Decay heat

Decay heat as a proportion of the nominal output calculated according to two different models: Retran with a general consideration of previous operation and Todreas assuming 2 years of operation before shutdown.

With decay heat ( English decay heat ) - sometimes simply reheat - one calls in the nuclear reactor technology, the decay heat that after completion of the nuclear fission reaction in the fuel even newly created. Since the neutron flux z. B. has almost come to a standstill by retracting the control rods , hardly any new cleavage reactions take place after the shutdown. Rather, the decay heat arises from the fact that the short-lived fission products present decay radioactively . Thermal output through downstream disintegration processes also occurs continuously in normal, continuous reactor operation; decay heat only means that heat that is newly generated when the system is switched off. Such decay heat generated in spent fuel in the spent fuel pool , in Castor or camps.

Colloquially, the decay heat is also referred to as "residual heat". This designation is misleading as it can be confused with the amount of heat stored in the reactor core.

Decay heat in the reactor core

Immediately after shutdown, the decay heat output is between 5% and 10% of the previous thermal output of the reactor, depending on the reactor type, the operating time and the nuclear fuel used. In a large reactor such as the EPR with 1600 megawatts (MW) of electrical power, i. H. around 4,000 MW of thermal output, around 50 MW of thermal output one hour after shutdown, and 20 MW after four days.

calculation

The remaining amount of a radionuclide at the beginning of the decay chain decreases over time according to an exponential function . For nuclides that are just being formed, the time course is a sum of increasing and decreasing exponential functions if only first-order reactions are taken into account. Neutron capture is a second order nuclear reaction, but is secondary to the nuclear fuel in the presence of neutron absorbers . When the cleavage product mixture is in a reactor, the numerous exponential functions with widely distributed time constants are superimposed to form a curve which, for practical purposes, e.g. B. can be approximated as a power function. Calculation rules are specified in the standards DIN 25463-1 and DIN 25463-2.

A simple approximation formula was given by Katharine Way and Eugene Wigner in 1946 : If a reactor is operated with the power for the duration , then the decay power is at the point in time after the reactor was switched off ${\ displaystyle T_ {0}}$ ${\ displaystyle P_ {0}}$ ${\ displaystyle P}$ ${\ displaystyle t}$

{\ displaystyle P (t) = 0 {,} 062P_ {0} \ left (t ^ {- 0 {,} 2} - \ left (T_ {0} + t \ right) ^ {- 0 {,} 2 } \ right).}

Here, T ₀ and t in seconds to use. The time range from 10 s to 100 days was specified for the validity, the uncertainty as 15% to 20%.

Way and Wigner have presented the derivation in detail. The assumptions and approximations in brief:

The mass numbers and the cleavage products were fixed at the maxima of the observed distributions. ${\ displaystyle A_ {L}}$ ${\ displaystyle A_ {H}}$

For the light (L) and heavy (H) cleavage products, the distribution of the number of protons was approximated as a Gaussian distribution.

{\ displaystyle Z}

The lifetimes of the radiators, which determine the kinetics, were set inversely proportional to the fifth power of the energy difference between the mother and daughter nucleus according to the Sargent rule , which in turn was calculated using the Bethe-Weizsäcker formula . ${\ displaystyle \ beta}$

For the mean post-decay power of the products of an individual initiating fission event, there is a decay proportional to if the initiating fission event occurred at the time , or ${\ displaystyle t ^ {- 1,2}}$ ${\ displaystyle t = 0}$

{\ displaystyle P_ {1} (t-t ') \ propto (t-t') ^ {- 1,2} \ ;.}

for a general start time . ${\ displaystyle t '}$

Assuming that nuclei were split evenly over an interval , the total decay power is obtained by integrating the different starting times : ${\ displaystyle {\ dot {N}} _ {0}}$ ${\ displaystyle [-T_ {0}, 0]}$ ${\ displaystyle t '}$

{\ displaystyle P (t) = {\ dot {N}} _ {0} \ int _ {- T_ {0}} ^ {0} P_ {1} (t-t ') \, dt' \ propto { \ dot {N}} _ {0} \ int _ {- T_ {0}} ^ {0} (t-t ') ^ {- 1,2} \, dt' = {\ dot {N}} _ {0} {\ bigl (} t ^ {- 0.2} - (T_ {0} + t) ^ {- 0.2} {\ bigr)} \ ;.}

