Modeling and Experiment of Fission Products Release and Interaction with Coolant For

Home , Nuclear fission

Modeling and experiment of fission products release and interaction with coolant for

defective fuel in Light Water Reactor (LWR)

Thesis

Presented in Partial Fulfillment of the Requirements for the Degree Master of Science in

the Graduate School of The Ohio State University

Sha Xue, B. S.

Graduate Program in Nuclear Engineering

The Ohio State University

2017

Thesis Committee:

Jinsuo Zhang, Advisor

Marat Khafizov, Co-advisor

Sha Xue

2017

Abstract

During the normal operation of light water reactor, fuel defects can reside on fuel cladding from various reason such as fuel-pellet mechanical interaction, the hydriding of the Zr clad, the grid fritting from the assembly support, the warp wire fritting with the clad and also the stress corrosion cracking (SCC). The formation of defects on fuel cladding will result water ingression to the gap and react with nuclear fuel and the cladding inner surface. The interaction of water and nuclear fuel will affect the fuel thermal properties and deteriorate the cladding by hydriding and change of oxygen potential in the fuel. The change of fuel thermal properties will decrease the thermal conductivity, lead the decrease of heat transfer coefficient which may increase the fuel melting risk. The volatile fission products and fission gas will release to the coolant through cladding defects and increase the coolant activity and the defective nuclear fuel becomes a fission product source term when reactor is under normal operation.

Experimental and modeling are applied to understand the behavior of a defective fuel pin.

The experimental part focuses on the dissolution test of rare earth fission products in simulated LWR coolant chemistry and the diffusion coefficient measurement of cesium iodide in simulated LWR coolant chemistry using Nuclear Magnetic Resonance (NMR) technique. Rare earth fission products significantly contribute the residual heat and large quantity of radioactivity after the core shut down or in severe accident, therefore, their

ii dissolution kinetic parameters in LWR are important to reactor safety and the understanding the source terms.

The solubility test of rare earth fission product species (La2O3, Nd2O3 and CeO2) in simulate LWR coolant water (1000 ppm H3BO3 and 2 ppm LiOH) under different temperatures (room temperature 23 oC, 40 oC, 60 oC and 80 oC), results show that

Neodymium oxide has the largest solubility in boric acid water and cerium oxide has the lowest solubility, the addition of boric acid will significantly increase the solubility of rare earth oxide in boric acid water.

The diffusion coefficient of cesium iodide in boric acid water is measured using NMR technique. The NMR Diffusion-Ordered Spectroscopy (DOSY) measurement of Cs+ in simulated LWR coolant chemistry shows the self-diffusion coefficient of Cs+ is about 3.04

× 10-11 m2/s, and shows little dependence on Cs+ concentration in the solution. The measured data is about 100 times smaller than Cs+ in free water, different solution composition, temperature difference, pH difference and also the measurement method difference may cause the difference.

The cesium transport and diffusion through the fuel matrix based on a fuel oxidation model is established. MOOSE/BISON code developed by Idaho National Laboratory is used to develop the cesium release model, the oxidation model results from the developed model agree with the results in reference which validate the model development using

MOOSE/BISON. The cesium release model shows the time dependent cesium release after fuel defects reside on the fuel cladding, the radioactivity release to the coolant will be significant in the long term operation. The releasing of Cs into the coolant is significant iii when the fuel-water contact area is about 5%. And the releasing of Cs into the coolant will be significant when the diffusion coefficient of Cs in the fuel matrix increases 10 times.

iv Dedication

Dedicated to the students at The Ohio State University

v Acknowledgments

I would like to first thank Prof. Zhang to offer me an opportunity to work with him in

OSU. He always passes his wisdom to me during my study and research, and supports my study.

I’d like to thank Prof. Khafizov and Prof. Smidts’s help to my research and guidance. I’d like to thank Boyuan Li always helping me in life and study. I’d like to thank Yixing

Shen, he offers lots of help to my academic study. Furthermore I’d like to express my gratitude to Dr. Wentao Zhou, Xiang Li, Yafei Wang, Jeremy Isler, Nik Shay, Evan Wu,

Dr. Yi Xie, Dr. Shaoqiang Guo, this accomplishment would not have been possible without them.

Finally, thanks all of you again, my life becomes more colorful and meaningful because your appearance in my life.

vi Vita

2012………………...... B.S. Nuclear Engineering, Xi’an Jiaotong University

2012 to 2015………………….. Research assistant in Institute of Nuclear Energy Safety

Technology, Chinese Academy of Sciences

2015 to present………………… Graduate Research Associate, Nuclear Engineering

Program, The Ohio State University

Fields of Study

Major Field: Nuclear Engineering

vii Table of Contents

Abstract ...... ii

Dedication ...... v

Acknowledgments...... vi

Vita ...... vii

List of Tables ...... x

List of Figures ...... xi

Chapter 1. Introduction ...... 1

1.1 Review of the fission products speciation and their chemical states in UO2 fuel. 6

1.2 Nuclear fission products speciation...... 7

1.2.1 Fission products speciation and chemical states in oxide fuels...... 8

1.2.2 Volatile fission products species ...... 10

1.2.3 High volatile fission products ...... 11

1.2.4 Semi-volatile fission products species ...... 15

1.2.5 Low volatile fission products including the lanthanides and the metallic

precipitates: Y, La, Ce, Pr, Nd, Pm, Sm, Zr, Tc, Ru, Nb...... 18

1.3 Jacobian-free Newton-Krylov (JFNK) methods ...... 22 viii 1.4 Experimental of fission product in simulated LWR coolant chemistry ...... 26

Chapter 2. Fundamental data measurement of fission product ...... 28

2.1 Solubility measurement of lanthanide oxide (La2O3, CeO2, Nd2O3) ...... 29

2.1.1 Experimental procedures for solubility measurement of lanthanide oxide

(La2O3, CeO2, Nd2O3) ...... 31

2.1.2 Result of solubility measurement...... 35

2.2 Diffusion coefficient measurement of cesium iodide (CsI) in simulated LWR

coolant chemistry using NMR technique...... 41

2.2.1 Experimental of diffusion coefficient measurement...... 44

2.2.2 Diffusion coefficient data analysis...... 45

Chapter 3. Cesium release model development...... 51

3.1 Model development-fuel oxidation ...... 54

3.2 Hydrogen transport in fuel cracks ...... 57

3.3 Heat generation and conduction in the fuel and clad ...... 59

3.4 Cesium release from the defective fuel ...... 64

3.5 BISON Kernel development...... 68

3.6 Model validation and cesium release result ...... 71

Chapter 4. Summary ...... 83

References ...... 87

ix List of Tables

Table 1 Inventories of the main fission products and actinides in oxide fuel and their expected segregation tendencies [13] ...... 9

Table 2 Solubility of RE oxides in Boric acid water in different temperatures ...... 37

Table 3 Solubility measurement of RE oxides in Boric acid water in different temperatures

(1000 ppm boric acid and 2 ppm lithium hydroxide) ...... 40

Table 4 Concentration verification for La and Nd ...... 40

Table 5 Cs+ self-diffusivity measurement for different CsI concentration ...... 48

Table 6 NMR DOSY measurement results comparison ...... 49

Table 7 Relative and absolute fission yield of cesium isotopes occurring in the thermal neutron fission of U235 [107] ...... 66

Table 8 Comparison of fuel centerline temperature between MOOSE/BISON results and reference work ...... 73

x List of Figures

Figure 1 Open top glass cell and accessories ...... 32

Figure 2 Schematic diagram of the solubility test ...... 33

Figure 3 Solubility of three RE oxide in 1000 ppm H3BO3 and 2 ppm LiOH ...... 37

o Figure 4. Dissolved La2O3 and Nd2O3 under room temperature (23 C) during different time duration...... 38

+ o o Figure 5 Cs diffusivity of 0.1 M CsNO3 D2O based standard (left: 26.9 C, right: 25 C)

...... 47

Figure 6 NMR signal attenuation fitting curve for 1 M CsI sample ...... 47

Figure 7 Cs+ self-diffusivity measurement for different CsI concentration ...... 48

Figure 8 Schematic of physical/chemical process in defective fuel [65]...... 54

Figure 9 Fuel radial temperature distribution for fuel element K31 of the model (radial cross-section view)...... 72

Figure 10 Fuel oxygen to metal ratio distribution of fuel element K31 ...... 74

Figure 11 Model predictions and O/M measurements for element K31 [65]...... 75

Figure 12 Average stoichiometry deviation of the fuel after 16 days with about 0.5 mm ×2 mm defect size ...... 76

Figure 13 Result for MOOSE/BISON simulation of fuel oxygen to metal ratio radial distribution for K31 after the defect formed after 28 days ...... 76

Figure 14 Cs retention concentration in the fuel for different fuel-water contact area ..... 79

xi Figure 15 Cs concentration distribution in the fuel after 16 days for fuel-water contact area

12.5% (Left: ¼ fuel, right: cross section view of the fuel) ...... 79

Figure 16 Cs concentration distribution in the fuel after 16 days for fuel-water contact area

100% (Left: ¼ fuel, right: cross section view of the fuel) ...... 80

Figure 17 Released Cs activity to coolant for different fuel-water contact area (Ci/ kg UO2)

...... 80

Figure 18 Cs retention concentration in the fuel for different diffusion coefficient ...... 81

Figure 19 Released Cs activity to coolant for different Cs diffusion coefficient (Ci/ kg UO2)

...... 82

xii Chapter 1. Introduction

Nuclear energy is a clean, safe, cost-competitive, reliable and independent source of energy of high efficiency. The biggest advantage of nuclear energy compared with the traditional fossil energy (gas, oil, coal) is no CO2, which is well known as the greenhouse gas that will be generated during the electricity generation process. Thus nuclear energy will be in great demand in the future for the purpose of conservation and sustain of natural resources and also for environment protection. Though nuclear energy is clean, it can be not clean resulting from the spent nuclear fuel (SNF) generated from the nuclear reactions during the fuel burnup in the reactors. During the nuclear operation process, fission products (FPs) and minor actinides (MA): neptunium, americium, cerium and many other elements [1] will generated by the nuclear reactions. FP and MA are highly radioactive and some of them with a half-life as long as billions of years. Therefore, the nuclear waste management and the safety of the reactors during operation always a big concern for the nuclear industry and the environment.

