IRI-131-2000-005

J.L. Kloosterman

Topic 3

Decay Heat Predictions: Experiments, Methods and Data

INTEGRAL VALIDATION AND DECAY HEAT STANDARDS

Frédéderic Joliot /Otto Hahn Summer School August 21-30, 2000 Cadarache, France

July 2000

FJ/OH Summer School ’2000 2000 Frédéric Joliot/Otto Hahn Summer School

August 21-30, 2000 Cadarache, France

Topic 3 Decay Heat Predictions: Experiments, Methods and Data

INTEGRAL VALIDATION AND DECAY HEAT STANDARDS

J.L. Kloosterman Interfaculty Reactor Institute

Delft University of Technology Mekelweg 15, NL-2629 JB Delft

Netherlands Tel: ++31 15 278 1191 Fax: ++31 15 278 6422

J.L.Kloosterman@iri.tudelft.nl

ABSTRACT After the shut down of a nuclear power plant, the radioactive decay of fission products, actinides and activation products produces heat that should be removed from the system. The fission products’ contribution dominates the decay heat source, while that of the actinides usually does not exceed 25%. The activation products become important only for long cooling times. Calculation of decay heat can be done by means of summation calculations, which take into account the buildup and decay of as many nuclides as possible, or by applying so-called decay heat standards. The latter are usually based on both experimental data and calculations. Although, the accuracy of summation calculations is within a few percent theoretically, in practice larger deviations are seen. Also differences between the decay heat standards and experiments exist, depending on the irradiation time, cooling time and the fissile actinide considered. 1 INTRODUCTION Calculation of decay heat as a function of cooling time is important for the prediction of the residual power in a nuclear reactor in case of (emergency) shutdown. Furthermore, an accurate prediction of decay heat is needed for the design of heat-removal systems during the handling and interim storage of spent fuel in nuclear reactors and in reprocessing plants, and during fuel transport. Current trends in reactor physics like the increase of the maximum fuel burnup, the use of MOX fuel in Light Water Reactors (LWRs), and the transmutation of minor actinides envisaged in nuclear reactors, call for continuous improvement in this field. During the operation of a nuclear reactor, a part of the energy released comes from the fissions caused by delayed neutrons and from the decay of radioactive fission products and actinides. When the chain reaction is halted, this heat source remains decaying with time scales dictated by the half-lives of the nuclides concerned. For a nuclear reactor with thermal power of 3000 MW, decay power exceeds 200 MW during the first few minutes. Obviously, the reactor designer should provide diverse means to extract this heat safely from the reactor core such that fuel melting never occurs. It is instructive to compare the decay heat with other reservoirs of stored energy in a nuclear reactor. Table 1.1 gives an overview of the stored energy expressed in full power seconds (fps) according to Pershagen (1989). The fuel has a relatively small buffer capacity, whilst that of the coolant and the reactor vessel and internals is much larger. The decay power and integral decay power per megawatt is shown as a function of cooling time in Fig. 1.1. After a cooling time of 0.5 day, the integral decay power exceeds already 0.0045 MWd ≈ 400 MWs = 400 full power seconds. This demonstrates the importance of decay heat if no cooling is present. If the core cooling is in operation, Fig. 1.2 shows the storage of decay heat in boiling water reactors. When the turbine condenser is not available as a heat sink, the excess steam is discharged from the reactor into the condensation pool to preserve the system pressure. Make-up coolant with a temperature of about 170 0C is injected to cool the core. This water together with the decay heat contributes to the heating of the condensation pool. After about 4 hours, the cooling power is already greater than the heat supplied, and the temperature of the condensation pool falls with the decreasing decay heat.

Table 1.1: Stored energy in a Boiling Water Reactor (BWR) expressed in full power seconds (fps) (Pershagen, 1989).

Item Stored Energy (fps) Fuel from operating temperature to 286oCa) 4.7 Fuel from 286oC to 100oC 4.2 Reactor coolant from 286oC to 100oC 112 Subcooling of reactor coolant during normal operation 5.8 Reactor vessel and internals from 286oC to 100oC 43 a) The value of 286oC corresponds to the saturation temperature of water at a system pressure of 7 MPa.

A simple formula to calculate the integral decay power per megawatt (thermal) can be derived from Henry (1986): ( ) ( )0.80.083 sdE t t= (1.1)

where t is the cooling time (s) after an infinitely long irradiation time. Note that the unit used in Fig. 1.1 should in fact be the same as that used in Eq. (1.1) (MWd/MW=d). Exercise 1.1: Convert Eq. (1.1) to units of day and verify the integral decay power curve in Fig. 1.1. Exercise 1.2: Estimate the amount of water needed to remove by evaporation the integral decay power after one week. How does it change with water pressure?

Figure 1.1: Decay power and integral decay power per megawatt (thermal) as a function of time (Forsberg, 1991).

The decay heat power comes mainly from five sources: 1. Unstable fission products, which decay via β- and γ-ray emission to stable isotopes.

The emission is mainly a consequence of the fact that actinides are relatively rich in neutrons, which leave the fission products in an unstable state with too many neutrons. The electrons released from radioactive β- decay contributes an average energy of about 8 MeV per fission event. This energy is immediately converted locally to heat. The delayed γ-ray emission contributes about 7 MeV to the average energy release per fission (Henry, 1986). By means of the photoelectric effect (most important for γ-rays of low energy < 0.3 MeV), the energy from Compton scattering (most important at intermediate to high energies 0.3-10 MeV) and pair production (most important at energies > 10 MeV) is transferred to charged particles (mainly electrons) that are directly absorbed locally. In total, the energy release rate of the β- and γ-ray emission equal about 7% of the total power production. The activity of fission products can be estimated if the half-life of the nuclide is very short compared with the irradiation time, or when the half-life is very long. In the first case, the nuclide saturates and the activity reaches an equilibrium value determined by (Pershagen, 1989):

310A yP= (1.2) where A is the activity of the nuclide in TBq, y is the yield in percent of fissions, and P is the heat generation (MW). In the second case, the activity of the nuclide increases linearly with time as follows:

210t

A yPT

=õ

(1.3)

where t is the irradiation time and Tõ

the half-life of the nuclide. When a reactor is

shutdown, a large number of short-lived fission products contribute to the total decay power. After long times, however, when all short-lived nuclides have decayed, only a few long-lived nuclides are important. For times exceeding 106 seconds, only a dozen nuclides dominate (Schmittroth, 1976). An important conclusion that can be derived from Eqs. (1.2) and (1.3) is that for short cooling times, the decay heat will not depend on the irradiation time, while for long decay times, the decay heat will be proportional to the irradiation time.

Exercise 1.3: Derive Eqs. (1.2) and (1.3).

2. Unstable actinides that are formed by successive neutron capture reactions in the uranium and plutonium isotopes present in the fuel. In uranium-fuelled reactors, the contributions due to U-239 with half-life of 23.5 min and Np-239 with half-life of 2.4 days dominate this source; in reactors loaded with thorium, the dominant isotopes are Th-233 and Pa-233 with half lives of 2.23 min and 27.1 days, respectively. However, with the recycling of plutonium and minor actinides like americium, many hazardous actinides are formed through (n,α), (n,γ) and (n,2n) reactions that may contribute significantly to the heat source in reprocessing plants after the fission products have been separated. Examples are the α-emitting Pu-238, americium and curium isotopes, and the curium and californium isotopes that decay via spontaneous fission (Kloosterman et al., 1997). For fast reactors or thermal reactors loaded with MOX

fuel, the actinides U-239 and Np-239 may contribute several tens of percents to the decay heat.

Figure 1.2: Decay power and cooling power in the condensation pool of a boiling water reactor with internal circulation pumps (Pershagen, 1989).

3. Fissions induced by delayed neutrons. As mentioned before, the fission fragments

produced by fission are relatively rich in neutrons, which gives rise to β- emission in some cases immediately followed by neutron emission. There are believed to be about twenty fission products that emit neutrons. These products are called delayed-neutron precursors (Weaver, 1986). In practice, however, the delayed neutron emission can be represented adequately by use of six effective precursor groups (Duderstadt and Hamilton, 1976) with half-lives for U-235 of 55, 22, 6.0, 2.2, 0.50, and 0.18 seconds. The fraction of delayed neutrons relative to that of the promptly emitted neutrons is very small, only 0.7% for U-235 and 0.25% for Pu-239, but due to the softer energy distribution of the delayed neutrons, the importance is larger than the direct yields suggest. According to point-kinetics with one effective group of delayed neutrons, the fission power as a function of time t after a large negative shutdown reactivity 0ρ reads (Todreas and Kazimi, 1989):

( ) ( ) 0 00

0 0

exp expP t P t tρ ρ ββ λ

β ρ β ρ − = − − − − Λ

(1.4)

where β is the fraction of delayed neutrons,λ the corresponding decay constant, and Λ the mean neutron generation time. The second exponential decays very quickly and is not important for decay heat analyses. The first exponential term decays with a time constant of about one minute, during which this heat source equals that produced by fission product decay (if a shutdown reactivity of 9$ is assumed, the amplitude of

the first term equals about 0.1). However, within minutes from shutdown fissions from delayed neutron emission are reduced to a negligible amount. Figure 1.3 shows the fission power after shutdown for various values of the shutdown reactivity (Sesonske, 1973). Because of its specific nature, it is usually neglected from general decay heat studies. Exercise 1.4: Estimate the value of one dollar reactivity in units of pcm (10-5) for an LWR fuelled with UO2 fuel and with MOX fuel. Exercise 1.5: Substitute in Eq. (1.4) typical values for light water reactors and verify that the second term vanishes within 0.01 second.

4. Reactions induced by spontaneous fission neutrons. A number of actinides, which

may be produced in the reactor during operation, decay by means of spontaneous fission with a corresponding liberation of neutrons. The activation reactions induced by these neutrons form a decay heat source, which, in general, is negligible compared with the other decay heat sources. In many cases, the neutrons liberated pose a shielding problem much more serious than a decay heat problem.

Figure 1.3: Reactor power due to delayed-neutron induced fissions after shutdown with a shutdown reactivity value as shown in the figure (Sesonske, 1973).