The number of split cores per second can be related to the reactor power (assumed to be constant over time): ${\ displaystyle {\ dot {N}} _ {0}}$

{\ displaystyle P_ {0} = \ langle E_ {s} \ rangle \ cdot {\ dot {N}} _ {0} \ ;.}

This is the mean energy that can be thermally used per split (about 200 MeV per split). Therefore, the decay output can also be related to the reactor output, as stated above. The correct pre-factor results from the correct mean individual decay power and the mean, thermally usable energy per fission. ${\ displaystyle \ langle E_ {s} \ rangle}$

Examples of decay heat after a long period of operation

After 11 months of operation near the nominal output in a typical fuel assembly cycle, the following values result from the above formula (output values and time periods are based on the fuel content of a typical large reactor):

Time after shutdown	Decay heat ( percent )	Thermal power at 4000 MW before shutdown (MW)	Time for the heating of 2500 m³ of water from 15 ° C to 100 ° C
10 seconds	3.72%	149	100 min
1 minute	2.54%	102	146 min
1 hour	1.01%	40	6 h
1 day	0.44%	18th	14 h
3 days	0.31%	13	20 h
1 week	0.23%	9	26 h
1 month	0.13%	5	49 h
3 months	0.07%	3	89 h

Decay heat in the cooling pool

Uncooled, spent (“spent”) fuel elements would heat up to the melting point for several months after the end of operation after being discharged from the reactor core. In order to dissipate their decay heat, these fuel elements have to be stored for several years in the water-filled decay pool belonging to every nuclear power plant. The heat output from the cooling pool is actively dissipated; in newer systems it is used economically to preheat the reactor feed water (cooling basin feed water preheater cooling circuit ).

Individual evidence

↑ RETRAN-02. Nuclear Power Industry Engineering & Consulting. CSA, accessed March 27, 2011 .
↑ Neil E. Todreas, Mujid S. Kazimi: Nuclear Systems I, Thermal Hydraulic Fundamentals . 2nd Edition. Hemisphere Publishing Corporation, New York 1990, ISBN 0-89116-935-0 .
↑ Nuclear fission and decay heat. Society for Plant and Reactor Safety, March 22, 2011, accessed on November 28, 2013 .
↑ R. Zahoransky (Ed.): Energy technology. 5th edition. Vieweg and Teubner, 2010, ISBN 978-3-8348-1207-0 , page 81
↑ Katharine Way, Eugene P. Wigner: Radiation from Fission Products. Technical Information Division, United States Atomic Energy Commission, Oak Ridge (Tennessee) 1946.
^ K. Way, EP Wigner: The Rate of Decay of Fission Products. In: Physical Review . Volume 73, 1948, pp. 1318-1330.

Remarks

↑ The efficiency of the reactor would correspond accordingly to around 30%, see also efficiency examples
^ Contents of an Olympic swimming pool

[RETRAN-1] RETRAN-02. Nuclear Power Industry Engineering & Consulting. CSA, accessed March 27, 2011 .

[TODREAS-2] Neil E. Todreas, Mujid S. Kazimi: Nuclear Systems I, Thermal Hydraulic Fundamentals . 2nd Edition. Hemisphere Publishing Corporation, New York 1990, ISBN 0-89116-935-0 .

[3] Nuclear fission and decay heat. Society for Plant and Reactor Safety, March 22, 2011, accessed on November 28, 2013 .

[5] R. Zahoransky (Ed.): Energy technology. 5th edition. Vieweg and Teubner, 2010, ISBN 978-3-8348-1207-0 , page 81

[6] Katharine Way, Eugene P. Wigner: Radiation from Fission Products. Technical Information Division, United States Atomic Energy Commission, Oak Ridge (Tennessee) 1946.

[7] K. Way, EP Wigner: The Rate of Decay of Fission Products. In: Physical Review . Volume 73, 1948, pp. 1318-1330.

[4] The efficiency of the reactor would correspond accordingly to around 30%, see also efficiency examples

[8] Contents of an Olympic swimming pool