The Pressurized Water Reactor (PWR) is the most widely used commercialized nuclear power plant type. Most of the possible fission products release from the nuclear reactor accident scenarios and if there is a failure for the protective barriers for example the vent of the containment, the fission products will release into the atmosphere. The Three Mile

Island (TMI) accident (1979) and the Chernobyl accident (1986) are the examples of the failure of containment and result the escape of the FP from the reactor. The releasing FP is 1 called the “source term”. Source term became part of the regulatory after the issuance of

WASH-1400 in 1975 [1]. After the TMI accident which only a small amount of iodine release was observed, the source term under the severe accident situation has raised great interest in the nuclear accident analysis.

It is important to predict and evaluate the fission products release after accident by knowing their release mechanism and their transport mechanism. There are four release phases after severe accident happens: (1) Coolant activity release. (2) Gap activity release. (3) Early in- vessel release. (4) Ex-release phase. (5) Late in-vessel release. [1]. At the beginning of reactor accident, the vent or the break of the primary coolant loop will result the leakage of coolant associated with the leakage of radioactivity, the typical loss of coolant accident is called “LOCA” which will result in the start of the emergency core cooling system

(ECCS). As the accident propagates, the loss of coolant accident will lead to less cooling down of the reactor core, the fuel cladding will melted due to the unremoved heat generated from the fuel pellets and the second radioactivity protective barrier fails the accumulated fission products in the gap will release to the coolant system. During the early in-vessel release stage, the fuel start to degrade with the accident going on, the melting of the fuel and the interaction between the fuel and coolant will result in a large amount release of fission products to the containment, the fission gases such as xenon and krypton will release to the containment immediately and other high volatile fission products like iodine, cesium will release to the containment afterwards. During this stage of the release, the melting nuclear fuel will sink to the bottom of the reactor vessel, however, after the reactor vessel bottom is melted by the heat, the failure of the bottom head will result in the release of fission products from the debris of the core and react will the concrete structural material 2 which is called the ex-in vessel release phase. The low volatile fission products may interact with concrete and release to the containment during ex-release phase and also the volatile fission products can also deposited to the concrete and release to the containment afterwards in the late-release phase.

Besides the above fission products release stages, fission products can also release to the containment through the “high pressure melt ejection (HPME)” system. When the bottom head of the reactor vessel failed, the molten reactor fuel and structural materials will injected to the containment through the reactor cooling system (RCS), the radioactive aerosols will added to the containment. The other phenomenon which will result in the release of fission products is the steam explosion which is result from the reaction between the coolant water and the molten core materials. This will induce the release of more airborne fission products. The small explosion will not increase the fission products release inventory much however, during a large scale of steam explosion, a significant amount of fission products will release to the containment very quickly associated with the release of large amount of droplet which will increase the radioactivity of the containment atmosphere and the coolant water.

However, the nuclear accident is not the only source term of the reactor, during the normal operation process, the fission products can also release to the coolant system or the containment due to the defective nuclear fuel. During the normal operation, fission products are retained in the fuel or some fission gases and volatile fission products can transport to the fuel gap, as long as the fuel cladding remain its integrity, the radioactive

3 fission products can retain in the gap, however the fact is that, during the reactor operation, the defects will appears on the fuel claddings.

The defects on a Zircaloy-clad are resulted from various reasons, such as the hydriding of the Zr clad, the grid fritting from the assembly support, the wrap wire fritting with the clad, pellet-cladding interaction (PCI) and the induced stress corrosion cracking (SCC) [2]. The defects on the fuel cladding will result in the entering of coolant water into fuel cladding interior. When the water interact with the cladding inners surface, the hydriding of the Zr cladding will decrease the tensile stress of the cladding and also increase the embrittlement, make the cladding less protective for the fuel. Several severe cladding degradation has been reported caused by the secondary hydriding of the cladding [2].Also the connection between the fuel and the coolant water will lead the depressurize of the gap, decrease the gap thermal conductivity, the decreasing of gap conductivity will result partial temperature increase of the fuel, increase the fuel melting risk because the heat cannot conducted to the coolant sufficiently.

The contact of water with the fuel will lead the interaction of fuel and water, the fuel will be oxidized, the oxygen to metal ratio (O/M) will increases, the diffusivity of fission products will be enhanced and however the thermal conductivity of the fuel decreases which lead to the increase fuel operating temperature. The larger the fuel temperature, the more the fuel expanded and the fission gap bubble swelling in the pellets, vice versa, cause more PCI. Therefore, from the viewpoint aforementioned, the accurate knowledge of defective fuel behavior, the PCI mechanism and the understanding of fission products release behavior is essential for the reactor safety.

4 This work is based on the knowledge of defective fuel oxidation and fission products release and transport to the coolant. The fuel oxidation and fission products release process is modelled using the Multiphysics Object-Oriented Simulation Environment (MOOSE) and BISON-a finite element-based nuclear fuel performance code developed by Idaho

National Laboratory since 2008 [3]–[7]. MOOSE is a parallel computational framework intended to solve of nonlinear partial differential equations systems which is based on the

Jacobian-free Newton-Krylov (JFNK) mathematical principles. MOOSE provides flexibility and efficiency even in largely coupled variable and large time scale problems.

Based on the huge and excellent computation capacity of MOOSE, the finite element nuclear fuel performance code BISON is developed to modelling the nuclear fuel performance problems for the next generation nuclear fuel. BISON has a large capacity in modelling different fuel types, for example, the UO2 fuel for LWR, the TRISO-coated particle fuel, the plated form metal fuel, also extend the ability to understanding how the irradiation impacts the fuel and structural materials in the irradiation experiment and also be applied to understand the novel fuel concepts.

To understanding the fission products behavior and transport mechanism, the fission products speciation and their behavior needs detailed classification and understanding.

There are about 30 fission product species, they form varieties of fission products chemical species. Some of them are highly radioactive, some of the activation products will be generated among neutrons, structural materials, and cladding materials. These wastes will be stored in spent fuel sites or the fuel reprocessing sites.

5 The releasing of radionuclides to the coolant and their interaction with the coolant or structures is important because radionuclides may cause serious corrosion problems to the fuel cladding or other structures which may decrease their integrities. Also radionuclides may release to the environment from the containment and coolant system causing environment issues. Therefore, this paper will review the current study of fission products speciation, experiment and modeling of fission products.

The first section will describe the fission products species for understanding the behavior of fission products in LWRs; the second section describes the releasing mechanism of the fission products release to the coolant by experiment and modeling; the third part discusses the reaction between radionuclides and coolant and the transport features of the radionuclides in the coolant, speciation and chemical states in LWRs. The thermodynamic properties are essential for understanding the kinetic properties of different kinds of fission products.

1.1 Review of the fission products speciation and their chemical states in UO2 fuel.

During the nuclear reaction process, fission products generated during the irradiation from the nuclear fission process. The quantity and the distribution of the fission products depending on the neutron flux and energy during the nuclide reactions for different fissile materials in the fuel [8]. During the fuel burnup, more than 20 fission products will be generated. The generation of fission products and their chemical state will influence the fuel properties: (1) The O/M ratio will influence the chemical potential of the fuel which will result in the different chemical species of the fission products in the fuel. (2) The changing of the chemical state of the fission products in the fuel can induce the physical

6 properties variation, e.g. fuel thermal conductivity, fission gas induced swelling, fuel creep and also the melting point [8]. (3) The chemical states of the fission products can also influence the fission products release behavior whenever in the accident situation during the reactor transients or the defective fuel situation under the normal operation period. (4)

Also the knowledge of the chemical state in the fuel is also critical in examination the dissolution kinetics and the residues as well as the precipitation during the spent fuel processing [9].

1.2 Nuclear fission products speciation

Lots of analytical techniques have been applied to examine the chemical state of irradiated fuels, the previous established radiochemical methods and micro-sampling are being superseded by the various analytical ceramography and optical methods e.g. XPS, XRD,

TEM, SEM, etc.[8]. Various kinds of the post irradiated fuel elements from LWR, high temperature reactor (HTR) and fast breeder reactor (FBR) were analyzed using those techniques. The fission products in oxidation fuel are typically categorized four groups.

(1) Volatile FPs which is also called the fission gas group including Kr and Xe. The fission gas bubbles will affected the fuel microstructure, the fuel chemistry will in return influence the diffusion of gas bubbles[10]. And the fission gas will release completely at high temperature condition which has been verified[11].

(2) High volatile fission products including Cs, I, Sb and Te. Cs and I are very important fission products due to their long half-life and highly volatile properties. The oxidation atmosphere will enhance the release of Cs and I. Also Cs can react with other

7 fission products in the fuel easily to form various kinds of other chemical compounds such as Cs2MoO4, Cs2TeO3 [11].

(3) Semi-volatile fission products: Ru, Mo, Ba, Sr, Pd, Rh. The behavior of the semi-volatile fission products is highly depends on the chemical potential of the fuel, they can became very volatile in oxidative atmosphere[11].

(4) Low volatile fission products including the lanthanides and the metallic precipitates: Y, La, Ce, Pr, Nd, Pm, Sm, Zr, Tc, Ru, Nb. The low volatile fission products are the most stable fission products in the fuel because of their compounds have high melting point or will reside the solid solution in the UO2 [12], however the release fraction can become large during accident situation due to their high fission yield.

At low temperature (< 1000°C), fission products diffusion in the fuel matrix is athermal and will be enhanced with fission, but it was observed from experiments that diffusivity of some FPs like Xe, Kr and I are similar and can be affected by the thermal shock. Moreover, fission gas, cesium and iodine are predicted to release from the irradiated fuel at the higher temperatures to gap [12].

