Most of the methods that are currently used in decay heat calculation are based on numerical integration methods. These methods require large computer times in providing accurate result. A typical example is the ORIGEN2 computer code. In numerical integration methods, we need to divide entire cooling times into small time steps to get accurate solutions. Thus, for long cooling times we need to have many time steps. In particular, ORIGEN2 uses secular or transient equilibrium approximation whenever possible to reduce the number of time steps.
To eliminate these shortcomings, in this study we find the decay heat at any time of interest after shutdown by evaluating analytic relations that are derived based on the assumption of no backward decay reactions in the case of fission products and on the assumption of no cyclic (feedback) chains in the mixture of forward (β-) reactions and backward(α) reactions in the case of actinides.
The analytic relations are obtained for each nuclide in terms of decay-chain-paths. Thus the computer time to evaluate the analytic relations are approximately linearly proportional to the number of the nuclides. To reduce further the computer time, the decay-chain-paths are constructed only once for a chosen reactor model and stored in an external file. This file is called in and evaluated easily be the analytic relations to obtain decay heat for different cases. This method has been computerized in a program called KIGEN.
The method was applied to the decay heat calculation of a typical pressurized water reactor and its results were compared with those of ORIGEN2. The agreement between the two results is excellent. For fission products the relative errors are less than 0.5% until cooling times of $10^7$ years. For actinides they are less than 1% for cooling times of $10^4$ years, but thereafter they increase rather rapidly due to the fact that the current version of KIGEN considers only part of backward (α) decay reactions and forward (β-) reactions. This will be improved in a future study.
