# An introduction to Spent Nuclear Fuel decay heat for Light Water Reactors: a review from the NEA WPNCS

Dimitri Rochman, Alejandro Algora, Francisco Àlvarez-Velarde, Aurelie Bardelay, Øystein Bremnes, Oscar Cabellos, Daniel Cano-Ott, Luigi Capponi, Coralie Carmouze, Stefano Caruso, et al.

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## To cite this version:

Dimitri Rochman, Alejandro Algora, Francisco Àlvarez-Velarde, Aurelie Bardelay, Øystein Bremnes, et al. An introduction to Spent Nuclear Fuel decay heat for Light Water Reactors: a review from the NEA WPNCS. EPJ N - Nuclear Sciences & Technologies, 2024, 10 (9), pp.1-83. 10.1051/epjn/2024010. hal-04737266

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# An introduction to Spent Nuclear Fuel decay heat for Light Water Reactors: a review from the NEA WPNCS

Dimitri Rochman¹, Alejandro Algora²,³, Francisco Àlvarez-Velarde⁴, Aurélie Bardelay⁵, Øystein Bremnes⁶, Oscar Cabellos⁷, Daniel Cano-Ott⁴, Luigi Capponi⁸, Coralie Carmouze⁹, Stefano Caruso¹⁰, Andrew Cummings¹¹, Ron Dagan¹², Muriel Fallot¹³, Luca Fiorito¹⁴, Lydie Giot¹³, Kevin Govers¹⁵, Silja Häkkinen¹⁶, Volker Hannstein¹⁷, Axel Hoefer¹⁸, Tan Dat Huynh¹⁹, Raphaëlle Ichou⁵, Germina Ilas²⁰, Pauli Juutilainen¹⁶, Lukasz Koszuk²¹, Marjan Kromar²², Sébastien Lahaye¹⁹, James Lam²³, Frédéric Laugier²⁴, Agnés Launay²⁵, Vincent Léger²⁶, David Lecarpentier²⁷, Jaakko Leppanen¹⁶, Fadhel Malouch¹⁹, Julie-Fiona Martin²⁸, David McGinnes²⁹, Robert William Mills⁸, Futoshi Minato³⁰, Yasushi Nauchi³¹, Pedro Ortego³², Plamen Petkov³³, Pablo Romojaro¹⁴, Shunsuke Sato³¹, Marcus Seidl³⁴, Ahmed Shama³⁵, Teodosi Simeonov³⁶, Anders Sjöland³⁷,³⁸, Virginie Solans³⁹, Fabian Sommer¹⁷, Sven Tittelbach⁴⁰, Aimé Tsilanizara¹⁹, Efstathios Vlassopoulos³⁵, Vanessa Vallet⁹, Alexander Vasiliev¹, Tomoaki Watanabe³⁰, and Gašper Žerovnik²²

¹ Reactor Physics and Thermal hydraulic Laboratory, Paul Scherrer Institut, Villigen, Switzerland

² Instituto de Fisica Corpuscular, IFIC (CSIC-Univ. Valencia), Valencia, Spain

³ Institute for Nuclear Research (Atomki), H-4001 Debrecen, Hungary

⁴ CIEMAT - Centro de Investigaciones Energéticas, MedioAmbientales y Tecnológicas, Madrid, Spain

⁵ Institut de Radioprotection et de Sureté Nucléaire, 92260 Fontenay aux Roses, France

⁶ EDF, DIPNN-DT, 69007 Lyon, France

⁷ Universidad Politecnica de Madrid, Madrid, Spain

⁸ National Nuclear Laboratory, Workington, UK

⁹ Commissariat à l'énergie atomique et aux énergies alternatives, Cadarache, 13108 Saint-Paul-lez-Durance, France

¹⁰ Kernkraftwerk Goesgen-Däniken AG, Däniken, Switzerland

¹¹ Nuclear Transport Solutions (NTS), Risley, UK

¹² KIT-Karlsruhe Institue of Technology, Karlsruhe, Germany

¹³ Subatech (CNRS/IN2P3, IMT Atlantique, Université de Nantes), 44307 Nantes, France

¹⁴ SCK CEN, Belgian Nuclear Research Center, Mol, Belgium

¹⁵ Federal Agency for nuclear Control, Brussels, Belgium

¹⁶ VTT Technical Research Centre of Finland Ltd., Espoo, Finland

¹⁷ Gesellschaft für Anlagen- und Reaktorsicherheit (GRS) gGmbH, Garching bei München, Germany

¹⁸ Framatome, Erlangen, Germany

¹⁹ Université Paris-Saclay, CEA, Service d'Études des Réacteurs et de Mathématiques Appliquées, 91191 Gif-sur-Yvette, France

²⁰ Oak Ridge National Laboratory, Oak Ridge, TN, USA

²¹ University of Warsaw, Warsaw, Poland

²² Jožef Stefan Institute, Ljubljana, Slovenia

²³ Rolls Royce, Derby, UK

²⁴ EDF - DPNT - DCN - PAD, 93200 Saint Denis, France

²⁵ Orano NC Recycling, 50444 Beaumont Hague, France

²⁶ Orano NPS, 78180 Montigny-le-Bretonneux, France

²⁷ EDF R&D, 91120 Palaiseau, France

²⁸ Division of Nuclear Science and Education, OECD Nuclear Energy Agency (NEA), 75775 Paris, Cedex 16, France

²⁹ AXPO Power AG, Baden, Switzerland

³⁰ Japan Atomic Energy Agency, Ibaraki, Japan

³¹ Central Research Institute of Electric Power Industry (CRIEPI), Tokyo, Japan

³² Science Engineering Associates S.L. (SEA), Madrid, Spain

³³ Sofia University "St. Kliment Ohridski", Sofia, Bulgaria

³⁴ PreussenElektra GmbH, Hannover, Germany

³⁵ Nagra - Nationale Genossenschaft für die Lagerung radioaktive Abfälle, Wettingen, Switzerland

³⁶ Studsvik Scandpower, Inc., Newton, Massachusetts, USA

³⁷ Swedish Nuclear Fuel and Waste Management Co. (SKB), Sweden, Sweden

³⁸ Dept. of Nuclear Physics, Lund University, Lund, Sweden

³⁹ Uppsala University, Uppsala, Sweden

⁴⁰ WTI GmbH, Jülich, Germany

e-mail: dimitri-alexandre.rochman@psi.ch
Received: 9 January 2024 / Received in final form: 28 May 2024 / Accepted: 2 July 2024

**Abstract.** This paper summarized the efforts performed to understand decay heat estimation from existing spent nuclear fuel (SNF), under the auspices of the Working Party on Nuclear Criticality Safety (WPNCS) of the OECD Nuclear Energy Agency. Needs for precise estimations are related to safety, cost, and optimization of SNF handling, storage, and repository. The physical origins of decay heat (a more correct denomination would be *decay power*) are then introduced, to identify its main contributors (fission products and actinides) and time-dependent evolution. Due to limited absolute prediction capabilities, experimental information is crucial; measurement facilities and methods are then presented, highlighting both their relevance and our need for maintaining the unique current full-scale facility and developing new ones. The third part of this report is dedicated to the computational aspect of the decay heat estimation: calculation methods, codes, and validation. Different approaches and implementations currently exist for these three aspects, directly impacting our capabilities to predict decay heat and to inform decision-makers. Finally, recommendations from the expert community are proposed, potentially guiding future experimental and computational developments. One of the most important outcomes of this work is the consensus among participants on the need to reduce biases and uncertainties for the estimated SNF decay heat. If it is agreed that uncertainties (being one standard deviation) are on average small (less than a few percent), they still substantially impact various applications when one needs to consider up to three standard deviations, thus covering more than 95% of cases. The second main finding is the need of new decay heat measurements and validation for cases corresponding to more modern fuel characteristics: higher initial enrichment, higher average burnup, as well as shorter and longer cooling time. Similar needs exist for fuel types without public experimental data, such as MOX, VVER, or CANDU fuels. A third outcome is related to SNF assemblies for which no direct validation can be performed, representing the vast majority of cases (due to the large number of SNF assemblies currently stored, or too short or too long cooling periods of interest). A few solutions are possible, depending on the application. For the final repository, systematic measurements of quantities related to decay heat can be performed, such as neutron or gamma emission. This would provide indications of the SNF decay heat at the time of encapsulation. For other applications (short- or long-term cooling), the community would benefit from applying consistent and accepted recommendations on calculation methods, for both decay heat and uncertainties. This would improve the understanding of the results and make comparisons easier.

# 1 Introduction

The characterization of Spent Nuclear Fuel (SNF) assemblies is an inherent process of the safety assessment pertaining to the back-end of the nuclear fuel cycle. It concerns the SNF assembly handling and storage, design and operation at reprocessing facilities or final repositories, and is also of prime importance for safeguard and fuel cycle decisions [1]. Many quantities play a key role in such characterization, including the fuel composition, dose, (sub) criticality level, fission gas release, fuel, and cladding behavior, corrosion, material accountability, and decay heat.

The decay heat from nuclear fuel can be defined as the recoverable energy released from the decay of radionuclides during irradiation and after the reactor cycle's shutdown and corresponds to the released thermal power (historically called decay heat, and more accurately defined today as thermal power). During the operation of a reactor cycle, heat is released in the core mainly from the prompt fission process; the contribution from decay heat is of lesser importance, nevertheless reaching about 7% of the total thermal power in the case of typical Light Water Reactors (LWR) [2], during cycle operation and up to its end. On the contrary, once the reactor cycle is stopped (as part of planned maintenance, reload, or unplanned safety shutdown), the prompt fission heat source dies away and the energy from the decay of fission products, actinides,

activation products and possibly delayed fission becomes the sole heat source. It decreases approximately as a sum of exponentials with different characteristic time parameters as a function of cooling time after the end of the cycle and is emitted at different rates either by assemblies in their end-of-life or by assemblies planned to be used again in following cycles.

Decay heat is a substantial amount of power (being in the order of MW or tens of MW, depending on the reactor core power), and for the next seconds to hours or days (defined as short cooling periods), it can eventually damage the primary and secondary safety barriers if not properly evacuated, resulting in the release of radioactive materials to the environment. Then from days to years of cooling time, the decay heat needs to be taken into account for the SNF handling and wet or dry storage, by having sufficient heat removal capacities. Therefore the design of storage pools, transport casks and surface dry pad storage has to account for this potential hazard. For longer cooling periods, the SNF can be reprocessed or disposed of. In both cases, the decay heat needs to be accounted for. The main influential parameters for its quantification are the following:

1. integral fuel irradiation level, or burnup (in MWd/t), especially important after a long cooling period,

2. initial fuel composition, including its enrichment and initial mass of actinides,

3. cooling time,
4. fuel assembly irradiation rate (in MW/t) during the reactor operation, especially important at short cooling times (just after the reactor shutdown or during the fuel unloading for instance),

5. use of burnable poisons (mainly during the first irradiation cycle),

6. other manufacturing and irradiation parameters (such as dimensions, densities, temperatures, and void).

During the past decades, national and international programs were dedicated to studying and understanding the evolution of the SNF decay heat, covering specific ranges for the most relevant parameters, in agreement with the industry standards at that period of exploitation. Such programs included measurements (see Sect. 5), estimations based on different calculation methods (such as summation or standard methods, see Sect. 6), and validation programs (see Sect. 8). For instance, national programs, as in France, provided research and understanding of the long-term behavior of SNF for storage and geological disposal, including decay heat [3], and international collaborations were framed at the Nuclear Energy Agency (NEA) with dedicated meetings and benchmarks, as presented in references [4–7]. As shown in these studies, before the year 2000, the initial fuel enrichments for UO₂ fuel rarely exceeded 3.8% in ²³⁵U, with average assembly burnup values generally lower than 55 MWd/kgU. Consequently, measurements and computational efforts were focused on these values and below. Missing are also direct decay heat measurements on MOX assemblies, or also on VVER or CANDU assembly types.

This observation leads to the **first justification** for developing new efforts toward a re-evaluation of the decay heat prediction capabilities. Since the year 2000, the nuclear fuel design and usage have changed with the evolution of the nuclear industry. The initial enrichment steadily increased until it reached 5.0% in ²³⁵U, and the assembly average burnup nowadays extends to 70 MWd/kgU, and occasionally to higher values. Additionally, the use of MOX fuel has increased in some countries, whereas other ones also have it stored from past use. An example is presented in Figure 1 for typical assemblies used before the years 2000 (low enrichment, low burnup, see the curve labeled “case 1”) and 20 years later (higher enrichment, higher burnup, see curves labeled “case 2” and “case 3”).

In the case of UO₂ fuel, one can see a significant increase in decay heat between cases 1 and 2, especially for cooling time from 1 to 100 years. This has consequences for the storage of SNF assemblies, as during this period, such assemblies may potentially be moved from one place to another and eventually from cask to canisters, with canisters going into long-term repository. Accordingly, new calculations are needed, implying new validation efforts, hopefully, based on new decay heat measurements. As presented in the same figure (bottom part), the decay heat coming from MOX fuel is also higher than UO₂ fuel (in the presented cases, for cooling periods longer than one month). In this case, there are no available direct decay heat measurements at the assembly level, making the validation of calculations with direct measurements unfeasible.

<figure><img src="image_3.png" /><figcaption>**Fig. 1.** Examples of calculated decay heat for typical UO₂ assemblies (top), having different burnup and enrichment values; bottom: comparison between typical MOX and UO₂ SNF assemblies.</figcaption></figure>

These examples illustrate today's need with respect to the SNF characterization, including among other quantities, nuclide concentrations and decay heat. The precise knowledge of the decay heat for fuel with low and high initial ²³⁵U enrichments, low and high burnup values, and short and long cooling times, directly affect the safety and economy of the back-end of the fuel cycle.

The **second justification** for new efforts in the prediction of SNF decay heat comes from the need for smaller uncertainties and well-assessed biases in measurements and calculations. This stems from stringent safety rules and higher economic constraints. An example of the impact of the knowledge of SNF decay heat concerns the number of required canisters for the final geological disposal. In a simplistic approach, each canister, for instance containing four PWR SNF assemblies, must have a total decay heat value lower than a given limit; high uncertainties or biases on the SNF decay heat values will increase the number of required canisters. Considering that 1% change in the estimation of the SNF decay heat can change the number of required canisters roughly by the same amount, the economical implications of the decay heat knowledge become straightforward.

A **third justification** for the re-assessment of the SNF decay heat originates from the need for a larger experimental database for validation. As mentioned in Section 5, the majority of measurements for SNF decay heat come from the Clab facility in Sweden, with additionally a limited number of cases from two decommissioned American facilities. Due to their high quality and small
uncertainties, the values from the Clab facility represent the current state of the art with respect to measurements and are used for all code validations. While it is a tremendous advantage to be able to access these measurements and all necessary information on the irradiated assemblies, there is an inherent risk in using experimental values coming from a single facility, as possible correlations between measured values are not mitigated with other experimental sources. Additionally, these measurements do not cover all characteristics of today's SNF assemblies, in terms of initial enrichment, burnup, and fuel type.

In this context, the working group SG12 has been organized under the auspice of the OECD Nuclear Energy Agency (NEA) and the Working Party on Criticality Safety (WPNCS) [8], and is dedicated to "Spent nuclear fuel decay heat: assessing the confidence level in experimental and computational estimations (SNF-DH)". In order to narrow the field of study of SG12, the primary focus is the existing SNF assemblies from current LWRs, and the main goals of SG12 are as follows:

* Allowing interested participants to exchange their experience related to the prediction of SNF decay heat (current knowledge, interests, and needs).

* Provide a state-of-the-art report for the estimation of the decay heat from existing SNF (the present report), including an overview on the calculation capabilities, possible sources of uncertainties and a description of the available experimental data.

* When applicable, raise awareness for relevant needs, in terms of calculations and measurements.

* Finally, provide recommendations for improving the SNF decay heat estimation, with respect to measurements, simulations, input information, and best practices.

Such studies are part of other international efforts, such as the International Atomic Energy Agency (IAEA) Coordinated Research Project on Spent Fuel Characterization (running from 2020 to 2024), as well as the European Union joint Strategic Programme of Research and knowledge management activities, dedicated to supporting radioactive waste management studies, called EURAD (running from 2019 to 2024). Another important international project concerns the measurements and the evaluations of decay heat at Clab, Sweden, between SKB, Vattenfall, and EPRI. When completed, one of the outcomes of this project will be the measured decay heat for a number of new SNF assemblies as well as the necessary information to perform decay heat calculations.

## 2 Motivation

As mentioned in the introduction, the estimation of the SNF decay heat is important at various cooling periods, from seconds after a reactor shutdown, up to millions of years later for the safety case of geological repositories. Our capability to calculate this quantity (linked to other ones such as nuclide inventory), as well as to provide well-justified uncertainties and biases has direct implications on the simulations of accident scenarios, as well on the

safety of the back-end of the fuel cycle, and naturally on involved cost. Our ability to excel in such estimations, and to improve safety and cost are the main motivations for presenting the state of the art from the aspects of measurement, simulation, and validation.

The availability of a limited number of measurements for SNF decay heat is directly affecting the confidence level of simulations. Such experiments are expensive and currently only one facility exists worldwide. The domain of validation is therefore restrained, potentially leading to increased safety margins. Raising awareness of the need for new and independent measurements is consequently the first priority of this work.

Understanding and informing about the different possibilities in simulations and the impact of different parameters is the second priority. Various methods, guidelines, and recommendations exist among institutes and countries, leading to different calculated decay heat values, even when starting from the same measurement database. Such variations of results should be made visible and explained to specialists and non-specialists.

Both previous points directly affect validation results. The scarcity of experimental values, as well as different simulation methods, may lead to different consequences for the outcome of a validation procedure (such as safety factors, confidence intervals, or uncertainties). Additionally, different validation procedures can also have different impacts on application quantities. Again, making such differences explicit, and understanding them is the third priority of this work.

Additional details are given in the following paragraphs, articulated around these three axes: measurements, simulations and validation.

### 2.1 General observations on current knowledge

Validation of the existing codes with measured SNF decay heat is currently considered a necessity by most existing national and international regulations (see for instance the IAEA Safety Guide Refs. [9,10]). Part of the motivation to continue performing analysis and measurements for SNF decay heat is due to today's trend of increasing burnup and initial enrichment values, and also due to the need to improve current predictions. To illustrate our current capabilities for predictions, Figure 2 represents one aspect of the validation of codes used in the calculations of SNF decay heat.

This figure presents the histogram for C/E ratios (being Calculated over Experimental values) for SNF decay heat coming from calorimetric studies. All (tabulated) values from the open literature are used for this figure, mixing PWR and BWR assemblies, different simulation codes, nuclear data libraries, calculation procedures, and experimental sources. Such results do not represent the outcome of a validated procedure, but rather a snapshot on the existing published data. In total, 1490 calculated over experimental ratios were found, and the average of such histogram is 1.003, with a standard deviation of 0.059. Such figures indicate at first sight that the simulation capabilities can satisfactory reproduce
<figure><img src="image_4.png" /><figcaption>**Fig. 2.** Histogram of the ratios of calculated (C) over experimental (E) decay heat values from literature studies for calorimetric measurements of full fuel assemblies. Both PWR and BWR assemblies are included.</figcaption></figure>

measured decay values for SNF with calorimetric measurements. One standard deviation is found to be close to 6%, and almost 86% of the data are within $\pm 1\sigma$. By considering two standard deviations, almost 97% of the cases are covered; a three-sigma interval leads to 98.8% of the cases (five sigmas cover 99.6%). Numbers are changing if ones differentiate between PWR and BWR SNF assemblies, as indicated in Table 1.

As observed in previous work, the spread of $C/E$ is larger for BWR than for PWR. This is certainly linked to the fact that BWR cases are more challenging to simulate, for instance, due to the heterogeneity of the irradiation conditions (such as radial and axial void variations). Depending on the application, such numbers can be considered as adequate or not. It is nevertheless important to understand the limitations of the experimental database used to perform such validation. In some cases, considering one standard deviation is not enough, as too many cases are left outside the $\pm 1\sigma$ band. Table 2 is presenting the number of $C/E$ cases (from Tab. 1) which are included in various multipliers of $\pm\sigma$.

It can be seen that if a specific application requires that more than 99% of the cases are covered, one needs to consider $3\sigma$ for the PWR SNF assemblies (corresponding to $1.000\pm0.138$), and $5\sigma$ for the BWR SNF assemblies (corresponding to almost $1.009\pm0.395$). Such large uncertainties, in terms of standard deviations, can have important consequences on facility designs, and it is therefore of high interest to improve the prediction capabilities.

Another quantity of high interest is the average value presented in Table 1. It can be defined as an average simulation bias, which is for instance of less than 2% in the case of the PWR SNF assemblies. The mentioned references are based on calculations performed with available measured SNF cases, implying a strong correlation between the presented values. More recently, a blind benchmark performed with 5 PWR SNF assemblies at the Clab facility, with more than 30 participants, has indicated an aver-

age bias of 0.978 ($\pm 0.022$) [15]. Later re-analysis of the experimental values (as of mid-2023) indicates an overestimation of the measurements, but such original value based on a blind exercise is in disagreement with the average values from Table 1. It is indicating that a more adequate understanding of possible bias sources is required.

## 2.2 Limitations

The main impediment to the results presented in the previous section lies in the limits of the application of the existing experimental database. Such validation (average $C/E$ values and standard deviations) is based on a very limited set of measurements:

* Three facilities worldwide delivered 268 publicly available measurements for 164 SNF assemblies, up to the year 2006 (see for instance lists in Refs. [13,14])<fnref n="1" />. See Tables 11 and 12 for details,

* among these three facilities, two do not exist nowadays (GE-Morris and HEDL-EMAD),

* out of 268 measurements, more than 50% come from the Swedish Clab facility and 40% from the American GE-Morris facility (currently shutdown),

* only $UO_2$ SNF assemblies for PWR and BWR were measured (no MOX fuel, no other design such as for VVER),

* the highest enrichment is 4%, which is lower than the ones typically used in current reactors,

* the highest assembly average burnup is 51 MWd/kgU, which is also lower than the values reached in current reactors,

* the cooling time ranges from 2 to 27 years, which does not cover all cooling ranges of interest.

As mentioned, the estimation of decay heat is relevant for fuel management over a large period of cooling periods: short (e.g. for Loss Of Coolant Accident or Reactivity Insertion Accident), intermediate (for on-site SNF storage) and long (for off-site storage or disposal such as deep geological repository); some general information related to such needs is provided in the following section.

## 2.3 Needs

Note that the influential parameters (see the bullet list in the introduction) do not have the same weight depending on whether one considers the SNF just after the reactor shutdown or after a long cooling period in the SNF pool.

### 2.3.1 Decay heat for short cooling times

A conservative evaluation of decay heat is paramount for the proper design of heat removal systems of nuclear power plants (for an adequate mitigation of loss of coolant accidents for instance). The typical period of interest in safety studies goes from the reactor shutdown to about ten days.