1.2.1 Fission products speciation and chemical states in oxide fuels.

Oxide fuels are widely used in sodium cooled reactor and water cooled reactors. According to the study of Middleton et al., in oxide fuels, niobium, zirconium, barium, yttrium, strontium, cerium, praseodymium, neodymium, samarium, and lanthanum will all exist in oxide form. Molybdenum, cesium, and rubidium will be elemental in the high temperature regions of the fuel pellet and will exist in oxide form in the cool regions. Palladium, rhodium, ruthenium, tellurium, and technetium will be elemental. The metals will

8 agglomerate to form inclusions in the fuel matrix. The inventories and fission yield of the main fission products and actinides in oxide fuel is listed in Table 1 [13].

Table 1 Inventories of the main fission products and actinides in oxide fuel and their

expected segregation tendencies [13]

9 1.2.2 Volatile fission products species

The volatile fission products also called noble gases species including Xe and Kr, they are chemically inert and easily transported from the fuel into the gap. During the fuel burnup process, the fission gas will redistributed in the fuel pin which will leads to significant gas release for defective cladding of fuel pins, the gases will immediately transported into the coolant, but a significant quantity will remain trapped in the fuel matrix. If the fuel continues to be heated through melt, the gases will immediately release to the coolant [14].

For compete fuel pins, the fission gas will transported to the fuel-clad gap, the accumulation of the fission gas in the gap will lead to the buildup of the plenum pressure, which will decrease the fuel thermal conductivity and result in the fuel operate at an increasingly higher temperature [14]. The increasing pressure in the gap will also cause the increasingly risk of the cladding stress which can enhanced the cladding brittleness.

Kr-85 has a long half-life of 10.73 years, the radiological effects range over the mid and long term [15]. Kr-85 will release two β- with an average energy of 47.5 keV and 251.4 keV, and also release gamma ray with an energy of 514 keV. The daughter of Kr-85 is stable Rb-85 nuclide.

Xe has short half-lives for the main isotope Xe-133m (T1/2 = 2.19 days), Xe-133 (T1/2 =

- 5.24 days) and Xe-135 (T1/2 = 9 h), and releasing β with an energy of 346 keV and various gamma rays with an energy range from 813 keV to 81 keV. Xe-133m and Xe-133 have a stable daughter Cs-133, however Xe-135 has a very long lived daughter Cs-135 (T1/2 = 2.3

× 106 years) which emitting β-.

10 1.2.3 High volatile fission products

The high volatile fission products group including I, Cs, Te, Sb, Rb and Ag [9], [11], [15]–

[17]. Cesium and Iodine are the most important fission products in this group with regard to their radiological hazards. The two major isotopes for iodine is I-134 (T1/2 = 1 h) and I-

131(T1/2 = 8 days), due to their short half-lives, the radiological hazards will become very significant in the first few days of the reactor accident, but the influence become negligible after 1 month. Also the releasing of iodine will take away about 15% of the reactor decay after 1 day of the emergency shut down [15].

Some fraction of iodine may exist in the fuel matrix in the vapor state, however the majority will form a stable salt compound with the alkali metal cesium, e.g. cesium iodine at equilibrium state [18]. Because the Gibbs free energy of formation for CsI is quite negative, leading this reaction to proceed to completion. From the fission yield table for oxide fuel, the elemental yield for cesium from fission is about six times that of iodine, therefore, during the accident situation all of the iodine should be removed from the gas phase CsI in the fuel matrix [19]–[21].

Cesium has a mid-term lived isotope, Cs-134 (T1/2 = 2.0652 years), two long lived isotopes

6 Cs-137 (T1/2 = 30.08 years) and Cs-135 (T1/2 = 2.3 × 10 years). Also cesium has two short term isotopes Cs-138 (T1/2 = 30 min) and Cs-136 (T1/2 = 13 days), the various cesium species make Cs an extremely important fission product since both of the short term and long term radiological effects. Also Cs is very volatile and easily react with other fission products in the fuel. The possible chemical forms of Cs in the fuel are CsI, Cs2UO4,

Cs2ZrO3, Cs2MoO4 [22] and also elemental form Cs [23], Cs2Te [24] and Cs2TeO3 [25].

11 During the accident situation, Cs will release as elemental form Cs, CsOH, CsI, Cs2MoO4,

Cs2Te, Cs2TeO3, Cs2TeO4. CsBO2 [11]. Previous study has shown that when Cs releasing in to the containment, the Boron in the coolant will react with Cs the form stable compound

CsBO2 which will impact the chemistry of cesium and iodine. Also, cesium can also react with the concrete and the structural materials in the reactor core, forming Cs2CrO4,

Cs2Fe2O4, Cs2Si4O9 [26].

Tellurium (Te) is another important fission product species. Tellurium will remain as

Cs2Te, Cs2TeO3, Cs2TeO4 , SnTe or elemental species alloyed with other metals in the oxide fuel depending on the oxygen potential in the fuel [11], [15], [22], [27]–[30].

Tellurium is another very important fission product which Cs2Te is one of most abundant fission product release to the containment, the production of Cs2Te is shown in equation

(1) [31]. Te-132 (T1/2 = 78 hours) is a precursor of I-132 (T1/2 = 2.28 hours) and emitting

β- particles [31], also there are some short live tellurium isotopes in the reactor: Te-131

(T1/2 = 25 min), Te-133m (T1/2 = 55.4 min) and Te-134 (T1/2 = 42 min) [28]. Previous experiments found that tellurium and cesium start to migrate at a linear power at about 30 kW/m, and that once the fission products are in bubble form, the diffusion of Te and Cs will close to the diffusion rate of krypton. The volatile fission products can transport along the grain boundaries with the driving force of temperature gradient of the fuel and accumulated in the gap [28].

Tellurium has been proved can react with the zircaloy cladding at high temperature which may result SCC [15], [22], [28], [29], [32]–[34], the experiment showed the reaction phase between Zr and Te as Zr1-xTe below 673 K, and at higher oxygen potential and high

12 temperature, cesium telluride is unstable and a majority tellurium is in the chemical form of zirconium telluride compounds which result from the main reaction between tellurium and the surface zircoloy rather than with the bulk material, and the releasing fraction of tellurium is high if the cladding is about 60% oxidized[13], [28], [35]–[37].

When the fuel is breached, the increasing oxygen potential in the fuel will lead to the oxidizing of Zircaloy when the temperature above 1150 K. Then the Zr-Te compound will react with water/steam and released. Since hydrogen will be generated during the zircaloy hydration process, a very high volatile H2Te will be formed, however the unstable species is unlikely be the major releasing form of tellurium. The possible reactions are listed in from reaction from (2) to (4) [28-29]:

Te (l) + Cs2MoO4 (s) → Cs2Te(s) + O2(g) + MoO2 (s) (1)

Zr (s) + H2O (s) → ZrO2(s) + H2 (g) (2)

푍푟푇푒2 + 2퐻2푂 (푠) → 푍푟푂2(푠) + 2퐻2 (푔) + 푇푒2 (3)

2퐻2 (푔) + 푇푒2 ⟷ 2퐻2 Te (4)

13 Tin (Sn) is one of the fission products generated during the nuclear reaction, the presence of Tin (Sn) will leads to the production of SnTe which will dominate the production of

Cs2Te under high hydrogen potential or high oxygen/steam condition, but the dominant process is also depends on the production of cesium [25], [29], tellurium can only release as elemental form at high oxygen partial pressures above the equilibrium potential of

Sn/SnO2 [22].

Antimony (Sb) is another volatile fission product in the fuel, the three main isotopes of Sb are: Sb-122 (T1/2 = 2.72 days), Sb-124 (T1/2 = 60.2 days) and Sb-125 (T1/2 = 2.76 years).

Sb-125 is the precursor of stable Te-125 which can react will zircaloy fuel cladding [38].

Although, Sb has a relatively low fission yield compared with other fission products, it is a short-term and long-term radiological hazard fission product and easy to deposited in the downstream loop [39]. Sb is sensitive to oxygen potential at high temperatures, experiment has shown the release of Sb in increasing steam environment, Sb can retain in fuel clad which is similar to Te and the releasing fraction will increased when the fuel cladding is oxidized[36], however the lower releasing of Sb was observed during the experiment also indicated Sb is likely bound with other metallic melts, e.g. alloys with nickel and silver

[13], [40]. Also the presence of Sn will also result the delay release of Sb [15]. Sb-125 can be used as an indicator of Te which is more difficult to measurement during the fission products release measurement [39].

Rubidium (Rb) is another high volatile fission products, it reacts with Te to form tellurides in the fuel and behaves like cesium [30]. The fission product monitoring project initiated by Argonne National Laboratory showed that the Rb-88 (T1/2 = 18 min), and Rb-89 (T1/2 =

14 15 min) are significant activity contributors, but since their half-lives are very short, they will not induce radiological hazard.

1.2.4 Semi-volatile fission products species

The semi-volatile fission products including Ru, Mo, Ba, Sr, Ba, Pd, Rh [16], and among the semi-volatile fissions products, Ru, Mo and Ba are the most important ones.

Ruthenium (Ru) is highly radiotoxic and chemotoxic fission product which also has a relatively high fission yield [41], [42] and will remain in metallic form in the fuel[43]. The major isotopes of Ru are Ru-106 (T1/2 = 369 days) and Ru-103 (T1/2 = 39.3 days), which are short term and mid-term radiological hazard [44]. During the accident situation, Ru will become highly volatile and will rapidly release under highly oxidizing conditions [42] as oxidized form RuO2 and Ru2O3 under oxidized condition [43]. The interaction between ruthenium oxide with the containment building materials (stainless steel and epoxy paint) could lead to Ru compound deposition in the surfaces because its affinity to iron oxide and organic compounds, and will be oxidized by the air to form radiotoxic RuO4 (g) [44], therefore the highly toxic property and containment building trap make Ru a very important semi-volatile fission products.