5. Structural and cladding materials in the reactor that may have become radioactive due

to (n,α), (n,p), (n,γ) and (n,2n) reactions. In many cases, it is the trace impurity elements present that activate and release decay heat. Unlike the fission products, the majority of these activation products decay directly to stable isotopes. The contributions of the structural materials are important for decommissioning and waste disposal, but are generally negligible compared with the contribution of the fission products. This is especially the case for short cooling times of importance in LOCA studies (<105 seconds). After a few hours, decay heat due to activation contribute a few percents to the total decay heat.

In early times only the contribution due to the fission products was taken into account, but nowadays it poses no serious problem (neither due to the nuclear data missing nor to the calculation method) to include the actinides’ contribution. Heat production due to delayed neutron induced fission or spontaneous fission is usually neglected. Activation of light elements in structural materials plays a role only in special circumstances, and is usually excluded from decay heat analyses. Finally, it should be noted that under reactor accident conditions, vapors and aerosols released from the core region contain various fission products, which may be deposited on structural materials. This reduces the decay heat levels in the core region, at the expense of increased heating of the primary circuit, posing a possible threat to the integrity of the structures (Lillington, 1995).

2 DECAY HEAT CALCULATIONS

2.1 Instantaneous burst of fission If we consider a system containing a single fissile actinide, on average, each fission creates exactly the complete fission product yield distribution characteristic of that nuclide. Figure 2.1 shows the fission product yields of three actinides as a function of the atomic mass number. These curves resemble the average fission product composition in the fuel if no activation takes place. With the presence of decay, the fission product composition changes, but not the cumulative yields shown in figure 2.1. These do change, however, by neutron activation. Figure 2.2 shows the normalized fission product composition due to fission of U-235 in a thermal neutron flux of 1012 cm-2⋅s-1 and 3⋅1013 cm-2⋅s-1. The concentrations of fission products with large absorption cross sections reduce considerably, while the concentration of nuclides with low activation cross-section increase. Exercise 2.1: Why do the cumulative yields in Figure 2.1 do not change with decay? Which nuclides cause the dips in Fig. 2.2?

Figure 2.1: Cumulative fission product yields due to thermal fissioning of U-233, U-235 and Pu-239 (JEF2.2).

Figure 2.2: Normalized cumulative fission product composition after irradiation of U-235 for 1000 days in a thermal neutron flux.

In the absence of neutron capture, the beta and gamma decay heat produced per fission event is only a function of the decay time. Let b(t) and g(t) be these decay heat sources, respectively. The total decay heat function per fission event f(t) is simply the sum of b(t) and g(t). If a fissile nuclide is being irradiated for a time I with a constant fission rate, the decay heat at a time t’ seconds following the irradiation can be calculated by regarding the irradiation as a series of fission bursts (see Fig. 2.3). For each fission burst, the contribution to the beta decay power per unit fission rate equals b(t)dt. Then the total beta decay power at decay time t’ normalized per unit fission rate becomes:

( ) ( )’

’

, ’I t

t

B I t b t dt+

= ∫ (2.1)

A similar expression is found for the gamma decay heat G(I,t’) and the total decay heat F(I,t’). If the irradiation time is small compared with the decay time t’, the function B, and similarly for G(I,t’) and F(I,t’), can be approximated by: ( ), ’ ( ’ / 2)B I t I b t I= ⋅ + (2.2)

This simply states that for a short irradiation time and a long decay time, the decay heat can be approximated by the burst function evaluated at time t’+I/2. The function B(I,t’) can be written as the difference of two integrals:

( ) ( ) ( ) ( ) ( )0 0 0 0’ ’ ’ ( ) ’

’ ’ ’ ’

, ’I t I t I t I I I t

t I t t I t

B I t b t dt b t dt b t dt b t dt+ + + − + +

+ +

= − = −∫ ∫ ∫ ∫ (2.3)

By taking the limit of I0 to infinity, the function B(I,t’) can be written as the difference of two terms at infinite irradiation: ( ) ( ) ( ), ’ , ’ , ’B I t B t B I t= ∞ − ∞ + (2.4)

Similar formulae apply for the gamma decay power G(I,t’) and the total decay power F(I,t’). For long irradiation times (I>>t’), the second term on the right hand side of Eq. (2.4) will be small compared with the first term, which implies that B(I,t’) can be approximated by B(∞,t’). It is noted that the functions b(t’), g(t’) and f(t’) are expressed in units of (MeV/second), and that the corresponding integral quantities B(I,t’), G(I,t’) and F(I,t’) are expressed in units of (MeV/fission) per (fission/second), i.e., effectively in units of (MeV/second).

Figure 2.3: A finite irradiation represented by a series of fission bursts (Tobias, 1980).

2.2 Burnup calculations Depletion of fissile nuclides During reactor operation, the nuclide inventory changes due to fuel depletion and fission product buildup. The mix of nuclides at the end of the irradiation period determines the decay heat, so for accurate determination of decay heat, the concentrations of all nuclides, both actinides and fission products, must be calculated. For depletion of a single fissile actinide:

( ) ( ) ( ) ( ) ( ) ( ), ,

AZ Z A A A A A A

a Z Z Z Z Z

dN tN t t N t t N t

dtσ λ α= − Φ − = − (2.5)

where N is the concentration of the nuclide with atomic number Z and mass number A, σ its microscopic cross section, and λ its decay constant. The total neutron flux is given by Φ. The parameter α can be viewed as a removal constant determined by the absorption rate (including both the fission and neutron capture rates) and the decay constant of the nuclide: ( ) ( ) .A A A

Z Z Zt tα σ λ= Φ + (2.6)

The concentration of the nuclide becomes:

( ) ( ) ( )( )00 exp ’ ’ ,

tA A AZ Z ZN t N t dtα= −∫ (2.7)

which is still a formal solution that cannot easily be calculated because the neutron flux depends on the concentration of the nuclide. Two standard approximations are used in depletion studies to solve Eq. (2.7) (Duderstadt and Hamilton, 1976). The first is the constant flux approximation (Φ(t)=Φ0), which gives the following expression for N(t):

( ) ( ) ( ) ( ) ( ) ( ),00 exp 0 exp exp .A A A A Z A A

Z Z Z Z a ZN t N t N t tα σ λ= − = − Φ − (2.8)

When nuclide decay can be neglected, which (of course!) is the case for natural occurring fissile nuclides, this solution simplifies to:

( ) ( ) ( ),00 exp .A A Z A

Z Z aN t N tσ= − Φ (2.9)

The other approximation used in depletion calculations is the constant power solution: ( ) ( ),

0 constant,Z A Aa a ZP w N t tσ= Φ = (2.10)

where wa is the energy released per neutron absorbed by the fissile nuclide. The solution of Eq. (2.5) is given by:

( ) ( ) ( ) ( )0 10 exp 1 expA A

Z Za

PN t N t t

wλ λ

λ= − − − − (2.11)

which, in the absence of decay, simplifies to:

( ) ( ) 00 .A AZ Z

a

PN t N t

w= − (2.12)

In other words, the fissile nuclide density decreases linearly with time, while decreasing exponentially in case of the constant flux approximation.

A comparison of both solutions is schematically shown in Fig. 2.4. For small irradiation times, both give the same solution, but for large irradiation times, the constant flux solution gives larger nuclide densities than the constant power approximation. In practice, many computer programs solve the depletion equations with a constant flux during short time intervals. The value of the flux during each time interval may be determined from the power given in the input, or calculated from lattice or neutron spectrum codes. Buildup of actinides As mentioned before, the dominant nuclides contributing to the actinide decay power in uranium-fuelled reactors are U-239 and Np-239, at least for decay

times < 106 seconds, after which beta decay of U-237 and Pu-241, and alpha decay of the other plutonium isotopes become important. The nuclide densities can easily be estimated when the production rate of U-239 in uranium-fuelled reactors is assumed to be constant in time. Let R be this constant production rate, so that the U-239 nuclide density can be expressed as:

( ) ( )239

239 2399292 92239

92

1 expR

N I Iλλ

= − − (2.13)

and that of Np-239:

( ) ( ) ( )( )

239 239 239 23823993 92 92 93239 92

93 239 239 23993 92 93

exp exp1 .

I IRN I

λ λ λ λλ λ λ

− − − = +

− (2.14)

Here time I is the irradiation time. Following shutdown, both species undergo radioactive decay with the release of beta and gamma radiation, leading to more complex expressions for the nuclide densities as a function of decay time (Tobias, 1980). The same formulae hold for the Th-233 and Pa-233 nuclide densities in reactors containing thorium. Exercise 2.2: Derive expressions for the U-239 and Np-239 nuclide densities similar to Eqs. (2.13) and (2.14) that include the decay effect after the irradiation. Eqs. (2.13) and (2.14) can be simplified considerably, when it is recognized that the nuclide density of U-239 saturates very quickly due to its short half life. Then the activities of U-239 and Np-239 are given by:

Figure 2.4: Depletion of a single fuel isotope according to the constant flux approximation and the constant power approximation (Duderstadt and Hamilton, 1976).

( ) ( )239 239 23992 92 92’ R exp ’A t tλ= − (2.15)

and:

( ) ( ) ( )239 239 239 23993 92 93 93’ 1 exp exp ’ ,A t R I tλ λ = − − − (2.16)

where t’ is the decay time. Note that the Eq. (2.16) can be simplified further if the irradiation time is much longer than the half-life of Np-239 (2.4 days), in which case the activity of Np-239 also decays exponentially after the irradiation. Exercise 2.3: When the nuclide Np-239 saturates, why is its activity during irradiation and decay virtually independent of the concentration of U-239? Buildup of fission products During reactor operation, a fission product may be created through its direct fission yield, or through neutron capture or decay by other nuclides. It may itself undergo transformation through radioactive decay or by neutron capture. Because the fission product decay heat is determined by a large number of nuclides whose concentrations vary more rapidly than those of the fissile actinides analytical expressions of nuclide concentrations for the purpose of decay heat evaluation are of little use. Instead, computer programs must be used to solve the differential equations governing the buildup and decay of fission products and actinides, as well as the structural materials. An exception to the above is the buildup of Cs-134 by activation of Cs-133. The concentration of Cs-133 as a function of the irradiation time is similar to that of U-239, except for the fact that the removal of Cs-133 is not due to decay, but by activation:

( ) ( )133

133 1335555 55133

55

1 exp .R

N I Iσσ

= − − Φ Φ (2.17)

Using this expression, the concentration of Cs-134 at the end of the irradiation reads:

( ) ( ) ( )134 134 134 133 13455 55 55 55 55134 134 133

55 55 55

1 11 exp exp expN R I I Iα σ α

α α σ = − − − − Φ − − − Φ

(2.18)

where the α indicates the total removal “cross section” given in Eq. (2.6). The activation of Cs-133 is easily calculated, and gives a significant contribution at cooling times of about 108 seconds (i.e. several years). Section 2.4 describes the effects of neutron captures by fission products in more detail. Exercise 2.4: Give an expression for the Cs-133 production rate (R) in Eq. (2.17).