<footnote n="1">¹ A number of measurements are not yet fully available, at the time of this report, such as from references [12,15].</footnote>
<table><caption>**Table 1.** Calculated over experimental ratios for LWR SNF assemblies (average and 1 standard deviation).</caption><thead><tr><th></th><th>LWR</th><th>PWR</th><th>BWR</th><th>Cases (PWR+BWR)</th></tr></thead><tbody><tr><td>Figure 2</td><td>1.003 ± 0.059</td><td>1.000 ± 0.046</td><td>1.009 ± 0.079</td><td>1490 (980+510)</td></tr><tr><td>Reference [11]</td><td>0.989 ± 0.059</td><td>0.999 ± 0.021</td><td>0.982 ± 0.074</td><td>236</td></tr><tr><td>Reference [12]</td><td>0.999 ± 0.018</td><td>1.001 ± 0.012</td><td>0.999 ± 0.024</td><td>121</td></tr><tr><td>Reference [13]</td><td>0.992 ± 0.055</td><td>1.020 ± 0.015</td><td>0.981 ± 0.077</td><td>199</td></tr><tr><td>Reference [14]</td><td>1.007 ± 0.071</td><td>1.014 ± 0.018</td><td>1.001 ± 0.097</td><td>263</td></tr></tbody></table>

<table><caption>**Table 2.** Coverage factors for PWR and BWR SNF assemblies correspond to the cases from Figure 2.</caption><thead><tr><th></th><th>LWR</th><th>PWR</th><th>BWR</th></tr></thead><tbody><tr><td>Average ±1σ</td><td>1.003 ± 0.059</td><td>1.000 ± 0.046</td><td>1.009 ± 0.079</td></tr><tr><td>1σ coverage</td><td>86%</td><td>91%</td><td>79%</td></tr><tr><td>2σ coverage</td><td>97%</td><td>98.4%</td><td>93.1%</td></tr><tr><td>3σ coverage</td><td>98.8%</td><td>99.5%</td><td>97.5%</td></tr><tr><td>4σ coverage</td><td>99.4%</td><td>99.7%</td><td>98.8%</td></tr><tr><td>5σ coverage</td><td>99.6%</td><td>99.9%</td><td>99.1%</td></tr></tbody></table>

The number of contributing radionuclides is well over a thousand just after the reactor shutdown, and that number decreases rapidly, as presented in Figure 3 reproduced from reference [16].

During this short cooling time period, the decay heat is nearly proportional to the reactor power before the reactor shutdown (“thumb rule” to be used with caution), as most of the contributing radionuclides are short-lived. For the same reason, it depends less on fuel burnup.

### 2.3.2 Decay heat for intermediate cooling times

In the 5 to 25-day period after reactor shutdown, the main application of decay heat evaluation is the safe unload- ing of the core into the nearby pool. Systems must take into account penalized values to cover fuel variability in power and irradiation during the fuel transfer. In case of suspected fuel leakage, the assembly decay heat must be lower than a given threshold to enable a vacuum-canister sipping procedure. In this intermediate period, the decay heat is still strongly linked to the assembly power before the reactor shutdown. However, the irradiation level has an increasing influence on cooling time.

Safety systems must be able to remove the decay heat of the complete unloaded core added to one of the fuel assemblies already stored in the pool. Once the fuel is partially reloaded back into the core, the safety systems still have to remove the decay heat from the definitively unloaded assembly batch and the fuel already stored in the pool.

### 2.3.3 Decay heat for long cooling times

Long cooling times correspond to fuel assemblies that have cooled down several months or years. Typical needs for decay heat evaluation are:

* Design of spent fuel pool heat exchangers,

* design of canisters and cylinders for fuel managing and fuel storage,

* design of casks for fuel transport,

* verification of fuel compliance with the heat thresholds of the mentioned containers.

The decay heat for long cooling times is not very sensitive to the fuel power before shutdown. It is mainly dependent on fuel burnup. Other decay heat evaluation needs for long cooling times are related to fuel reprocessing, radioactive material vitrification and naturally radioactive waste storage or repository. As mentioned in the introduction, the estimation of the SNF decay heat is important at various cooling periods, from seconds after a reactor shutdown, up to millions of years later for the safety case of geological repositories. Our capability to calculate this quantity (linked to other ones such as nuclide inventory), as well as to provide well-justified uncertainties and biases has direct implications on the simulations of accident scenarios, as well on the safety of the back-end of the fuel cycle, and naturally on involved cost. Our ability to excel in such estimations, and to improve safety and cost are the main motivations for presenting the state of the art from the aspects of measurement, simulation and validation.

The availability of a limited number of measurements for SNF decay heat is directly affecting the confidence level of simulations. Such experiments are expensive and currently only one facility exists worldwide. The domain of validation is therefore restrained, potentially leading to increased safety margins. Raising awareness on the need of new and independent measurements is consequently the first priority of this work.

Understanding and informing about the different possibilities in simulations and the impact of different parameters is the second priority. Various methods, guidelines and recommendations exist among institutes and countries, leading to different calculated decay heat values, even when starting from the same measurement database. Such variation of results should be made visible and explained for specialists and non specialists. Both previous points directly affect validation results. The scarcity of experimental values, as well as different simulation methods may lead to different consequences for the outcome of a validation procedure (such as safety factors, confidence intervals or uncertainties). Additionally, different validation procedures can also have different impacts on application quantities. Again, making such differences explicit, and understanding them is the third priority of this work.
<figure><img src="image_5.png" /><figcaption>**Fig. 3.** Number of nuclides that have to be computed to obtain a fraction (99%, 99.9%,..., 100% – ε, with ε = 10⁻¹²%) of the total decay heat computed by DARWIN with the JEFF-3.0 nuclear data library. Left: short cooling time in seconds from 0.1 to 10¹³ seconds. Right: long cooling time in days from 1 day to 10¹¹ years.</figcaption></figure>

Additional details are given in the following para-
graphs, articulated around these three axes: measure-
ments, simulations, and validation.

**2.4 General observations on current knowledge**

Validation of the existing codes with measured SNF decay heat is currently considered as a necessity by most of existing national and international regulations (see for instance the IAEA Safety guide Refs. [9,10]). Part of the motivation to continue performing analysis and measurements for SNF decay heat is due to today's trend of increasing bumpup and initial enrichment values, and also due to the need in improving current predictions. To illustrate our current capabilities for predictions, Figure 2 represents one aspect of the validation of codes used in the calculations of SNF decay heat.

This figure presents the histogram for C/E ratios (being Calculated over Experimental values) for SNF decay heat coming from calorimetric studies. All (tabulated) values from the open literature are used for this figure, mixing PWR and BWR assemblies, different simulation codes, nuclear data libraries, calculation procedures, and experimental sources. Such results do not represent the outcome of a validated procedure, but rather a snapshot of the existing published data. In total, 1490 calculated over experimental ratios were found, and the average of such histogram is 1.003, with a standard deviation of 0.059. Such figures indicate at first sight that the simulation capabilities can satisfactorily reproduce measured decay values for SNF with calorimetric measurements. One standard deviation is found to be close to 6%, and almost 86% of the data are within ±1σ. By considering two standard deviations, almost 97% of the cases are covered; a three-sigmas interval leads to 98.8% of the cases (five sigmas cover 99.6%). Numbers are changing if ones differentiate between PWR and BWR SNF assemblies, as indicated in Table 1.

As observed in previous work, the spread of C/E is
larger for BWR than for PWR. This is certainly linked
to the fact that BWR cases are more challenging to sim-

ulate, for instance due to the heterogeneity of the irradiation conditions (such as radial and axial void variations). Depending on the application, such numbers can be considered adequate or not. It is nevertheless important to understand the limitations of the experimental database used to perform such validation. In some cases, considering one standard deviation is not enough, as too many cases are left outside the ±1σ band. Table 2 is presents the number of C/E cases (from Tab. 1) which are included in various multipliers of ±σ.

It can be seen that if a specific application requires
that more than 99% of the cases are covered, one needs
to consider 3σ for the PWR SNF assemblies (correspond-
ing to 1.000±0.138), and 5σ for the BWR SNF assemblies
 corresp onding to almost 1.009±0.395). Such large uncer-
tainties, in terms of standard deviations, can have impor-
tant consequences on facility designs, and it is therefore
of high interest to improve the prediction capabilities.

Another quantity of high interest is the average value
presented in Table 1. It can be defined as an average sim-
ulation bias, which is for instance less than 2% in the case
of the PWR SNF assemblies. The mentioned references
are based on calculations performed with available mea-
sured SNF cases, implying a strong correlation between
the presented values. More recently, a blind benchmark
performed with 5 PWR SNF assemblies at the Clab facil-
ity, with more than 30 participants, has indicated an aver-
age bias of 0.978 (± 0.022) [15]. Later re-analysis of the
experimental values (as of mid 2023) indicates an over esti-
mation of the measurements, but such original value based
on a blind exercise is in disagreement with the average
values from Table 1. It is indicating that a more adequate
understanding of possible bias sources is required.

**2.5 Limitations**

The main impediment of the results presented in the pre-
vious section lies in the limits of application of the existing
experimental database. Such validation (average C/E val-
ues and standard deviations) is based on a very limited
set of measurements:
* Three facilities worldwide delivered 268 publicly available measurements for 164 SNF assemblies, up to the year 2006 (see for instance lists in Refs. [13,14])<fnref n="2" />. See Tables 11 and 12 for details,

* among these three facilities, two do not exist nowadays (GE-Morris and HEDL-EMAD),

* out of 268 measurements, more than 50% come from the Swedish Clab facility and 40% from the American GE-Morris facility (currently shutdown),

* only UO₂ SNF assemblies for PWR and BWR were measured (no MOX fuel, no other design such as for VVER),

* the highest enrichment is 4%, which is lower than the ones typically used in current reactors,

* the highest assembly average burnup is 51 MWd/kgU, which is also lower than the values reached in current reactors,

* the cooling time ranges from 2 to 27 years, which does not cover all cooling ranges of interest.

As mentioned, the estimation of decay heat is relevant for fuel management over a large period of cooling periods: short (e.g. for Loss Of Coolant Accident or Reactivity Insertion Accident), intermediate (for on-site SNF storage), and long (for off-site storage or disposal such as deep geological repository); some general information related to such needs is provided in the following section.

## 2.6 Needs

Note that the influential parameters (see the bullet list in the introduction) do not have the same weight depending on whether one considers the SNF just after the reactor shutdown or after a long cooling period in the SNF pool.

### 2.6.1 Decay heat for short cooling times

A conservative evaluation of decay heat is paramount for the proper design of heat removal systems of nuclear power plants (for an adequate mitigation of loss of coolant accidents for instance). The typical period of interest in safety studies goes from the reactor shutdown to about ten days. The number of contributing radionuclides is well over thousand just after the reactor shutdown, and that number decreases rapidly, as presented in Figure 3 reproduced from reference [16].

During this short cooling time period, the decay heat is nearly proportional to the reactor power before the reactor shutdown (“thumb rule” to be used with caution), as most of the contributing radionuclides are short-lived. For the same reason, it depends less on fuel burnup.

### 2.6.2 Decay heat for intermediate cooling times

In the 5 to 25 days period after reactor shutdown, the main application of decay heat evaluation is the safe unloading of the core into the nearby pool. Systems must take in account penalized values to cover fuel variability in power

and irradiation during the fuel transfer. In case of suspected fuel leakage, the assembly decay heat must be lower than a given threshold to enable a vacuum-canister sipping procedure. In this intermediate period, the decay heat is still strongly linked to the assembly power before reactor shutdown. However, the irradiation level has an increasing influence with cooling time.

Safety systems must be able to remove the decay heat of the complete unloaded core added to the one of the fuel assemblies already stored in the pool. Once the fuel is partially reloaded back into the core, the safety systems still have to remove the decay heat from the definitively unloaded assembly batch and the fuel already stored in the pool.

### 2.6.3 Decay heat for long cooling times

Long cooling times correspond to fuel assemblies that have cooled down several months or years. Typical needs for decay heat evaluation are:

* design of spent fuel pool heat exchangers,

* design of canisters and cylinders for fuel management and fuel storage,

* design of casks for fuel transport,

* verification of fuel compliance with the heat thresholds of the mentioned containers.

The decay heat for long cooling times is not very sensitive to the fuel power before shutdown. It is mainly dependent on fuel burnup. Other decay heat evaluation needs for long cooling times are related to fuel reprocessing, radioactive material vitrification, and naturally radioactive waste storage or repository.

## 3 Definition

In the following, the meaning of a number of quantities related to decay heat is explained. Even though the level of details can be appreciably extended, a minimum amount of information is provided in the following, allowing the reader to understand each term, and possibly to explore mentioned citations for additional details.

### 3.1 Spent nuclear fuel

In the present context, several complementary definitions of “Spent Nuclear Fuel” assembly (or simply *SNF*) can be used:

* *SNF*, also called spent fuel or depleted fuel, is a nuclear fuel that has been irradiated in a *nuclear reactor* (usually at a nuclear power plant or an experimental reactor) and that may be replaced by fresh fuel if it can no longer sustain *fission* in that environment due to physical, regulatory/licensing or economical limitations. Nuclear fuel becomes spent when its fissionable nuclides have been partially consumed and fission-product poisons have accumulated in it. *SNF* is characterized by its *burnup* (see Sect. 3.5) which is a measure of its utilization level.

<footnote n="2">² A number of measurements are not yet fully available, at the time of this report, such as from references [12,15].</footnote>
* SNF is a nuclear fuel withdrawn from a nuclear reactor following irradiation. SNF has not been chemically separated from its constituent elements by reprocessing: it includes the special nuclear material, by-product material, source material, and other radioactive materials associated with fuel assemblies.

SNF can also be called “Used Nuclear Fuel” (or UNF) and both terms are often interchangeable. They nevertheless do not refer to the same views, as the term SNF implies the concept of waste to be disposed of, whereas UNF suggests a possible reuse. Different institutions use either terms (NRC [17], IAEA [18], NWMO [19]), or a mix of both (US DOE). In this document, SNF is used with the broader meaning “nuclear fuel that has been irradiated in a nuclear reactor”.

## 3.2 Spent nuclear fuel characterization

Decay heat is one of the most important quantities for SNF characterization (or SFC for Spent Fuel Characterization). There is not a unique definition for the SFC, and one can refer to the ASTM C 1682:21 *Standard Guide for Characterization of Spent Nuclear Fuel in Support of Interim Storage, Transportation, and Geologic Repository Disposal* [20], which guides testing (involved in characterizing the physical and chemical nature of SNF) in support of its interim storage, transport, and disposal in a geologic repository. In this context, the experimental and computational characterization efforts can be defined as:

> Any test conducted principally to furnish information for a mechanistic understanding of alteration (for example, electrochemical polarization tests, leach tests, solubility tests, etc)

where the “alteration” is defined as any change to the form, state, or properties of the material under consideration. A non-exhaustive list of possible test fields is given below:

* Physical appearance, Extent, and distribution of visible cladding damage

* Weight/size/dimensions of SNF assemblies

* Radionuclide and fissile content

* Criticality-safety

* Metallography/optical microscopy

* Water content and drying characteristics

* Oxidation kinetics

* Ignition characteristics

* Dissolution characteristics

* Deliquescence and advective flow.

One of the challenging aspects of the SFC is the change of the SNF characteristics as a function of cooling time. Several experimental tests can be done at a certain time, and they need to be combined with theoretical models to understand the long-term evolution of given observables. Typical examples concern the change in the nuclide concentrations (due to natural decay), or in oxidation, directly affecting criticality values for hundreds of thousands of years.

Understanding the characteristics of SNF is essential in all spent fuel management activities, the SFC being a prerequisite for such safe and economical management. The IAEA Joint Convention on the Safety of Spent Fuel Management and the Safety of Radioactive Waste Management in 1997 defines spent fuel management as follows [21]:

> “spent fuel management” means all activities that relate to the handling or storage of spent fuel, excluding off-site transportation.

One can also note that the important characteristics in spent fuel management mainly depend on the evaluated quantities. Important characteristics for criticality-safety in spent fuel pools may differ from those important in transport, dry storage, or final disposal repository.

## 3.3 Decay heat

The term “decay heat”, generally expressing the recoverable energy generated by the decay of nuclides from nuclear fuel, does not correspond to the correct modern terminology. The term heat is nowadays used to describe energy transfer, for instance, based on the mechanism of conduction or radiation (without the transfer of matter). As an energy, the proper unit of heat is Joule, or sometimes calorie. A better designation is “decay power”, therefore correctly expressed in Watts, or eventually in Watt per ton (of matter). As the term “decay heat” was historically used from the 1940s, it is still employed today, with the understanding that the quantity of interest is expressed in Watt.

The term “thermal power” ( or “residual thermal power”) is also sometimes used (as in the DIN standard [22]), although the word “thermal” refers to the power generated in the reactor core, commonly called thermal power (to differentiate it from the electrical power). Specific definitions can be found in different guides or countries:

* US DOE: it is considered that decay heat is a particular problem associated with nuclear reactors. Even though the reactor is shut down, heat is produced from the decay of fission fragments (note that this definition does not include the contribution from actinides). Limits for each particular reactor are established to prevent damage to fuel assemblies due to decay heat [23]. This reference provides two definitions of decay heat generation rate. The first definition is related to the physical process of decay heat generation as a result of a fission reaction and obtained products that contain excess energy. The second definition is related to the energy excess in the form of heat, which appears to be a safety feature. There should be established limits, based on the engineering design, not to be exceeded. Therefore, the decay heat generation rate is not only a physics feature but also an engineering concept.

* US NRC: the heat produced by the decay of radioactive fission products after a reactor has been shut down (March 2021). As mentioned, it should be noted that
such a definition does not include the contribution of actinides.

* US NRC Regulatory guide 3.54, revision 2: the heat generation rate of the spent fuel assembly is the recoverable thermal energy (from radioactive decay) of the assembly per unit of time and per unit of fuel mass. Heat generation rate has also been referred to as decay heat rate, afterheat, or afterheat power.

* ASN, (France, not translated to avoid modifications): La puissance résiduelle est la puissance thermique développée par un réacteur nucléaire après l'arrêt, provenant essentiellement de la radioactivité du combustible nucléaire et des autres matériaux ainsi que des fissions résiduelles.

* According to the ISO standard of 1992 [24], “The decay heat power of nuclear fuels is the thermal power produced by radioactive decay of fission and activation products of the nuclear fuel following the shutdown of a nuclear reactor” (note that the contribution from actinides is also missing).

– In the German DIN standard [22,25], the decay power is defined as the “thermal power generated by the decay of nuclides in the nuclear fuel”.

It should be noted that if these definitions differ in their formulation and on some specific points, they all agree on the physical phenomenon: released energy from the nuclear components and other materials after the reactor shutdown (although many definitions do not include the contribution from actinides, and one can consider as well that the decay heat is also produced during a reactor cycle).

## 3.4 Decay heat standards

Standard methods and reference guides for the calculation of SNF decay heat have been established in different countries; details can be found in Section 6.3. They provide acceptable procedures for calculating such decay heat (mathematical methods, range of applications, and often examples), which sensibly differ from the summation method (see Sect. 6.4.1). The main advantages of these methods are that they can be applied given a limited set of parameters representing the SNF and its irradiation, such as average burnup, cooling time, initial enrichment, and partial fission contributions from the main actinides. They do not necessitate neutron transport and fuel depletion calculations and can provide values a short calculation time. Examples of such methods are the ANS-5.1 [26], ISO [27], NRC-3.54 [28], and the DIN 25463-1 [22] standards.

## 3.5 Burn up (or burnup)

The burnup is a measure (not in the experimental meaning) of the utilization level of the fuel. Depending on the perspective of the final user, different approaches are commonly encountered to quantify the burnup. One of them reflects the number of fissions that have taken place:

* It can be expressed as the fission density, i.e. the number of fissions in a given volume. Units such as fiss./cm³ or fiss./m³ are commonly used in the research reactor community; those are simply obtained by integrating, over time, the fission rate, itself being the product of neutron flux with the fuel macroscopic fission cross-section.

* It may also be described as the relative fraction of actinides that has fissioned. Radiochemists often use the term “Fissions per Initial Heavy Metal Atom”, or FIMA, unit in spent fuel assays, before converting that to more practical units for the end-users.

However, by far, the most common approach to commercial fuel burnup is to describe its specific thermal energy output. Indeed, for commercial reactor operations, the total thermal core power is known through the thermal balance at the core inlet and outlet. Integrated over time for a given cycle, one obtains the cycle thermal energy generation, which translates into the cycle performance. That latter quantity is often characterized by the number of effective full-power days i.e., the equivalent number of days at nominal power corresponding to the cycle thermal energy output. The relative distribution of fissions and, hence, the nominal power in the core is known from core physics calculations and/or from in-core instrumentation. The product of the fuel assembly nominal power, for example in MW, with the number of effective full-power days enables a fast evaluation of the thermal power output of each assembly, as well as its specific thermal output if divided by the fuel mass or by the initial heavy-metal mass. The natural units to express the burnup level for commercial reactors are therefore MWd/kgHM, or variants involving GW or $t_{HM}$ (HM refers to Heavy Metals). Those units are also often used from licensing and/or regulatory perspectives.

An equivalence, or conversion factors, between those units, can easily be established if one assumes an effective energy release of 200 MeV per fission event and a density of 10 960 kg/m³ for UO₂ fuel:

$$1\% \text{ FIMA} \leftrightarrow 2.310^{26} \text{ fiss./m}^3 \\ \leftrightarrow 9.4 \text{ MWd/kg}_{\text{HM}} \\ \approx 10 \text{ MWd/kg}_{\text{HM}}. \qquad (1)$$

As presented in reference [29], “fuel burnup measures how much energy is extracted from nuclear fuel and is a measure of fuel depletion.”.

As a simple representative example of this quantity, it can be considered that the fission of a single nucleus of $^{235}$U induced by a thermal neutron releases about 200 MeV of recoverable energy. To produce 1 Watts of power, a total of $3.1 \times 10^{10}$ fissions per second is needed. To reach an energy (or burnup) of 1 MWd (megawatt-day), one needs about $2.5 \times 10^{21}$ fissions. If every nucleus undergoes fission, the same amount of nuclei is necessary, which is roughly contained in 1 gram of any fissile material. It is important to note that this relation between burnup and the number of fissions is only a rough approximation. The average recoverable energy per fission depends on the fissioned nuclide as well as on the contribution
from other, non-fission, neutron-induced reactions, which
depends also on system design and operational param-
eters. The actual value may vary by up to about 5%. In
addition to these definitions, the following distinctions are
often useful:

* Core burnup: averaged burnup over entire core (for all fuel assemblies).

* Assembly burnup: averaged burnup over a single fuel assembly.

* Assembly node burnup: average burnup value for a vertical segment of an assembly. A vertical segment usually represents 10 cm to 20 cm.

* Pin burnup: averaged burnup over a single fuel pin or fuel rod.

* Local burnup: burnup values within a single fuel pellet.

The assembly burnup is one of the most important quantities for the determination of the assembly decay heat. It can unfortunately not be directly measured and is either calculated or derived from the measurements of related quantities. Due to its importance for the estimation of assembly decay heat, some general information is provided hereafter. Details can be found for instance in references [30,31].

