# Decay Heat

This page provides the chapter on decay heat from the "DOE Fundamentals Handbook: Thermodynamics, Heat Transfer, and Fluid Flow," DOE-HDBK-1012/2-92, U.S. Department of Energy, June 1992.

Other related chapters from the "DOE Fundamentals Handbook: Thermodynamics, Heat Transfer, and Fluid Flow" can be seen to the right.

DOE Handbook: Heat Transfer

## Decay Heat

Decay heat production is a particular problem associated with nuclear reactors. Even though the reactor is shut down, heat is produced from the decay of fission fragments. Limits for each particular reactor are established to prevent damage to fuel assemblies due to decay heat.

### Reactor Decay Heat Production

A problem peculiar to power generation by nuclear reactors is that of decay heat. In fossil fuel facilities, once the combustion process is halted, there is no further heat generation, and only a relatively small amount of thermal energy is stored in the high temperature of plant components. In a nuclear facility, the fission of heavy atoms such as isotopes of uranium and plutonium results in the formation of highly radioactive fission products. These fission products radioactively decay at a rate determined by the amount and type of radioactive nuclides present. Some radioactive atoms will decay while the reactor is operating and the energy released by their decay will be removed from the core along with the heat produced by the fission process. All radioactive materials that remain in the reactor at the time it is shut down and the fission process halted will continue to decay and release energy. This release of energy by the decay of fission products is called decay heat.

The amount of radioactive materials present in the reactor at the time of shutdown is dependent on the power levels at which the reactor operated and the amount of time spent at those power levels. The amount of decay heat is very significant. Typically, the amount of decay heat that will be present in the reactor immediately following shutdown will be roughly 7% of the power level that the reactor operated at prior to shutdown. A reactor operating at 1000 MW will produce 70 MW of decay heat immediately after a shutdown. The amount of decay heat produced in the reactor will decrease as more and more of the radioactive material decays to some stable form. Decay heat may decrease to about 2% of the pre-shutdown power level within the first hour after shutdown and to 1% within the first day. Decay heat will continue to decrease after the first day, but it will decrease at a much slower rate. Decay heat will be significant weeks and even months after the reactor is shutdown.

The design of the reactor must allow for the removal of this decay heat from the core by some means. If adequate heat removal is not available, decay heat will increase the temperatures in the core to the point that fuel melting and core damage will occur. Fuel that has been removed from the reactor will also require some method of removing decay heat if the fuel has been exposed to a significant neutron flux. Each reactor facility will have its own method of removing decay heat from both the reactor core and also any irradiated fuel removed from the core.

### Calculation of Decay Heat

The amount of decay heat being generated in a fuel assembly at any time after shutdown can be calculated in two ways. The first way is to calculate the amount of fission products present at the time of shutdown. This is a fairly detailed process and is dependent upon power history. For a given type of fuel, the concentrations, decay energies, and half lives of fission products are known. By starting from a known value, based on power history at shutdown, the decay heat generation rate can be calculated for any time after shutdown.

An exact solution must take into account the fact that there are hundreds of different radionuclides present in the core, each with its own concentration and decay half-life. It is possible to make a rough approximation by using a single half-life that represents the overall decay of the core over a certain period of time. An equation that uses this approximation is Equation 2-16.

$$\dot{Q} = \dot{Q}_o \left({1 \over 2}\right)^{ \text{time} \over \text{half-life} }$$
(2-16)

where:

 $$\dot{Q}$$ = decay heat generation rate at some time after shutdown $$\dot{Q}_o$$ = initial decay heat immediately after shutdown time = amount of time since shutdown half-life = overall decay half-life of the core

Example:

A 250 MW reactor has an unexpected shutdown. From data supplied by the vendor, we know that decay heat at time of shutdown will be 7% of the effective power at time of shutdown and will decrease with a 1 hr half life. Effective power at time of shutdown was calculated to be 120 MW. How much heat removal capability (in units of Btu/hr) will be required 12 hours after shutdown?