Numerical procedures The general equation describing time-dependent nuclide concentrations during irradiation and decay reads:

( )i i j j i i

j f j x j j j j a i i ij i j i j i

dN tN N f N N N

dtγ σ σ λ σ λ

≠ ≠ ≠

= Φ + Φ + − Φ −∑ ∑ ∑ (2.19)

The first three terms on the right hand side of Eq. (2.19) describe the production of the nuclide i by fissioning, neutron interactions ((n,γ), (n,α), (n,p), (n,2n), (n,3n), reactions etc), and decay of other nuclides. The last two terms describe the destruction rate of the nuclide by neutron absorption (including fissioning) and by radioactive decay. Because the nuclide densities vary with time, the one-group neutron cross-sections, and the neutron flux are essentially time dependent, which makes Eq. (2.19) non-linear and its solution non-trivial. Therefore, in most modern computer codes, the neutron flux Φ is averaged over (some region of) space and energy, and usually kept constant during small time steps. Then Eq. (2.19) is solved for the nuclide densities at the end of the particular time step, after which the neutron spectrum in the fuel is recalculated and the neutron interaction cross sections used in the burnup calculation are updated. The new value for the neutron flux is calculated from the power (obtained from the spectrum calculation or given in the input of the burnup code), and the nuclide densities at the end of the next time step are calculated. In this way, the nuclide densities at the end of the irradiation are obtained. Although most of the computer programs solve Eq. (2.19) iteratively in the way described above, differences exist in the solution methods used. Some codes, for example, solve Eq. (2.19) analytically while other codes apply a numerical procedure. Differences also exist in the detail included in the calculations. Some codes have a limited number of nuclide chains and neutron reactions, but can give more accurate space-dependent solutions. The WIMS code system, for example, only takes into account (n,γ), (n,2n) and fission reactions, and only a limited number of nuclides, but calculates the nuclide densities for very large numbers of geometrical cells. This stems from the fact that reactor lattice codes like WIMS, focus on the calculation of reactivity effects of nuclides, rather than on the accurate prediction of (exotic) nuclides with a negligible influence on reactivity. Other codes like CINDER, DARWIN, FISPACT, ORIGEN, and RIBD (so-called point-depletion codes) include a large number of nuclides, and take into account a large number of neutron interactions, but have a limited capability to obtain space-dependent nuclide inventories. Most codes have special provisions to treat short-lived nuclides (usually by putting the concentrations of these nuclides directly to their equilibrium values) to reduce CPU time and to avoid numerical errors. Increased performance of computers has led to the development of Monte Carlo neutron spectrum codes coupled to point-depletion codes to undertake accurate burnup calculations in complex three-dimensional geometries (see for example Kloosterman (1996), and Hesse et al (2000)). The first type of code calculates the neutron spectrum, neutron flux, and the self-shielded neutron cross sections, which are subsequently passed to the burnup code that calculates the nuclide densities at the end of the current time step. Together with new extended nuclear data libraries (Hoogenboom and Kloosterman, 1997), this is expected to improve inventory calculations, especially for new applications such as the recycling of plutonium and transmutation of minor actinides. Another option is to perform the burnup calculations in the Monte Carlo code itself (Mori et al, 1999).

Summation calculations The final step in decay heat analyses, after the inventories of the actinides and fission products have been calculated for the specified conditions of reactor operation and cooling, consists of summing the products of the activity of each nuclide and the mean energy release per desintegration Ei of that nuclide. The total decay heat is then given by: i i i

i i i i i ii i i

H E N E N E Nα β γλ λ λ= + +∑ ∑ ∑ (2.20)

Exercise 2.5: Estimate the average energy release per disintegration for α, β and γ decay. 2.3 Uncertainties in summation calculations

For cooling times ranging from 10 days to a few years, the actinides contribute a fraction of about 10% to the total decay heat in uranium-fuelled reactors. Assuming a realistic uncertainty of about 10% in the actinides decay heat contribution, its uncertainty to the total decay power does not exceed one percent. For this reason, most of the uncertainty analyses focus on the fission products. Uncertainties in fission product decay heat are due to uncertainties in the nuclear data and the irradiation history. Nuclear data uncertainties can further be categorized into those due to fission product yields, half-lives, and decay energies. Table 2.1 gives an overview of the status in the late seventies. At that time, the main uncertainty was due to decay energies, although the data of Yamamoto and Sugiyama (1978) suggest that the major uncertainty for decay times larger than 103 seconds was due to the yields. Despite this discrepancy, it was generally agreed that the yield data for thermal fission of U-235 are not the dominant source of uncertainty, particularly if correlation effects are accounted for as will be explained later. The uncertainty due to the half-lives tends to be relatively insignificant for most cooling times. Besides the yields, half-lives and decay energies, there is another source of uncertainty, namely that due to the nuclear cross-section data. As mentioned before, depletion calculations are usually done with a constant flux during a time step using one-group cross sections collapsed with the neutron spectrum calculated for that time step. This means that the uncertainties in the one-group cross sections of the nuclides are partly due to uncertainties in the basic nuclear data and partly due to the errors in the neutron spectrum calculation method and uncertainties in the irradiation history. In general, the effect of including the neutron interactions with nuclei is to increase the decay heat produced. The effect in a thermal reactor is only a few percent for cooling times less than 105 seconds and less than 2% for decay times less than 103 seconds. In fast reactors, the effect is believed to be even smaller (Tasaka (1977), Schmittroth (1976)). For this reason, the uncertainties in nuclear cross-section data do not contribute significantly to the decay heat uncertainty. Figures 2.5 and 2.6 give a graphical representation of the uncertainties in summation calculations as a function of the decay time for thermal and fast fission, respectively. Although some discrepancies exist between the different studies for similar irradiation time, all the curves display similar trends. The uncertainty first decreases to a minimum for cooling times between 103 and 106 seconds after which it increases again.

As mentioned at the beginning of this section, another source of uncertainty is that due to the various unknowns in the irradiation history. Because the effect of neutron capture reactions on fission product decay heat is quite modest, the uncertainties related to neutron spectrum effects can usually be neglected, despite the fact that the actinide inventory may be quite sensitive to spectrum effects (Tobias, 1980). A more important effect is that due to the fuel rating. The concentrations of the short-lived actinides and fission products at saturation are proportional to the reactor power (see Eq. (1.2)), which implies that the uncertainties in the concentration of these nuclides are proportional to the uncertainty in the fuel rating too. For longer cooling times up to 30 years, the actinide decay heat is

proportional to the square of the reactor power, which implies that a 2% uncertainty in the fuel rating gives rise to a 4% uncertainty in the actinide decay heat. Exercise 2.5: Show that the concentration of a nuclide formed by two subsequent neutron capture reactions is proportional to the square of the neutron flux. Uncertainties in the irradiation time also have an impact on the resulting uncertainties in decay heat, but only for long cooling times. For short cooling times, the decay of the short-lived fission products, which are relatively insensitive to the irradiation time (see Eq. (1.2)), dominate the decay power. The activity of the non-saturating nuclides is proportional to the irradiation time (see Eq. (1.3)), while that of the nuclides in between (“slowly” saturating nuclides) depends on the irradiation time as shown in Eq. (2.16) [ ( )1 exp Iλ− − behavior]. Therefore, the effect of this source of error on the activity of

these nuclides is largest for short irradiation times when the short-lived fission products already dominate the decay heat production.

Table 2.1: Status in the late seventies of uncertainties in fission product decay heat summation calculations for thermal fission of U-235 (Tobias, 1980).

Another source of error may be due to uncertainties in the history of the power rating during burnup. Not surprisingly, however, it will be the power rating at the end of the irradiation that dominates the decay heat heat for short cooling times. As may be deduced from the analysis above for long cooling times the decay heat is rather insensitive to the power rating history of the fuel. However, it is sensitive to the mean value of the power rating and the irradiation time. Sensitivity studies are mainly performed for the well-known fissile uranium and plutonium isotopes (U-235 and Pu-239). To see how much the fission product yields of one nuclides differ from the other, a correlation coefficient (µ) is defined that measures the agreement or difference between the

fission yields of two isotopes:

( ) ( )

,

22 ,

. ’

’

i ii

i ii i

y y

y yµ = =

∑

∑ ∑y yy y

(2.21)

Figure 2.5: Total uncertainty in fission product decay heat summation calculations for thermal neutron fission (Tobias, 1980).

Figure 2.6: Total uncertainty in fission product decay heat summation calculations for fast neutron fission (Tobias, 1980).

Figure 2.7 shows the correlation coefficient between fission-product yields induced by thermal neutrons (T), fast neutrons (F) and high-energy neutrons (H) relative to the thermal-induced yields of U-235. The general tendency is that the larger the difference is between the atomic masses of U-235 and the isotope under consideration, the smaller the µ is. This, of course, is what one would intuitively expect. To get some feeling about the meaning of the correlation coefficient µ, one can compare the yields of U-233, U-235 and Pu-239 in Fig. 2.1 with the correlation coefficients in Fig. 2.7 (0.900 for thermal fission of U-233, and 0.854 for thermal fission of Pu-239). In general, the differences between thermal and fast fission are much smaller than the differences between thermal fission and high-energy fission. The same correlation coefficient µ can also be

used to assess the differences between evaluated nuclear data libraries. This coefficient is shown in Fig. 2.8 for the independent fission yields between the ENDF/B-VI and the JNDC (version 2) nuclear data files. As can be seen, the differences are relatively small, which is most probably due to the fact that the source of the yields in the two data files is identical. Therefore, the correlation coefficient in that case, is more a measure of the differences introduced by the processing codes, rather than a measure for the differences between the independent fission yields.