### 3.5.1 Calculated burnup

As indicated in the following, the assembly burnup can be
calculated by performing a full-core calculation (such as
in core follow-up calculations), or part of the rod burnup
can be assessed with a single-assembly calculation (such
as during lattice code validation). The second one still
depends on the information provided by the core simula-
tor, implying that the knowledge of the calculated assem-
bly burnup cannot be better than the performance of the
core simulator. Biases and uncertainties for the calculated
burnup should not be assumed negligible.

#### From lattice code

Lattice codes are often used for the calculation of nuclide
concentrations in specific samples obtained from irradi-
ated rods or assemblies (in Post Irradiation Examination,
or PIE). Such calculations are of importance as they are
often used in code validation (see Sect. 8), which may
eventually impact the conditions of SNF transport and
storage. These calculated concentrations are then com-
pared to measured ones, for instance for samples contained
in the SFCOMPO database [32]. In such lattice calcula-
tions, the sample burnup is first obtained based on core
simulator data (see next paragraph). The accepted prac-
tice is that to compensate for the lack of knowledge of
the full irradiation conditions, the sample burnup can be
modified so that the calculated concentration of a spe-
cific nuclide matches its measured value, for instance for
a burnup indicator, such as ¹⁴⁸Nd.

In this approach, the sample burnup value cannot be
known better than the concentration uncertainty of the
selected nuclides (varying from tens of a percent, up to
5%). Such sample value is of course different from assem-
bly burnup, and the extrapolation is not straightforward,

<figure><img src="image_6.png" /><figcaption>**Fig. 4.** Comparison between the CASMO5 (single-assembly calculation, left) and SIMULATE (full-core calculation right) pin burnup values for the GU3 sample. The sample location is indicated with an orange square [33].</figcaption></figure>

due to the normalization effect to a measured nuclide con-
centration, and to the axial and radial burnup distribu-
tions. An example of the radial burnup distribution is pre-
sented in Figure 4 for the ARIANE sample GU3 [33].

On the left is a lattice calculation performed with the
code CASMO5, assuming reflective boundaries outside the
assembly of interest (usually, no information for the neigh-
boring assemblies is provided for PIE analysis). Conse-
quently, there is a symmetry for the burnup distribution
of the concerned segment. On the right is the calculated
burnup distribution from the code SIMULATE, consider-
ing the realistic assemblies surrounding the assembly of
interest. It can be observed that the two burnup distribu-
tions are different, illustrating the burnup simplification
obtained in lattice calculations.

Concerning the normalization of the lattice calcula-
tion to the measured concentration of burnup indicators
(¹⁴⁸Nd, ¹³⁷Cs, or a few Nd isotopes), helps assess solely
the effect of a specific code, its nuclear data library and
the modeling method, based on irradiation parameters
(usually) provided by a core simulator. The normalization
removes the effect observed on the right side of Figure 4
(neighboring assemblies). But it also does not allow to
disentangle fission contributors (such as ²³⁵U and ²³⁹Pu,
as their productions of ¹⁴⁸Nd are roughly equivalent); the
power history (and the sample burnup) can consequently
be incorrect, even if the agreement with specific nuclide
concentrations is acceptable. A way to bypass this issue is
to normalize the power history to match the ratio of mea-
sured nuclides concentrations which are differently pro-
duced from ²³⁵U and ²³⁹Pu, such as ⁹⁰Sr over ¹⁵⁰Nd [34]
(different fission yields for the two main fission contribu-
tors can help to better assess if individual contributions
are correctly captured during the simulation).

#### From core simulator

The assembly burnup, as well as the assembly node bur-
nup profile, can be calculated based on various in-core
detectors (e.g. fission chambers), measured core thermal
output (based on temperature and flow measurements),
<table><caption>**Table 3.** Example of single assembly burnup calculations for a UO₂ and a MOX assembly. Both are initially enriched at 4% in fissile materials. Calculations are performed with CASMO5. “Fis.” corresponds to the fissile nuclides and “Fer.” to the fertile nuclides.</caption><thead><tr><th rowspan="3">Assembly<br>burnup<br>MWd/kgHM</th><th colspan="4">UO<sub>2</sub></th><th colspan="4">MOX</th></tr><tr><th colspan="4">Contribution from</th><th rowspan="2">Total mass<br>Fis.+Fer.<br>%</th><th colspan="4">Contribution from</th><th rowspan="2">Total mass<br>Fis.+Fer.<br>%</th></tr><tr><th><sup>235</sup>U</th><th><sup>238</sup>U</th><th><sup>239</sup>Pu</th><th><sup>241</sup>Pu</th><th><sup>235</sup>U</th><th><sup>238</sup>U</th><th><sup>239</sup>Pu</th><th><sup>241</sup>Pu</th></tr></thead><tbody><tr><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>100</td><td>0</td><td>0</td><td>0</td><td>0</td><td>100</td></tr><tr><td>1</td><td>0.9</td><td>0.1</td><td>0</td><td>0</td><td>99.8</td><td>0</td><td>0.1</td><td>0.8</td><td>0.1</td><td>99.7</td></tr><tr><td>2</td><td>1.9</td><td>0.1</td><td>0</td><td>0</td><td>99.7</td><td>0</td><td>0.1</td><td>1.7</td><td>0.2</td><td>99.6</td></tr><tr><td>5</td><td>4.5</td><td>0.2</td><td>0.3</td><td>0</td><td>99.3</td><td>0.1</td><td>0.4</td><td>3.9</td><td>0.6</td><td>99.2</td></tr><tr><td>10</td><td>8.1</td><td>0.7</td><td>1.2</td><td>0</td><td>98.7</td><td>0.3</td><td>0.7</td><td>7.8</td><td>1.2</td><td>98.7</td></tr><tr><td>15</td><td>11.4</td><td>1.0</td><td>2.5</td><td>0.1</td><td>98.1</td><td>0.4</td><td>1.2</td><td>11.3</td><td>2.1</td><td>98.2</td></tr><tr><td>20</td><td>14.4</td><td>1.4</td><td>3.9</td><td>0.3</td><td>97.6</td><td>0.5</td><td>1.7</td><td>14.6</td><td>3.2</td><td>97.7</td></tr><tr><td>25</td><td>17.0</td><td>1.8</td><td>5.6</td><td>0.6</td><td>96.9</td><td>0.6</td><td>2.0</td><td>18.0</td><td>4.1</td><td>97.1</td></tr><tr><td>30</td><td>19.4</td><td>2.1</td><td>7.6</td><td>0.9</td><td>96.4</td><td>0.8</td><td>2.4</td><td>21.2</td><td>5.4</td><td>96.5</td></tr><tr><td>35</td><td>21.5</td><td>2.5</td><td>9.6</td><td>1.4</td><td>95.8</td><td>0.9</td><td>2.9</td><td>24.2</td><td>6.7</td><td>96.0</td></tr></tbody></table>

and validated core simulator. Alternatively, the methods to calculate the assembly burnup may vary from one code to another, and have evolved over time (a possible consequence is a change of attributed assembly burnup over time).

Because the estimation of the burnup often relies on core simulators for the vast majority of burned assemblies, the decay heat of such SNF can be directly affected by the burnup values obtained from such simulations. A recent analysis of the possible errors in assembly reactivity, based on in-core measurements can be found in reference [35]. Such analysis provides an estimated error in assembly reactivity as a function of the assembly node burnup, using in-core flux map measurements for different PWR cores. The method is based on varying assembly burnup values and calculating the impact on the comparison between the measured and calculated power maps. The impact of such variations is compared to the nominal values (best estimate burnup values) and possible biases are derived. The conclusion of this study mainly concerns the reactivity biases at hot full power (HFP) and cold conditions. Assembly burnup values were modified by a factor between 0.85 and 1.15, but an agreement between calculated and measured in-core flux was found with factors generally within ±5%.

Although a detailed study should be performed to analyze the distribution of such factors (not available from the mentioned reference), this study indicates that a certain degree of freedom exists for the estimation of the assembly burnup, probably within the range of a few percent.

### 3.5.2 Example of calculated burnup

As presented earlier, a very simple calculation indicates that the fission of all nuclei contained in 1 gram of fissile material provides about 1 MWd. This is naturally a simplification,

as other reactions happen in the fuel, due to the mixture of initial nuclides ($^{235}$U and $^{238}$U, and in some cases Pu isotopes), and the build-up of fission products. Neutron capture on actinide nuclides and fission products also produces energy, which modifies the simple previous account. Two examples of calculated burnup values from realistic assemblies are presented in Table 3: one UO₂ and one MOX assembly, both initially enriched at 4% in fissile materials. These examples were obtained from lattice calculation (single assembly) with the code CASMO5.

One can then observe that for realistic assemblies and irradiation conditions, more than one nuclide contributes to the total released energy. Modern depletion codes can consider the contribution from different nuclides and provide relatively precise burnup values. Naturally, the underlying nuclear data used for these calculations (Q-values, energy release as a function of the neutron energy, fission and capture cross sections) are not perfectly known, which can modify the calculated assembly burnup. As previously mentioned, changes in an assembly burnup value directly affect the assembly decay heat.

As a last example of calculated burnup, the case of burnup values from core simulators is considered in the following. For a realistic PWR cycle, two different calculations are performed with the same core simulation code, but different versions (nonetheless the same nuclear data library), called in the following V1 and V2. Often, a new code version implies an additional update in the input file for the cycle description, and the input file was therefore modified. Both calculations were validated against in-core data and showed similar performances. There were nevertheless changes in the calculated burnup values, both for assembly average and pin-wise values, and differences in percent are presented in Figure 5.

As observed, the changes for the average assembly burnup are within ±2%, with higher deviations at low burnup. The pin burnup values present a larger spread. This is an
<figure><img src="image_7.png" /><figcaption>**Fig. 5.** Burnup differences for assembly and pin values, for a realistic cycle calculation, from two different versions of the same core simulator.</figcaption></figure>

indication that the assembly burnup values from a core simulator are not uniquely defined, and a certain amount of uncertainty is also propagated to decay heat values.

### 3.5.3 Measured burnup

The term “measured burnup” is by itself not correct, as burnup or fissile content values are not directly measured, but can be derived from other measured quantities combined with specific calculations and assumptions. Such measurements concern the neutron and gamma radiations emitted from an assembly. The build-up of minor actinides during the depletion of the assembly leads to the emission of a number of $\alpha$ particles due to the relatively short half-life of such nuclides (e.g. isotopes of Am, Cm). The rate of $\alpha$ emission is generally high enough to produce a significant amount of neutrons and gamma rays from $(\alpha,n)$ reactions and spontaneous fission. A strong dependence between the neutron emission rate and the burnup exits can be used to infer the assembly’s average burnup [36]. In practice, complications can arise as the measurements of gamma-ray spectra represent a mixture of fission products, activation products, and actinides that have built up during the assembly irradiation.

Different techniques exist to measure gamma-ray or neutron emissions (see for instance Ref. [37]). In active neutron detection, an external neutron source is used, consequently increasing the neutron flux from neutron-induced fission events occurring in the residual fissile material; the time dependence of the neutron count rate is used to infer the quantity the amount of fissile material. In the case of gamma-ray measurements, specific gamma-ray energies are measured, corresponding to the decay of well-known fission products. Such fission products need to be produced in significant amounts (high fission yield), having a half-life long enough to allow gamma-ray measurements, and gamma-ray energies which are easy to identify. $^{137}$Cs is consequently a good candidate (half-life of 30.07 years, with a gamma-ray energy of 661.7 keV), being the main gamma-ray emitter after a few years of cooling time.

During this type of measurement, background subtraction can be significant, implying long counting times to reach adequate statistical accuracy. Details can be found in Section 5.2.2 and in Appendix C. A third method used to experimentally infer the assembly burnup is the passive neutron measurement technique. It consists in detecting emitted neutrons from spontaneous fission of minor actinides, mainly from $^{244}$Cm, with a half-life of 18.1 years. $^{244}$Cm emits more than 90% of the neutrons from an irradiated assembly for cooling times ranging from 10 years to 100 years. Its concentration is highly sensitive to the assembly burnup, but also measurement factors (such as detector positioning). Additionally, the SNF irradiation conditions need to be well known to correctly calculate the concentration of $^{244}$Cm.

## 4 Physical origin of decay heat, key contributors

The complexity of the decay heat process originates from the fact that one handles with byproducts of radioactive decay, which can be understood from the quantum mechanics theory. In particular, one refers to the internal energy levels of the nuclei. As the density of those levels increases with the atomic mass (with an important dependence on nuclear structure [38]), one expects an enhanced number of decay transitions mainly for mid and heavy nuclides. Such decays are subject to uncertainties, probabilities, and half-life definitions of decay patterns, which are not obvious.

The decay process and its uncertainties become more cumbersome as far as decay heat is concerned as very often the daughter product is also radioactive and can generate even more heat by further shorter decay processes. Ultimately, as will be shown in this section one has to deal with some unique decay pairs, or even to some extent decay chains, each of which, with its branching ratios and own heat production over different time scales.

As mentioned in the introduction, the integral amount of heat is well known to be around 7% of the operational power and a detailed analysis is not relevant. For long storage periods, the contribution of specific nuclides becomes considerably important. Considering again the quantum mechanics nature of the decay phenomenon, one has to separate the radioactive nuclides into different groups according to their decay types. Such an analysis includes the half-life time and decay mode. Further, one can analyze the mobility of such radioactive elements within and out of the repository. In the following subsections, the relevant elements are divided into actinides, fission products, and activation products. In addition, the specific pairs of radioactive materials with enhanced importance at different periods after shutdown are presented. The last part of this section demonstrates a quantitative analysis of those nuclides, which dominate the decay heat during the first 100 years, the realistic foreseen time of the temporary storage. The simulation is based upon a decay process of a PWR fuel assembly. For completeness, the decay heat at 300 years cooling time shows that the actinides are
<table><caption>**Table 4.** Fission Energy Release from the ENDF/B-VII.1 evaluated library. The neutron capture value is obtained from reference [39].</caption><thead><tr><th>Energy modes</th><th>Fractions</th><th><sup>235</sup>U<br>(MeV)</th><th><sup>238</sup>U<br>(MeV)</th><th><sup>239</sup>Pu<br>(MeV)</th><th><sup>241</sup>Pu<br>(MeV)</th><th>Time</th></tr></thead><tbody><tr><td><i>E</i><sub>kin</sub> fission fragments</td><td>80%</td><td>169.1</td><td>169.8</td><td>175.5</td><td>175.3</td><td>Instant</td></tr><tr><td><i>E</i><sub>kin</sub> Fission Neutrons</td><td>2–3%</td><td>4.8</td><td>4.6</td><td>6.2</td><td>6.0</td><td>Instant</td></tr><tr><td>Beta decay of FPs</td><td>3–4%</td><td>6.5</td><td>8.5</td><td>6.7</td><td>7.6</td><td>Delayed</td></tr><tr><td>Gamma-rays prompt</td><td>3–4%</td><td>6.6</td><td>6.7</td><td>5.2</td><td>6.4</td><td>Instant</td></tr><tr><td>Gamma-rays delayed</td><td>3–4%</td><td>6.3</td><td>8.2</td><td>5.3</td><td>6.6</td><td>Delayed</td></tr><tr><td>Neutrinos</td><td>4–5%</td><td>8.7</td><td>11.4</td><td>7.1</td><td>8.8</td><td>Delayed (unrecoverable)</td></tr><tr><td>Neutron capture</td><td>3–5%</td><td></td><td>6–11</td><td></td><td></td><td>Instant/Delayed</td></tr></tbody></table>

practically dominating more than 95% of the decay heat from that time slot, and the importance of other nuclides, in particular $^{137}$Cs/$^{137m}$Ba and $^{90}$Sr/$^{90}$Y, fade away. Table 4 presents a list of the main energy fractions for each production mode during irradiation in a typical LWR.

It is relatively clear that the available energy from $\beta$ decays and isomeric transitions represents about 7 to 8% of the total energy (approximately corresponding to the calculated decay heat from the Borst-Wheeler equation at the time of the reactor shutdown, see Eq. (6) in Sect. 6).

## 4.1 Overview

Several publications prior to the year 2000s and the older regulatory guides considered decay heat as a single integral quantity, see, for instance, references [40,41]. More recently, as detailed in Section 6.4.1, the implementation of the summation method in computer codes for decay heat predictions provides a means to further isolate the nuclides responsible for most of the SNF decay heat power as a function of cooling time. Additionally, current decay heat standards treat the decay heat as a sum of individual components based on the physics of the decay process and nuclide generation under neutron irradiation (see details in Sect. 6.3).

Several studies have determined the most important medium-to-long-term decay heat contributors for spent LWR fuel and were used as a source in the following, see for instance reference [42]. This reference ranks individual nuclides by their contribution to the decay heat power. It also addresses the need for accurate source term predictions in commercial LWRs with higher levels of fuel enrichment and burnup.

Figure 6 summarizes the findings from reference [42] for 5 years following reactor shutdown.

As indicated in the figure, the decay heat power fractions of $^{90}$Sr and $^{90}$Y are added up as the two nuclides quickly reach a secular equilibrium. The same holds for $^{137}$Cs and $^{137m}$Ba and $^{144}$Ce and $^{144}$Pr. The fractions of the total decay heat power produced by individual nuclides are displayed as a function of burnup and ini-

<figure><img src="image_8.png" /><figcaption>**Fig. 6.** Contributions to the UO$_2$ SNF decay heat for 5 years of cooling time. Numbers 3, 4, and 5 correspond to the initial $^{235}$U enrichment.</figcaption></figure>

tial enrichment. Results are equivalent for both BWR and PWR and suggest a marginal dependence of the nuclide importance to decay heat on the LWR reactor type for cooling times longer than 1 year.

In the following paragraphs, the key nuclides contributing to the total decay heat of spent LWR uranium-fuel are discussed. Their production routes in a typical LWR are highlighted based on summation calculations using the simplified PWR model, as proposed in reference [43].

## 4.2 Delayed fission

A part of the decay heat comes from delayed fission events, induced by delayed neutrons. As delayed neutron precursors have relatively short half-lives, the delayed fission contribution is limited to the first 100 seconds after shutdown (in the case of a heavy water reactor, the photo-neutron source due to deuterium is large enough to affect the neutron population immediately after shutdown). The importance of delayed fission for decay heat after shutdown is presented in references [44,45]. In reference [39], it was also shown that taking into account the delayed fission in reactivity-initiated accident (RIA) simulations significantly changes the calculated decay heat for a short time (a few seconds).
<figure><img src="image_9.png" /><figcaption>Fig. 7. Actinide production scheme in irradiated reactor fuel.</figcaption></figure>

## 4.3 Actinides

During the irradiation of uranium fuel, transuranic nuclides build up mostly as a combination of multiple neutron capture reactions (n,γ) in the initial uranium and radioactive decay. Other threshold reactions such as (n,2n) or (n,p) occur at a much lower rate, making these production routes often negligible. In low-enriched uranium fuel, most of the neutron captures occur in $^{238}$U, producing fissile nuclide $^{239}$Pu from the rapid decay of $^{239}$U and $^{239}$Np. Many of the actinides created as a result of nuclear transmutation have much shorter half-lives than those of the uranium isotopes present in fresh fuel and can significantly contribute to the decay heat of spent LWR fuel. An overview of the transmutation mechanisms for the actinides buildup in irradiated nuclear fuel is shown in Figure 7. Only a few actinides are responsible for decay heat in $UO_2$ fuel at any cooling time in comparison with a large amount of significantly contributing fission products.

Within the first few years following reactor shutdown fission products are the primary source of decay heat and the radioactive decay of actinides only generates a small fraction of it. In the first few hours/days of cooling this contribution comes mainly from the radioactive decay of the $^{239}$U and $^{239}$Np produced from the transmutation<fnref n="3" /> of $^{238}$U [47,48]. As for other short-lived nuclides, their concentration and their role in decay heat is a function of problem-specific parameters such as the reactor-specific power. The $^{239}$U/$^{239}$Np contribution dies out within a few days, after which alpha-emitter $^{242}$Cm, with a half-life of 142 days, contributes up to 90% of the actinide decay heat power up to 1 year. All other actinides with a non-negligible concentration at shutdown decay with longer half-lives and their contribution is only relevant for the long-term decay heat. In general in MOX fuel the actinide contribution exceeds the fission product decay heat power already after a few years of cooling. More than 99.5% of the total actinide decay heat in spent LWR fuel from 30

days up to more than 200 years from discharge is produced by seven actinides: $^{241}$Am, $^{242}$Cm, $^{244}$Cm, $^{238}$Pu, $^{239}$Pu, $^{240}$Pu and $^{241}$Pu [28].

$$^{239}\text{U}/^{239}\text{Np}$$

Days after discharge the actinide decay contribution comes primarily from the decay of short-lived nuclides $^{239}$U and $^{239}$Np, which have radioactive half-lives of 23.46 min and 2.356 days, respectively. $^{239}$U is produced from neutron capture in $^{238}$U and quickly beta decays into $^{239}$Np emitting beta and gamma radiation. The daughter nuclide $^{239}$Np further beta decays into $^{239}$Pu also releasing beta-electrons and gamma-rays. This decay sequence is reported in equation (2) and not only it represent the only significant production route of $^{239}$U and $^{239}$Np during irradiation, but also of the fissile nuclide $^{239}$Pu.

$$^{238}\text{U} \xrightarrow{(n,\gamma)} ^{239}\text{U} \xrightarrow{(23.46 \text{ min})} ^{239}\text{Np} \xrightarrow{(2.356 \text{ day})} ^{239}\text{Pu} \quad (2)$$

The $^{239}$U and $^{239}$Pu decay heat power was derived analytically in the decay heat standards [24,26,49], which cover explicitly their contribution to the decay heat of LWRs. A value for the $^{239}$U and $^{239}$Np short-term decay heat of spent LWR fuel strongly depends on the reactor operation condition. However, publications from the early 2000s and earlier show that it can represent up to more than 90% of the actinide decay heat power fraction (equivalent to about 20% of the total decay heat power) after the first day of cooling and it goes down to about 70% within 5 to 10 days [44,47,48].

$$^{239}\text{Pu}/^{240}\text{Pu}$$

$^{239}$Pu is continuously created from the irradiation of $^{238}$U following the production route already presented in equation (2). Further irradiation of the nuclear fuel gives rise to plutonium isotopes $^{240}$Pu, $^{241}$Pu, and $^{242}$Pu as a result of neutron captures starting with $^{239}$Pu.

During nuclear fuel irradiation in a LWR this is essentially the only plutonium production route. $^{239}$Pu buildup gradually saturates with burnup as its fission rate

<footnote n="3">³ For uranium fuel with high $^{235}$U enrichment, the actinide's short-term contribution to decay heat power comes from the transmutation products of $^{235}$U, i.e. $^{237}$U and $^{238}$Np [46].</footnote>
<figure><img src="image_10.png" /><figcaption>Fig. 8. Build-up of the Pu isotopes in a LWR as a function of the assembly burnup.</figcaption></figure>

increases. On the other hand, the production of the heavier plutonium isotopes accelerates at higher burnup values: an effect that is visible in Figure 8 for $^{242}$Pu because of its lower disappearance rate.