Solution:

1. First determine the decay heat immediately following shutdown.

(120 MW)(.07) = 8.4 MW decay heat at shutdown

2. Then use Equation 2-16 to determine the decay heat 12 hours later.
$$\begin{eqnarray} \dot{Q} &=& \dot{Q}_o \left({1 \over 2}\right)^{ \text{time} \over \text{half-life} } \nonumber \\ &=& 8.4 ~\text{MW} \left({1 \over 2}\right)^{ 12 ~\text{hr} \over 1 ~\text{hr} } \nonumber \\ &=& 2.05 \times 10^{-3} ~\text{MW} \left({ 3.413 \times 10^6 ~\text{Btu/hr} \over 1 ~\text{MW} }\right) \nonumber \\ &=& 7000 ~{ \text{Btu} \over \text{hr} } \end{eqnarray}$$

The second method is much simpler to use, but is not useful for forecasting heat loads in the future. To calculate the decay heat load at a given point after shutdown, secure any heat removal components from the primary system or spent fuel pool and plot the heatup rate. If the mass of the coolant and the specific heat of the coolant are known, the heat generation rate can be accurately calculated.

$$\dot{Q} = m ~c_p ~{ \Delta T \over \Delta t }$$
(2-17)

where:

 $$\dot{Q}$$ = decay heat (Btu/hr) m = mass of coolant (lbm) cp = specific heat capacity of coolant (Btu/lbm-°F) ΔT = temperature change of coolant (°F) Δt = time over which heatup takes place (hr)

Example:

Three days after a planned reactor shutdown, it is desired to perform maintenance on one of two primary heat exchangers. Each heat exchanger is rated at 12,000 Btu/hr. To check the current heat load on the primary system due to decay heat, cooling is secured to both heat exchangers. The primary system heats up at a rate of 0.8°F/hr. The primary system contains 24,000 lbm of coolant with a specific heat capacity of 0.8 Btu/lbm-°F. Will one heat exchanger be sufficient to remove the decay heat?

Solution:

$$\begin{eqnarray} \dot{Q} &=& m ~c_p ~{ \Delta T \over \Delta t } \nonumber \\ &=& (24,000 ~\text{lbm}) \left( 0.8 ~{\text{Btu} \over \text{lbm-}^{\circ}\text{F}}\right) \left({ 0.8^{\circ}\text{F} \over 1 ~\text{hr} }\right) \nonumber \\ &=& 15,360 ~{ \text{Btu} \over \text{hr} } \end{eqnarray}$$

One heat exchanger removes 12,000 Btu/hr.

One heat exchanger will not be sufficient.

### Decay Heat Limits

Reactor decay heat can be a major concern. In the worst case scenarios, it can cause melting of and/or damage to the reactor core, as in the case of Three Mile Island. The degree of concern with decay heat will vary according to reactor type and design. There is little concern about core temperature due to decay heat for low power, pool-type reactors.

Each reactor will have some limits during shutdown that are based upon decay heat considerations. These limits may vary because of steam generator pressure, core temperature, or any other parameter that may be related to decay heat generation. Even during refueling processes, heat removal from expended fuel rods is a controlling factor. For each limit developed, there is usually some safety device or protective feature established.

### Decay Heat Removal

Methods for removing decay heat from a reactor core can be grouped into two general categories. One category includes methods which circulate fluid through the reactor core in a closed loop, using some type of heat exchanger to transfer heat out of the system. The other category includes methods which operate in an open system, drawing in cool fluid from some source and discharging warmer fluid to some storage area or the environment.

In most reactors, decay heat is normally removed by the same methods used to remove heat generated by fission during reactor operation. Additionally, many reactors are designed such that natural circulation between the core and either its normal heat exchanger or an emergency heat exchanger can remove decay heat. These are examples of the first category of methods for decay heat removal.

If a reactor design is such that decay heat removal is required for core safety, but accidents are possible that will make the closed loop heat transfer methods described above unavailable, then an emergency cooling system of some sort will be included in the reactor design. Generally, emergency cooling systems consist of some reliable source of water that is injected into the core at a relatively low temperature. This water will be heated by the decay heat of the core and exit the reactor via some path where it will either be stored in some structure or released to the environment. Use of this type of system is almost always less desirable than the use of the closed loop systems described above.

Students should research systems, limits, and protective features applicable to their own specific facilities.