Figure 2.7: The correlation coefficient (Eq. (2.21)) between the thermal fission yields of U-235 and the fission yields due to thermal neutrons (T), fast neutrons (F) and high-energy neutrons (H) based on ENDFB-VI (Oyamatsu and Sagisaka, 1996).

Recently, decay heat uncertainties were estimated from the data in the ENDF/B-VI nuclear data library containing fission yields for 50 nuclides and decay data for 891 fission products (Ohta et al, 1996). Although the uncertainties in the beta and gamma decay energies and in the decay data (half-lives) of the nuclides had to be estimated, the result seems in reasonable agreement with those already achieved twenty years ago. The uncertainties in thermal neutron induced fission of U-235 and fast neutron induced fission of Am-241 are shown in Fig. 2.9. The U-235 results are in reasonable agreement with the results shown in Fig. 2.5. Again the uncertainties for short and long cooling times are much higher than for cooling times between 104 and 108 seconds. The peaks in the uncertainties of

the gamma decay heat component of U-235 are due to Nb-101, Sr-93, Y-97, Y-95 and Cs-137 (Oyamatsu et al, 1997). Furthermore, the uncertainties for the minor actinides are about 2 to 5 times larger than the uncertainties for U-235 and Pu-239. It is noted that for the uncertainty in the total decay heat (the summed beta and gamma components), correlation effects are neglected, which implies that the figures overestimate the decay heat uncertainty (because a strong negative correlation can be expected between the beta and gamma decay heat uncertainties). The (negative) correlation between the yields, due to the sum of the independent yields in a decay chain should equal the mass chain yield, and the total sum of the all mass chain yields being set to equal 2, are taken into account. The effects of this correlation are shown in Fig. 2.10 as function of the cooling time. The uncertainty in the delayed neutron activity at cooling times between 0.1 to 100 seconds is typically 2 to 3 times larger than the uncertainty due to beta and gamma decay heat for the same nuclides (Miyazono et al, 1997).

Figure 2.8: The correlation coefficient (Eq. (2.21)) between the independent fission yields of nuclides of the ENDF/B-VI and JNDC (version 2) nuclear data files for fission due to thermal neutrons (T), fast neutrons (F), and high-energy neutrons (H) (Oyamatsu and Sagisaka, 1996).

Figure 2.9: The uncertainties in decay heat calculations for thermal neutron induced fission of U-235 and fast neutron fission of Am-241 (Ohta et al, 1996).

Figure 2.10: Uncertainties in decay heat calculations due to fission yields for thermal neutron induced fission of U-235 and of Pu-239 (Ohta et al, 1996). Recently, a hybrid method for the calculation of decay heat has been published, based on the fact that the decay heat power is a linear function of the independent fission yield. This implies that the fission yields of a nuclide can be written as a linear combination of the fission yields of N other nuclides, such that the residue is minimized. The decay heat of the specific nuclide can be calculated from the resulting coefficients as a weighted sum of the decay heat of the N other nuclides. In this way, the decay heat of nuclides with no experimental decay heat data can be calculated as a weighted sum of the decay heat of nuclides with decay heat data that are well known from experiments (Takeuchi et al, 1999). The method has been shown to give good results for beta decay heat calculations (within 3-5% compared with summation calculations), but exhibits a slightly larger discrepancy for gamma decay heat calculations (within 4-8%).

Table 2.2: Uncertainties in decay heat calculations for several nuclides and energy ranges of the neutrons inducing fission (Ohta et al, 1996). Nuclide Neutron energy β γ β+γ U-235 Thermal 1-6 1-6 1-6 U-238 Fast 1-5 2-5 2-4 Pu-239 Thermal 2-12 2-13 2-7 Np-237 Fast 3-12 3-9 3-9 Am-241 Fast 4-13 4-20 4-13 Am-243 Fast 5-13 5-16 4-12 Cm-244 Fast 4-13 5-20 5-13 Cm-246 Fast 5-14 6-17 5-12 Cm-248 Fast 5-15 6-15 5-12 2.4 Influence of neutron capture reactions Comparing Figs. 2.1 and 2.2, the influence of neutron capture reactions on the fission product composition can be seen. In general, neutron captures increase the fission product decay heat, because stable isotopes are transmuted to unstable ones. However, there are a few exceptions among which the most important one is Xe-135 (Tasaka, 1977). This isotope, with a half-life of about 9 hours and a very large thermal absorption cross-section, either decays to Cs-135 or transmutes to the stable isotope Xe-136. Hence neutron capture reactions have a twofold effect. First, the fission product decay heat for cooling times up to 105 seconds decreases, because less Xe-135 decays to Cs-135. Secondly, the fission products decay heat between 105 and 107 seconds decreases, because a lower Cs-135 concentration yields a lower production of the unstable isotope Cs-136 with half-life of 13 days that is produced through neutron capture by Cs-135. Figure 2.11 shows the effect of neutron capture reactions in an LWR as a function of the cooling time for both U-235 and Pu-239, and for U-235 with zero Xe-135 cross section, while Fig. 2.12 shows the influence of the thermal neutron flux. From these figures, some important conclusions can be drawn. First, the effect of neutron capture reactions on the fission product decay heat is negligible for cooling times of importance for Loss Of Coolant studies (LOCA) (< 104 seconds). Secondly, between 104 and 107 seconds, the effect of neutron capture reactions is to increase the fission product decay heat, but by no more than ten percent for a very high thermal neutron flux (see Fig. 2.12). Thirdly, only after 107 seconds, when the decay heat power has already reduced by a factor of 100, the activation of the fission products increases the decay heat power, but for realistic fluxes and irradiation times by no more than 50%. These three conclusions also hold when the neutron flux is increased instead of the irradiation time (Tasaka, 1977). Figures 2.13 and 2.14 show the effects of the irradiation time on the fission product decay heat for both an LWR (Fig. 2.13) and a fast reactor LMFBR (Fig. 2.14). It is seen that for practical neutron fluxes and irradiation times, the effects of neutron capture on the decay heat are smaller in a fast reactor than in a thermal reactor. This is mainly due to the lower values of the neutron capture cross sections in a fast reactor.

Figure 2.11: The effect of neutron capture on the fission product decay heat (Tasaka, 1977).

Figure 2.12: The effect of the thermal neutron flux on the fission product decay heat in an LWR (Tasaka, 1977).

Figure 2.13: The effect of the irradiation time on the fission product decay heat in an LWR (Tasaka, 1977).

Figure 2.14: The effect of the irradiation time on the fission product decay heat in an LMFBR (Tasaka, 1977).

3 DECAY HEAT EXPERIMENTS 3.1 Introduction Although decay heat measurements have been performed in the early forties (Tobias, 1980), in this chapter we will discuss the basic aspects of decay heat measurements performed and documented in the late seventies. As we will see later on, the experiments documented by Dickens et al (1977, 1978, 1981), and Yarnell and Bendt (1978) played an important role in the adoption of the ANS5.1-1979 decay heat standard. Almost without exception, the experiments were specifically designed to yield information about the fission-product decay heat component only, which of course is much easier than to design an experiment that would yield only the actinide decay heat component. Fortunately, it is quite easy to estimate this component as only U-239 and Np-239 dominate this source. The decay-heat energy release from nuclear fission, in most cases thermal neutron fission, can be measured by two complementary methods:

• Integral measurement of the total beta and gamma-ray energy release by, for example, calorimetric methods. This is a simple and direct approach, but no distinction can be made between the energy release due to betas and gamma rays. Difficulties with this method arise from the (gamma) energy loss from the calorimeter and from the time constant associated with this meter. In 1978, Yarnell and Bendt used this method for short cooling times.

• Differential energy measurements of beta and gamma rays released during decay of fission products for specified counting time intervals following specified irradiation time intervals. The total energy release rate can be obtained by integrating over all beta and gamma ray energies. Clearly, one needs detectors accurately calibrated for a broad energy range and corrected for dead-time etc.

The two methods are complementary in the sense that the first method calls for long irradiation times leading to saturated fission product concentrations, while the second method calls for short irradiation times. Because the decay heat standards discussed in Chapter 4 based on these measurements are given for infinite irradiation times, a relationship between the irradiation time and the counting time is needed. Assuming a constant production rate 1R of a single nuclide with decay constant λ1, the amount produced during the irradiation time period Tirrad equals:

( )11 1

1

1 exp .irrad

RN Tλ

λ = − − (3.1)

After a time waitT , this number is reduced by a factor of ( )1exp waitTλ− . Integrating over

time period countT , gives the nuclides’ emission yield ( , , )irrad wait countY T T T :

( ) ( ) ( )11 1 1 1

1

( , , ) 1 exp exp 1 exp .irrad wait count irrad wait count

RY T T T T T Tλ λ λ

λ = − − − − − (3.2)

Clearly, symmetry is observed between the irradiation time irradT and the counting time

countT , which implies:

1 1( , , ) ( , , ).irrad wait count count wait irradY T T T Y T T T= (3.3)

Thus, for the emission yield of the daughter nuclide produced by decay:

( ) ( ) ( )

( ) ( ) ( )

2

1 12 2 2

2 1 2

1 11 1 1

2 1 2

( , , )

1 exp exp 1 exp

1 exp exp 1 exp ,

irrad wait count

irrad wait count

irrad wait count

Y T T T

RT T T

RT T T

λλ λ λ

λ λ λλ

λ λ λλ λ λ

=

+ − − − − − −

− − − − − − −

(3.4)

so that it can be concluded that both for nuclides directly produced by fission, and for the daughter nuclide produced by decay, symmetry can be observed between the irradiation time Tirrad and the counting time Tcount. In practice, this means that decay heat due to an infinitely long irradiation time can equally well be reproduced by a short irradiation time and an infinitely long counting time. The situation is illustrated in Fig. 3.1. Exercise 3.1: Verify Eq. (3.4). Why are Eqs. (3.3) and (3.4) not valid when neutron capture plays an important role?