Molybdenum (Mo) is a high fission yield material and easy to react with Cs to form

Cs2MoO4 and MoO2, they are stable fission products in oxide fuel and is very important for the oxygen potential in the fuel and even performs as the oxygen buffer of the fuel [28],

[45], [46]. The fission product isotopes of Mo are stable species in the fuel, and Mo can be volatile under oxidized condition [9], [13], [37], [47].

15 Barium (Ba) and strontium (Sr). Ba and Sr have very similar properties [22]. Ba is also a high fission yield fission product and easy to react with other fission products in the fuel, and similar to Mo. Barium significantly contribute to the decay heat after reactor shut down, Ba-140 and La-140 contribute about 20% of the residual power[22]. Ba-140 has a half-life of T1/2 = 12.75 days, and La-140 has a half-life about T1/2 = 1.68 days, therefore the evolution of Ba is important during the accidents. Besides, Ba and Mo are biological hazard which is harmful to human lungs and bones [48]. Ba is little dissolute in the nuclear fuel and their precipitates in fuel has the forms of barium oxide BaO, barium zirconate

BaZrO3, barium urinate BaUO3 in fuel. Ba tends to release under reducing conditions while

Mo in oxidizing conditions. BaZrO3 is mainly from the reaction with zircaloy and can be trapped in the fuel cladding [42] [49][9][22].

In high temperature and high pressure steam environment, the release of barium oxide and strontium oxide may be enhanced, once they contact with steam, hydroxide will be formed.

And also the oxidation of zircaloy will in return affect the release behavior of barium and strontium [27]. When Ba and Sr release to the coolant system, they are possible to deposit in the downstream loop depending on their chemical form. When Ba in the reduced atmosphere, the volatilely will increase, because the metal form Ba is more volatile than the oxide form [39][36].

Strontium has three major fission product isotopes: Sr-90 (T1/2 = 28 years), Sr-89 (T1/2 =

51 days) and Sr-88 is a stable nuclide. Strontium is another very important fission products,

Sr is a calcium mimic which is incorporated in bone growth, therefore is very harmful to human body [50]. Sr will be as insoluble SrO form in the UO2 fuel. Hydroxide will be

16 formed if the SrO react with high temperature and high pressure steam, the oxides would deposit in the loop as barium oxide [9], [27], [40].

Although Ba and Sr have similar properties, the difference between Ba and Sr are shown below [27]:

(1) The solubility of barium salts in water is larger than that of strontium salts in

water.

(2) The thermal stability of barium oxide is better than strontium oxide.

(3) The reaction between barium with hydrogen is more fierce than that of

strontium reaction with hydrogen.

Palladium (Pd) and rhodium (Rh) are actinides and belong to the noble metal fission product in UO2 fuel. Pd-107 is the second longest lived (T1/2 = 6.5 million years) and but with least radioactive energy (33 keV β- decay, specific activity 5×10−5 Ci/g) among the

7 long-lived fission products [51]. Pd will alloyed with other metal fission product, fuel and cladding materials , the typical metallic compound is Mo-Tc-Ru-Rh-Pd which can be formed in the low oxygen conditions [8] [52]. Rhodium, palladium and technetium showed a similar behaviour to that of barium or molybdenum: Rh releases were greater in reducing conditions while Pd and Tc releases were greater in oxidizing conditions, though their release seems lower under all conditions studied [2], [22].

17 1.2.5 Low volatile fission products including the lanthanides and the metallic

precipitates: Y, La, Ce, Pr, Nd, Pm, Sm, Zr, Tc, Ru, Nb.

The release fraction of low volatile fission products is much lower compared with the high volatile fission products. The release of volatile fission products mainly depend on the solid-state diffusion in the UO2 fuel and the release of low volatile fission products will more depend on the partial pressures of the fission products and the transportation from the fuel surface to the stream system [37]. During the accident situation, volatile fission products will be released immediately in high temperature and high pressure environment, then the low volatile fission products will become condensed and concentrated on the fuel surface, therefore the subsequent release of volatile fission products will enhance the release of low volatile fission products [37] [11]. The release of low-volatile fission product release mechanism also believed due to the volatilization of UO2. The volatilization is treated as the vaporization of UO3 (g) from the fuel matrix which is related to the oxygen partial pressure in the fuel [16].

The low-volatile fission products significantly contribute the core residual heat and activity, especially for lanthanides (lanthanum, cerium and neodymium) which has high fission yield in the UO2 fuel. Therefore, low-volatile fission products are also very important in the long-term reactor accident scenario evaluation [53].

Lanthanum is a mid-range fission yield product with about 6.4% of the fission yield[53].

Lanthanum contributes about 15%~25% of the residual heat after reactor shut down

(Geiger, 2016) [53]. Lanthanum mainly forms La2O3 in UO2 fuel, and soluble in UO2 fuel.

18 Cerium (Ce) has two major radioactivity fission product isotopes, Ce-144 (T1/2 = 285 days) and Ce-141 (T1/2 = 32.5 days) which are the short term and mid-term radioactive hazard, and both of the two fission products have a high fission yield about 5.5% and 5.9%. Cerium also has a big contribution to the core residual power and activity after shut down. The radioactivity release for more than 10% of the reprocessing plant are due to Ce-144, when the reactor shut down, Ce-144 contributes about 16% after one month and 18% after three months. Cerium also contribute about ~18% and ~26% of the core residual power after the reactor shut down in one and three months via the decay of Ce-144 to Praseodymium-144

(Pr-144) [53]. Cerium mainly form Ce2O3 and CeO2 in UO2 fuel. The volatility of Ce will increasing in reductive atmosphere [11].

Technetium-99 (Tc-99) is another long lived fission product, with a half-life of 2.11×105 years, and as metal precipitate in the fuel, the fission yield of Tc-99 is about 6% [42], [54],

[55]. The isotopes of Tc contribute a significant amount of the activity in the primary coolant which has been calculated of VVER1000-V446 [56].

The metallic precipitation Mo-Pd-Rh-Ru-Tc in the fuel will affect the distribution of other fission product such as the (Ba,Sr)(Zr,Mo)O3 oxide phase in the fuel, therefore the metallic phase in the fuel can in turn affect the chemical potential, microstructure, and thermal properties of the fuel [57].

During the reactor operation, there are many factors will result in the zircaloy fuel cladding failures, such as cladding hydriding, debris fretting, pellet-cladding interaction (PCI) due to the fuel pellets swelling, and the SCC induced by corrosion products [2]. Therefore the coolant will flows through the defects and react with fuel and cladding interior, which will 19 cause cladding oxidation, fuel oxidation and result in the change in thermal properties of the fuel and the change of gap heat transfer coefficient. Except the oxidation of fuel, high volatile fission product and some semi-volatile fission products will release to the coolant increasing activity of primary coolant [58]. Besides, the fission product release will be enhanced by fuel oxidation process [13].Therefore, the understanding of fuel oxidation and fission product release mechanism for defective fuel is very import. Since there are a lot of difficulties in building a fission product release experimental facility, because the high safety risks for the high temperature and pressure water system, therefore, modeling can be an very effective method to simulate the fission product releasing process and fuel oxidation [2], [13], [47], [56], [58]–[68].

There are many kinds of modelling tools and codes for evaluation of fission product releasing and transporting the coolant system after accident, such as ASTEC code for fission products release modelling [16], [48], [69]–[71], MELCOR code for severe accident analysis [72], CORSOR code to simulate the release of fission products and structural materials during the in-vessel phase during LWR severe accidents [39], [73],

[74], PHEBUS code to study the degradation of core structure materials and fuel from the early phase of reactor accident [70], [75]. However, no official tools for fission products release from a defective nuclear fuel during normal operation.

Idaho National Laboratory has developed a Multiphysics Object Oriented Simulation

Environment (MOOSE) since 2008. The purpose of developing MOOSE is to develop nuclear energy related engineering applications more efficiently. It has been applied to many areas of science and engineering including: material science such as microstructure

20 evolution, phase filed model development, chemistry, solid mechanics, superconductivity, etc. (http://mooseframework.com/about/). In reactor fuel performance simulation, many governing equations need to be coupled together to describe heat generation, thermal response of the fuel chemical species diffusion, mechanical contact between fuel and cladding, and the solid mechanics of the fuel during burnup [3]. The various governing equations are always nonlinear, the nonlinear material properties will add more nonlinearity which are always strongly coupled with each other. In computational nuclear engineering will always dealing with multiscale models and diversity time scales [3].

These kinds of modelling problems are typically solved using operator split methods, which is simplifying the solution by decoupling and solving the modified equations separately [3]. The mentioned “loosely coupled” method of solving equations is based on the interactions between first system and second system until the repeated process give a convergence that both the systems are satisfied. However, if the system is coupled tightly, this approach will make the system converges very slowly and this issue will be enlarged when coupled systems are on different time scales [3].

The other way to solve this nonlinear system is apply a tightly coupled solution procedure when using loosely coupled method to solve the problem [3]. This procedure will solve the problems simultaneously by generate nonlinear algebraic matrix which will be solved using a strongly convergent nonlinear solver. MOOSE is developed to solve all systems fully coupled and intended to be designed for engineering applications, which has the following features [3]:

21 (1) The large problems need to be solved paralleled and scaled during the solving

process, but it can be used on desktop computers and parallel machines because of

the economics consideration during the development. Also, since MOOSE is

developed for easier engineering application, the implicit strongly convergent

method and parallel scalability is also very important.

(2) MOOSE is developed based on modern software development principles and is also

related to other applications which based on it, therefore MOOSE should meet

accepted QA requirement.

(3) MOOSE is aimed to solve engineering problems which includes geometry creation,

mesh generation, mesh quality and adaptation, visualization and result analysis.

Thus, the above mentioned factors will influence MOOSE efficiency.

