlo calculations and with measured values.

TABLE OF CONTENTS

• Introduction
• Effective Diffusion Parameters
• Internal Boundary Conditions
• Control Rod Worth Evaluations
• Summary and Conclusions
• References
• Appendix: Blackness Coeffs and Eff Diff Parameters in Slab Geom