Figure 3.1: A representation of irradiation, waiting and counting times in decay heat experiments (Dickens et al, 1977).

3.2 Decay heat measurements by Dickens et al To measure the decay heat from U-235 and Pu-239, Dickens et al, (1977, 1978) irradiated small samples of U-235 and Pu-239 for short periods of time (1, 5/10 and 100 seconds) in the fast pneumatic tube facility of the Oak Ridge Research Reactor. The thermal neutron flux was about 3⋅1013 cm-2.s-1 with the ratio between the thermal flux and the epi-thermal ranging from 36 to 40. The mass of the samples ranged from 1 to 10 µg for U-235 and from 1 to 5 µg for Pu-239. The samples were irradiated several times (Tirrad), with a waiting time following the end of irradiation (Twait), and counting times began at the end of the waiting time (Tcount). The resulting spectra were integrated over the energy range to obtain the energy release for betas and gamma rays for every combination of ( ), ,irrad wait countT T T . After the irradiation and the decay heat power

measurements, each sample was shipped to the low background counting room in order to determine the number of fissions in the sample. This was done by measuring the peak yields of Mo-99 (140.5 keV), Te-132 (49.7 keV) and Zr-97 (658 keV) for 8 hours or longer. The number of fissions Nf could be determined from:

( )exp( ) 1

1 expwait

fcount Y

Y TN

T BC

λλ ε

=− −

(3.5)

where Y is the measured peak yield, λ is the appropriate decay constant, Twait is the sample cooling time till the beginning of the measurement,ε is the detector efficiency for the gamma ray energy of interest, B is the branching ratio for the desired gamma ray and

YC is the cumulative fission yield for the isotope. For practical reasons, the beta and gamma rays were measured separately. For the beta measurements, two samples had to be prepared and irradiated. One without magnetic deflection to measure the joint contribution of betas and gamma rays, and one with magnetic deflection to measure only the gamma ray contribution. The difference of the two measurements yielded the requested beta decay heating. To estimate the contribution of epi-thermal neutron induced fissions to the decay heat, summation calculations were performed to determine the difference between decay heat due to thermal-induced neutron fission and fast-neutron induced fission of U-235. This difference turned out to be only 1% for cooling times between 2 and 104 seconds. Because of this small difference the effect of epi-thermal neutron induced fission of U-235 on the total decay heat was assumed to be negligible. Moreover, the total number of fissions induced by epi-thermal neutrons was estimated to be less than 1.5% of the total number of fissions. The results were presented integrally and differentially. A compact description of the experiments and the results is given in Kloosterman (1996), while some results are presented in Table 3.1. 3.3 Decay heat measurements by Yarnell and Bendt Yarnell and Bendt (1978) measured the fission decay heat of U-233, U-235 and Pu-239 by means of a calorimetric technique. Small samples of the fissile materials (with mass of 87 mg for U-233 and 66 mg for Pu-239) sealed in gas-tight stainless steel to avoid the release of gaseous fission products were irradiated for 20,000 seconds at constant thermal neutron flux. After this, the samples in their envelope were transferred to a liquid helium bath contained in a thermally isolated copper block that absorbed about 97% of the beta and gamma radiation emitted by the fission products in each sample. The absorbed energy evaporated liquid helium from the reservoir and a hot-film anemometer measured the evolution rate of the boil-off gas. It is important that the calorimeter has a short time constant compared with the measurement time. Furthermore, the temperature of the irradiated sample has to be brought to that of liquid helium before the measurements can start. The decay heat was calculated from the gas flow using the heat of vaporization of helium. The number of fissions in the sample was determined radiochemically after the calorimetric measurements were completed. In this way, only minor corrections were required to obtain the true decay heat. Again a summary of the experimental details can be found in Kloosterman (1996), while some results are given in Table 3.2.

Table 3.1: Fission product decay heat (MeV/fission) following an infinitely long irradiation as a function of the cooling time (Dickens et al, 1977, 1978, 1981). Some values are interpolated with time dependence according to Eq. (4.3) for the cooling time in the table.

Cooling time (s) U-235 Pu-239 Pu-241 2 11.20 9.666 11.46 5 10.10 8.778 10.15 10 9.119 8.040 9.095 20 8.118 7.289 8.066 50 6.582 6.305 6.742 100 5.949 5.550 5.790 200 5.156 4.877 4.975 500 4.293 4.077 4.087

1000 3.681 3.459 3.444 2000 3.073 2.821 2.801 5000 2.365 2.107 2.088 10000 1.9222 1.713 1.690

Table 3.2: Fission product decay heat (MeV/fission) following an irradiation of 2⋅104 seconds as a function of the cooling time (Yarnell and Bendt, 1978).

Cooling time (s) U-233 U-235 Pu-239 10 8.225 20 6.431 6.934 6.482 50 5.335 5.607 5.366 100 4.539 4.652 4.488 200 3.810 3.842 3.739 500 2.949 2.914 2.885

1000 2.310 2.254 2.206 2000 1.678 1.623 1.527 5000 0.9795 0.9018 0.7973 10000 0.5909 0.5317 0.4566

The results in Table 3.2 are significantly lower than the results in Table 3.1, which is due to the fact that the first-mentioned results are for an irradiation time of only 2⋅104 seconds, while the results in Table 3.1 are for an infinitely long irradiation. The contribution of nuclides with long half-lives will be missing in Table 3.2. In fact, a systematic difference exists between the spectroscopic results of Dickens and the calorimetric results of Yarnell and Bendt, the latter being larger than the former. The difference is larger than the uncertainty in each of the measurements (about 3%). In fact, the difference has never been resolved, and is often called in the literature the LANL-ORNL discrepancy or the calorimetric-spectroscopic discrepancy (Yoshida and Tasaka, 1992).

3.4 Integral decay heat measurement in SuperPhénix In a fast reactor with little thermal leakage, it is possible to measure the decay heat by recording the temperature at various places in the system. If this is done once with a known power supply to measure the inertia of the system, the experiment can be repeated with an unknown power. In this way the decay heat produced in the core after a shutdown can be measured. Such an experiment has been performed at SuperPhénix in the eighties (Gillet et al, 1990). After a reactor scram, the steam generators cooled the reactor until, after 3 hours, the primary sodium reached a temperature of 300 0C. Then the steam generators were drained and, because they could not remove any heat, the sodium temperature rose to 340 0C after which the emergency decay heat removal system became operational. When the sodium cooled to 300 0C, the emergency heat removal system was shut off, and the sodium temperature rose again. The variation in the temperature of the sodium is shown in Fig. 3.2, while Fig. 3.3 shows the decay heat obtained from the recorded data. The experimental error ranges from 7 to 13%. Although these kinds of calorimetric experiments are attractive because they differ from the experiments described in Sections 3.2 and 3.3, it is quite difficult to take into account the correct operating history of the reactor and the isotopic composition of the fuel. Calculations reported in literature underestimate the experimental values by about 5%, which is well within the uncertainty margin of the measurements.

Figure 3.2: Sodium temperature during the decay heat measurements in SuperPhénix (Gillet et al, 1990).

Figure 3.3: Decay heat power obtained from the measurements in SuperPhénix (Gillet et al, 1990).

In Japan, a series of calorimetric decay heat measurements has been done on spent fuel subassemblies of the JOYO experimental fast reactor (Aoyama et al, 1999). C/E ratios also ranged between 0.9 and 0.96. Both Pu-238 and Am-241 were found to give a significant contribution (6 to 17%) to the decay heat produced for cooling times from 26 to 258 days.

4 DECAY HEAT STANDARDS 4.1 Simple formulae The half-lives of fission products range from a small fraction of a second to millions of years. Clearly, to calculate the fission product decay power accurately for cooling times ranging from seconds to tens of years, summation calculations are required to take into account the contributions of all nuclides for which decay data is available. However, for a limited range of the cooling time, some fission products dominate, which enables one to use simplified formulae. In Chapter 1 it was already mentioned that for cooling times exceeding 106 seconds, only a dozen nuclides dominate (Schmittroth, 1976). In this section, some simple formulae will be shown, valid for a limited range of cooling times only. Todreas and Kazimi (1989) give for the beta decay power b(t) (See Eq. (2.1)) the following expressions accurate within a factor of two for cooling times between 10 seconds and 100 days. For the beta decay power, the formula is:

( ) ( )1.2 -1 -11.40 MeV.s .fissionb t t−= (4.1)

with the cooling time t expressed in seconds. It is implicitly assumed that the mean energy of beta particles equals about 0.4 MeV. For the corresponding gamma decay power g(t), the expression reads:

( ) ( )1.2 -1 -11.26 MeV.s .fission ,g t t−= (4.2)

where a mean energy per gamma decay of about 0.7 MeV has been assumed. In 1963, Glasstone and Sensonske presented these formulae with the cooling time expressed in days, as well as a more accurate one for cooling times between 1 and 100 seconds that includes beta decay contributions due to U-239 and Np-239. Using Eq. (2.1) for b(t) and the corresponding equation for g(t), one can calculate the decay heat power after a reactor operation time I. The following expression, originally published by Way and Wigner (1951), is obtained for the total fission product decay heat:

( ) ( ) ( )0.20.2 -12.66, MeV.fission

0.2F I t t t I

−− = − + (4.3)

or, expressed as a fraction of the fission power of the reactor during operation:

( ) ( ) 0.20.2, 0.066F I t t t I−− = − + (4.4)

Note that Pershagen (1989) erroneously uses a ten times larger constant in Eq. (4.4). Taking an infinitely long reactor operation time, and integrating over the cooling time, one obtains the integral decay power given in Eq. (1.1). Glasstone and Sesonske (1981) provide a variant to Eq. (4.4):

( ) ( ) 0.30.3, 0.137F I t t t I−− = − + (4.5)

as well as a more complex function with four terms. Finally, note that the decay heat power after a fission pulse, Eqs. (4.1) and (4.2), varies roughly with a t-1 dependence. For this reason, the product t⋅f(t) is often plotted instead of f(t). Exercise 4.1: Calculate the decay heat per MWth reactor power 1 hour, 1 day and 1 month after shut down. The reactor operated for 3 years. Compare Eqs. (4.4) and (4.5).