(4) MOOSE must meet the software validation and verification requirement which

required a robust verification of the MOOSE framework.

1.3 Jacobian-free Newton-Krylov (JFNK) methods

Jacobian-free Newton-Krylov method (JFNK) is the method used in MOOSE, which is aimed to solve the coupled nonlinear systems. JFNK methods has been widely used in many computational areas of engineering problems. To solve the coupled nonlinear partial differential equations (PDE), the nonlinear algebraic equations matrix should be solved, which will needs many considerations. Firstly, the linear system to be used during Newton iteration is required. If the solution variables number increase, the associated matrix involves the Jacobian entries also increases. The increasing of size will result in large requirement of system memory. Moreover, it is time consuming when the nonlinear system

22 with complex material properties, it is time consuming to compute the full Jacobian and for highly nonlinear problems when considering complex material properties. Newton–

Krylov methods are named of Newton’s method based Krylov method for solving the linear systems[3].

To application of JFNK in MOOSE is start by generating a weak form of the PDEs and derive it into the residual function form. Further, the boundary conditions needed to be added to modify the residual function. The problem is shown as the following equations from (5) to (11) [3] [76]:

푭(퐱) = 0 (5)

with F: ℝ푁 → ℝ푁, where N represents the how many unknowns exist in the system. The

Jacobian of this system is written as,

휕푭(퐱) (6) 풥(퐱) = 휕퐱

The Newton iteration is derived as,

풥(퐱(풌))훿퐱(풌) = −푭(퐱(풌)), (7)

23 and

퐱(풌+ퟏ) ← 퐱(풌) + 훿퐱(풌), (8)

Where k denotes the Newton iteration times.

However, the high cost of forming the Jacobian for relatively large grids making the above algorithm inefficient for many cases. Therefore, Krylov iterative solvers can be applied to solve the problem, which just needs the action of the Jacobian matrix on a vector [3]. The finite-difference approach to evaluate the matrix-vector product 풥(퐱(풌))퐕 is shown as [3],

퐅(퐱(풌) + ε퐕) − 퐅(퐱(풌)) (9) 풥(퐱(풌))퐕 ≈ ε

To use the expression effectively, the residual vector needs to be scaled to other variables.

And ε is chosen to satisfy the machine precision during computation [76].

This form has many advantages [3]:

(1) No need to do analytic derivatives to form J

(2) No time needed to compute J (just residual computations)

(3) No space needed to store J

24 The finite Element Method is an effective numerical way to obtain the approximate solutions of PDEs. FEM is similar like polynomial fitting which is finding coefficients for basic functions.

Therefore, the combination of the coefficients and the basis function form the solution of the PDEs. Quadrature can be used to find the integrals of the PDEs numerically. Newton’s method can be appled to find the solutions of nonlinear equations and the JFNK methods provide an effective way to solve the derivative equations [3]. In MOOSE, a preconditioner

M-1 applied to [3]:

풥(퐱(풌))M−ퟏ(Mδ퐱(풌)) = −퐅(퐱(풌)), (10)

Where M−1 represents the preconditioning process. The expression becomes [3]:

퐅(퐱(풌)+휺M−ퟏ푽)−퐅(퐱(풌)) (11) 풥(퐱(풌))M−ퟏ푽 ≈ , 휀

When choosing M−ퟏ, M−ퟏ푽 should be suitable approximation to 풥(퐱(풌))퐕 [56].

MOOSE provides an open source framework for developing an advanced simulation tools to various engineering problems. MOOSE uses a hierarchical, block-structured input file.

Within each blocks, any number of name/value pairs can be listed. The syntax is

25 completely customizable or replaceable which users can develop their own-needed

MOOSE blocks to solve different problems. MOOSE expects six basic blocks: mesh block, variables block, kernels block, boundary conditions block, executioner block and outputs block. The core idea of MOOSE is developing the kernels. The kernel block declares PDE operators to be used in the simulation, the parameter is to specify the type of kernel instantiate [76].

BISON is a finite element-based nuclear fuel performance code has been developed by

INL based on MOOSE since 2009 [6]. Therefore, bison is also a parallel, finite element- based tool to solve the coupled nonlinear PDEs for nuclear fuel behaviors. BISON supports multidimensional geometry such as one-, two- and three dimension geometry [6]. The temperature and burnup dependent thermal properties, fission product induce fuel swelling, fuel densification, thermal and irradiation creep, fracture, and fission gas production and release can be solved by BISON [77]. For cladding materials, BISON can solve materials properties such as plasticity, irradiation growth, and thermal and irradiation creep problems. Also, gap heat transfer, mechanical contact, and the evolution of the gap/plenum pressure with plenum volume, gas temperature, and fission gas addition is also included

[78], [77]. The input file of BISON is similar as MOOSE input file, and the similar running process.

1.4 Experimental of fission product in simulated LWR coolant chemistry

Except modelling work, also experiment work is performed to understand the fission product release mechanism and the fission product properties in LWR coolant chemistry.

The experimental work includes: dissolution test for lanthanide oxide (lanthanum oxide

26 (La2O3), Cerium oxide (CeO2) and Neodymium oxide (Nd2O3)) in simulated LWR coolant chemistry condition (about 1000 ppm boric acid (H3BO3), 200 ppm lithium hydroxide

(LiOH)) under room temperature and elevated temperatures (40 oC 60 oC, 80 oC).

And the diffusion coefficient measurement of Cs+ in boric acid water by dissolving cesium iodide in LWR coolant chemistry condition is measured using Nuclear Magnetic

Resonance (NMR) technique for different cesium iodide concentration. The long lived fission product cesium is considered for because Cesium is a high volatility fission product and has relative high fission yield also the high radioactivity.

27 Chapter 2. Fundamental data measurement of fission product

To examine the fission product release for the defective fuel in LWR, several experiments have been conducted:

(1) Dissolution test for lanthanide oxide (lanthanum oxide (La2O3), cerium oxide (CeO2) and neodymium oxide (Nd2O3)) in simulated LWR coolant chemistry (about 1000 ppm boric acid (H3BO3), 200 ppm lithium hydroxide (LiOH)) under room temperature and elevated temperatures (40 oC 60 oC, 80 oC) were carried out. Although lanthanide oxide are the low-volatile fission products in the fission products group, they significantly contribute the residual heat and the radioactivity after reactor shut down which is very important to nuclear safety. Because the fundamental data of lanthanide oxides in reactor coolant is rare, it is important to know the solubility of the fission product solubility in reactor coolant. This test is aim to get the dissolution kinetics of the lanthanides in simulated LWR coolant chemistry.

(2) Diffusion coefficient measurement for cesium iodide using Nuclear Magnetic

Resonance (NMR) spectroscopy technique. Cesium is one of the most important fission products, the most commonly released volatile chemical species of Cs fission product is cesium iodide (CsI) which will react with water immediately and form cesium ion in water, however, the diffusivity of Cs+ in LWR coolant is seldom reported. The self-diffusivity of

Cs+ in free water is reported about 7 × 10−10 푚2/푠 to 1.7 × 10−9 푚2/푠 at 18 oC [79].

28 Though electrochemical technique is an effective method to measure the diffusivity, this method is only effective when there is a redox couple during the electrochemical test. Since

Cs+/Cs couple has very negative redox potential, about -3.026 V vs SHE,it is impossible to get a Cs+/Cs redox couple in low ionic solution such as the LWR coolant, therefore other method should be employed to measure the diffusion coefficient of Cs+ in LWR coolant which is very important for understanding the Cs transport kinetics in aqueous solution.

NMR can be used to measure the diffusivity utilize magnetic field gradients which the electromagnetic field is spatially dependent [80]. Modern NMR spectrometers can measure self-diffusion coefficient for molecules in solution [81]. Diffusion measurements can be routinely accessible with conventional high-resolution NMR spectrometers equipped with actively shielded pulsed field gradient (PFG) probeheads [82]–[84]. Therefore, NMR measurement is taken to measure the self-diffusion coefficient of cesium iodine in simulated LWR coolant chemistry.

2.1 Solubility measurement of lanthanide oxide (La2O3, CeO2, Nd2O3)

Lanthanide oxide are the low volatile fission product in UO2 fuel, however, due to their high fission yield and their important role after reactor shut down - the significant contribution to the residual heat and the radioactivity after reactor shut down. Because of the similarities between actinide series and RE elements chemistries, the behavior of RE elements in aqueous solution may be used to understand the behavior of some of the actinide elements. In particular, Nd3+ ion shows very similar chemical and geochemical properties with Americium ion (Am3+), besides, RE ions are also can be analogue to

29 Plutonium ion (Pu3+) and Curium ion (Cm3+) [85], [86]. Under high pressure and high temperature conditions, the solubility of many oxides can become very appreciable in water

[87] which makes the solubility measurement of RE oxide in LWR coolant more important.

When contact with water, lanthanide oxide will probably form hydroxide, and then the ions

+ 0 - 2- will hydrolysis in the solution to form Ln(OH)2 , Ln(OH)3 , Ln(OH)4 , Ln(OH)5 ,

3- 5+ 4+ 3+ 6+ 5+ 4+ Ln(OH)6 , Ln2OH , Ln2(OH)2 , Ln2(OH)3 , Ln3(OH)3 , Ln3(OH)4 , Ln3(OH)5 ,

6+ 8+ Ln5(OH)9 and Ln6(OH)10 which have been proposed for different RE element in water.