For $^{240}$Pu and $^{241}$Pu, which have respectively large capture and fission cross sections in a thermal LWR, the production and disappearance rates already balance out for burnup values of the order of a few tens of GWd/tHM or lower, depending on the fuel’s initial enrichment.

$^{239}$Pu and $^{240}$Pu are both long-lived alpha-particle emitters with half-lives, of 24 110 and 6560 years, respectively. They release alpha particles with average energies of 5.156 MeV and 5.238 MeV. Because of the magnitude of these half-lives the decay of $^{239}$Pu and $^{240}$Pu is irrelevant during the fuel irradiation but becomes important to the SNF decay heat power already after 100 years of cooling with a contribution of a few percent and up to 20% after one thousand years. These numbers do not significantly vary with burnup and initial enrichment.

### $^{241}$Am

$^{241}$Am naturally decays into long-lived $^{237}$Np with a half-life of 432.8 years. For one disintegration of $^{241}$Am an alpha particle is emitted with an average energy of about 5.48 MeV. Independently on whether the fuel is irradiated in a reactor or left to decay, the only significant production route of $^{241}$Am is from the radioactive beta decay of $^{241}$Pu (half-life of 14.33 years).

About 70 years after shutdown $^{241}$Am becomes the largest source of decay heat power in spent LWR fuel and it remains as such for a few thousand years. After one hundred years it generates almost half of the total decay heat power [42,43], and about 70% of the actinide decay heat power fraction [44]. Its relative importance to decay heat is significantly affected by the SNF burnup. At high burnup and depending on the fuel’s initial enrichment the $^{241}$Am buildup during irradiation slows down as the $^{241}$Pu loss via neutron-induced fission increases. The $^{241}$Am relative contribution to the decay heat power in SNF with 70 GWd/tHM burnup and 5% initial enrichment drops to about 30% at 100 years of cooling time [42].

### $^{242}$Cm

The only significant production process of $^{242}$Cm in an LWR is from the neutron irradiation of $^{241}$Am. Neutron capture reactions in $^{241}$Am create $^{242}$Am, in its ground state with a probability higher than 90%. $^{242}$Am either beta decays into $^{242}$Cm or produces $^{242}$Pu from electron capture with a ratio of 83/17% and a half-life of 16.01 hours. The amount of $^{242}$Am in its first metastable state (i.e. $^{242m}$Am at 48.6 keV) formed during irradiation decays by internal conversion to its ground state with a probability of 99.5% and a longer half-life of 141 years. Despite being the only production process of $^{242}$Cm after shutdown, the decay chain of $^{242m}$Am is negligible to decay heat. $^{242}$Cm decays with a half-life of 162.9 days and emits alpha particles with a peak energy of 6.11 MeV (74% emission probability) which constitutes the majority of the recoverable decay energy. Already a few years after discharge essentially all of the $^{242}$Cm would be converted into $^{238}$Pu.

As for the other curium isotopes, $^{242}$Cm in nuclear fuel is generated from multiple neutron captures and, as such, its production accelerates at higher burnup levels. The $^{242}$Cm decay heat power fraction in spent LWR fuel is the highest after several hundred days of decay and it constitutes 80–90% of the actinides share [47]. This contribution remains below 5% of the total decay heat power [43,50] as fission products are still the largest decay heat source within this time scale. For irradiated MOX fuel, $^{242}$Cm can contribute to more than 15% of the total decay heat at 1 year of cooling. For both fuel types, the relative importance of $^{242}$Cm for decay heat drops already a couple of years after discharge.

### $^{238}$Pu

$^{238}$Pu naturally decays with a relatively long half-life of 87.7 years, principally by emitting alpha radiation and by a marginal fraction undergoing spontaneous fission. The emitted alpha particles have an average energy of 5.58 MeV per disintegration making $^{238}$Pu a considerable heat source with a specific power of about 0.55 W/g [51]. More than 90% of the $^{238}$Pu content in spent LWR fuel is produced via the neutron activation of $^{237}$Np shown in equation (3).

$$^{237}\text{Np} \xrightarrow{(n,\gamma)} ^{238}\text{Np} \xrightarrow{(2.1 \text{ days})} ^{238}\text{Pu}. \quad (3)$$

In turn, $^{237}$Np builds up either from a series of neutron capture reactions in $^{235}$U or as a result of the (n,2n) reaction in $^{238}$U. The fraction of decay heat power produced by $^{238}$Pu strongly increases with burnup. This effect is enhanced at longer cooling times to the detriment of $^{241}$Am, which ultimately saturates. The $^{238}$Pu contribution after 5 years of cooling varies from a few percent at low burnup up to more than 8% at high burnup. After 100 years it produces from 20% to 30% of the total decay heat power for a burnup range between 50 and 70 GWd/tHM.
$^{244}$Cm

At burnup higher than 30–40 GWd/tHM (or lower bur-
nup for initial enrichments below 5%) $^{244}$Cm becomes the
most present curium isotope in irradiated nuclear fuel. In
SNF, $^{244}$Cm is practically entirely generated from neutron
captures at $^{243}$Am, followed by the disintegration of the
resulting $^{244}$Am in equation (4). Both isomers of $^{244}$Am
beta decay into $^{244}$Cm with similar half-lives (i.e. 10.1
hours the ground state and 26 min the metastable state).

$$
^{243}\text{Am} \xrightarrow{^{(n,\gamma)}\text{Am}} ^{244}\text{Am} \xrightarrow[\text{(10.1 h/26 min)}]{\beta} ^{244}\text{Cm}. \quad (4)
$$

Basically, all the $^{243}$Am in irradiated fuel is created from
the sequence of neutron captures in the plutonium iso-
topes reported in equation (5).

$$
^{241}\text{Pu} \xrightarrow{^{(n,\gamma)}} ^{242}\text{Pu} \xrightarrow{^{(n,\gamma)}} ^{243}\text{Pu} \xrightarrow[\text{(4.96 h)}]{\beta} ^{243}\text{Am}. \quad (5)
$$

Other production routes including $^{242}$Am electron capture decay, neutron captures in americium or lighter curium isotopes are negligible. $^{244}$Cm decays with a half-life of 18.1 years emitting alpha particles with an average energy of 5.9 MeV.

4.4 Fission products

Radioactive fission products are mainly neutron-rich
nuclides that carry most of the energy generated by the
fission reaction in the form of kinetic energy. The majority
of these fission products decay to more stable states via a
combination of isomeric transitions and beta radioactive
decays within seconds from their creation and up to a few
hundred years. The gamma and beta-radiation released
in the decay process is much smaller than that of a fis-
sion reaction, but it represents the largest share of decay
heat load in uranium fuel up to nearly 100 years of cool-
ing time. For typical LWRs the fission products generate
up to 80% of the integrated decay energy between 1 and
10 years, that is when the decay heat power release is
still large and a limiting factor for the licensing of storage
installations [52].

For low-enriched uranium fuels in LWRs, more than
99% of the fission products contributing to the SNF
decay heat are generated from neutron-induced fissions
of four major fissioning nuclides: $^{235}$U, $^{239}$Pu, $^{238}$U, and
$^{241}$Pu [28]. For each of these four nuclides, Figure 9 and
Table 3 show how their fission rate fraction evolves as a
function of burnup.

Up to more than 90% of fission events at the begin-
ning of irradiation happens in the driver fissile nuclide
$^{235}$U [53]. As $^{235}$U is consumed with burnup, more and
more fissions occur in the $^{239}$Pu (and in a later stage in
$^{241}$Pu) produced by neutron capture in $^{238}$U. For a lower
initial enrichment, the fraction of fissions in plutonium
becomes dominant at lower burnups. About 10% or fewer
fission events occur in $^{238}$U because of its large abundance
of uranium fuel, a figure that remains essentially constant
with burnup.

<figure><img src="image_11.png" /><figcaption>**Fig. 9.** Fission rate fraction as a function of burnup for the UO₂ model in reference [43].</figcaption></figure>

Fission products contribute to the spent fuel ther-
mal output to an extent that depends on their half-life
and density in the fuel. Their decay heat power rapidly
degrades because of the radioactive decay of the more
significant energy emitters. Several decay steps along a
decay chain are generally involved before reaching a sta-
ble nuclide. For cooling times longer than 30 days (and up
to a few tens of years) about 95% of the total decay heat
power is produced by 10 to 15 fission products, i.e. $^{89}$Sr,
$^{91}$Y, $^{95}$Zr, $^{95}$Nb, $^{103}$Ru, $^{106}$Rh, $^{140}$Ba, $^{140}$La, $^{141}$Ce, $^{144}$Ce,
$^{144}$Pr [54,55]. By the end of the decay chains, longer-lived
radioactive nuclides are typically formed such as $^{90}$Sr and
$^{137}$Cs.

At cooling times between 1 and 70 years following shutdown, the fission products responsible for most of the decay heat power are only a handful. The dominant contributors are mostly parent-daughter pairs in secular equilibrium including $^{137}$Cs/$^{137m}$Ba, $^{90}$Sr/$^{90}$Y, $^{106}$Rh/$^{106}$Ru, and $^{144}$Ce/$^{144}$Pr [56]. Since their precursors have fully decayed out along their decay chains, the content of these fission products in SNF can be qualitatively assessed from the analysis of their cumulative fission yields.

A significant decay heat power contribution also comes
from nuclides created by neutron capture reactions in fis-
sion products during the irradiation of the fuel, such as
$^{154}$Eu and $^{134}$Cs. The latter is identified by the decay
heat standards as the dominant decay heat-generating
nuclide resulting from neutron capture by fission prod-
ucts [24,26,57].

For cooling times between 1 and 5 years, the largest
share of decay heat is produced by the decay chains of
the relatively short-lived fission products $^{144}$Ce and $^{106}$Ru,
and by the decay of activation product $^{134}$Cs generated by
neutron irradiation of the stable fission product $^{133}$Cs. 10
to 30 years after shutdown the decay chains of $^{137}$Cs and
$^{90}$Sr alone generate more than half of the decay heat rate
of spent LWR fuel. $^{137}$Cs and $^{90}$Sr have similar half-lives
and contribute in almost equal parts to the decay heat
power for several decades until the role of the actinides
becomes dominant. The $^{137}$Cs and $^{90}$Sr relative contribu-
tion increases marginally for less irradiated fuel because
of the lower $^{134}$Cs buildup. For irradiated MOX fuel, the
importance of these two nuclides drops by a factor of three
because of the coincident contribution of actinides such as
$^{238}$Pu and $^{244}$Cm.
<figure><img src="image_12.png" /><figcaption>**Fig. 10.** Build up of the <sup>106</sup>Rh nuclide in a LWR as a function of the assembly burnup, for the main four fissioning nuclides.</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>**Fig. 11.** Build up of the <sup>144</sup>Ce nuclide in a LWR as a function of the assembly burnup, for the main four fissioning nuclides.</figcaption></figure>

### <sup>106</sup>Ru/<sup>106</sup>Rh

<sup>106</sup>Ru is a short-lived fission product that emits beta radiation with a half-life of about one year. Practically the whole <sup>106</sup>Ru content in spent LWR fuel is produced from fission reactions with cumulative product yields of 0.41% and 4.34% [58], respectively for thermal neutron-induced fissions in <sup>235</sup>U and <sup>239</sup>Pu (see Fig. 10).

The heat generation from <sup>106</sup>Ru is for a large majority produced by the radioactive decay of its daughter <sup>106</sup>Rh. <sup>106</sup>Ru disintegrates to the ground state of <sup>106</sup>Rh emitting low-energy beta particles, and without releasing gamma radiation [59]. Its disintegration via neutron-induced reactions is negligible. The <sup>106</sup>Rh half-life of only 30.1 seconds, much shorter than the half-life of <sup>106</sup>Ru, implies a secular equilibrium between the two radionuclides. <sup>106</sup>Rh decays by beta decay into <sup>106</sup>Pd. About 10% of the decays goes to excited states that further decay releasing gamma rays. The recoverable energy released with the radioactive decay of <sup>106</sup>Rh is 1.41 MeV and 0.21 MeV, respectively for light particles and electromagnetic radiation. The radioactive chain <sup>106</sup>Ru/<sup>106</sup>Rh is ranked second amongst the decay heat power contributors for UO<sub>2</sub> fuel at one year of cooling. The fraction of the total decay heat power after 5 years of cooling slightly increases with lower burnup and initial enrichment.

### <sup>144</sup>Ce/<sup>144</sup>Pr

The <sup>144</sup>Ce/<sup>144</sup>Pr decay chain produces the largest contribution to the decay heat power of spent LWR fuel 1 year after shutdown, with a growing relative importance for fuel with lower burnup. With cumulative yields of 5.48% and 3.76%, respectively for <sup>235</sup>U and <sup>239</sup>Pu thermal neutron-induced fissions, <sup>144</sup>Ce is generated mostly as a fission product, see Figure 11.

Only a relatively small fraction results from the activation of fission product <sup>143</sup>Ce. <sup>144</sup>Ce decays by beta decay into the ground state of <sup>144</sup>Pr with a branching ratio of 98.85%, while the remaining 1.15% goes into the <sup>144m</sup>Pm (half-life of 7.2 minutes) at 59 keV above the ground state. In turn, <sup>144</sup>Pr beta decays into long-lived <sup>144</sup>Nd (half-life of 2.29 × 10<sup>15</sup> years). Since the half-life of the daughter nuclide <sup>144</sup>Pr is much shorter than the one of its parent <sup>144</sup>Ce, i.e. respectively 17.29 min and 284.89 days, the

two nuclides attain a secular equilibrium within about two hours [60]. The radioactive decay of both nuclides involves gamma-ray transitions of low intensity, and while <sup>144</sup>Ce emits low energy beta electrons, the largest decay heat recoverable energy is associated with the high energy beta electrons of <sup>144</sup>Pr, i.e. average recoverable energy of light particles of 1.026 MeV.

### <sup>134</sup>Cs

Since <sup>134</sup>Cs comes after the stable nuclide <sup>134</sup>Xe in the A = 134 decay chain, its generation as a fission product from the A = 134 chain is limited to the direct contribution from fission, i.e. its cumulative fission yield equals its independent fission yield. In practice, because of the small value of this fission yield, the only significant <sup>134</sup>Cs production path in a nuclear reactor is from neutron capture in the stable fission product <sup>133</sup>Cs. Being at the end of the A = 133 mass chain, which only includes short-lived nuclides, the <sup>133</sup>Cs cumulative fission product yield is relatively well known, especially for a thermal neutron-induced fission of <sup>235</sup>U, i.e. 6.653%. Its cumulative yield for a <sup>239</sup>Pu thermal neutron-induced fission is 6.844%, thus making the <sup>133</sup>Cs production relatively invariant to the type of the fissioning system. <sup>133</sup>Cs is an effective neutron absorber with a sufficiently large capture cross section for the formation of the <sup>134</sup>Cs in its ground state and, with a probability lower than 1%, of its first metastable state at 138.7 keV [61]. <sup>134</sup>Cs is constantly removed via radioactive decay and, during irradiation, additionally by neutron capture (see Fig. 12).

<sup>134</sup>Cs mainly beta decays with a relatively short half-life of 2.064 years into excited states of <sup>134</sup>Ba. Electron capture transition is also possible with very low probability, but it is irrelevant for practical purposes. The recoverable energy per disintegration consists of 163.5 keV and 1.555 MeV, respectively for light particles and electromagnetic radiation, with signature energies of 1365.2 keV (emission probability 3.02%) and 604.7 keV (emission probability 97.6%).

The <sup>134</sup>Cs relative contribution to the decay heat rate of spent LWR fuel is the highest after about 3 years of cooling. After 5 years it ranks third, behind the decay chains of <sup>90</sup>Sr/<sup>90</sup>Y and <sup>137</sup>Cs/<sup>137m</sup>Ba. Its production scheme makes its dependence on burnup close to quadratic (Fig. 12). As
<figure><img src="image_14.png" /><figcaption>Fig. 12. Build up of the ¹³⁴Cs nuclide in a LWR as a function of the assembly burnup, for the main four fissioning nuclides.</figcaption></figure>

<figure><img src="image_15.png" /><figcaption>Fig. 13. Build up of the ¹³⁷Cs nuclide in a LWR as a function of the assembly burnup, for the main four fissioning nuclides.</figcaption></figure>

a consequence, its relative importance increases for higher burnup. In irradiated MOX fuel, the ¹³⁴Cs fractional contribution is about two-fold lower compared to UO₂ fuel.

$$^{137}\text{Cs}/^{137m}\text{Ba}$$

¹³⁷Cs has a low neutron capture cross-section (0.27 b at thermal energy), a relatively long half-life of about 30 years and large cumulative fission product yields that are only marginally dependent on the fissioning nuclide and neutron energy (i.e. 6.09% and 6.58% respectively for ²³⁵U and ²³⁹Pu thermal neutron-induced fission, see Fig. 13). Production from neutron capture by fission products in the A = 136 mass chains is excluded because of the low neutron absorption cross sections.

These characteristics, together with the possibility of its clear identification via non-destructive gamma-ray measurements, make ¹³⁷Cs universally used for fuel burnup measurements [62], as its concentration shows a near-linear dependence on burnup [53]. The only decay mode of ¹³⁷Cs is via beta transition, with average recoverable energy for light particles of 179.89 keV, and the release of low-energy gammas-rays. The decay process yields stable nuclide ¹³⁷Ba in its ground state with a probability of 5.64% and short-lived ¹³⁷mBa with a probability of 94.36%. With a half-life of 2.552 min, ¹³⁷mBa transitions into its ground state emitting a signature 661.7 keV gamma-ray with an emission probability of 85.1%, whose magnitude surpasses any generated bremsstrahlung [63].

<figure><img src="image_16.png" /><figcaption>Fig. 14. Build up of the ⁹⁰Sr nuclide in a LWR as a function of the assembly burnup, for the main four fissioning nuclides.</figcaption></figure>

Due to its short half-life, ¹³⁷mBa cannot be treated separately and always in equilibrium with ¹³⁷Cs.

Already after 5 years of cooling the ¹³⁷Cs decay chain contributes to at least 20% of the total decay heat power in irradiated spent LWR fuel. This figure is only weakly affected by the initial enrichment and slightly decreases for higher burnup because of the growing importance of ¹³⁴Cs. The ¹³⁷Cs decay chain remains central for the characterization of SNF decay heat rate up to 100 years of cooling. In MOX fuel its relative importance diminishes to a maximum of 10% because of the larger actinides build-up and because of the contribution of the ²³⁸Pu, already present in the fresh fuel, to the decay heat power.

$$^{90}\text{Sr}/^{90}\text{Y}$$

The only significant production path of ⁹⁰Sr in nuclear reactors is via neutron-induced fission reactions. The ⁹⁰Sr production strongly depends on the fissioning system, with a larger cumulative product yield for a ²³⁵U thermal neutron-induced fission (5.68%) than for a ²³⁹Pu thermal neutron-induced fission (2.08%), see Figure 14.

Because of its negligible absorption cross-section, ⁹⁰Sr builds up almost linearly for small burnup, that is when the number of fissions in ²³⁹Pu is significantly smaller than the number of fissions in ²³⁵U.

With a half-life of 28.8 years, ⁹⁰Sr undergoes beta decay without the emission of gamma rays. Its daughter product (⁹⁰Y in its ground state) also beta decays into the stable nuclide ⁹⁰Zr, with a half-life of 2.67 days and a negligible gamma-ray yield. The average recoverable energy of light particles from the decay chain includes both contributions of ⁹⁰Sr and ⁹⁰Y, respectively of 193.5 keV and 933.8 keV. As the half-life of ⁹⁰Y is much shorter than that of ⁹⁰Sr, both nuclides are normally in secular equilibrium. As for ¹³⁷Cs/¹³⁷mBa, also ⁹⁰Sr/⁹⁰Y contributes to slightly higher fractions to the total decay heat for less irradiated fuel. In irradiated MOX fuel, the fraction of decay heat coming from the ⁹⁰Sr decay chain is much less significant because of the lower ²³⁹Pu fission product yield.

$$^{154}\text{Eu}$$

¹⁵⁴Eu has a negligible direct fission product yield as its decay chain is blocked by the stable nuclide ¹⁵⁴Sm. Then, its production is almost exclusively driven by the neutron
<figure><img src="image_17.png" /><figcaption>**Fig. 15.** Build up of the <sup>154</sup>Eu nuclide in a LWR as a function of the assembly burnup, for the main four fissioning nuclides.</figcaption></figure>

absorption in <sup>153</sup>Eu (312.6 b at thermal energy), whose production from thermal neutron-induced fission in <sup>239</sup>Pu is larger than in <sup>235</sup>U: cumulative fission yields of 0.38% and 0.15%, respectively (see Fig. 15). <sup>154</sup>Eu has a large neutron-absorption cross-section of 1353.1 b at thermal energies and it is continuously depleted during irradiation. Because of the <sup>154</sup>Eu relatively long half-life of 8.6 years, radioactive decay plays a minor role in the nuclide loss during the reactor operation, with the primary destruction channel being neutron-induced capture reactions. <sup>154</sup>Eu disintegrates almost entirely (>99.9%) via beta decay to excited states of the stable nuclide <sup>154</sup>Gd. Of the emitted beta decay energy, on average 270.242 keV and 1.244 MeV are recoverable respectively from light particles and electromagnetic radiation. Given its relatively long half-life and strong gamma-ray signature, <sup>154</sup>Eu is frequently used as a burnup monitor for long cooling times [64,65].

## 4.5 Activation products

Light elements are also present together with the nuclear fuel inside the core, in the form of rod cladding (usually made of zirconium alloys), or grids (also called spacers) to hold together rods (usually also made of zirconium alloys, or stainless steel). These elements were selected for their neutronic characteristics (low absorption) and also because they are corrosion-resistant materials. But still, neutrons can interact with these structural materials, via neutron capture, and create radionuclides which will eventually decay and produce an amount of decay heat.

Additionally, in the case of some older generation 3 loop PWR, part of the reactor internals are made of hard metal alloys, which contain a substantial amount of cobalt. Specific fuel assembly spacers can also be found with cobalt impurities, as high as 10 000 ppm. The nuclide <sup>60</sup>Co is therefore of time, both for immediate dose rate, but also as an activation product.