4.2 Decay Heat Standards Data from several experiments were examined in the 1960s to provide an accurate basis for predicting fission product decay heat power. In 1971, the results were adopted by the American Nuclear Society (ANS) to assemble the first decay heat standard (ANS5.1/N18.6) based on the recommendations by Shure, which after some minor modifications was submitted to the American National Standards Institute (ANSI) in 1973. Figure 4.1 shows the fission product decay heat power as a function of cooling time according to that standard.

Figure 4.1: Fission-product decay power as a function of cooling time after shutdown according to the draft ANS5.1/N18.6 (Todreas and Kazimi, 1989).

The ANS5.1/N18.6 draft later updated to the ANS5.1-1973 draft standard contained a single curve to represent all uranium-fuelled reactors. Uncertainties ranged from +20% to -40% for cooling times less than 103 seconds, from +25% to -50% for cooling times larger than 107 seconds, and from +10 to -20% for cooling times in between. Because the range of cooling times less than 104 seconds is especially important for the evaluation of Emergency Core Cooling Systems (ECCS) in case of Loss of Coolant Accidents (LOCA), the fission-product decay heat calculated for these purposes was set to 1.2 times the values calculated by the ANS5.1-1973 draft standard for infinite irradiation (Dickens et al, 1991). New measurements in the seventies led to a new compilation that resulted in the adopted standard in 1979 (ANS5.1, 1979), which was reaffirmed in 1985. Figures 4.2 and 4.3 compare the two standards. Figure 4.2 shows that the ANS5.1-1979 standard gives slightly lower values for short cooling times (up to 103 seconds). Also shown in Fig. 4.2 is the uncertainty band assigned to the draft standard from 1973. It should be noted here that the ANS5.1-1973 draft standard is applicable to all fissionable nuclides, while the

ANS5.1-1979 standard has three separate standards for thermal fission of U-235 and Pu-239, and fast fission of U-238. Therefore, a fair comparison requires a decay heat computation over the lifetime of reactor fuel. Taking into account that in a thermal uranium-fuelled reactor, a fraction of the fission power is due to fast fission of U-238, and thermal fission of Pu-239, the ANS5.1-1973 draft standard is quite representative for cooling times up to 10 seconds (see Fig. 4.3). For longer times, the ANS5.1-1973 is expected to give an underestimation of the decay heat production. Exercise 4.2: Estimate the contribution to the fission power in a thermal uranium-fuelled reactor due to fast fission of U-238 and due to thermal fission of Pu-239.

Figure 4.2: Fission-product decay heat according to the ANS5.1-1973 draft standard and to the ANS5.1-1979 adopted standard (Dickens et al, 1991).

Figure 4.3: Fission product decay heat according to the ANS5.1-1973 draft standard and the ANS5.1-1979 adopted standard (Todreas and Kazimi, 1989).

In the ANS5.1-1979 standard, the U-235 evaluations for cooling times up to 105 seconds are based on summation calculations and measurements performed in the seventies by Lott et al (1973), Friesenhahn et al (1976), Dickens et al (1977), Yarnell and Bendt (1977), and Schrock et al (1978), and for Pu-239 by Dickens et al (1978), Yarnell and Bendt (1978), and Fiche et al (1976). For cooling times greater than 105 seconds, the standard is based solely on summation calculations supported by experimental data (see Figs. 4.4 and 4.5). The U-238 evaluation is also based solely on summation calculations. Shure et al (1979) compared the ANS5.1-1979 standard with experiments reported in the literature by Gunst et al (1975). Figure 4.4 shows the ratio of calculations and experiments for U-235 data, while Fig. 4.5 shows the same for Pu-239 data. Despite the fact that for the cooling times considered the standard is based on summation calculations only, the agreement is quite good. The average C/E ratios are 1.009 for U-235 and 0.995 for Pu-239. In the ANS5.1-1979 standard, the decay heat power after a fission delta pulse, f(t), for thermal fission of U-235 or Pu-239 and for fast fission of U-238 is fitted as a weighted sum of 23 exponential functions:

( ) ( )23

1

exp ,i ii

f t a tλ=

= −∑ (4.6)

where the αs and λs are the fit coefficients different for each fissile actinide. The fission power after a reactor operation time I can be represented by:

( ) ( ) ( )23

1

, exp 1 exp .ii i

i i

F I t t Iα λ λλ=

= − − − ∑ (4.7)

The fission product decay heat after an infinitely long reactor operation time can be obtained by setting I equal to 1013 seconds (!). The maximum cooling time considered by this standard is 109 seconds. Note that according to Eq. (4.6), the decay heat is fitted by pseudo fission products decaying to a stable daughter nuclide. However, one cannot ascribe real fission products to each term in Eq. (4.6). In other decay heat standards, the fit coefficient may become even negative!

Figure 4.4: Ratio of calculations and experiments of U-235 fission product decay heat (Shure et al, 1979).

Figure 4.5: Ratio of calculations and experiments of Pu-239 fission product decay heat (Shure et al, 1979).

Figure 4.6: Ratio of fission product decay heat according to the ANS5.1-79 standard and calculations (Dickens et al, 1991).

Figure 4.7: Ratio of fission product decay heat with and without activation of fission products (Tasaka et al, 1991).

The effect of neutron capture is not included in the ANS5.1-1979 standard, but an upper bound is given that provides conservative values of decay power in case of long operation of a uranium-fuelled LWR at high neutron flux. Figure 4.6 shows a comparison between these conservative values and some summation calculations representing a realistic fuel irradiation period and neutron flux. Indeed, the ANS5.1-1979 standard is seen to be very conservative. As we will see later on, the correction factor applied by the Japanese standard (Tasaka et al, 1991) is much more realistic. Figure 4.7 shows the ANS5.1-1979 correction factor compared with the Japanese ones for realistic operation conditions. Clearly, for cooling times less than 104 s (important for LOCA analyses), the effect of neutron capture is quite small. This was already seen in Section 2.4. It is generally accepted that the ANS5.1-1979 standard for thermal fission of U-235 and Pu-239 can be used for fast fission of these isotopes with an accuracy of about 1% (Dickens et al, 1977, Dickens et al, 1991). Indeed, in Fig. 2.7 we see that the correlation coefficient between the fission-product yields due to thermal fission and fast fission of U-235 is quite close to one. For Pu-239, the correlation coefficient between thermal fission yields of U-235 and thermal fission yields of Pu-239 (0.854) is almost equal to the coefficient between thermal fission yields of U-235 and fast fission yields of Pu-239 (0.858). Since the release of the ANS5.1-1979 standard, new measurements have been reported in literature by, amongst others, Baumung (1981) (thermal fission of U-235 using a calorimetric method) and Akiyama et al (1981) (fast fission of U-235, Pu-239 and U-238). For a more complete list, see the ANS5.1-1993 standard or Dickens et al (1991). The ANS5.1-1979 standard is in very good agreement with the results of Baumung, and with the U-235 and Pu-239 results of Akiyama for long cooling times (>4⋅103 s). For shorter times, the standard overestimates the measured values. For U-238, the ANS5.1-1979 standard agrees very well with Akiyama for cooling times longer than 200 seconds. To arrive at a best estimate set for the decay heat due to thermal fission of U-235 and Pu-239, Tobias (1989) analyzed all experimental data available at that time. It turns out that the ANS5.1-1979 standard agrees very well with these best estimates for cooling times longer than 6 seconds, being larger for cooling times between 3 and 6 seconds, and smaller for cooling times less than 3 seconds (Dickens et al, 1991). Despite the good agreement between the ANS5.1-1979 standard with experiments, a new standard was adopted in 1993 (ASN5.1-1993) with the following extensions:

• The cooling time was extended from 109 seconds to 1010 seconds, so that the standard can be used for the analysis of decay heat for off-site spent fuel storage.

• Decay heat data due to thermal fission of Pu-241 were included. • Decay heat data due to fast fission of U-238 were based on both experimental

(Akiyama et al, 1981) data and summation calculations. • Decay heat data due to thermal fission of U-235 and Pu-239 were revised, based

on the best estimate sets of Tobias (1989) for short cooling times and on new summation calculations for long cooling times.

In the ANS5.1-1993 standard, the effect of neutron capture by fission products is represented the same way as it was in the ANS5.1-1979 standard (see Figs. 4.6 and 4.7), but with the possibility to modify this factor. Meanwhile, a few other decay heat standards were released in Germany (DIN25463, 1990) and in Japan (Tasaka et al, 1991). The German standard contains the ANS5.1-1973 fit coefficients for the thermal fission of

U-235 and Pu-239 and fast fission of U-238. In addition, it contains fit coefficients for thermal fission of Pu-241 based on experiments for cooling times less than 104 seconds (Dickens et al, 1981) and on summation calculations for longer cooling times. Furthermore, the German standard contains fit coefficients for the uncertainties. The Japanese standard is based on summation calculations solely, and describes the fission product decay heat for the thermal fission of U-235, Pu-239 and Pu-241, and the fast fission of U-238 and Pu-240 with a similar equation to Eq. (4.6), but with 33 exponential terms (of which some are negative!) instead of ’only’ 23. The maximum cooling time is 1013 seconds (300,000 years). Due to a lack of known short-lived fission products in summation calculations, the Japanese standard seems to underestimate the fission product decay heat for cooling times up to 104 seconds compared with the other standards (Storrer, 1993). This is shown in Figs. 4.8 and 4.9 for U-235 and Pu-239, and in Figs. 4.10 and 4.11 for Pu-241 and U-238. Also note the rather large difference for short cooling times between the old ANS5.1-1973 standard, and the ANS5.1-1993 and JAERI (1991) standards. Furthermore, it is noted that the DIN standard equals the ANS5.1-1979 standard for U-235, Pu-239 and U-238. In the Japanese standard, the effect of neutron capture by fission products can be included by means of a correction factor that can be calculated with a simple program provided on a floppy disk with the standard. Figure 4.7 compares this correction factor for a PWR, BWR and an FBR for typical reactor operation times with the conservative correction factor given in the ANS5.1 standards. Because the Japanese standard is based on summation calculations only, fit parameters are given for the decay heat due to beta particles and gamma rays separately. The decay heat due to U-239 and Np-239 can be calculated by simple formulae, like Eqs. (2.13) and (2.14) and the formulae derived in Exercise 2.2. The decay energies are 0.447 MeV for U-239 and 0.426 MeV for Np-239.