Due to the low solubility of RE oxide in water, polymeric hydrolysis products would not be expected in the solution [86]. The Hydrolysis of RE element in near neutral solution is significant, therefore, hydrolysis should be taken in natural waters with pH > 6.The reactor coolant has a pH about 7, therefore, the hydrolysis of RE in reactor coolant is also possible and also the hydrolysis of RE in high temperature could be enhanced [86]. The hydrolysis process of trivalent RE ion species can be expressed in equation (12) to (14) [88], [89]:

3+ − Ln2O3(s) + 3 H2O(liq) = 2Ln (aq) + 6OH (aq) (12)

3+ 3x−y + x Ln + y H2O ⇄ Lnx(OH)y + yH (13)

30 3+ − 3x−y x Ln + y OH ⇄ Lnx(OH)y (14)

The RE oxides all has very low solubility in water, their solubility are not well agreed for

-6 -6 all the study, the solubility of Nd2O3 is reported about 5.75 × 10 mol/L and 2.7 × 10

mol/L in room temperature water(25 oC) and praseodymium oxide ha even smaller

solubility in water, about 6.1 × 10-7 mol/L in room temperature [90]. Cerium is reported

can be considered as the best plutonium surrogate of the plutonium (Pu) [91] because its

ionic radius and coordination number is very similar as Pu. Besides, in nuclear waste

management industry, cerium is one of the fission products species whose redox state will

significantly affects the waste container-silicate glass compositions [91]. Therefore, all of

the rare earth species fission products are important for the nuclear industry.

2.1.1 Experimental procedures for solubility measurement of lanthanide oxide

(La2O3, CeO2, Nd2O3)

1) Preparation of the base aqueous media using1000 ppm H3BO3, and 200 ppm LiOH.

One liter of the stock solutions of boric acid and lithium hydroxide based on double

distilled Millipore water and pH control using a pH meter. The H3BO3 is of 99.99%

purity, LiOH.7H2O 99.99% purity is 99.99% which are all purchased from

purchased from Fisher Scientific.

2) Use a clean open top glass cell, washed three times using double distilled Millipore

water and dried before the test. The glass cell is intend for electrochemical test

which is fabricated by Pine Instrument INC. which is shown in Figure 1. The six

31 port open top cell enables the user to equip the cell with a variety of accessories

(condenser, pH measurement, thermometer, etc.) since during the test, temperature

control and condense is needed to avoid the escape of solution. The glass cell is

corrosion resistive and chemical stable which is suitable for the test.

Figure 1 Open top glass cell and accessories

3) Add the prepared solution into the glass cell, using a temperature adjustable hot

plate (Fisher Scientific) to control the temperature of the solution in the cell. The

temperature is set to 23 oC, 40 oC, 60 oC, and 80 oC during each test. The

temperature control of the hot plate is within ± 0.5 oC.

32 4) Preheat the solution. After the temperature reach the desired temperature, add 20

mg of the metal oxide powder to the heated solution and stir the solution using a 1

inch magnet and record the start time. The stirring magnet is used to mimic the

coolant flow in the reactor, and which can also avoid the oxide power sedimentation

on the glass cell bottom and make the power disperse in the solution, the

experiment set up is shown in Figure 2.

Figure 2 Schematic diagram of the solubility test

5) Clean a batch of Teflon 30 ml volume bottles to put the samples, the bottoms

should be cleaned three times using Millipore double distilled water and dried

upside down on Kim wipe.

6) Sampling schedule:

33 a. Sampling after 5 min, 10 min, 30 min, 1 hours, 5 hours, 24 hours, 48 hours to

determine the time range of interest.

b. Removal of 15 ml of the solution from the glass cell using a syringe. Then put a

0.1 um Millipore syringe filter on the syringe. Filtrate the solution to the clean

30 ml bottle as soon as possible to avoid the cooling down of the sample. Since

the concentration can be varied with different temperature.

c. Add 2 v/v % super pure nitic acid to the sample to stabilize the sample solutions

and mix the solution thoroughly for 20 seconds. Name the sample clearly with

certain manner.

7) Preparation of ICP standards and samples.

a. ICP standards will be prepared at Menden Hall laboratory, OSU

The Concentration range for ICP-MS: 10 ppb – 1 ppm and the concentration

range for ICP-OES: 0.05 – 10 ppm. Since lanthanide oxide has low solubility,

therefore ICP-MS is preferred to sample analysis.

b. The ICP standards prepared are with concentrations of 1 ppb, 10 ppb, 50 ppb,

250 ppb, 10 ppm, each with a volume of 100 ml.

c. Weigh the ICP standards empty bottom first and rest to zero. Use the pipette

remove 1 ml of the 1000 ppm La, Ce, Nd standards to the bottle, add 2 v/v % of

the super pure nitric acid to the. Then add the double distilled water to the bottle

to dilute the standard to 100.8 g. Mix the solution thoroughly for about 20

seconds. Then follow this step to prepare other ICP standards. Record the

readings of the scale after each step when the number is stabilized.

34 d. Before the ICP measurement, the samples collected should be diluted, because

the boric acid has much higher concentration (1000 ppm compared with ~1

ppm) than the interested element, and it will influence the ICP measurement

during the measurement process. The samples were diluted for two batches, 100

times diluted and 10 times diluted. During the measurement, check the lowest

diluted sample first.

e. ICP measurements at Menden Hall laboratory, OSU.

2.1.2 Result of solubility measurement.

Two batches of solution with different boric acid concentration are prepared for the solubility test, one is boric acid with a concentration of about 16000 ppm (16 g/L) and 450 ppm (0.45g/L) LiOH, since it is reported that boric acid could enhance solubility of some chemical compound [92]. Another base solution is with 1000 ppm boric acid and 2 ppm of lithium hydroxide according to the references [93], [94]. The pH of the solutions are from

6.8~7.1. The solubility measurement of three RE oxides in 16000 ppm (16 g/L) boric acid and 450 ppm (0.45g/L) LiOH is shown in room temperature and 40 oC is shown in Table

2. The solution concentration during the different time range is shown in Figure 4. The concentration of three lanthanide element La, Ce, Nd and solubility of three oxide species under different temperatures with 1000 ppm boric acid and 2 ppm lithium hydroxide is shown in Table 3. A comparison of the solubility between the three oxides is shown in

Table 2.

The solubility of the samples are measurement using ICP-ms method which has high accuracy and efficiency. Neodymium oxide has the highest solubility in average from two

35 set of data, can Cerium oxide has the lowest solubility in boric acid water. Also, the higher concentration of the boric acid, the more the dissolved oxide in water which has already been discussed above.

Figure 4 shows the dynamic oxide dissolved process of lanthanum oxide and cerium oxide, the stirring magnet is fixed at a rotating speed of 250 rpm/min, the two oxide dissolved fast at the beginning 100 min, which almost reach 80% of the final concentration, i.e. the solubility, after 100 min of the test, the oxide dissolves much slower than the first 100 min, the oxide dissolves slowly and reach the equilibrium at about 1500 min (25 hours, approximate 1 day) for lanthanum oxide and neodymium. Since cerium has very low solubility compared with the other two oxide, the detection limit of cerium ion in water is below the limit of ICP-MS detectable limit. However, based on the similar chemical properties of the lanthanides group, the time for cerium oxide to reach the equilibrium should also around 1 day, though the concentration is very low. During a severe reactor accident, the first 72 hours are very important, Ce and La will contribute 20%~30% of the residual heat and during the accident situation, the large injection of the boric acid water into the reactor core will enhance the dissolved of RE fission products in coolant which can increase the activity of the coolant significantly and will be potential radiological hazard of the environment.

36 Table 2 Solubility of RE oxides in Boric acid water in different temperatures

Boric acid: 16 g/L, LiOH: 0.45 g/L Solubility Test Temperature La2O3 Nd2O3 CeO2 (mg/L) (mg/L) (µg/L) 23 oC 16.23 23.95 99.3 40 oC 25.33 37.26 139.8

1 Ce

log10(Solubility) La

0.1 0 0.01 0.02 0.03 0.04 0.05 0.06 1/T (1/oC)

Figure 3 Solubility of three RE oxide in 1000 ppm H3BO3 and 2 ppm LiOH

Figure 3 shows the comparison of solubility of three RE oxide in 1000 ppm H3BO3 and 2 ppm LiOH, the samples of the measurement are taken around 3 days of the dissolution test which the oxide should reach the equilibrium solubility based on the data in Figure 4.

37 During the test, to verify there is no problem with the sampling process, another batch of the samples were collected, and concentration is measured for several samples, the comparison of the concentration of the two batches sample is shown in Table 4, which sample batch A is the data source in this work. The verification of the two samples show the sampling process is reasonable which proves the data is reliable.

o Figure 4. Dissolved La2O3 and Nd2O3 under room temperature (23 C) during different time duration.

From the solubility measurement data, the solubility of cerium oxide and neodymium oxide didn’t change much during when increase the temperature. And Neodymium oxide has the largest solubility in boric acid water on average. However, the lanthanum oxide solubility

38 slows large dependency on temperature change, when the temperature is 40 oC and 60 oC, the solubility increase greatly from 65.5 ppb at 20 oC to 2881.5 ppb at 40 oC, and then decrease a little to 695ppb at 40 oC, the solubility at 80 oC is about 57.97 ppb. However, due to the similarity of structure and chemical properties of lanthanide oxide, the large solubility increase when solution temperature increases from 20 oC to 80 oC is unlikely to happen, even the temperature increases, the solubility change will not too big during low temperature range which can be compared with the solubility of Neodymium oxide and

Cerium oxide in boric acid water.

Besides, based on (12) and (13), La2O3 can react with water to form La(OH)3, the lanthanide trivalent ions will hydrolysis in aqueous solution, from the hydrolysis results for La(OH)3 in water when the temperature from 293 K to 600 K, the increase of temperature will decrease the solubility constant Ks [97], which means when the temperature increases the solubility of La(OH)3 in water decreases.

o Based on the above analysis, the solubility increase of La2O3 when temperature at 40 C and 60 oC may probably due to the experimental error: (1) caused by sample contamination from the environment during the test, (2) contamination from the ICP capillary from the previous high concentration ICP standards during the test, (3) The sample analysis error from the ICP-MS test, because the measurement of ICP-MS is highly sensitive with the temperature, pressure change in the system.

o o From the above analysis, the two unreasonable point (40 C, 80 C) of La2O3 solubility measurements are omitted. The solubility of three lanthanide oxide species in 1000 ppm

39 boric acid, 2 ppm LiOH water shows no significant temperature dependent under low

o temperature (less than 100 C). The average solubility of Nd2O3, La2O3 and CeO2 is about

251.2 ppb, 57.9 ppb, 4.6 ppb separately in 1000 ppm boric acid, 2 ppm LiOH water. Also, the increasing of boric acid concentration in the solution will increase the solubility of rare earth oxide in the solution, which during the reactor accident condition, the dissolution of low-volatile and semi-volatile fission products in the solution can be increased significantly.