## 4.6 Example of nuclide contributions for typical PWR burnup simulation

To illustrate the contributions described in the previous paragraphs, a number of examples are provided in the following. The relevant nuclides are shown from 6 months

<table><caption>**Table 5.** Heat generated by the most dominant nuclides (98.2% of the generated heat), 6 months after reactor shut down for a representative 55 MWd/kgHM burnup.</caption><thead><tr><th>Z</th><th>Nuclide</th><th>Half-life</th><th>Decay heat (kW)</th></tr></thead><tbody><tr><td>59</td><td><sup>144</sup>Pr</td><td>17.28 min</td><td>107.4</td></tr><tr><td>45</td><td><sup>106</sup>Rh</td><td>30 sec</td><td>101.6</td></tr><tr><td>55</td><td><sup>134</sup>Cs</td><td>2.06509 y</td><td>53.5</td></tr><tr><td>41</td><td><sup>95</sup>Nb</td><td>34.9907 d</td><td>40.1</td></tr><tr><td>96</td><td><sup>242</sup>Cm</td><td>162.928 d</td><td>36.0</td></tr><tr><td>40</td><td><sup>95</sup>Zr</td><td>64.0324 d</td><td>21.5</td></tr><tr><td>56</td><td><sup>137m</sup>Ba</td><td>2.552 m</td><td>12.4</td></tr><tr><td>39</td><td><sup>90</sup>Y</td><td>2.67083 d</td><td>12.2</td></tr><tr><td>58</td><td><sup>144</sup>Ce</td><td>285. d</td><td>9.6</td></tr><tr><td>39</td><td><sup>91</sup>Y</td><td>58.5104 d</td><td>8.1</td></tr><tr><td>96</td><td><sup>244</sup>Cm</td><td>18.0004 y</td><td>7.1</td></tr><tr><td>94</td><td><sup>238</sup>Pu</td><td>87.698 y</td><td>4.8</td></tr><tr><td>44</td><td><sup>103</sup>Ru</td><td>39.2604 d</td><td>4.7</td></tr><tr><td>38</td><td><sup>89</sup>Sr</td><td>50.5706 d</td><td>4.1</td></tr><tr><td>55</td><td><sup>137</sup>Cs</td><td>30.0406 y</td><td>3.8</td></tr><tr><td>63</td><td><sup>154</sup>Eu</td><td>8.59302 y</td><td>3.5</td></tr><tr><td>38</td><td><sup>90</sup>Sr</td><td>28.7898 y</td><td>2.3</td></tr></tbody></table>

to several tens of years of cooling. The main characteristic calculations were performed for a typical theoretical PWR operating up to 55 MWd/kgHM (with an average enrichment of 4% and a total mass of 20 tons). The calculations employed the standard option of the NUCLEONICA Program [66] for the spent fuel inventory, using the JEFF-3.1 nuclear data library. The list of nuclides in Table 5 presents more than 98% of the nuclides contributing to the decay heat at 6 months cooling time and therefore are the main nuclides to be looked at for cooling times in this range.

Four nuclides have a very short half-life and their precursors should be examined too. <sup>144</sup>Pr with a half-life time of 17.28 min is a decay product of <sup>144</sup>Ce, which appears also on the list and has thereafter a particular importance, contributing about 25% to the total generated heat. This pair is mentioned in Section 4.4.

Another important nuclide is rhodium <sup>106</sup>Rh with a half-life time of 30 seconds. Its precursor is ruthenium <sup>106</sup>Ru with a half-life time of 1.02 years. At such time after shutdown, the decay of <sup>106</sup>Ru is of crucial importance and, through the daughter decay of <sup>106</sup>Rh, accounts for about 22% of the whole generated heat. This pair is mentioned as well in Section 4.4.

The third nuclide is the isomer <sup>137m</sup>Ba. This is a daughter product of <sup>137</sup>Cs. Its importance is not as large as the contributions of the above-mentioned two nuclides, as it represents only about 4% of the heat at this period of time. Nevertheless, the <sup>137</sup>Cs have a half-life time of about 30 years and, through <sup>137m</sup>Ba, the main contributor to heat production at later time periods as will be
<table><caption>**Table 6.** Same as Table 5, but for 2 years of cooling time.</caption><thead><tr><th>Z</th><th>Nuclide</th><th>Half-life</th><th>Decay heat (kW)</th></tr></thead><tbody><tr><td>45</td><td><sup>106</sup>Rh</td><td>30 s</td><td>36.7</td></tr><tr><td>55</td><td><sup>134</sup>Cs</td><td>2.06509 y</td><td>32.3</td></tr><tr><td>59</td><td><sup>144</sup>Pr</td><td>17.28 m</td><td>28.3</td></tr><tr><td>56</td><td><sup>137m</sup>Ba</td><td>2.552 m</td><td>12.0</td></tr><tr><td>39</td><td><sup>90</sup>Y</td><td>2.67083 d</td><td>11.8</td></tr><tr><td>96</td><td><sup>244</sup>Cm</td><td>18.0004 y</td><td>6.7</td></tr><tr><td>94</td><td><sup>238</sup>Pu</td><td>87.6984 y</td><td>4.9</td></tr><tr><td>55</td><td><sup>137</sup>Cs</td><td>30.0406 y</td><td>3.6</td></tr><tr><td>96</td><td><sup>242</sup>Cm</td><td>162.928 d</td><td>3.5</td></tr><tr><td>63</td><td><sup>106</sup>Eu</td><td>8.59302 y</td><td>3.1</td></tr><tr><td>58</td><td><sup>144</sup>Ce</td><td>285 d</td><td>2.5</td></tr><tr><td>38</td><td><sup>90</sup>Sr</td><td>28.7898 y</td><td>2.2</td></tr><tr><td>51</td><td><sup>125</sup>Sb</td><td>2.758 y</td><td>0.9</td></tr></tbody></table>

discussed below. Further details of the pair $^{137}$Cs/$^{137m}$Ba are also found in Section 4.4.

The same arguments mentioned above for $^{137}$Cs are also valid for $^{90}$Y and its precursor $^{90}$Sr. Again, as for $^{137}$Cs, the $^{90}$Sr has a half-life time of about 28 years, which increases its importance at longer decay times (see also $^{90}$Sr/$^{90}$Y in Sect. 4.4).

The calculations for the same operational conditions as in Table 5 were repeated for a cooling time of 2 years. In this case, Table 6 shows the growing importance of $^{137}$Cs and $^{90}$Sr while the nuclides with half-lives of up to a few months like $^{89}$Sr, $^{103}$Ru etc. die away. Table 6 presents the spent fuel vector after 2 years for elements contributing about 98.2% of the heat produced, where indeed the contributions of $^{89}$Sr and $^{103}$Ru are marginally small and the contributions from these nuclides are neglected.

Past 5 years of decay time, $^{137}$Cs and $^{90}$Sr become the most dominating nuclides as far as the generated heat is concerned.

In a benchmark calculation led by SKB Sweden [15], the nuclides that contribute to the decay heat were isolated and analyzed by several codes. The importance of the main nuclides can be seen for five cases, from 4 years, up to 22 years of cooling time, in Table 7. The pairs $^{137}$Cs/$^{137m}$Ba and $^{90}$Sr/$^{90}$Y generate about 40% up to 61% of the decay heat at the time range of 4.5 to 21.5 y respectively. Again, as shown by the former calculation, the contribution of $^{134}$Cs (half-life time 2 y) vanishes in this period as well as the contribution of $^{106}$Ru.

After 20 years, the importance of the decay heat has a direct impact on the geological disposal beyond the interim storage. As far as the nuclides are concerned, the minor actinides become more dominant. Nevertheless, the pairs $^{137}$Cs/$^{137m}$Ba and $^{90}$Sr/$^{90}$Y generate about 50% of the heat. However, the overall heat is about two orders of magnitude smaller in comparison with the decay heat after 2 years. With half-lives of about 30 years, the influence of $^{137}$Cs and $^{90}$Sr decreases strongly towards 300 years, while

<table><caption>**Table 7.** The main decay heat generators between 4.5 and 20 years cooling time based on the SKB Benchmark [15]. The percent number given each nuclide emphasizes the partial contribution of heat of only one specific nuclide to the total heat produced at a certain time after shutdown.</caption><thead><tr><th></th><th colspan="2">~4.5 y</th><th colspan="2">~8.5 y</th></tr><tr><th></th><th>Decay time</th><th></th><th>Decay time</th><th></th></tr></thead><tbody><tr><td><sup>134</sup>Cs</td><td>21%</td><td><sup>137</sup>Cs/<sup>137m</sup>Ba</td><td>29%</td><td></td></tr><tr><td><sup>137</sup>Cs/<sup>137m</sup>Ba</td><td>20%</td><td><sup>90</sup>Sr/<sup>90</sup>Y</td><td>26%</td><td></td></tr><tr><td><sup>90</sup>Sr/<sup>90</sup>Y</td><td>19%</td><td><sup>244</sup>Cm</td><td>15%</td><td></td></tr><tr><td><sup>106</sup>Ru/<sup>106</sup>Rh</td><td>11%</td><td><sup>238</sup>Pu</td><td>12%</td><td></td></tr><tr><td><sup>244</sup>Cm</td><td>10%</td><td><sup>134</sup>Cs</td><td>8%</td><td></td></tr><tr><td><sup>238</sup>Pu</td><td>7%</td><td><sup>241</sup>Am</td><td>4%</td><td></td></tr><tr><td><sup>144</sup>Ce/<sup>144</sup>Pr</td><td>6%</td><td><sup>154</sup>Eu</td><td>3%</td><td></td></tr><tr><td><sup>154</sup>Eu</td><td>2%</td><td></td><td></td><td></td></tr><tr><td><sup>241</sup>Am</td><td>1%</td><td></td><td></td><td></td></tr><tr><td></td><td colspan="2">~10 y</td><td colspan="2">~13.5 y</td></tr><tr><td></td><td>Decay time</td><td></td><td>Decay time</td><td></td></tr><tr><td><sup>137</sup>Cs/<sup>137m</sup>Ba</td><td>31%</td><td><sup>137</sup>Cs/<sup>137m</sup>Ba</td><td>29%</td><td></td></tr><tr><td><sup>90</sup>Sr/<sup>90</sup>Y</td><td>29%</td><td><sup>90</sup>Sr/<sup>90</sup>Y</td><td>26%</td><td></td></tr><tr><td><sup>244</sup>Cm</td><td>13%</td><td><sup>238</sup>Pu</td><td>18%</td><td></td></tr><tr><td><sup>238</sup>Pu</td><td>11%</td><td><sup>244</sup>Cm</td><td>13%</td><td></td></tr><tr><td><sup>134</sup>Cs</td><td>5%</td><td><sup>241</sup>Am</td><td>7%</td><td></td></tr><tr><td><sup>241</sup>Am</td><td>5%</td><td><sup>154</sup>Eu</td><td>2%</td><td></td></tr><tr><td><sup>154</sup>Eu</td><td>2%</td><td><sup>134</sup>Cs</td><td>1%</td><td></td></tr><tr><td><sup>240</sup>Pu</td><td>1%</td><td><sup>240</sup>Pu</td><td>0%</td><td></td></tr><tr><td></td><td colspan="2">~21.5 y</td><td></td><td></td></tr><tr><td></td><td>Decay time</td><td></td><td></td><td></td></tr><tr><td><sup>137</sup>Cs/<sup>137m</sup>Ba</td><td>32%</td><td></td><td></td><td></td></tr><tr><td><sup>90</sup>Sr/<sup>90</sup>Y</td><td>29%</td><td></td><td></td><td></td></tr><tr><td><sup>238</sup>Pu</td><td>14%</td><td></td><td></td><td></td></tr><tr><td><sup>244</sup>Cm</td><td>12%</td><td></td><td></td><td></td></tr><tr><td><sup>241</sup>Am</td><td>9%</td><td></td><td></td><td></td></tr><tr><td><sup>240</sup>Pu</td><td>2%</td><td></td><td></td><td></td></tr><tr><td><sup>154</sup>Eu</td><td>1%</td><td></td><td></td><td></td></tr></tbody></table>

as mentioned above, the actinides start to dominate the heat generation of the spent fuel.

At periods of about 40 to 50 years, the quantity of SNF that can be disposed of together depends on its heat load and on the geological conditions. Salt rocks can conduct heat better than clay. However, for the safety of a waste disposal, the mobility of potential radioactive materials within the hosting rock becomes one of the crucial criteria for the loading scheme within the disposal casks, with the aim of controlled heat removal and radioactive dose in the storage gallery. Those issues are beyond the scope of this chapter.

However, the change of the governing nuclides as far as their heat decay is concerned is emphasized in Tables 8 to 10, for 40, 100 and finally 300 years of decay time. The
<table><caption>**Table 8.** Same as Table 5, but for 40 years of cooling time.</caption><thead><tr><th>Z</th><th>Nuclide</th><th>Half-life</th><th>Decay heat (kW)</th><th>Z</th><th>Nuclide</th><th>Half-life</th><th>Decay heat (kW)</th></tr></thead><tbody><tr><td>56</td><td><sup>137</sup><i>Ba</i></td><td>2.552 m</td><td>5.0</td><td>39</td><td><sup>90</sup><i>Y</i></td><td>2.67083 d</td><td>4.7</td></tr><tr><td>94</td><td><sup>238</sup><i>Pu</i></td><td>87.6984 y</td><td>3.6</td><td>95</td><td><sup>241</sup><i>Am</i></td><td>432.804 y</td><td>3.4</td></tr><tr><td>96</td><td><sup>244</sup><i>Cm</i></td><td>18.0004 y</td><td>1.5</td><td>55</td><td><sup>137</sup><i>Cs</i></td><td>30.0406 y</td><td>1.5</td></tr><tr><td>38</td><td><sup>90</sup><i>Sr</i></td><td>28.7898 y</td><td>0.9</td><td>94</td><td><sup>240</sup><i>Pu</i></td><td>6563.04 y</td><td>0.4</td></tr><tr><td>94</td><td><sup>239</sup><i>Pu</i></td><td>24113.5 y</td><td>0.2</td><td>63</td><td><sup>154</sup><i>Eu</i></td><td>8.59302 y</td><td>0.1</td></tr></tbody></table>

<table><caption>**Table 9.** Same as Table 5, but for 100 years of cooling time.</caption><thead><tr><th>Z</th><th>Nuclide</th><th>Half-life</th><th>Decay heat (kW)</th><th>Z</th><th>Nuclide</th><th>Half-life</th><th>Decay heat (kW)</th></tr></thead><tbody><tr><td>95</td><td><sup>241</sup><i>Am</i></td><td>432.804 y</td><td>3.6</td><td>94</td><td><sup>238</sup><i>Pu</i></td><td>87.6984 y</td><td>2.2</td></tr><tr><td>56</td><td><sup>137</sup><i>Ba</i></td><td>2.552 m</td><td>1.3</td><td>39</td><td><sup>90</sup><i>Y</i></td><td>2.67083 d</td><td>1.1</td></tr><tr><td>94</td><td><sup>240</sup><i>Pu</i></td><td>6563.04 y</td><td>0.4</td><td>55</td><td><sup>137</sup><i>Cs</i></td><td>30.0406 y</td><td>0.4</td></tr><tr><td>94</td><td><sup>239</sup><i>Pu</i></td><td>24113.5 y</td><td>0.2</td><td>38</td><td><sup>90</sup><i>Sr</i></td><td>28.7898 y</td><td>0.2</td></tr><tr><td>96</td><td><sup>244</sup><i>Cm</i></td><td>18.0004 y</td><td>0.2</td><td>95</td><td><sup>243</sup><i>Am</i></td><td>7365.09 y</td><td>0.03</td></tr></tbody></table>

<table><caption>**Table 10.** Same as Table 5, but for 300 years of cooling time.</caption><thead><tr><th>Z</th><th>Nuclide</th><th>Half-life</th><th>Decay heat (kW)</th><th>Z</th><th>Nuclide</th><th>Half-life</th><th>Decay heat (kW)</th></tr></thead><tbody><tr><td>95</td><td><sup>241</sup><i>Am</i></td><td>432.804 y</td><td>2.6</td><td>94</td><td><sup>238</sup><i>Pu</i></td><td>87.6984 y</td><td>0.4</td></tr><tr><td>94</td><td><sup>240</sup><i>Pu</i></td><td>6563.04 y</td><td>0.4</td><td>94</td><td><sup>239</sup><i>Pu</i></td><td>24113.5 y</td><td>0.2</td></tr><tr><td>95</td><td><sup>243</sup><i>Am</i></td><td>7365.09 y</td><td>0.03</td><td>56</td><td><sup>137</sup><i>Ba</i></td><td>2.552 m</td><td>0.01</td></tr><tr><td>39</td><td><sup>90</sup><i>Y</i></td><td>2.67083 d</td><td>0.009</td><td>55</td><td><sup>137</sup><i>Cs</i></td><td>30.0406 y</td><td>0.004</td></tr><tr><td>93</td><td><sup>239</sup><i>Np</i></td><td>2.35498 d</td><td>0.003</td><td>94</td><td><sup>242</sup><i>Pu</i></td><td>3.735e+5 y</td><td>0.002</td></tr></tbody></table>

daughter products <sup>90</sup>Y and <sup>137</sup><i>Ba</i> from <sup>90</sup>Sr and <sup>137</sup><i>Cs</i> respectively die away after 300 years equal to about 10 half-life time periods of those pairs.

# 5 Measurements

Measured data of decay heat are of prime interest for the understanding of the energy released by SNF and for the validation of decay heat codes, standard methods, and nuclear data. The quality of such data ultimately determines the confidence users have in their simulation tools. Substantial efforts to measure total energy releases from irradiated samples, and also separated contributions from isomeric transitions and β decays, were made more than 50 years ago: pulse and long irradiations on small enriched actinides samples, using thermal or fast neutrons, from 0.1 seconds to tens of thousands of minutes of cooling time, and more recently on full scale irradiated spent fuel assemblies.

Despite these extensive campaigns, limited experimental data are available for the validation of simulation codes and nuclear data libraries. Some of the first measurements suffer from large uncertainties (concerning today's capabilities), inconsistencies, and more recently, integral decay heat measurements on full SNF present high cor-

relations between themselves due to the limited number of facilities and studied cases. It was also noticed that the existing set of measured SNF decay heat values does not cover the characteristics of today's fuel: high enrichment, high burnup, and interest in short and long cooling times.

In the following, a list of the most representative experiments is presented, with some details. Readers will notice that pulse irradiation of small samples were not performed for decades and that integral SNF decay heat measurements nowadays rely on a unique facility (Clab, Sweden), notwithstanding the worldwide importance of SNF storage.

## 5.1 Calorimetric measurements

First calorimetric measurements were performed in the 50s using galvanometers and ion chambers for irradiated uranium rods, or the decay energy absorbed by the full-scale reactor, see references [67,68] for details. These experiments were able to cover a cooling range from 0.1 to 10⁸ seconds. These types of measurements are not described in the following but are the predecessor of more modern calorimetric measurements for SNF assemblies. A general overview of more recent integral measurements of decay
<table><caption>**Table 11.** Summary of existing integral decay heat measurements using calorimetric methods.</caption><thead><tr><th>Facility</th><th>Fuel type</th><th>Cooling years</th><th>Burnup MWd/kgU</th><th>Enrichment wt.%<sup>235</sup>U</th><th>Reactor type</th><th>Measured Watt</th><th>Reference</th></tr></thead><tbody><tr><td>Clab</td><td>SNF UO<sub>2</sub></td><td>11 – 27</td><td>20 – 47</td><td>2.1 – 3.1</td><td>BWR</td><td>55 – 285</td><td>[76]</td></tr><tr><td>Clab</td><td>SNF UO<sub>2</sub></td><td>13 – 26</td><td>20 – 51</td><td>2.1 – 3.4</td><td>PWR</td><td>210 – 715</td><td>[76]</td></tr><tr><td>Clab</td><td>SNF UO<sub>2</sub></td><td>4 – 21</td><td>50 – 55</td><td>3.6 – 3.95</td><td>PWR</td><td>660 – 1660</td><td>[15,80]</td></tr><tr><td>Clab</td><td>SNF UO<sub>2</sub></td><td>–</td><td>–</td><td>–</td><td>LWR</td><td>–</td><td>[12]</td></tr><tr><td>GE-Morris</td><td>SNF UO<sub>2</sub></td><td>2 – 11</td><td>15 – 47</td><td>3.4 – 4.0</td><td>BWR</td><td>45 – 390</td><td>[52,72,73]</td></tr><tr><td>GE-Morris</td><td>SNF UO<sub>2</sub></td><td>3 – 8</td><td>27 – 39</td><td>1.1 – 2.5</td><td>PWR</td><td>360 – 930</td><td>[52,72,73]</td></tr><tr><td>HEDL</td><td>SNF UO<sub>2</sub></td><td>3 – 5</td><td>26 – 28</td><td>2.5</td><td>PWR</td><td>640 – 1550</td><td>[70,74]</td></tr><tr><td>SuperPhenix</td><td>full core</td><td>3 – 24 hours</td><td>–</td><td>–</td><td>SFR</td><td>1 – 2 × 10<sup>7</sup></td><td>[85]</td></tr><tr><td>JOYO</td><td>SNF MOX</td><td>0.1 – 2</td><td>58 – 66</td><td>13 – 19</td><td>SFR</td><td>150 – 1400</td><td>[81–84]</td></tr><tr><td>MERCI</td><td>rod UO<sub>2</sub></td><td>0.02 – 43 days</td><td>3.5</td><td>3.7</td><td>PWR</td><td>4.6 – 172</td><td>[86]</td></tr></tbody></table>

heat for entire SNF assemblies, using calorimeters is presented in Table 11. Some details are provided below.

### 5.1.1 General information

#### United States

Comprehensive summary of measurements performed in the U.S. has been compiled by Roddy and Mailen in 1987, representing the HEDL and GE-Morris Operation facilities [69]. A schematic overview of both calorimeters is presented in Figure 16 [70,71].

The General Electric spent fuel storage facility in Morris, Illinois (GE-Morris facility) used a pool calorimeter and in total 111 different decay heat measurements were performed between 1980 and 1985 on 14 PWR fuel assemblies (reactors Point Beach 2 and San Onofre 1) and 61 BWR assemblies (reactors Cooper, Dresden and Monticello) [52,72,73]. Seven decay heat measurements were also reported on five PWR assemblies from the Turkey Point 3 reactor. These measurements were performed between 1980 and 1983 using a boil-off calorimeter operated at the Engine Maintenance Assembly and Disassembly facility (EMAD) on the Nevada Test site of the Handford Engineering Development Laboratory (HEDL facility) [70,74]. No measurements were reported in the USA after the decay heat measurements of spent fuel coming from the Monticello reactor and the calorimeters have been decommissioned since.

A summary of the US decay heat measurements associated with fuel design description, and reactor operating data needed to perform decay heat calculations benchmarks are given in the validation report of the SCALE code for LWR Spent Nuclear Fuel by Gauld et al. in reference [52]. This validation study is based on the data compiled by the Energy Information Administration of the U.S. Department in Nuclear Fuel Data Survey Form RW-859 of 2004. Complementary information is also available in the Schmittroth and Roddy reports published by HEDL and ORNL laboratories [69,70,74].

The systematic bias for the GE-Morris measurements is about ±4% in the 200 W range and ±2% around 700 W. For the HEDL decay heat measurements, ±10% in the

<figure><img src="image_18.png" /><figcaption>**Fig. 16.** Sketch of the HEDL [70] (left) and GE-Morris calorimeter [71] (right).</figcaption></figure>

100 W range was reported and drops to ±5% for values greater than 1000 W, as mentioned in reference [52].

Finally, it is worth noticing the use of an underwater calorimeter at the Bettis Atomic Power Laboratory [75] for the measurements on small samples (a few grams for $^{233,235}$U and $^{239}$Pu).