Figure 4.8: The fission product decay heat for the thermal fission of U-235 according to several standards.

Figure 4.9: The fission product decay heat for the thermal fission of Pu-239 according to several standards

Figure 4.10: The fission product decay heat for the thermal fission of Pu-241 according to several standards.

Figure 4.11: The fission product decay heat for the fast fission of U-238 according to several standards.

5 DECAY HEAT VALIDATION 5.1 Development of nuclear data libraries Since the late seventies, studies of fission product decay heat have resulted in considerable progress, mainly due to improvements in the nuclear data libraries. Evaluated nuclear data have improved due to more accurate experimental measurements of the decay properties of nuclides, and the application of β-decay theories to supplement the incomplete decay data. Furthermore, the number of evaluated nuclides has been extended. Table 5.1 gives an overview of the number of nuclides in various recently evaluated nuclear data files. From the comparison between JEF-1 and the other libraries, it is seen that current efforts have focused on extending the libraries to include nuclides with estimated decay energies. After the modernizing of the evaluated nuclear data libraries, the nuclear data libraries of the summation codes have also been updated. A couple of years ago, for example, Hoogenboom and Kloosterman (1997) updated the ORIGEN-S libraries with nuclear data based on JEF-2.2 and EAF-3 and extended the fission product library by the inclusion of a further 201 nuclides. Table 5.1: Comparison of the number of fission products in various modern evaluated nuclear data libraries (Storrer (1994), and Nichols (2000)). Item JEF-1 JEF-2 JNDC-FP-

V2 ENDF-B/VI

Evaluated fission products 700 860 1227 891 Radioactive fission products 540 730 1080 764 Stable fission products 120 130 147 127 FP with known decay energy 540 611 536 443 FP with estimated decay energies 0 119 544 384 5.2 Validation of decay heat data from ENDF/B-VI, JEF-2.2 and JNDC FP V2 (IRI) The three evaluated nuclear data libraries for decay heat calculations have been tested by using the functional module ORIGEN-S of the SCALE code package to solve the Bateman equations during irradiation and a subsequent decay interval (Leege et al, 1998). ORIGEN-S uses a library with cross sections and decay data for all nuclides based on the JEF-2.2 and the EAF-3 libraries (Hoogenboom and Kloosterman, 1997). However, for this study, the nuclear data library could be replaced by one based entirely on JEF-2.2, or ENDF/B-VI or JNDC FP. To compare the data in the three evaluated data libraries in a valid manner, the nuclides in the standard ORIGEN-S library that were not present in JEF2.2, ENDF/B-VI or JNDC FP were effectively removed from the ORIGEN-S library The decay heat production from the Dickens experiments and from the Yarnell and Bendt measurements were calculated with these three libraries. As the experimental results are reported in MeV per fission, the results needed to be normalized, which was obtained by comparing the total burnup in the foils with the burnup from the ORIGEN-S calculations. By including the material from the seals of the foils in the calculation it was found that their activation plays no role in the decay heat. The neutron spectral parameters were also varied during the irradiation, but this led to only minor changes in the total decay heat.

The results from the Dickens benchmarks are shown in Figs. 5.1 and 5.2. For U-235, the calculations overestimate the experiments with 10 to 25%. The best results are from the ENDF/B-VI evaluated data. A remarkably large discrepancy of almost 50% is found for long irradiation times (100 seconds) and long waiting times (5000 seconds). In general, the calculations for Pu-239 are in better agreement with the measurements than for U-235.

Figure 5.1: Decay heat from the thermal fission of U-235 for irradiation times of 1, 10 and 100 seconds (Dickens et al, 1977) compared with summation calculations.

Figure 5.2: Decay heat from the thermal fission of Pu-239 for irradiation times of 1, 5 and 100 seconds (Dickens et al, 1978) compared with summation calculations.

The results from the Yarnell and Bendt benchmarks are shown in Figs. 5.3 to 5.5 for U-233, U-235 and Pu-239, respectively. For U-233, the calculations show discrepancies ranging from –10 to –5% when using the JEF-2.2 and ENDF/B-VI data, and from -5 to 0% for the JNDC data. For U-235, the JEF-2.2 results are slightly better, showing discrepancies ranging from -5 to 0%, just like the JNDC results. The results from ENDF/B-VI show somewhat larger discrepancies. All three libraries perform worse for Pu-239, with discrepancies ranging from -15 to 10% for short to long cooling times.

Figure 5.3: Decay heat from the thermal fission of U-233 for an irradiation time of 20,000 seconds (Yarnell and Bendt, 1978) compared with summation calculations.

Figure 5.4: Decay heat from the thermal fission of U-235 for an irradiation time of 20,000 seconds (Yarnell and Bendt, 1978) compared with summation calculations.

In conclusion, the decay heat is overestimated by calculation for both U-235 and Pu-239 in the Dickens benchmark (short irradiation times) by about +10 to 25%, while the decay heat is underestimated for all three actinides used in the Yarnell and Bendt benchmark (long irradiation times) by about -5 to -10%, except for the decay heat from Pu-239 at very long waiting times. For long cooling times (after 1000 s) the agreement between experiments and calculations is rather good. In general, the best solutions are obtained from the calculations using the JNDC data library, which contains significantly more fission products than the other two evaluated data libraries. Apparently, the number of fission products in the three evaluated data libraries is not yet sufficient for decay heat calculations.

Figure 5.5: Decay heat from the thermal fission of Pu-239 for an irradiation time of 20,000 seconds (Yarnell and Bendt, 1978) compared with summation calculations.

5.3 Validation of decay heat data from JEF2.2 and EAF3 (IRI) With the updated nuclear data library for the ORIGEN-S code, the experiments performed by Dickens et al (1977, 1978) and Yarnell and Bendt (1978) were simulated to test the new data libraries based on the JEF2.2 and EAF3 libraries (Hoogenboom and Kloosterman, 1997). The purpose of these calculations was not to test the JEF2.2 evaluated nuclear data library, but to test the best-available nuclear data library for decay heat calculations used at Interfaculty Reactor Institute in Delft. This library is based on the original ORIGEN-S data libraries, updated and extended as much as possible with nuclear data from the JEF2.2 and the EAF-3 files. The Dickens benchmark and the Yarnell and Bendt benchmark were recalculated in the same way as described in the previous section. The results for the Dickens benchmark are shown in Figs. 5.6 and 5.7, for U-235 and Pu-239, respectively. Although no C/E plots are available, the discrepancies between calculation and measurement are only 5% for cooling times up to 1000 seconds, being slightly larger thereafter. For Pu-239, the agreement is even better, between -5 and +5%. For the Yarnell and Bendt results, the comparison with calculation is shown in Figs. 5.8 and 5.9 for U-235 and Pu-239, respectively. Discrepancies for U-235 are around 5%, which means that the calculations underestimate the experimental results. For Pu-239, the difference between calculation and experiment is larger for short cooling times. In general, the differences between calculation and experiment are smaller than those presented in the previous section, which seems to be due to the fact that the nuclear data library used in this section contains more nuclides.

Figure 5.6: Decay heat from the thermal fission of U-235 for irradiation times of 1, 10 and 100 seconds (Dickens et al, 1977) compared with summation calculations.

Figure 5.7: Decay heat from the thermal fission of Pu-239 for irradiation times of 1, 10 and 100 seconds (Dickens et al, 1978) compared with summation calculations.

Figure 5.8: Decay heat from the thermal fission of U-235 for an irradiation time of 20,000 seconds (Yarnell and Bendt, 1978) compared with summation calculations.

Figure 5.9: Decay heat from the thermal fission of Pu-239 for an irradiation time of 20,000 seconds (Yarnell and Bendt, 1978) compared with summation calculations.

5.4 Validation of decay heat data from JEF2.2 (CEA) In the framework of benchmark testing of JEF2.2, CEA also performed extensive calculations to test the JEF2.2 file for decay heat purposes. Besides the benchmarks of Dickens et al (1977, 1978), and Yarnell and Bendt (1978), the experiments of Akyama et al (1981) have also been used. Results are shown in Figures 5.10 to 5.14 for U-235 and Pu-239 (Nimal et al, 1993). As mentioned before, instead of the function b(t) defined by Eq. (2.1), the function t.b(t) is often plotted, because at first order b(t) behaves like t-1 with cooling time. However, this implies that the presentation changes also because of measurement errors in t. Having this in mind, Fig. 5.10 shows the U-235 decay heat due to a thermal-neutron induced fission burst. Clearly, the JEF2 results are in better agreement than the older library (CEA699), but still a discrepancy exists between calculations and measurements around 100 seconds cooling time. The decay heat after an infinitely long irradiation time is shown in Fig. 5.11, indicating that the calculations overestimate the experiments especially for short cooling time. Figs. 5.12 and 5.13 show the same results for Pu-239. At first sight, JEF2.2 appears to have improved the agreement between calculation and experiment for the whole range of cooling times, but between 15 and 3000 seconds, the calculations underestimate the decay heat due to gamma rays. This observation has been found to occur when using other evaluated files for cooling times between 300 and 3000 seconds, and seems to arise from missing β-strength in the decay of some fission products (Yoshida et al, 1999). The improvement shown by the JEF2.2 results in Fig. 5.13 is not sufficient to give a perfect match between measurements and calculations. As might be expected from the results in the previous section, the calculations underestimate the measured values from Yarnell and Bendt (1978) for short cooling times, as can be seen in Fig. 5.14.

Figure 5.10: Fission product decay heat of U-235 after a thermal neutron induced fission burst. Comparison of calculations (Nimal et al, 1993) and experiments.

Figure 5.11: Fission product decay heat of U-235 after an infinitely long irradiation. Comparison of calculations (Nimal et al, 1993) and experiments (Dickens et al, 1977).