Table 3 Solubility measurement of RE oxides in Boric acid water in different temperatures (1000 ppm boric acid and 2 ppm lithium hydroxide)

Boric acid: 1000 ppm, LiOH 2 ppm Temperature Concentration (ppb) Concentration (µg/L) o ( C) La Nd Ce La2O3 Nd2O3 CeO2 20 65.5 253.8 4.772 76.9 296.5 5.9 40 2881.5 192.9 4.657 3381.8 225.3 5.7 60 695.6 290.7 4.52 816.4 339.6 5.6 80 57.97 257.5 5.272 68.0 300.8 6.5

Table 4 Concentration verification for La and Nd

Sample batch A Sample batch B Error (%) La (20 oC) 65.5 64.6 1.37 Nd (80 oC) 257.4 257.6 0.1

40 2.2 Diffusion coefficient measurement of cesium iodide (CsI) in simulated LWR

coolant chemistry using NMR technique.

Many method can be applied to measure the diffusion coefficient in aqueous solution, such as Taylor Dispersion Analysis (TDA)[95], electrochemical technique [96], conductivity measurement for derivation of the diffusivity [79], and also the Nuclear Magnetic

Resonance (NMR) spectroscopy [97] measurement of the diffusivity.

Taylor dispersion method is based on that solvent is transported by convection and diffusion, the axial spreading is due to the radial diffusion and convection which will results in the injected solute pulse developing a symmetrical concentration distribution. The basic governing equation is shown in (15) and (16) [95]:

푑퐶 푑2퐶 (15) = 푘 푑푡 푑푥2

푟2푢2 (16) 퐷 = 48푘

Where

C = Concentration of a certain chemical species

r = capillary radius

u = mean speed of the fluid flow

41 k = dispersion coefficient

The electrochemical method is based on the redox couples in the solution which has already been discussed above. During the electrochemical test, the current of some electrode reactions are diffusion controlled, the diffusion controlled process typically has the following relationship which is shown in equation (17) and (18) [96]:

휕퐶(푥,푡) 퐽 = −퐷 (For one dimension) (17) 휕푥

푖(푡) = −푛퐹퐴퐽(0, 푡) (18)

where

A = Electrode area

F = Faraday constant

n = Stoichiometric number of electrons involved in the electron transfer reaction

Conductivity measurement is another method to get the diffusion coefficient. The relation between the ionic equivalent conductivity and diffusivity is given by Nernst-Einstein equation shown in equation (19) [79]:

퐹2 (19) Λ0 = 푧2퐷 ( ) 푚,𝑖 𝑖 𝑖 푅푇

where

42 zi = Charge number of ion i

T = Temperature

F = Faraday’s constant

R= Universal gas constant

Di = Diffusion coefficient of ion i

0 Λ m,i = Molar conductivity of ion i

The base of Nuclear Magnetic Resonance (NMR) spectroscopy is that many nuclei have spin and they are all electrically charged. The energy will transferred between the base energy and higher energy level if apply an external magnetic field.

There will a signal generated for this energy transfer which will be processed to yield an

NMR spectrum for the nucleus concerned. For diffusion coefficient measurement,

Diffusion Ordered Spectroscopy (DOSY) is always used. The NMR signal intensity is attenuated depending on the diffusion time, Δ, and the gradient parameter, δ, g, as described by equation (20) [81], [84]:

−퐷훾2푔2훿2(∆−훿/3) (20) 퐼 = 퐼0푒

where

I = Observed intensity

43 I0 = Unattenuated signal intensity

Δ = Diffusion time

δ = Gradient length

g = Gradient strength

γ = Gyromagnetic ratio of the observed nucleus

All of the four methods has advantages and disadvantages. TDA and NMR are both widely used, but diffusion coefficient measurement of NMR is also depends on the solubility of the chemical in the solution. Electrochemical technique involves the redox species formation which is not easy to form in low ionic aqueous solution, and conductivity measurement yield the largest uncertainty because the solution is easily contaminated by various chemical in the environment. Since cesium iodide has very negative redox potential

(−3.026 V vs SHE) which is impossible to use electrochemical method, the large solubility of CsI in aqueous solution makes NMR the best method to get the diffusion coefficient.

2.2.1 Experimental of diffusion coefficient measurement.

(1) Standard preparation. Clean the NMR tubes using acetone and died in air

with caution.

(2) Dissolve the cesium nitrite standard in to heavy water (D2O), deuterium can

be used for field frequency lock make the spectrum resolution better.

Deuterated solvents can also avoid the spectrum broadening by regular

hydrogen. Therefore, use deuterium oxide to dissolve the solute.

44 (3) Prepared the cesium iodide solution (0.01 M, 0.1M, 0.2M, 0.4M, 1M) in

boric acid and lithium hydroxide water.

(4) Measure the diffusion coefficient i Chemical and Biomolecular Engineering

and Chemistry Building in OSU.

2.2.2 Diffusion coefficient data analysis.

The diffusivities are measured in Dept. Chemistry and Biochemistry, the Ohio State

University. The Bruker Advance III HD 600 NMR facility is employed for the measurement. Before the Cs+ diffusivity measurement, gradient strengths were calibrated by running DOSY experiments using 1% H2O/D2O sample, in which the diffusion coefficient of the monodeuterated water (HOD) will be measured and compared with the literature data to make sure the diffusivity measurement results are reliable. The calibration result shows the doped water diffusivity in 25 oC is about 1.66×10-9 m2/ s, the doped water diffusivity from previous measurements is reported as 1.91×10-9 m2/ s [98], [99]. Though there is some difference between the calibration value and the reference value, the difference between the measurement and reference data is acceptable, which means the

NMR facility is ready to for DOSY measurement.

After the facility calibration, the diffusivity of 0.1 M cesium nitrite (CsNO3) dissolved in deuterium oxide (D2O) standard is measured. The reason using deuterium oxide as the solvent is because NMR spectra are recorded for compounds dissolved in a solvent, the using of deuterated solvent instead of the ordinary 1H-containing solvent can avoid the

NMR signal disturbed by ordinary solvent [80], [81], [97].

45 + The Cs diffusivity of 0.1 M CsNO3 in D2O standard is measured for two times, the first measurement shows the Cs+ diffusivity is about 3.078×10-11 m2/s under 26.9 oC. The

+ second measurement is conducted 8 days later, result shows Cs diffusivity of 0.1 M CsNO3 standard is about 2.78×10-11 m2/s under 25 oC. The diffusivity fitting curves of two 0.1 M

CsNO3 standard is shown in Figure 5. The difference in operation temperature is due to the facility adjustment issue. The two separate measurements show a small difference of the

Cs+ diffusivity, since diffusivity is temperature dependence, therefore the difference is reasonable and the standard measurement also indicate the correctness of Cs+ diffusivity measurement experimental set up.

+ After get the Cs diffusivity of 0.1 M CsNO3 standard, the diffusivity of different CsI samples in 1000 ppm H3BO3, 2 ppm LiOH can be measured use the same experimental set up and the diffusivity is obtained by shimming tuning [99] because of the presence of ordinary 1H. The diffusivity fitting curve of 1M CsI is shown in Figure 6. The decaying of the curve represents the signal attenuation due to ion diffuse in NMR facility. A summary of the diffusivity of Cs+ is shown in Table 5.

+ o o Figure 5 Cs diffusivity of 0.1 M CsNO3 D2O based standard (left: 26.9 C, right: 25 C)

Figure 6 NMR signal attenuation fitting curve for 1 M CsI sample

47 Figure 6 shows the fitting result of attenuated NMR signal of the Cs+ during the setting diffusion time. The diffusivity of Cs+ can be obtained from equation (20) by NMR signal data fitting.

Table 5 Cs+ self-diffusivity measurement for different CsI concentration

Fit diffusivity of Cs in Sample concentration sample solution (M) (× 10-11 m2/s) 0.01 3.368 0.1 3.111 0.2 2.693 0.4 2.753 1 3.293 Average : 3.04 × 10-11 m2/s

Figure 7 Cs+ self-diffusivity measurement for different CsI concentration

48 Table 6 NMR DOSY measurement results comparison

The diffusion coefficient depends on many factors: molecular shape, molecular size, solvent viscosity, solution properties as salt concentration, pH, temperature, etc [96].

Therefore the diffusivity difference between the Cs+ in this work and reference work [79] may due to different reasons:

(1) Quite different solution composition. The addition of 1000 ppm and 2 ppm LiOH

will possibly result the Cs+ bounding and interaction will boric acid molecules

which will result a decrease of Cs+ diffusivity. Study of 5.53 mM CsCl and 27.67

-10 mM SC4 mixture result a Cs+ diffusivity about 1.28× 10 m2/s by NMR

measurement, which proves the different solution composition can influence the

diffusivity of Cs+ [100].

(2) pH difference can result a diffusivity difference. The CsI solution based on boric

acid and lithium hydroxide result a pH about 6.9~7.2 for different CsI

concentration. However the pH in reference work is not reported which should be

different from the pH in this study.

49 (3) Different measurement method. This work use NMR DOSY measurement which

is high accuracy, the reference work from conductivity measurement in1996, the

different measurement methods could lead to different error in Cs+ diffusivity.

(4) Temperature difference between this work (26.9 oC) and reference work (25.3 oC).

Ion diffusivity is sensitive to temperature change, the two difference temperatures

will probably influence the difference in diffusivity.