#### Sweden

In 2004, SKB initiated a program at the Clab facility (Central Interim Storage Facility for Spent Nuclear Fuel) to provide decay heat data in support of the characterization of spent fuel applicable to the design and operation of wet and dry facilities and also for the future national fuel repository at Forsmark [76]. The Clab calorimeter used a design similar to the GE-Morris one. Up to 2006, 145 calorimeter measurements on full-length assemblies were reported for 34 PWR assemblies (reactors Ringhals 2 and Ringhals 3) and 50 BWR assemblies (reactors Barsebäck 1, Barsebäck 2, Forsmark 1, Forsmark 2, Forsmark 3, Oskarshamn 2, Oskarshamn 3, Ringhals 1); experimental
<table><caption>**Table 12.** Summary of existing decay heat measurements using calorimetric methods on LWR SNF assemblies.</caption><thead><tr><th>Facility</th><th>Reactor type</th><th>Reactor</th><th>SNF design</th><th>Enrichment (<sup>235</sup>U wt.%)</th><th>Burnup (MWd/kgU)</th><th>Cooling time (years)</th><th>Number of assemblies</th><th>Number of measurements</th></tr></thead><tbody><tr><td rowspan="5">GE-Morris</td><td>PWR</td><td>Point Beach 2</td><td>14 × 14</td><td>3.4</td><td>32 – 39</td><td>4</td><td>6</td><td>6</td></tr><tr><td>PWR</td><td>San Onofre 1</td><td>14 × 14</td><td>3.9 – 4.0</td><td>27 – 32</td><td>3 – 8</td><td>8</td><td>8</td></tr><tr><td>BWR</td><td>Monticello</td><td>7 × 7</td><td>2.3</td><td>9 – 21</td><td>10 – 11</td><td>6</td><td>13</td></tr><tr><td>BWR</td><td>Cooper</td><td>7 × 7</td><td>1.1 – 2.5</td><td>12 – 28</td><td>2 – 7</td><td>56</td><td>81</td></tr><tr><td>BWR</td><td>Dresden 2</td><td>7 × 7</td><td>2.1</td><td>5</td><td>8</td><td>1</td><td>2</td></tr><tr><td rowspan="6">HEDL Clab</td><td>PWR</td><td>Turkey Point</td><td>15 × 15</td><td>2.5</td><td>26 – 28</td><td>2 – 6</td><td>4</td><td>6</td></tr><tr><td>PWR</td><td>Ringhals 2</td><td>15 × 15</td><td>3.1 – 3.3</td><td>34 – 51</td><td>16 – 27</td><td>18</td><td>33</td></tr><tr><td>PWR</td><td>Ringhals 3</td><td>17 × 17</td><td>2.1 – 3.4</td><td>20 – 47</td><td>13 – 26</td><td>16</td><td>38</td></tr><tr><td>BWR</td><td>Ringhals 1</td><td>8 × 8</td><td>2.3 – 2.9</td><td>21 – 45</td><td>13 – 24</td><td>17</td><td>45</td></tr><tr><td>BWR</td><td>Oskarshamn 2, 3</td><td>Many</td><td>2.2 – 2.9</td><td>15 – 47</td><td>12 – 27</td><td>14</td><td>15</td></tr><tr><td>BWR</td><td>Forsmark 1,2,3</td><td>Many</td><td>2.1 – 3.0</td><td>20 – 38</td><td>11 – 15</td><td>11</td><td>12</td></tr><tr><td></td><td></td><td>Barsebäck 1, 2</td><td>8 × 8</td><td>2.3 – 3.2</td><td>20 – 41</td><td>11 – 25</td><td>7</td><td>9</td></tr></tbody></table>

values, assembly data and operation history were reported in reference [76], as well as in SCALE analysis [76–78].

In 2014, additional measurements performed between 2006 and 2010 were reported by Ilas et al. [79]. They mainly concern the same SNF as in previous references but with more recent measurements. These cases (not yet publicly available at the time of writing) would be interesting as they represent multi-measurements over a few years.

In 2017, five new measurements for 5 different PWR assemblies were proposed by SKB for the so-called “blind decay heat calculation benchmark”, and results were published in reference [15,80]. These PWR assemblies corresponded to higher enrichments and burnup values compared to the previous Clab reported data in reference [76], therefore nicely complementing the existing set. More recently, reference [12] is referring to new Clab measurements performed from 2015 to the present. It is also indicated that the description of such 60 new measurements will be published soon.

## Japan

These Japanese-reported experiments are the only ones currently performed on MOX assemblies [81–84]. Such assemblies were designed to be used in the experimental sodium-cooled fast reactor JOYO and therefore do not correspond to designs of LWR MOX fuel. Enrichments in <sup>235</sup>U and Pu were reported sensibly higher than for LWR for the measured assemblies (13 to almost 30%). These measurements are reported in Table 11 but cannot simply be used or compared to measurements for LWR assemblies.

## France

In France, two different types of measurements were realized: one on the decay heat for the full core of the sodium-cooled fast reactors Phénix and Superphénix [85] and one on a single UO₂ rod [86]. One can add measurements performed at the ZOE reactor on small samples (a few grams) with a dedicated calorimeter [87].

In the case of Phénix and Superphénix, experiments on decay heat measurements on French Sodium Fast Reactors (SFR) were performed between 1979 and 1996. However, due to the final shutdown of Phénix scheduled in 2010, it was decided to perform a new test as part of the Phénix end-of-life experiments: the PUIREX experiment [88]. A calorimetric method based on the thermal balance of the reactor circuits was used. No actual calorimeter such as in Clab or GE-Morris was needed. The decay heat of the full core was deduced for low power (about 10 MW) and predicted calculations were validated. This type of experiment, giving access to the decay heat of the entire reactor is only feasible in sodium-fast reactors thanks to the sodium inertia in the pool configuration of the reactor. As in the case of the JOYO measurements, such results are not of relevance to the present work but correspond to the only published decay heat data for a full core.

The second published measurement, part of the MERCI program, concerns the irradiation of a single UO₂ rod, at the periphery of the experimental reactor OSIRIS [86]. Characteristics of the irradiation can be seen in Table 11. The decay heat was measured using the MOSAÏC calorimeter (by means of heat transfer to water). The main advantage of this case consists of its short cooling time and low burnup, helping to validate decay heat calculations linked to <sup>235</sup>U fission products.

The experimental uncertainties for the measured decay heat are also relatively low: between 1 and 3%.

### 5.1.2 Details

#### MERCI-1 experiment (France)

A fresh PWR UO₂ fuel rod sample (active length of 40 cm) with a 3.7 wt.% content in <sup>235</sup>U and zircaloy-4 cladding, within a stainless steel containment, was irradiated during 55 equivalent full power days in the periphery of the OSIRIS reactor [86]. The layout of the MERCI device in the OSIRIS pool is reported in Figure 17.

The discharge burnup of the MERCI fuel rod was about 3.6 GWd/tHM. The fuel rod was transferred in 26 min from its irradiation location to a hot cell to be inserted
<figure><img src="image_19.png" /><figcaption>**Fig. 17.** Layout of the MERCI device at the OSIRIS facility [86].</figcaption></figure>

into the MOSAİC calorimeter. The released decay heat was measured from 27 min to 45 days after shutdown. Over this period the decay heat decreases from about 200 W to 4 W. Post-irradiation examinations were also performed at the CEA/LECI laboratory in order to measure the concentrations of the main actinides (uranium, plutonium) and burnup trackers (neodymium, cesium) in a sample located at the middle of the fuel rod. These post-irradiated examinations allowed an accurate evaluation of the fuel rod burnup and axial distribution. The fuel rod axial distribution was also measured by gamma-ray scanning inside the OSIRIS pool with a high-purity germanium detector system.

The OSIRIS reactor is an experimental reactor with a thermal power of 70 MW. It is a light water reactor, open-core pool type. The MERCI device was located in the periphery of the OSIRIS reactor core and was made up of two mechanical components: the fuel rod to be transferred and its support structure, equipped with core instrumentation, i.e. rhodium self-powered neutron detectors to measure the thermal neutron flux, cobalt detectors for safety purposes, one removable fission chamber, and activation dosimeters to measure the axial neutron fluence profile.

The MOSAİC calorimeter was designed [89] and patented by the CEA [90]. The MOSAİC calorimeter design is based upon the heat pipe principle where the cold element is the condenser and the warm element is a tungsten cylinder, which also reduces gamma-ray leakage thanks to its high density (about 18 g/cm³), see Figure 18. The tungsten absorbs about 96% of the total gamma-ray emission. The gamma-ray leakage was evaluated by calculation. The MOSAİC calorimeter was designed with the particular goal to have a precision of 1% and to have mini-

<figure><img src="image_20.png" /><figcaption>**Fig. 18.** Sketch of the MOSAİC calorimeter [89].</figcaption></figure>

mal heat losses. The residual heat is deduced by a heat balance measurement on the secondary system using accurate instrumentation such as platinum resistance thermometers and Coriolis flowmeters.

Two analysis of the MERCI-1 experiment were performed, one with the 3D full pointwise Monte Carlo code TRIPOLI-4® [91] and one with the deterministic 2D lattice code APOLLO2 [92] coupled with the depletion code PEPIN2 [93], which performs the depletion calculation with very precise depletion chains describing the buildup and disappearance of more than 3800 nuclides and the exact depletion history of the MERCI-1 experiment.

The axial neutron flux calculated by TRIPOLI-4 is corrected in order to fit with the measured axial gamma-ray scanning. At the end of the depletion and cooling period, the nuclide concentrations are compared to the measured ones, and the neutron fluence is adjusted in order to minimize the discrepancies on the main actinides and burnup trackers.

In addition to this calculation, the gamma-ray leakage and the activation of the structural components are also evaluated by computation. The gamma-ray leakage has been evaluated with TRIPOLI-4 and PEPIN2 (JEFF-3.1.1 nuclear data library) by integrating the energy of the gamma-rays that escape the first enclosure of the MOSAİC device. The calculated gamma-ray heat loss fraction (gamma-ray heat loss/total decay heat) is plotted in Figure 19. The gamma-ray leakage is comprised between 2% (around 42 days) and 4% (around 30 min). The gamma-ray leakage follows mainly the gamma heat loss of the ¹⁴⁰La, which has high gamma-ray energy (1.6 MeV). The ¹⁴⁰La is also the main contributor to the decay heat between 17 hours and the end of the measurement period. The energy produced by the activation of the cladding has also been evaluated with PEPIN2 calculations. It appeared that the contribution of the cladding to the total decay heat is comprised of between 0 and 2.25% at the maximum around 1.5 hours of cooling.

Between 27 min and 45 min a measurement bias was observed due to an unexpected thermal transient after the introduction of the MERCI fuel rod inside the calorimeter: the MERCI fuel rod stored heat during the transfer phase from the reactor pool to the hot cell. Thus, during the first 800 seconds, the measurement overestimates the effective residual heat produced by the MERCI fuel. This unforeseen energy storage amount cannot be
<figure><img src="image_21.png" /><figcaption>Fig. 19. Gamma-ray heat loss fraction [86].</figcaption></figure>

calculated or estimated because of a lack of appropriate instrumentation.

The measurement uncertainty with the MOSAÏC calorimeter is between ±1% and ±2% depending on the cooling time. This uncertainty has been evaluated from the propagation through the MOSAÏC calorimeter numerical model of measurement errors (temperature, mass flow rate) and thermo-physical properties (density, specific heat, enthalpy, thermal conductivity). The uncertainty due to the neutron flux adjustment is ±0.7%. Bias due to the calculation scheme has been estimated to be under ±0.2%. This point has been checked by using two different methods for the neutron calculation (Monte Carlo and deterministic), in addition to several sensitivity studies on the calculation scheme choices.

The nuclear data uncertainties were recently reevaluated with both deterministic and stochastic methods that produced very similar results [94]. The nuclear data uncertainty on the decay heat of the MERCI fuel is about 4% at the beginning of the measurement period and rises up to 11% at the end of the measurement period. The main contributors to the variance of the decay heat are the independent fission yields of $^{235}$U in the thermal range (for this calculation, independent fission yields are not correlated, which maximizes the total uncertainty in this time period). All these uncertainties are independent of each other and result in a global uncertainty calculated by quadratic summation comprised between 5% and 12% at 2 standard deviations.

The calculation-over-experiment discrepancies ($C/E - 1$) are plotted in Figure 20. The gray area represents the total uncertainty at two standard deviations. A satisfactory agreement is observed between 5 and 42 days of cooling where the discrepancies are under ±1%. The maximum discrepancy is about 6% at 12.5 hours of cooling. Between 45 min and 36 hours, the discrepancies are included in the analysis uncertainty at 2 standard deviations. Between 36 hours and 42 days, the discrepancies are within the analysis uncertainty at 1 standard deviation.

MERCI-1 is the first experiment that enables the integral validation of decay heat issued from the disintegration of $^{235}$Uth fission products and the $^{239}$U/$^{239}$Np decay. This program demonstrated the feasibility of such an experiment, at very short cooling times and with a very low experimental uncertainty. Nevertheless, additional experiments at higher burnup or with depleted UO₂ fuel or MOX

<figure><img src="image_22.png" /><figcaption>Fig. 20. Calculation over measurement discrepancies (red line) associated with the total uncertainty (measurement, modeling, and nuclear data) at two standard deviations [94].</figcaption></figure>

fuel are mandatory. Indeed, a recent work has been performed on the MERCI-1 experiment in order to quantify the similarity of this experiment to a UO₂ fuel irradiated in a PWR regarding nuclear data [95]. The results show that the similarity of the MERCI-1 experiment with the UO₂ fuel decreases drastically with the burnup of the UO₂ fuel. Even at 10 GWd/tHM, the contributions of the $^{239}$Pu fission products cannot be neglected, which makes the MERCI-1 experiment not appropriate to validate codes for the decay heat of PWR UO₂ fuels at burnup higher than 10 GWd/tHM.

Concerning additional decay heat measurements performed at the PHENIX reactor (France), called the PUIREX experiment, details can be found in Appendix A.

## The Clab experiments (Sweden)

The intermediate fuel storage facility at Clab allows for performing calorimetric measurements of nuclear fuel assemblies for BWRs and PWRs [76]. As mentioned, the design of the Clab calorimeter is similar to that used at GE-Morris. A five-meter-long cylinder is placed inside a water pool and can contain the full length of a nuclear fuel assembly, thus allowing for a non-destructive measurement, see Figure 21. The calorimeter is hermetically sealed to prevent water in the pool from coming into contact with the water inside the calorimeter during the measurement. A centrifugal pump circulates water in the calorimeter to maintain a homogeneous temperature in the measurement chamber. Sixteen temperature sensors are located in the water inside the calorimeter, on the internal and external surfaces of the calorimeter, and in the water outside the calorimeter to measure the increase in temperature. The calorimeter is calibrated with an electric heater with well-known power. Dose rate monitors are placed outside the calorimeter to measure the quantity and radial distribution of the gamma-ray radiation that escapes from the calorimeter. Corrections are applied for the fraction of the released gamma-ray heat absorbed outside of the calorimeter.

The decay heat of a nuclear fuel assembly is determined with the temperature increase method. The measured increase rate of the temperature is compared to the corresponding calibration measurements and the decay
<figure><img src="image_23.png" /><figcaption>**Fig. 21.** Sketch of the Clab calorimeter [76].</figcaption></figure>

power is determined. The gamma-ray radiation field is also measured and the power escaped gamma-ray heat is determined. The total decay heat power is derived from the sum of the measured decay power and the measured power from the escaped gamma rays. This method has the advantage of being relatively independent of the gamma-ray heat leakage since leakage also occurs during calibration. On the other hand, compensating factors must be added to account for the fact that fuel assemblies have a different volume, mass, and material composition than the electric heater. The realistic measurement time necessary to carry out a calorimetric measurement for one fuel assembly is one day.

After the measurement campaign involving the “blind decay heat benchmark” in 2017, a new analysis of the experiments, including calibration, escaped gamma-rays (simulations) and detectors was undertaken until 2023, in collaboration with EPRI. New measured decay heat values are planned to be publicly distributed, with low uncertainties (in the vicinity of a few percent).

## The calorimeter project in Switzerland

The development, installation, and commissioning of a new full-scale calorimeter to measure the decay heat of spent fuel assemblies at Gösgen Nuclear Power Plant (KKG) is currently under consideration. This calorimeter would allow the measurement of UO₂ PWR fuel with very high burnup (up to ~70 GWd/t) and high enrichment (up to 5%), as well as MOX fuel. The concept of the

<figure><img src="image_24.png" /><figcaption>**Fig. 22.** Layout of KKG calorimeter (left) and cross-section of the shielding design (right).</figcaption></figure>

<figure><img src="image_25.png" /></figure>

calorimeter is aimed at achieving a high level of measurement precision.

The mechanical structure of the Gösgen calorimeter is shown in Figure 22 and consists of a shaft for holding the fuel assembly, with vacuum insulation to minimize heat transfer between the calorimeter and the vessel basin and a lid that is closed to perform the measurement. The lid is made of polyethylene and is pressed against a seal by a slight underpressure, preventing uncontrolled mass transfer with the basin contents. This implies that if there is no active circulation, the lid is released, and the fuel is cooled by natural convection (internal KKG safety condition). The calorimeter has a modular design and can be operated in three different modes (three main feed/intake points, as illustrated in Fig. 22). One of the three possible functionalities is depicted in Figure 22, where the mass flow is depicted by arrows (mass flow from the lower inlet line to the upper section line). A lead, steel-coated, shielding is also designed to absorb almost 100% of the gamma-ray losses (to increase the measurement accuracy). The decay heat is determined by temperature differences between outlet and inlet lines and the water mass flow, in a reached steady-state system.

The measuring station will be set up at the edge of the container basin of the external wet storage facility. The calorimeter will be mounted on a fuel rack normally used for fuel inspection, under ~7 m water. More details will be published in the coming years if the project successfully continues.

## 5.2 Gamma-ray and beta-particle measurements

Apart from the calorimetric measurements presented in the previous section, for “large” samples, a number of other experiments, using specific calorimeters were also performed on small samples (as previously mentioned at Bettis [75], ZOE [87], but also in the UK [96]). Dedicated γ-ray and β-electron emission detectors were also used. Some details are provided in the following.
### 5.2.1 Historical measurements

In the 1960s and 1970s, a number of experiments were performed to measure the decay energy release rates from fission events, from short irradiation of small samples. These data are extremely useful for code validation (see for instance Ref. [97]), as presented later in Section 6.4.4. Additionally, a number of experiments, with some code inputs were compiled by the IAEA under the CoNDERC project. A summary of some measurements is presented in Table 13 and in mentioned references.

Note that additional measurements were performed on other actinides, such as $^{232}$Th, $^{233,238}$U and $^{237}$Np. Depending on the type of experiment, the total energy release rates, with or without the β-electron and γ-ray components are measured and presented. Selected measurements are presented in this section and a more detailed description of a number of experiments can be found in reference [118].

#### Liquid scintillator

A number of measurements for the total energy release were performed with a large absorption scintillator, absorbing virtually all beta-electrons and gamma-rays [75, 103, 105, 110, 119]. Typically, such calorimeters were very large (a few thousand liters), and made of different modules of plastic cylinders coupled to photomultiplier tubes. A rabbit system was used to bring irradiated samples to this instrument in a matter of seconds. Samples (for instance enriched uranium deposited on aluminum backing) were irradiated with a moderated neutron source (for instance $^{252}$Cf surrounded by water) for various periods, each of them followed by a calorimetric measurement.

#### Separated β-electron and γ-ray measurements

In order to obtain the contributions from the β-electron and γ-ray emissions, some measurements were performed with scintillators such as NaI for γ-ray detection, and with Si(Li) detectors for β-electrons. Small samples were irradiated with thermal or fast neutrons, and transported with a pneumatic system in front of the dedicated detectors. Measurements were separately performed for β-electron and for γ-ray detection, see, for instance, references [108, 120, 121]. A different approach is followed in reference [96], based on Calvet microcalorimeter measurements: it corresponds to a multicel calorimeter using a uranium shell surrounding the sample and absorbing a large part of the emitted γ-rays.

#### Compilation and data selection

The previous experiments for the total or β-electron and γ-ray energy release rates are currently extensively used for code and nuclear data validation (mainly fission yields and decay data), as presented in Figures 28, 31 and 32. They are nevertheless not directly compared to calculations, but the comparisons are based on specific compilations, or evaluations, as from Tobias et al. [122], on selected and trusted sets of measurements from Dickens, Akiyama, and Schier (Lowell) [107, 123–127]. For more

details on the validation of nuclear data with these data, see Sections 6.4.3 and 6.4.4.

### 5.2.2 Detection of gamma-rays from short-lived fission products

The description provided in the following concerns the detection of gamma rays from short-lived fission products at KUCA and KURNS-LINAC in Japan. More details on these studies can be found in reference [128].

#### Introduction

For new types of reactor cores, the residual heat removal system must be designed carefully to prevent elevation of the temperature of fuel cladding. For the design, the residual heat during the initial quarter of an hour after the shutdown of the core is naturally of high relevance. The residual heat is mainly determined by the decays of fission products (FPs) with a half-life of less than an hour. The yields of FPs and their decay data (yields and decay types) have comprehensively been evaluated up to now. However, isotopic validations of those yields and data are not trivial.

Recently, radiations were measured at Kyoto University Critical Assembly facility (KUCA) and at Kyoto University LINAC pulsed neutron source facility for specific purposes. As byproducts, gamma rays from short-lived FPs were measured. In the following, the measurements were reported.

#### Critical experiments

Some of neutron-induced reactions are followed by emissions of gamma rays of intrinsic spectra to the reactions. Thus, gamma-ray spectrometry would give information on the ratio of rates of some reactions occurring in neutron multiplication systems including a critical core. Then a mocked-up was built for the critical core in a light water tank at KUCA and the gamma rays outside the tank were measured as shown in Figure 23 left.

428 sheets of plate-type fuel of uranium (U) and aluminum (Al) alloy were loaded vertically to the core bottom base made of stainless steel. The $^{235}$U enrichment of the fuel is 93 wt.%. An HPGe with 30% relative efficiency was used for the gamma-ray detection. The photoelectric (PE) peaks of gamma-rays from capture reactions of $^{1}$H, $^{27}$Al, $^{53}$Cr, $^{56}$Fe, and $^{58}$Ni and $^{235}$U were detected as well as the single and the double escape peaks (DE, SE) of those. Gamma-ray peaks from de-excitation of $^{16m}$O are also found. The pulse height spectrum from 2900 to 4900 keV is shown in Figure 23 right. The base continuum spectrum is due to the prompt gamma-rays from fission of $^{235}$U. Above the continuum part, small peaks stick out. Except for PE, DE, and SE components originated in the $^{27}$Al(n,γ) reaction, more than ten peaks are found. The spectrum was compared to the evaluation in JENDL/FPY+FPD-2011, followed by the identification of peaks of which the count rate is dominated by the decay of $^{88}$Br, $^{89}$Kr, $^{90,90m,91,92}$Rb, $^{95,97,98}$Y, and $^{136}$Te.

