4. METHOD OF SOLUTION
Multigroup integral transport theory has been chosen as the best tool to handle the evaluation of Gd behaviour in LWRs. Use is made of a modified version of the THERMOS code to ob- tain all the necessary spectral and geometrical detail, taking into account also the radial dependence of the poison concentration due to the radial dependence of spectrum and flux level within the pin (a different spectrum is evaluated in each mesh point). At each ir- radiation step, the space and energy neutron distribution is calcu- lated, the burnup of the isotopes in the fuel is consequently calcu- lated and the procedure is automatically repeated for the following time step and so on. The computer time is reduced since at each irradiation step the neutron distribution of the previous step is used as a guess for the convergence procedure.
In the transport calculations at each irradiation step the conver- gence is checked with respect to the mesh where the absorption rate as evaluated at the previous irradiation step is maximum; while at beginning of life this mesh is obviously the outermost one; as irradiation proceeds this most significant mesh moves toward the center.
The main output of the BEVE routine consists of the thermal macro- scopic cross sections of the poisoned cell versus burnup to be used for the computation of the fuel element in x,y geometry.
One BEVE run must be performed for each type of poisoned cell in the element. Each BEVE run supplies for each irradiation step the following information:
- The value of the fluence in the coupling region.
- The equivalent natural Gd concentration.
- The cell macroscopic constants for both energy schemes in BURNY (i.e. one or two thermal groups).
When calculating the fuel element in x,y geometry, if a poisoned cell is present, BURNY identifies what poison cell type it belongs to and then reads in the associated constants from the correspond- ing table supplied by BEVE.
In the thermal range two different cross section libraries are available, set up by the BELIB code and including Gd-155 and 157 and Gd-Nat. One uses a 22 group scheme and the other 30 groups with the standard THERMOS group structure.
In the epithermal and fast range the FORM code was used to cal- culate the group constants.
The two isotopes Gd-155 and 157 are assumed to burn independently (i.e. Gd-156 absorption neglected).
It should be stressed that BEVE provides information on the be- haviour of highly absorbing burnable poison in the thermal range.
Although some epithermal and fast effects are accounted for in the depletion by BEVE, the epithermal constants of the poisoned cell are not calculated by BEVE, but by BURNY.