Figure 5.12: Fission product decay heat of U-235 after a thermal neutron induced fission burst. Comparison of calculations (Nimal et al, 1993) and experiments.

Figure 5.13: Fission product decay heat of Pu-239 after an infinitely long irradiation. Comparison of calculations (Nimal et al, 1993) and experiments (Dickens et al, 1978).

Figure 5.14: Fission product decay heat of Pu-239 after an irradiation of 20,000 seconds. Comparison of calculations (Nimal et al, 1993) and experiments (Yarnell and Bendt, 1978). The experimental values are also given in Table 3.2. 5.5 Validation of decay heat standards (IRI) The decay heat standards ANS5.1-1973 and the Japanese standard (Tasaka et al, 1991) have been compared with the experimental results from Dickens et al. (1977, 1978), and Yarnell and Bendt (1978). For the Dickens benchmark, the results are shown in Fig. 5.15 for U-235 and in Fig. 5.16 for Pu-239. For the first-mentioned nuclide, both the ANS5.1-1979 results and the JAERI ones are 10 to 25% higher than the experimental results for 1, 10, and 100 seconds irradiation time. The JAERI analytical solution is slightly better than that from the ANS5.1-1979 standard. For the Pu-239 isotope, results are slightly better than the results for the U-235 benchmark. Note the different scales for the C/E plots. The results from the Yarnell and Bendt benchmarks are shown in Figs. 5.17 and 5.18. For U-235, both the ANS5.1-1979 and the JAERI analytical results are in good agreement with the experimental results, and most certainly the ANS5.1-1979 results. For the Pu-239, the ANS5.1-1979 standard shows a discrepancy of about –5% for the whole cooling time, while the JAERI standard shows a discrepancy between –10 to –5% for short to long cooling times. Apparently, the decay heat standards that have been adopted give better results for longer irradiation times.

Figure 5.15: Decay heat from the thermal fission of U-235 for irradiation times of 1, 10 and 100 seconds (Dickens et al, 1977) compared with standards.

Figure 5.16: Decay heat from the thermal fission of Pu-239 for irradiation times of 1, 5 and 100 seconds (Dickens et al, 1977) compared with standards.

Figure 5.17: Decay heat from the thermal fission of U-235 for an irradiation time of 20,000 seconds (Yarnell and Bendt, 1978) compared with standards.

Figure 5.18: Decay heat from the thermal fission of Pu-239 for an irradiation time of 20,000 seconds (Yarnell and Bendt, 1978) compared with standards.

6 DECAY HEAT IN DIFFERENT REACTORS As expected from previous chapters, the decay for short cooling times will mainly be determined by the fissile actinides in the fuel, and much less by the irradiation conditions such as the neutron flux density and the neutron spectrum. However, for long cooling times, these differences become significant, as shown in Fig. 6.1. Since the concentration of fission products and actinides are proportional to [1-exp(-λI)], with λ being the decay constant and I the irradiation time, there is a trend that decay heat increases with the irradiation time. On the other hand, the higher the fuel burnup, the larger the contribution of Pu-239 to the fission power (if the reactor was originally fuelled with UO2), which will generally decrease the fission product decay heat.

Figure 6.1: A comparison of fission-product decay heat from several reactor types. Note that the LWR is fuelled with U-233 mixed in thorium, while the LMFBR is fuelled with (U-Pu) MOX fuel (Tobias, 1980). Figure 6.2 shows the contribution of the actinide decay heat as a function of the cooling time. For a reactor loaded with uranium, the actinide contribution peaks at a percentage contribution of 20-25% at cooling times of about 105 seconds (1 day). This maximum shifts to about 106 seconds (1 month) for an LWR containing thorium. For cooling times larger then 109 seconds (30 years), the actinides dominate the decay heat production. Especially the minor actinides that are produced in the MOX-fuelled LMFBR give a large contribution at long cooling times.

Figure 6.2: Percentage contribution of the actinide decay heat from several reactor types. Note that the LWR is fuelled with U-233 mixed in thorium, while the LMFBR is fuelled with (U-Pu) MOX fuel (Tobias, 1980).

ACKNOWLEDGEMENT The author expresses his thanks to F. Storrer (CEA, Cadarache) for information provided via private communication.

LITERATURE Akiyama M. et al (1981), Report ORNL-TR-4784, Oak Ridge National Laboratory. Aoyama T. et al (1999), Proc. 1998 Symp. on Nucl. Data, JAERI Conf 99-002, Japan, 84-91. ANS5.1 (1979), Decay Heat Power in Light Water Reactors, American Nuclear Society. ANS5.1 (1993), Decay Heat Power in Light Water Reactors, American Nuclear Society. Baker S.M. and Spinra B.I. (1977), Report NUREG-0018-4. Baumung K. (1981), Report KFK-3262, FzK, Karlsruhe, Germany. Devillers C. (1977), Review paper No. 4, IAEA Advisory Group Meeting on Fission Product Nuclear Data, ECN, Petten, Report IAEA-213. Dickens J.K. et al (1977), Report ORNL/NUREG-14, Oak Ridge National Laboratory. Dickens J.K. et al (1978), Report ORNL/NUREG-34, Oak Ridge National Laboratory. Dickens J.K. et al (1981), Nucl. Sci. Eng., 78, 126-146. Dickens J.K. et al (1991), Nucl. Safety, 32 (2), 209-221. DIN25463 (1990), Deutches Institut für Normung, Germany. Duderstadt J.J. and Hamilton L.J. (1976), Nuclear Reactor Analysis, John Wiley&Sons. Fiche C. et al (1976), Report CEA SEN/022, CEA Cadarache, France. Forsberg C.W. (1991), Nucl. Technol., 96, 229-235. Friesenhahn S.J. et al (1976), Report EPRI NP-180, Electric Power Research Institute. Gillet G. et al (1990), Nucl. Sci. Eng. 106, 94-97. Glasstone S. and Sesonske A. (1963, 1981), Nuclear Reactor Engineering, Van Nostrand Company, Princeton, New Jersey. Gunst S.B. et al (1975), Nucl. Sci. Eng., 56, 241; Corrigendum Nucl. Sci. Eng., 64, 904. Henry A.F. (1986), Nuclear Reactor Analysis, MIT Press. Hesse U. et al (2000), Proc. PHYSOR 2000, Pittsburgh, Pennsylvania, USA, Sess. IV-B. Hoogenboom J.E. and Kloosterman J.L. (1997), Nucl. Eng. Design, 170, 107-118. Kloosterman J.L. (1996), Report ECN-NUC-RFA-96-16, NEA-1606:ZZ-ECN-BUBEBO, 1999. Kloosterman J.L. et al. (1996), Proc. Int. Conf. on the Physics of Reactors, Mito, Japan. Kloosterman J.L. et al. (1997), Proc. Int. Conf. on Future Nuclear Systems, Yokohama, Japan, 338-343. Leege P.F.A. et al. (1998), Proc. Int. Conf. on the Physics of Nucl. Science and Techn., Long-Island, USA, 1499-1505. Lillington J.N. (1995), Light Water Reactor Safety, Elsevier Science. Lott M. et al (1973), Journal of Nuclear Energy, 27, 597. Miyazono T. et al (1997), Proc. 1996 Symp. on Nucl. Data, JAERI, Japan. Mori T. et al (1999), Proc. Mathematics and Computation, Reactor Physics and Environmental Analysis in Nuclear Applications, Madrid, Spain, 987-996. Nichols, A.L. (2000), Private communication. Nimal B. et al (1993), JEF/DOC-442, NEA, Paris, France. Ohta H. et al (1996), Proc. 1995 Symp. on Nucl. Data, JAERI Conf 96-008, Japan, 290-295. Oyamatsu K. et al (1997), Proc. 1996 Symp. on Nucl. Data, JAERI Conf. 97-004, Japan. Oyamatsu K. and Sagisaka M. (1996), Proc. 1995 Symp. on Nucl. Data, JAERI Conf 96-008, Japan, 344-349. Pershagen B. (1989), Light Water Reactor Safety, Pergamon Press.

Schmittroth F., (1976), Nucl. Sci. Eng., 59, 117-139. Schmittroth F. and Schenter R.E. (1977), Nucl. Sci. Eng., 63, 276-291. Schrock V.E. et al (1978), Report EPRI NP-616, Vol. 1. Sesonske A. (1973), Nuclear Power Plant Design Analysis, Technical Information Center, United States Atomic Energy Commission. Shure K. et al (1979), Nucl. Sci. Eng., 71, 327-342. Storrer F. (1993), JEF/DOC-441, NEA, Paris, France. Storrer F. (1994), Proc. Int. Conf. on Nucl. Data for Science and Techn., Gatlinburg, USA. Takeuchi H. et al (1999), Proc. 1998 Symp on Nucl. Data, JAERI Conf 99-002, Japan, 124-129. Tasaka K. (1977), Nucl. Sci. Eng., 62, 167-174. Tasaka K. et al (1991), Report JAERI-M-91-034, Japan. Tobias A. (1980), Prog. Nucl. Ener., 5, 3-93. Tobias A. (1989), Report CEGB-RD-B-621089. Todreas N.E. and Kazimi M.S. (1989), Nuclear Systems I, Hemisphere Publishing. Trap T.J. et al (1977), Report OSU-NE-7701. Way K. and Wigner E.P. (1951), Rate of Decay of Fission Products, Radiochemical Studies: The Fission Products, Book 1, paper 43, page 43, McGraw-Hill. Weaver D.R. (ed.) (1986), Delayed Neutron Properties, Univ. of Birmingham. Yamamoto T. and Sugiyama K. (1978), Ann. Nucl. Energy 5, 621-637. Yarnell J.L. and Bendt P.L. (1977), Report LA/NUREG-6713, Los Alamos National Laboratory. Yarnell J.L. and Bendt P.L. (1978), Report NUREG/CR-0349, LA-7452-MS, Los Alamos National Laboratory. Yoshida T. and Tasaka K. (1992), NEA-DOC92-9, NEA, Paris, France. Yoshida T. et al (1999), Journ. of Nucl. Sci. and Techn. 36 (2), 135-142.