The peak-to-base ratio is small due to the intense prompt fission gamma-rays and the statistical errors of
<table><caption>**Table 13.** Summary of existing differential decay heat measurements for neutron-induced fission on specific systems. Measurements are given in MeV/s/fission.</caption><thead><tr><th>System</th><th>Measurement</th><th>Cooling time sec.</th><th>Publication year</th><th>Reference</th></tr></thead><tbody><tr><td><sup>235</sup>U(n<sub>th</sub>, f)</td><td>β & γ</td><td>0.3–10<sup>6</sup></td><td>1964–1981</td><td>[98–114]</td></tr><tr><td><sup>239</sup>Pu(n<sub>th</sub>, f)</td><td>β & γ</td><td>3–10<sup>6</sup></td><td>1973–1978</td><td>[103,115]</td></tr><tr><td><sup>241</sup>Pu(n<sub>th</sub>, f)</td><td>β & γ</td><td>3–12 × 10<sup>3</sup></td><td>1978</td><td>[116]</td></tr><tr><td><sup>235</sup>U(n<sub>14</sub> MeV, f)</td><td>β & γ</td><td>20–14 × 10<sup>3</sup></td><td>1984</td><td>[117]</td></tr><tr><td><sup>239</sup>Pu(n<sub>14</sub> MeV, f)</td><td>β & γ</td><td>35–14 × 10<sup>3</sup></td><td>1984</td><td>[117]</td></tr></tbody></table>

<figure><img src="image_26.png" /><figcaption>**Fig. 23.** Left: Side view of the critical core and HPGe detector. Yellow lines are of aluminum alloy. Right: Measured γ-ray spectrum for critical core.</figcaption></figure>

those peaks range from 2 to 20% for four hours of measurement with a power of 4.6 mW. In this measurement, the FP gamma-ray was measured during neutron irradiation so that FP of half-lives shorter than 4 seconds (<sup>97</sup>Y) was detected.

## Out-of-phase measurement for small sample

Gamma-ray spectra were measured for a small U sample of the natural <sup>235</sup>U enrichment irradiated by a pulsed neutron source at KU-LINAC. The neutron was generated by photo-interactions with a tungsten target and the fast neutron was slowed down in light water moderator. The pulse frequency was 50 Hz and the time from pulse generation to a gamma-ray detection was measured to determine incident neutron energy for the gamma-ray emission reaction. The flight path length was approximately 11 m. The time spectrum for the gamma-ray detection is shown in Figure 24 left.

The original purpose of this experiment was to detect <sup>238</sup>U(n,γ) gamma-rays for the thermal and the resonance energy neutrons and so peak structures are found in Figure 24 left. However, after decay out of the thermal neutrons, gamma-ray events were still detected, corresponding to out-of-phase events. In such a case, there is no neutron, indicating that the fission and capture reactions would not be induced. Such events are therefore due to some radioactive decay. Currently, it is expected that those decay were from FPs originating in <sup>235</sup>U in the sample although the initial enrichment was 0.72 wt.%. The gamma-ray spectra for the out-of-phase events are shown in Figure 24 right, where peak components can be observed. By the attenuation of the

<figure><img src="image_27.png" /><figcaption>**Fig. 24.** Left: Time of flight spectrum for estimation of energy of incident neutron. Right: γ-ray spectrum at time background. Nuclides in labels denote β-decay parents of delayed γ-rays.</figcaption></figure>

prompt fission component, the peak-to-base ratio of them is better than those in Figure 23 right. Comparing the measured data to the JENDL/FPY+FPD-2011, peaks dominated by <sup>89</sup>Kr, <sup>90,91</sup>Rb, <sup>95,97,98</sup>Y were identified. Gamma-rays were also measured during neutron irradiation, the gamma rays from <sup>97</sup>Y were also measured by this method.

## Future plan

The new techniques are potentially useful for the validation of fission product yields and their associated decay data. In these critical experiments, the estimation of the detection efficiency of the FP gamma-rays needs to be determined. A possible method is to rely on gamma-ray transport calculation with the PHITS or the MCNP-6 codes assuming or calculating spatial fission distribution. Currently, the normalization of the calculated efficiency is under study. Another issue is related to the background from <sup>27</sup>Al(n,γ) gamma-rays. Accordingly, critical experiments with fuels with different ratios of Al/U in another facility might be beneficial.

In the out-of-phase measurement, an open question is related to the amount of <sup>238</sup>U fission events since the neutron spectrum above 30 eV was not measured at the facility. To remedy this, it is planned to perform Cd filtered and non-filtered measurements were scheduled with enriched U samples. Those decay data have recently been re-evaluated in the JENDL-5 nuclear data library, and comparisons between the measured and calculated gamma-ray spectra will be highly beneficial.
# 6 Calculation methods

As the decay heat of SNF is seldom measured, the importance of its estimation through calculations is crucial. There are globally three different possibilities:

1. based on a single formula, with various degrees of complexity,

2. based on more advanced methods presented in various national and international standards,

3. and based on the summation method.

Historically, the first developments have led to the derivation of formulas, which depended on a limited number of parameters, and are therefore labeled in the following as “simple formula”. Such an approach followed the calculation capabilities at that time, as well as the past needs. Valuable information was obtained (such as the well-accepted value of “7%” residual heat after a reactor shutdown, or general aspects of exponential decay of the decay heat), and allowed some finer developments integrated into the decay heat standard methods. Such methods were developed over decades (from the 1970s to today) and will be presented in the following. Both simple formulas and standard approaches generally have a range of applicability and cannot be applied to any cooling time and fuel type.

More recently, the ability to perform accurate decay heat calculations based on a summation approach (coupled with a precise neutron transport and depletion calculations) has sensibly improved, mostly due to the availability of evaluated nuclear data as well as more affordable computer power. Such developments will also be presented in this section.

## 6.1 Simple formula

Under specific needs, the decay heat can sufficiently be well approximated by the known Borst Wheeler formalism [2] (see Appendix B for details):

$$P(t, T) = \frac{2.7P_0}{200 \times 1.6 \times 10^{-13}} \int_{t}^{t+T} \tau^{-1.2} d\tau \quad \text{MeV/s} \quad (6)$$

$$= 4.1 \times 10^{11} P_0 [t^{-0.2} - (t+T)^{-0.2}] \quad \text{MeV/s} \quad (7)$$

$$= 0.065 P_0 [t^{-0.2} - (t+T)^{-0.2}] \quad \text{W}, \quad (8)$$

where the Borst Wheeler function definition contains $P(t, T)$, the power emitted at time $t$ after the shutdown of a reactor that operated for time $T$, as well as $P_0$, the reactor power.

The origin of this expression comes from the idea of dealing with the heat contribution of isomeric transitions and $\beta$ decays. Borst and Wheeler (as well as Glasstone and Sasonke [129]) use the classical approach based on Way and Wigner [38]. The difference is the weight given to the $\beta(t)$ and the $\gamma(t)$ decay. Nevertheless, by combining both contributions of the $\gamma(t)$ and the $\beta(t)$ decay, one can get very similar results.

It is of course “tempting” to adjust this formula to measured values. The 200 MeV/fission used in the above

<figure><img src="image_28.png" /><figcaption>Fig. 25. Decay heat ratio $P/P_0$ as presented in equations (8)–(B.12), compared to the early ANS-5.1/N18.6 standard from 1971. The irradiation time $T$ is considered infinite ($10^{13}$ seconds).</figcaption></figure>

equation can be adjusted to the more correct energy release per fission 202 MeV/fission (for $^{235}$U thermal neutron induced fission in a typical LWR), etc., the 2.7 MeV/s can also be changed to other numbers beyond the 2.8 MeV/s as proposed by Glasstone [129]. Further ideas appear in more complicated expressions.

In reference [129], Glasstone introduces a more general method where two parameters, $a$ (multiplier) and $b$ (power parameter), can be changed. One can explain this procedure by the fact that the $\alpha$ decay is not included in the original considerations and as compensation, a better fitting to measured data occurs by tuning the existing parameters (see Fig. 25 for a simple comparison with different approaches).

Todreas and Kazimi [130] proposed a more detailed approach for the exact evaluation of the decay heat, at the very beginning of the shutdown phase.

They additionally define the heat generated by delayed neutrons in a very short time (0–80 seconds) after shutdown. In parallel, a more fundamental approach for the shutdown is given by Duderstadt & Hamilton [131], based on the point kinetic equation and derive the decay heat power by integrating the time over the changing reactivity during the fall of the shutdown control rods.

Except for the very sophisticated approach mentioned above, the approach of Way & Wigner [38] that was adopted by Borst Wheeler, Glasstone, and others to provide a very good solution for times from 0 to about $10^6$ seconds. Beyond that period, the impact of the $\alpha$ decay is noticeably growing, and as it is not included, the results are expected to be worse. In addition, the fact that most of the reactors are idle for maintenance for about 30 days between successive cycles is also a source of inaccuracy, as it is not taken into account in the formula shown above. In view of the mentioned limitations, the Borst Wheeler formula was tested against several measurements obtained from reference [15]. The decay time was between $10^8$ and $10^9$ seconds. The maintenance time between the cycles was ignored which indeed showed more conservative results. Overall, the decay heat ratio (decay heat to nominal power
heat of the reactor) was over-estimated by a maximum of 60%. Using the solution of Glasstone [129,132] (which is supposed to be applicable up to $8 \times 10^8$ seconds) underestimates the results by up to 60%, which is for safety reasons not conservative, and hence not recommended. Full adaptation to the measurable results can also be mathematically achieved by further adjustments of the time parameters, albeit without physical foundation.

Consequently, the safety considerations for waste disposal afford much higher accuracy, which can be only achieved by “tedious” burnup calculations. Nevertheless, some of these early studies of the pioneers of the nuclear technology can support and provide useful guidance for the range of decay heat one is concerned with, even at relevant long-time disposal.

## 6.2 Delayed fission

After a reactor shutdown, fission events can continue to happen, not initiated by prompt neutrons (emitted about $10^{-14}$ seconds after a fission event), but due to neutrons emitted by fission products after $\beta$ decays (delayed neutrons), by $(\alpha,n)$ or $(\gamma,n)$ reactions, or simply from spontaneous fission. Delayed neutrons can be emitted from milliseconds up to a few hundred seconds (for the longest-lived precursor $^{87}$Br), as long as precursors are produced. These sources of delayed neutrons can also induce fission events, called delayed fission, therefore contributing to decay heat. In practice, such contribution from $\beta$ decays is rapidly vanishing compared to other sources, as indicated in Figure 26.

In the present context, delayed fission is therefore different from the definition given in references [134,135], where it corresponds to a nuclear decay process that couples 13 decay and fission, mainly corresponding to an exotic decay mode of excited heavy actinides.

In reference [133], two examples for different fuel assemblies (one $UO_2$ and one MOX) are presented, with the calculated contributions from delayed fission to the total decay heat (see Fig. 26). As observed, although delayed fission is the main contributor shortly after shutdown, its contribution becomes negligible after about 100 seconds. It can be considered that delayed fission is of no importance for SNF storage, but on the contrary, it can be of high importance in the case or slow or fast transients [39].

## 6.3 Standards

Standard methods for decay heat calculation were originally developed to provide a means to determine decay heat values with an accuracy comparable to that of summation methods but with less computational effort and without the need for excessive nuclear data libraries.

Due to the limited number of input quantities the standard methods are often easier to use than summation methods, especially for users who are not experts in the field of decay heat. Some methods also provide guidance for a specific application. With regards to licensing

<figure><img src="image_29.png" /><figcaption>**Fig. 26.** Example of decay heat (with delayed fission); Top: for a $UO_2$ fuel, enriched at 3.5%, with a burnup value of 33 MWd/kgU. Bottom: Same for a MOX fuel enriched at 5.30% (Pu content) with a burnup value of 60 MWd/kgHM. Extracted from a French REP900 [133].</figcaption></figure>

procedures, depending on the regulatory framework in a given country, the usage of decay heat standards may also reduce the effort in a license application or in some cases even be mandatory.

Nowadays, calculations based on best-estimate codes, using the summation method, are more easily accessible than historically, rendering the use of standards less unavoidable. As presented in the following and in the example in Section 6.3.7, standard values can sensibly depart from values based on the summation method. It is also interesting to realize that standard methods often require as inputs quantities such as “power per irradiation steps”, or fission fractions per irradiation steps (fraction of $^{235}$U, $^{238}$U, $^{239}$Pu and $^{241}$Pu to the total fission rates, for each irradiation steps), which can only be accurately obtained from best-estimate codes (e.g. SCALE/POLARIS, CASMO5, Serpent).

### 6.3.1 Overview

A variety of standards (or standard methods) was developed over time, with numerous releases and updates. The latest releases at the time of the present work are as follows: the JAERI-M 91-034 from 1991 [57], the ANSI/ANS-5.1 from 2014 [136], the DIN 25462-1 and -2 from 2014 [22,25], the U.S. NRC RG 3.54, Rev. 2, from 2018 [28], and finally the ISO 10645, from 2022 [27].

Despite some differences in the methods and the level of self-sufficiency, the latest revisions of the standards adopted a common approach. The total decay heat power is computed as a sum of contributing sources instead of
the empirical formulation based on tabulated correction factors used in the earlier revisions. The identified major decay heat sources considered in the latest releases are:

* Fission products,

* actinides, and

* neutron capture (n,γ) on fission products.

The standards usually neglect spacial effects of energy dis- position (from γ radiation) and the decay heat contribu- tion from delayed neutrons and activated structural com- ponents. Each of these standards presents limits on the applicability, defined based on

* Reactor type (PWR or BWR),

* fuel type (UO₂ or MOX),

* decay time after irradiation,

* fuel properties, burnup, and enrichment.

The mentioned standards apply almost identical methods for the evaluation of the decay heat due to the decay of fission products, except those generated by neutron capture on fission products.

Similar semi-empirical methods are used, except in DIN 25463 1/2 (2014), for the decay heat due to neutron capture in fission products and fully empirical for the decay heat from the actinides. Indeed, the DIN standard is using explicit analytical methods for the evaluation of the decay heat from the decay of fission products generated by neutron capture in fission products as well as from the decay of the actinides.

In terms of self-sufficiency, the standards can be divided into entirely self-sufficient, such as the DIN 25463 1/2 (2014) and U.S. NRC RG 3.54 Rev.2 (2018), and standards requiring special input data, dependent on operating conditions, reactor type or fuel type, prepared by the user: ANSI/ANS-5.1 (2014) and ISO 10645 (2022). For example, the ANSI/ANS-5.1 (2014) requires knowledge (and justification) of the fission fractions for the major four fissionable nuclides $^{235}$U, $^{238}$U, $^{239}$Pu and $^{241}$Pu, at each irradiation interval, the production rate of $^{239}$U from capture on $^{238}$U at end of irradiation, as well as the number of fissions per initial fissile atom (FIFA). Similarly, the ISO 10645 (2022) requires the fission fractions however provides a formula for the production rate of $^{239}$U from capture on $^{238}$U.

Tables 14 and 15 summarize the main standard characteristics and applicability area; details will be provided in the following sections, but readers are encouraged to read the original standard publications for a full understanding.

In the case of MOX fuel for the DIN standard, the amount of Pu fissile content is defined as ($^{239}$Pu+$^{241}$Pu) divided by (U+Pu+Am). Therefore the amount of $^{241}$Am is indirectly included in the Pu fissile content. Increasing the amount of $^{241}$Am may lead to leaving the area of applicability by lowering the Pu fissile content. $^{241}$Am is not added to $^{239}$Pu and $^{241}$Pu in the numerator since it is not fissile in the sense that the capture cross section is usually larger than the fission cross section in the thermal spectrum (this is also reflected in cross-section data given in the standard).

### 6.3.2 DIN 25463-1 and -2 standards, 2014

The standard provides the basis for calculating the decay heat power of uranium oxide nuclear fuel in pressurized water reactors by taking into account the contribution of fission products from nuclear fission, the contribution of actinides, and the contribution of decay heat power resulting from neutron capture in fission products. By its definition, the standard is entirely self-sufficient hence requires no special, reactor, or fuel type, or operating conditions-dependent data to be supplied by the user.

#### History

The history of the German standard for the calculation of decay heat power, DIN-25463, begins in 1982:

* Fission products: from summation of 23 exponential terms for $^{235}$U, $^{238}$U and $^{239}$Pu from ANSI/ANS-5.1-1979,

* Actinides: $^{239}$U and $^{239}$Np,

* Correction term to account for actinides other than $^{239}$U and $^{239}$Np,

* Explicit formula with approximated neutron flux for $^{134}$Cs production,

* G-factor for neutron capture in fission products other than $^{133}$Cs.

DIN 25463 1990:

* $^{241}$Pu is added as fissionable nuclide

* Fission products: 24 exponential terms for $^{235}$U, $^{238}$U, $^{239}$Pu and $^{241}$Pu,

* Minor corrections.

DIN 25463-2 2008:

* newly developed standard for PWR MOX fuel.

DIN 25463-1/2 2014:

* Decay time < $2 \times 10^9$ sec. (≈63 years),

* MOX fuel

* Fission products: 24 exponential terms for $^{235}$U, $^{238}$U, $^{239}$Pu and $^{241}$Pu,

* Actinides: explicit depletion chains,

* Neutron capture in fission products: explicit activation chains,

* Extended range of applicability for enrichment and burnup.

Besides the standards for light water reactor fuel, there is also a DIN standard for nuclear fuels of high-temperature reactors with spherical fuel elements [137]. This standard will not be further discussed here since it is outside the scope of the present paper and has been withdrawn lately.

#### Applicability and limitations

The standards are applicable UO₂ and MOX fuel irradiated in pressure water reactors (PWR), under the following conditions:

* Not applicable to fuel depleted in BWRs,

* Decay time shorter than $2 \times 10^9$ s (≈ 63 years),

* Uranium enrichment: 3–5 wt.%,
<table><caption>**Table 14.** Main standard characteristics concerning their latest releases.</caption><thead><tr><th>Standard</th><th>Fission Products (FP)</th><th>Capture in FP.</th><th>Actinides</th></tr></thead><tbody><tr><td>ANSI/ANS-5.1 (2014)</td><td>23-term exponential fit</td><td>t ≤ 10<sup>4</sup>sec: G-factor<br/>t > 10<sup>4</sup>sec: Explicit: <sup>133–134</sup>Cs<br/>Correction for the rest</td><td>Explicit: <sup>239</sup>U, <sup>239</sup>Np<br/>Correction for the rest</td></tr><tr><td>DIN 25463 1/2 (2014)</td><td>24-term exponential fit</td><td>Depletion chains</td><td>Depletion chains</td></tr><tr><td>RG 3.54 Rev.2 (2018)</td><td>9-term exponential fit<br/>ANSI/ANS-5.1 (2014)</td><td>Explicit: <sup>133–134</sup>Cs<br/>Correction for the rest</td><td>semi-empirical for<br/>7 actinides</td></tr><tr><td>ISO 10645 (2022)</td><td>ANSI/ANS-5.1 (2014)</td><td>Explicit: <sup>133–134</sup>Cs<br/>Correction for the rest</td><td>Explicit: <sup>239</sup>U, <sup>239</sup>Np<br/>Correction for the rest</td></tr></tbody></table>

<table><caption>**Table 15.** Main standard limits and applicability concerning their latest releases.</caption><thead><tr><th>Standard</th><th>Reactor</th><th>Fuel</th><th>Decay time<br>(sec)</th><th>Burnup<br>(MWd/kgU)</th><th>Enrichment<br>(wt.%)</th></tr></thead><tbody><tr><td>ANSI/ANS-5.1 (2014)</td><td>LWR</td><td>UO<sub>2</sub></td><td>&lt;10<sup>10</sup> (≈316 y)</td><td>No limit</td><td>No limit</td></tr><tr><td>DIN 25463 1/2 (2014)</td><td>PWR</td><td>UO<sub>2</sub><br>MOX</td><td>&lt;2.10<sup>9</sup> (≈62 y)</td><td>&lt;80<br>&lt;60</td><td>3.0–5.0 (235U)<br>1.8–7.5 (fissPu)</td></tr><tr><td>RG 3.54, Rev. 2 (2018)</td><td>PWR<br>BWR</td><td>UO<sub>2</sub></td><td>1–110 years</td><td>10–65<br>10–55</td><td>2.0–5.0 (235U)</td></tr><tr><td>ISO 10645 (2022)</td><td>LWR</td><td>UO<sub>2</sub></td><td>&lt;10<sup>9</sup> (≈31 y)</td><td>&lt;62</td><td>&lt;5</td></tr></tbody></table>

* Fissile plutonium in HM: 1.8–7.5 wt.%,

* Fissile plutonium in total plutonium: 50–80 %,

* Fuel to moderator ratio: 1.8–2.4,

* Maximum burnup for UO₂: 80 MWd/kgHM, and for MOX: 60 MWd/kgHM,

* Maximum 235U in MOX fuel: 0.72 wt.%,

* Decay heat power from activation products in struc- tural materials and fission power from delayed neutron-induced fission are not included.

Methodology

The total decay heat rate/power $P_z$ after a decay time $t$ which follows a power period $T$, is a sum of contributions from fission products, actinides, and decay heat generated by nuclides formed by neutron capture in fission products:

$$P_z(t, T) = P_S(t, T) + P_R(t, T) \quad (9)$$

with

* $P_S$: the decay heat rate from fission products from fission of 235U, 238U, 239Pu, and 241Pu.

* $P_R$: the decay heat rate from actinides and neutron capture in fission products.

The decay heat from fission products $P_S$ is computed by approximating a pulse power function by a sum of 24 exponential terms multiplied by the reaction rates $R_i$ of the four main fissile nuclides and integrated over the power intervals $k$. The pulse power function, $f_i(t)$, represents the decay heat power per fission, following an instantaneous pulse of a significant number of fission events. The data

represent $f_i(t)$ and its assigned $1\sigma$ uncertainty for thermal fission of 235U, 239Pu, and 241Pu, and for fast fission of 238U. The decay heat power is obtained in (MeV/fission·s) and converted to W·s by $\epsilon = 1.6022 \times 10^{-13}$ W·s/MeV:

$$P_S(t, T) = \epsilon \cdot \sum_{k=1}^{N} \sum_{i=1}^{4} R_{i,k} \sum_{j=1}^{24} \frac{\alpha_{i,j}}{\lambda_{i,j}} (1 - e^{-\lambda_{i,j} T_k}) \cdot e^{-\lambda_{i,j} t_k} \quad (10)$$

with

* $\epsilon$: conversion coefficient from MeV/s to W,

* $\lambda_{i,j}, \alpha_{i,j}$: the coefficients in the 24-term exponential fit for the fission products decay heat power,

* $R_{i,j}$: the fission fractions of nuclide $i$ (235U, 238U, 239Pu and 241Pu) in step $k$,

* $T, t$: the time on power and cooling time, for the step $k$.

The fission fractions, $R_{i,j}$, are determined by burnup calculations, depleting the actinides.

The decay heat due to radioactive decay of actinides and decay of nuclides generated by neutron capture in fission products is treated explicitly by solving the burnup equations for the nuclide atom densities $N_n$ via prescribed depletion and decay paths, with cross sections, decay constants $\lambda_n$ and recoverable energies $Q_n$ provided by the DIN documentation:

$$P_R(t, T) = \epsilon \cdot \sum_n Q_n \cdot \lambda_n \cdot N_n(t, T) \quad (11)$$

with $N_n(t, T)$ the solution of system of burnup differential equations for $\frac{dN_n(t)}{dt}$.
The actinides included explicitly are: $^{234-239}$U, $^{237-239}$Np, $^{238-243}$Pu, $^{241,242,243,244}$Am, $^{242,244}$Cm. The nuclides included in the decay heat due to capture in fission products are: $^{110m}$Ag, $^{134}$Cs, $^{136}$Cs, $^{140}$La, $^{148,148m}$Pm and $^{154,156}$Eu.

The DIN provides a set of effective data: cross sections, neutron capture and fission along with the basic decay data such as atomic masses, decay constants, fission yields, and recoverable energies, in the form of interpolation tables. The data interpolation for UO₂ fuel is defined by enrichment and moderator-to-fuel ratio. An additional parameter, the fissile share in plutonium, is used in the interpolations for MOX fuel. The standard provides a formulation for the neutron flux which is determined for each burnup step by an iterative procedure. The uncertainty in the computed decay heat power is determined from the uncertainties of the sources contributing to decay heat power: fission products without neutron capture in fission products, actinides, neutron capture in fission products, and the uncertainty in the operating power. The uncertainty of the computed total decay heat is calculated by:

$$ \Delta P_Z(t, T) = n \cdot \sqrt{\Delta P_S^2(t, T) + \Delta P_R^2(t, T) + P_Z^2(t, T) \left(\frac{\Delta P}{P}\right)^2} \quad (12) $$

with

* $n$: the statistical uncertainty in term of [sigma],

* $\Delta P_S$: the uncertainty decay heat power from fission products,

* $\Delta P_R$: the uncertainty in decay heat power from actinides and neutron capture in fission products,

* $\frac{\Delta P}{P}$: the relative uncertainty in the nominal thermal power,

* $Q_i$, $\Delta Q_i$: nuclide energy per fission and uncertainty,

* $\lambda_{i,j}$, $\beta_{i,j}$: coefficients in the 24-term exponential fit for FP uncertainties,

* $R_{i,k}$: fission rate fraction of isotope ($^{235}$U, $^{238}$U, $^{239}$Pu and $^{241}$Pu) in step k,

* $t, T$: time on power and cooling time (same for step k: $t_k, T_k$).

For the uncertainty decay heat power from fission products ($\Delta P_S$), the expression is given by

$$ \Delta P_S(t, T) = \sum_i^4 \sqrt{P_{S,i}^2(t, T) \left(\frac{\Delta Q_i}{Q_i}\right)^2 + \Delta P_{S,i}(t, T)} \quad (13) $$

and

$$ \Delta P_{S,i}(t, T) = \epsilon \cdot \sum_{k=1}^{m} \sum_{i=1}^{4} R_{i,k} \sum_{j=1}^{24} \left( \frac{\beta_{i,j}}{\lambda_{i,j}} (1 - e^{-\lambda_{i,j} T_k}) \cdot e^{-\lambda_{i,j} t_k} \right) \quad (14) $$

For the uncertainty due to the actinides and neutron capture in fission products, $\Delta P_R$ can be expressed as follows, following the same definitions as previously mentioned:

$$ \Delta P_R(t, T) = 0.05 \cdot \left( 1 + \frac{t}{t + 5 \cdot 10^5} \right) \cdot P_r(t, T) \quad (15) $$

### 6.3.3 US NRC RG 3.54, revision 2, 2018

It is stated that the regulatory guide (RG) provides methods that are acceptable to the U.S. Nuclear Regulatory Commission (NRC) staff for calculating spent nuclear fuel heat generation rates for use as design input for an independent spent fuel storage installation (ISFSI). By its definition, the regulatory guide is entirely self-sufficient hence requires no special, reactor, fuel type, or operating conditions (apart from the power history) dependent data to be supplied by the user.

#### History

Revision 1, 1999

* Empirical formula with table interpolated factors with dependency on burnup and enrichment,

* Maximum burnups of 45 MWd/kgU (BWR), and 50 MWd/kgU (PWR).

Revision 2, 2018

* Extended ranges for burnup and enrichment,

* The empirical procedure is replaced by sum of contributing sources,

* Fission products: 9 exponential terms for $^{235}$U, $^{238}$U, $^{239}$Pu and $^{241}$Pu from ANSI/ANS-5.1-2014,

* Actinides: semi-empirical procedure for 7 actinides,

* Neutron capture: explicit for $^{134}$Cs production; tabulated correction factor for the rest,

* Activation products in structural materials: tabulated corrections factor.

#### Applicability and limitations

The methodology used in the guide is appropriate for computing the heat generation rates of fuel assemblies from LWRs as a function of burnup, specific power, decay time, and enrichment up to 5 weight-percent (wt.%) $^{235}$U in uranium.

* Applicable for UO₂ depleted in either PWR or BWR,

* Not applicable for MOX fuel,

* Decay times from 1 year to 110 years,

* Initial $^{235}$U enrichment: 2 to 5 wt.%,

* PWR, burnup applicability range: 10 to 65 MWd/kgU,

* BWR, burnup applicability range: 10 to 60 MWd/kgU,

* Average power: from 12 to 50 kW/kgU.

#### Methodology

The total decay heat, $P_T(t, T)$, after a decay time $t$ which follows a power period $T$, is computed as a sum of the following separate sources and corrected by a safety factor $F_S$:

$$ P_T(t, T) = [P_F(t, T) + P_C(t, T) + P_E(t, T) + P_A(t, T) + P_S(t, T)] \cdot F_S(t) \quad (16) $$

with

* $P_F$: decay heat power from fission products,

* $P_C$: decay heat power from neutron capture in $^{133}$Cs to product $^{134}$Cs,
* $P_E$: decay heat power from neutron capture in other fission products,

* $P_A$: decay heat power from actinides,

* $P_S$: decay heat power from activated structural materials, and

* $F_S$: a safety factor.

The decay heat from fission products, $P_F(t, T)$, is computed by approximating a pulse power function by a sum of 9 exponential terms multiplied by the reaction rates $R_i$ of the four main fissile nuclides and integrated over the power intervals $k$. The pulse power function, $f_i(t)$, represents decay heat power per fission following an instantaneous pulse of a significant number of fission events. The decay heat power is obtained in (MeV/fission·s) and converted to W·s by $\epsilon = 1.6022 \times 10^{-13}$ W·s/MeV:

$$P_F(t, T) = \epsilon \cdot \sum_{k=1}^{N} \sum_{i=1}^{4} R_{i,j} \sum_{j=i}^{9} \frac{\alpha_{i,j}}{\lambda_{i,j}} (1 - e^{-\lambda_{i,j} T_k}) \cdot e^{-\lambda_{i,j} t_k} \quad (17)$$

The method and the data are those developed for ANSI/ANS-5.1-2014. The nine group coefficients $\lambda_{i,j}$ and $\alpha_{i,j}$, provided by the standard, are applicable for SDC times longer than 1 year. The $P_C(t, T)$, the decay heat due to radioactive decay of $^{134}$Cs generated by neutron capture in $^{133}$Cs is given by the following equation:

$$P_c(t, T) = Y \cdot E \cdot \lambda_4 \frac{S}{Q} \left[ \frac{1 - e^{-(\lambda_4 + \sigma_4 \phi)T}}{\lambda_4 + \sigma_4 \phi} + \frac{e^{-\sigma_3 \phi T} - e^{-(\lambda_4 + \sigma_4 \phi)T}}{\sigma_3 \phi - (\lambda_4 + \sigma_4 \phi)} \right] e^{-\lambda_4 t} \quad (18)$$

with

* Y: effective cumulative $^{133}$Cs yield per fission (in percent),

* $\lambda_4$: decay time constant $^{134}$Cs ($s^{-1}$),

* $\sigma_3$: spectrum averaged (n,γ) cross section in $^{133}$Cs (barn),

* $\sigma_4$: spectrum averaged absorption cross section in $^{134}$Cs (barn),

* E: recoverable energy per decay for $^{134}$Cs (MeV),

* $\phi$: total neutron flux (n/cm$^2$·s),

* S: specific operating power (MeV),

* $Q_i$: specific energy per fission for the four fissionable nuclides (MeV),

and

$$\frac{S}{Q} = \frac{1}{T} \sum_{k=1}^{m} \sum_{i=1}^{4} \frac{S_{i,k}}{Q_i} T_k \quad (19)$$

$$S_{i,k} = S_k \cdot \frac{S_i}{S} \quad (20)$$

The quantity $S_{i,k}$ is the specific thermal operating power generated by the fission of nuclide i for irradiation interval $k$. The relative power fractions for each of the four fissionable nuclides $S_i/S$ is tabulated as a function of initial enrichment and burnup, and reactor types PWR and

BWR. The average specific power during step $k$ is determined from the burnup $B_k$ and irradiation time $T_k$.

$$S_k = \frac{8.64 \times 10^4 \cdot B_k}{T_k} \quad (21)$$

The $P_E(t, T)$, the decay heat power from neutron capture in fission products except for $^{133}$Cs is determined from the decay heat of the fission products $P_F$ and reactor independent factors tabulated as a function of decay time $H(t)$:

$$P_E(t, T) = P_F(t, T) \cdot H(t) \quad (22)$$

The decay heat from actinides is calculated as the sum of contributions from seven nuclides: $^{241}$Am, $^{238-241}$Pu, $^{242}$Cm, and $^{244}$Cm, tabulated via time and power factors. The time-dependent part is computed as:

$$P'_A(t) = \sum_{n=1}^{7} \hat{\beta}_n e^{-\lambda_n t} \quad (23)$$

with $\hat{\beta}_n$ are coefficients calculated as:

$$\hat{\beta}_1 = \beta_1 - \beta_2 \frac{E_1}{E_2} \frac{\lambda_1}{\lambda_1 - \lambda_2} \quad (24)$$

$$\hat{\beta}_2 = \beta_2 \left[ 1 + \frac{E_1}{E_2} \frac{\lambda_1}{\lambda_1 - \lambda_2} \right] \quad (25)$$

$$\hat{\beta}_n = \beta_n \quad \text{for } n = 3 - 7 \quad (26)$$

$\hat{\beta}_n$ are the tabulated constants depending on reactor, burnup and enrichment, $\lambda_1$ and $\lambda_2$ the decay time constant for $^{241}$Am and $^{241}$Pu, and $E_1, E_2$ the recoverable energy for $^{241}$Am and $^{241}$Pu. The decay heat power from the decay of actinides is obtained by applying a correction factor to the average power:

$$P_A(t, T) = P'_A(t) \cdot 1.82 S_{\text{avg}}^{-0.06} \quad (27)$$

with $S_{\text{avg}}$ the average power is computed as:

$$S_{\text{avg}} = \frac{1}{T} \sum_{k=1}^{m} S_k T_k \quad (28)$$

The $P_S(t, T)$ component, the decay heat power from activation in structural materials is designed to account mainly for the production of $^{60}$Co. The decay heat power is determined from the decay heat of the fission products $P_F$ and factors tabulated as a function of decay time $A(t)$:

$$P_s(t, T) = P_F(t, T) \cdot A(t) \quad (29)$$

As for the safety factor, $F_S(t)$, the definition given by the guide is: “An additional safety factor is applied to allow for uncertainties in the predicted values of the decay heat power obtained using the methods and data in this guide”. The safety factor is tabulated as a function of decay time.

The guide does not provide methods or data related to the uncertainties. It is quoted: “The uncertainty is found to be relatively small and largely independent of burnup over the range of the data. The methods are found to
yield conservative estimates of decay heat on average. The safety factor includes additional statistical allowance to ensure that the values obtained using the guide are conservative with respect to 95 percent of the measurement data at a 95-percent confidence level. The safety factor also addresses potential non conservatism resulting from the procedures of the guide and other approximations".

### 6.3.4 JAEA standard, JAERI-M 91-034, 1991

The decay heat and related quantities reported in this work correspond to recommendations from the “Committee of Standardization of Decay Heat Power in Nuclear Reactors”, organized by the “Atomic Energy Society of Japan” [49,138]. It applies to LWR (also to Fast Breeder Reactors), and corresponds to decay heat from fission products, including the decay of $^{239}$U and $^{239}$Np, but excluding the decay heat from actinides, from the activation products in structural materials, as well as from delayed neutron-induced fission.

Fission products from five origins are considered in this work: thermal neutron-induced fission of $^{235}$U, $^{239,241}$Pu and fast neutron-induced fission of $^{238}$U and $^{240}$Pu.

### 6.3.5 ANS standards

The standards provided by the American Nuclear Society (ANS) have evolved and refined over the past decades. We present here a very simplified history, to understand the developments of such ANS standards. Because the ANS standards are being developed using rules allowing each standard to be approved by the American National Standards Institute (ANSI), the standards are often referred to as ANSI/ANS, followed by a specific reference number and year.

Prior to the standard released in 1979, the first draft standard (ANS-5.1/N18.6) was based on predictions of fission products' decay heat by Shure [139]. Such “evaluation” effort was based on computational and experimental works [140,141]. The decay heat refers to reactors initially loaded with uranium fuels and operated at constant power ($P_0$), as expressed by the previous functions presented in previous paragraphs; Figure 25 presents the calculated decay heat as ratios of $P/P_0$, for the 1973 ANS-5.1 standard, as well as the calculated curves from the various equations. A detailed history of the development of the 1973 standard (as well as the following one of 1979) can be found in reference [142].

Such draft standard was suffering from two main inaccuracies: (1) that the decay heat contributions from different fission products were equal, and (2) that the neutron capture effects were negligible. The correction of such deficiencies has led to a new standard, issued in 1979 (ANSI/ANS-5.1-1979), and reaffirmed<fnref n="4" /> in 1985. Details of the new standard can be found in reference [143]. It mainly focuses on cooling time less than $10^4$ seconds, although it covers cooling periods up to $10^9$ seconds, based on an upper bound for the capture correction. It also explicitly accounts for differences in the fission products from $^{235}$U,

$^{238}$U, and $^{239}$Pu; neutron capture in fission products is taken into account using a correction factor, as it will be later done in many decay heat standards. Additionally, this 1979 standard considered changes in fissile content during the fuel life (this was a new development compared to the previous standard and to the previous functions presented in the above paragraphs). In the ANSI/ANS-5.1-1979 standard, the decay heat from fission products is represented in two ways.

Differences in the ANS standard versions (1979, 1994, 2005, 2014, and 2019) consist in the number of considered fissioning systems ($^{241}$Pu is taken into account from 1994), the considered measured and calculated decay heat values.

* ANSI/ANS-5.1-1994

* ANSI/ANS-5.1-2005

* ANSI/ANS-5.1-2014 (reaffirmed in 2019)

## History

This American National Standard provides values for the decay heat power from fission products and actinides following the shutdown of light water reactors operated with nuclear fuel consisting of uranium. ANSI/ANS-5.1 was first proposed in 1971, the revised proposal submitted in 1973, and officially released in 1979 notified as ANSI/ANS-5.1-1979.

* Applicable to $t < 10^9$ seconds,

* Fission products: summation of 23 exponential terms for $^{235}$U, $^{238}$U and $^{239}$Pu,

* Actinides: $^{239}$U and $^{239}$Np, and

* Neutron capture in fission products by a G-factor.

In the 1994 revision, the following changes were applied:

* Applicable to $t < 10^{10}$ s,

* $^{241}$Pu is added as fissionable nuclide,

* Updated $^{238}$U data, and

* Revised uncertainty data.

For the ANSI/ANS-5.1-2005, minor corrections and recommendations were implemented, whereas in the latest ANSI/ANS-5.1-2014 revision, correction terms to account for actinides other than $^{239}$U and $^{239}$Np were added, and the production of $^{134}$Cs was taken into account.

## Applicability and limitations

The standard is applicable to LWRs containing $^{235}$U as the initial major fissile material and $^{238}$U as the fertile material. The decay heat contributions from $^{235}$U, $^{238}$U, $^{239}$Pu, and $^{241}$Pu are treated explicitly; other fissionable nuclides are accounted for by treating them as $^{235}$U:

* Applicable for decay times shorter than $10^{10}$ seconds (about 316 years),

* Inapplicable for MOX fuel, and

* Decay heat power from activation products in structural materials and fission power from delayed neutron-induced fission is not included.

<footnote n="4">⁴ Reaffirmation means that no substantive changes are being made to the current document.</footnote>
Methodology

The total decay heat power from the fission products and actinides is calculated as:

$$P_T(t, T) = P'_d(t, T) + P_{dC}(t, T) + P_{dHE}(t, T) + P_{dA}(t, T) \quad (30)$$

where the contributing decay sources are from

- $P'_d(t, T)$: fission products from fissions of $^{235}$U, $^{238}$U, $^{239}$Pu, and $^{241}$Pu,

- $P_{dC}(t, T)$: neutron capture in fission products

$$P_{dC}(t, T) = \begin{cases} P'_{d}(t, T) \cdot G(t) & t \le 10^4 \text{ seconds} \\ P_{Cs}(t, T) + P_{dE}(t, T) & t > 10^4 \text{ seconds} \end{cases} \quad (31)$$

- $G(t)$: correction factor,

- $P_{Cs}(t, T)$: decay heat from capture in $^{133}$Cs,

- $P_{dE}(t, T)$: fission products other than $^{133}$Cs,

- $P_{dHE}(t, T)$: for $^{239}$U and $^{239}$Np, and

- $P_{dA}(t, T)$: for other actinides.

The decay heat from fission products, $P'_d(t, T)$, is computed by approximating a pulse power function by a sum of 23 exponential terms ($j = 1, \dots, 23$) multiplied by the fission fraction ($R_i$) of fissile nuclide ($i = 1, 4$) and integrated over interval ($k = 1, N$) at constant power.

$$P_d^i(t, T) = \epsilon \cdot \sum_{k=1}^{N} \sum_{i=1}^{4} R_{i,j} \sum_{j=1}^{23} \frac{\alpha_{i,j}}{\lambda_{i,j}} (1 - e^{-\lambda_{i,j} T_k}) \cdot e^{-\lambda_{i,j} t_k} \quad (32)$$

with

- $\epsilon$: conversion factor from MeV/s to W,

- $\lambda_{i,j}$ (and $\alpha_{i,j}$): coefficients in the 23-term exponential fit, ($i = 4, j = 23$),

- $R_{i,k}$: fission rate fraction of nuclide $i$ ($^{235}$U, $^{238}$U, $^{239}$Pu, $^{241}$Pu) in step $k$,

- $T, t$: time on power and cooing time, step $k$.

The four sets of 23 coefficients $\alpha_{i,j}$ and $\lambda_{i,j}$, are provided by the standard for the thermal fissions of $^{235}$U, $^{239}$Pu and $^{241}$Pu, and the fast fissions of $^{238}$U. The formulation is derived from the analytical solution of the integral for

$$P_i(t_k, T_k) = \int_0^T R_i(\tau) f_i(t + T - \tau) d\tau. \quad (33)$$

The integral gives the decay heat power of fission products resulting in of the fission of fissionable nuclide ($i$), during irradiation interval at constant power ($k$). The function $f_i(t)$ representing the decay heat power per fission following an instantaneous pulse of a significant number of fission events is defined as:

$$f_i(t) = \sum_{j=1}^{23} \alpha_{i,j} e^{-\lambda_{i,j} t}. \quad (34)$$

The fission fractions $R_i$ depends on the fuel type and the operating conditions and must be provided by the user.

The decay heat due to neutron capture in fission products, $P_{dC}(t, T)$, for shutdown times $t \le 10^4$ seconds is based on corrections to the decay heat of fission products $G(t)$-factor calculated as:

$$G(t) = (3.24 \cdot 10^{-6} + 5.23 \cdot 10^{-10} t) \cdot T^{0.4} \Psi. \quad (35)$$

The irradiation time $T$ is limited to $1.2614 \times 10^8$ seconds (about 4 years) and the Fissions per Initial Fissile Atom (FIFA) should be $\Psi < 3$. The FIFA and $\Psi$ must be evaluated and supplied by the user. For shutdown times $t > 10^4$ seconds, the standard provides a tabulated correction factor $H(t)$. In addition, the standard applies explicitly the contribution from $^{134}$Cs being produced by the neutron capture in $^{133}$Cs:

$$P_{dC}(t, T) = \begin{cases} P'_{d}(t, T) \cdot G(t) & t \le 10^4 \text{ seconds} \\ P_{Cs}(t, T) + P_{dE}(t, T) & t > 10^4 \text{ seconds} \end{cases} \quad (36)$$

with parameters as defined earlier:

- $P'_d(t, T)$: fission products from fissions of $^{235}$U, $^{238}$U, $^{239}$Pu and $^{241}$Pu,

- $P_{dCs}(t, T)$: decay heat from capture in $^{133}$Cs is defined by

$$P_{dCs}(t, T) = Y \cdot E \cdot \lambda_4 \frac{P}{Q} \left[ \frac{1 - e^{-(\lambda_4 + \sigma_4 \phi)T}}{\lambda_4 + \sigma_4 \phi} \cdot \frac{e^{-\sigma_3 \phi T} - e^{-(\lambda_4 + \sigma_4 \phi)T}}{\sigma_3 \phi - (\lambda_4 + \sigma_4 \phi)} \right] \cdot e^{-\lambda_4 t} \quad (37)$$

with

- $Y$: effective cumulative $^{133}$Cs yield per fission (in percent),

- $\lambda_4$: decay constant of $^{134}$Cs ($s^{-1}$),

- $\sigma_3$: spectrum averaged (n,γ) cross section in $^{133}$Cs (barns),

- $\sigma_4$: spectrum averaged absorption cross-section in $^{134}$Cs (barns),

- $E$: average energy per decay for $^{134}$Cs (MeV),

- $\phi$: effective neutron flux ($n/cm^2.s$):

$$\phi = \frac{1}{T_{\text{eff}}} \sum_{k=1}^{N} \phi_k T_k \quad (38)$$

$$\phi_k = \frac{S_k}{\epsilon_{\text{eff}}} \cdot 2.58 \cdot 10^{23} \quad (39)$$

- $S_k$: specific power density (MW/tU$_{initial}$)

- $\epsilon_{\text{eff}}$: effective enrichment (wt % of initial $^{235}$U)

- $P/Q$: effective fission rate defined as

$$\frac{P}{Q} = \frac{1}{T} \sum_{k=1}^{N} \sum_{i=1}^{4} \frac{P_{i,j}}{Q_i} \quad (40)$$

- $P_{i,j}$: specific operating power for nuclide $i$ (MeV),