From the above analysis, the NMR diffusivity measurement of Cs+ in boric acid water is reliable. Figure 7 and Table 6 shows Cs+ diffusivity in sample solution shows no significant concentration dependent features. The average Cs+ diffusivity is about 3.04 ×

10-11 m2/s. Cs+ diffusivity in free water is about 100 times larger than Cs+ in boric acid solution around room temperature.

50 Chapter 3. Cesium release model development

During reactor operation process, defects will appear on the fuel claddings. The defects on a Zircaloy-clad are resulted from various reasons, such as the hydriding of the Zr clad, the grid fritting from the assembly support, the wrap wire fritting with the clad, pellet-cladding interaction (PCI) and the induced stress corrosion cracking (SCC). The defects on the fuel cladding will result in the entering of coolant water into fuel cladding interior region. When water interact with the cladding inner surface, it will cause cladding hydriding, increase the cladding embrittlement resulting a less protective fuel cladding for the nuclear fuel, since fuel cladding is the second barrier prevent radioactivity nuclides or material releasing. The defects on fuel cladding has been reported to BWR, CANDU reactor and also PWR. The ingress of water into the gap will also lead to the depressurize of the gap, the fission gas such as Kr and Xe will accumulated in the gap, together with the plenum gas helium to offer a high gap thermal conductivity in order to transfer the heat generated from the fuel to the coolant efficiently. However, when the defects formed on the fuel cladding, the connection between the gap and coolant water will lead the heat transfer less efficiently.

The contact of water with high temperature fuel will also lead to the fuel oxidation which will also decrease the fuel thermal conductivity and increasing the fuel melt risks.

Besides, the defects on the cladding offer a path for the escape of radioactive material release to the coolant, such as the fission gas Kr and Xe, the increasing of oxygen to metal

51 (O/M) ratio after fuel oxidation the diffusivity of fission products can be enhanced, let the high volatile fission products Cs and I transport from fuel to the coolant. The larger the fuel temperature, the more the fuel will be expanded, the more the high volatile fission products transport to the coolant. Therefore, the defective fuel behavior is very important for reactor safety. In this work, cesium release is modelled using MOOSE/BISON software package developed by Idaho National Laboratory.

MOOSE is developed to solve various coupled variable problems even largely coupled variable and large time scale problem using Jacobian-free Newton-Krylov (JFNK) mathematical principles. Based on the excellent performance of MOOSE, BIOSN is developed for modelling the nuclear fuel performance. BISON is a finite element based code, and has large capacity and ability to solve different fuel behavior problems, such as

UO2 fuel for LWR, the TRISO-coated particle fuel for High Temperature Gas Reactor, the plate-type fuel. The primary purpose of BISON is solve coupled system of partial differential equations, those equation represent important physics related engineering scale nuclear fuel behavior. Fuel simulation in BSION typically consist of solving the energy momentum, mass conservation equations. Those equations are solved simultaneously using the finite element method (FEM) and JFNK approach on a discretized domain. The domain typically will represent the physical object will be modelled, such as the fuel block or the cladding, etc. Kernels, boundary conditions, material properties and many other blocks are consist the BISON input. Since BISON is based on MOOSE, therefore, BISON has all the modules which is developed in MOOSE, and has its own modules for nuclear fuel behavior modelling. The unique modules in BISON including plenum pressure,

52 coolant channel, mechanical contact between cladding and fuel, gap heat transfer module, material tensor module, fission rate module to calculate the fission rate during the burnup, burnup calculation module, neutron heat source calculation, arrhenius diffusion, nuclear materials block, fuel creep model, fuel irradiation module, fuel relocation model, etc.

BISON is a powerful tool for nuclear fuel behavior modeling, the modeling work in this work is depending on BIOSN and MOOSE in combination of the development of own kernels.

For nuclear fuel element, the volatile fission products can release from the fuel matrix into the gap between the fuel and cladding, when a defect appears on the cladding, the volatile fission product can migrate and transport from the gap to the defect and them release to the coolant. Research shows that diffusion is the dominant process of transporting the fission products within the fuel and clad-fuel gap [49], [61], [62], [101]. During the normal reactor operation, the gap pressure will increase with the increasing of burnup due to the releasing of fission products in the gap, the convective force by the increasing of pressure will not significantly contribute the fission product release [61]. During the modeling process of the fission product release, it is important to understand of the source tern from the fuel and their transport in the fuel-clad gap. The cesium release model is highly depend on the nuclear fuel behavior, a time-dependent solution of temperature distribution, the fuel oxygen-to-metal ratio and cesium release through a defect should be considered for the model. A schematic fission product of physical/chemical process in defective fuel is shown as Figure 8 [65].

Figure 8 Schematic of physical/chemical process in defective fuel [65]

3.1 Model development-fuel oxidation

Since the release of cesium from the fuel is temperature and time dependent, also the properties change during fuel burnup will also affect the volatility of fission product which has been already discussed previously. When the fuel clad is defected, water will ingress to the gap and contact with fuel, therefore, the cesium transport in the fuel matrix and the water mixture in the gap should be considered. When cesium transport to the fuel outer surface, the amount of cesium contact with water will dissolves or react with water, then the dissolved species will transport from the fuel outer surface-coolant boundary to the bulk solution. The amount of the fission products transport to the bulk is depends on the diffusion of cesium in the fuel-water interface boundary diffusion layer.

54 When the fuel cladding defected, the reaction between fuel and water will lead to the fuel metal-to-oxygen ratio changed, therefore, affect the fuel time dependent temperature, also, the water will react will the zircaloy cladding to produce hydrogen and in return affect the fuel temperature, therefore, the basic reaction between water-fuel and water-cladding should be considered first before develop the cesium release model.

When the water contact with the high temperature uranium oxide fuel, the basic reaction shown in equation (14) is considered [65]:

UO2 + xH2O ↔ UO2+x + xH2 (21)

For the oxygen reaction and oxygen transport in the fuel matrix and the interstitial transport, the normal diffusion due to the oxygen concentration gradient in the fuel matrix and the Soret effect due to the temperature gradient in the fuel matrix should be considered.

Soret effect is that the drive force of diffusion of a certain species in the matrix is temperature gradient [102][103]. The rod type fuel pin in LWR has the highest temperature in the centerline, and lowest temperature distribution in the fuel outer surface. The fuel water reaction and mass balance considering oxygen transport in the fuel is given by equation (22) and (24) [65]:

55 휕푥 푄 (22) 푐 = 푐 훻⃗ ∙ (퐷 (훻푥 + 푥 훻푇)) + 𝜎 푅푟푒푎푐푡 푈 휕푡 푈 푅푇2 푓 푓

where x is the stoichiometry deviation in UO2+x which indicates the oxygen reaction with

3 the UO2 fuel. cU is the molar density of uranium oxide fuel, in the unit of (mol/cm ). σf is the ratio of surface area of cracks of fuel to the unit volume of fuel (m-1) when the fuel

react body is cracked. Rf represents the reaction rate between fuel and water [65]. The kinetic reaction rate can be obtained by employing a surface-exchange model, the reaction rate

-1 -1 (molm s of O or H2) is given as [65]:

푟푒푎푐푡 (23) 푅푓 = 푐푈훼√(1 − 푞)푝푡(푥푒 − 푥), 푓표푟 푥 < 푥푒

where xe is the equilibrium stoichiometry deviation in UO2+x related the local oxygen potential in fuel cracks,  in equation (24) is the surface-exchange rate of oxygen (cm s-1) when the fuel temperature at T (K),  = 36.5 exp(-23500/T), pt indicates the total system pressure in fuel (atm). The diffusion coefficient of oxygen is given by equation (24) [65]:

퐷 = 2.5 exp(−16400/푇) (cm2 s-1) (24)

Q is the molar effective transport heat of oxygen in fuel matrix, which is originated from oxygen redistribution model (OXIRED) in TRANSURANUS code, the transport heat to drive the oxygen diffusion in fuel matrix is given by equation (25)[65]:

56 푄 = −3.5 × 1034exp(−68 + 34푥) (J mol-1) (25)

Although, the oxygen redistribution model is developed for U-Pu oxide fuel, however, the transport heat shows less dependent on the plutonium content in the fuel, therefore the above transport heat can be applied to UO2 fuel. The equilibrium stoichiometry deviation xe can be expressed in the following expression which is from the equilibrium thermodynamic analysis for the uranium-oxygen system[65]:

푎 + 푐휁 + 푒푇 + 푔휁2 + 푚푇2 + 푘휁푇 (26) 푥 = ( ) 푒 1 + 푏휁 + 푑푇 + 푓휁2 + 푝푇2 + 푛휁푇

where the parameters are: a = 0.033107, b = 0.268985, c = 0.0086795, d = -6.222 × 10-4, e

= -5.188 × 10-5, f = 0.020038, g = 4.5017 × 10-4, k = -7.8344 × 10-4, m = 1.842 × 10-8, n =

푞 -7.452 × 10-5, p = 1.3906 × 10-7, and 휁 = log ( ), where q is the hydrogen production 1−푞 mole fraction in the fuel cracks which will be evaluated in equation (27).

3.2 Hydrogen transport in fuel cracks

During the reaction between fuel and water, hydrogen will produced during the process which is shown in equation (14). The partial pressure ratio result from the hydrogen to steam ratio in the fuel is q/(1-q), which will affect the oxygen potential in equilibrium state in the fuel from equation (26), and also will govern the equilibrium stoichiometry xe in

UO2. Typically, UO2 fuel has porosity  which is defined as the ratio of pore volume in the

57 fuel and the fuel volume. Therefore, equation (27) shows the mass balance of hydrogen in fuel gap during the process [65]:

휕(푞푐푔) (27) 휀 = 휀훻⃗ ∙ (푐 퐷 훻⃗ 푞) + 𝜎 푅푟푒푎푐푡 휕푡 푔 푔 푓 푓

where 휀 is fuel porosity, q is hydrogen mole fraction of the total gas in the fuel-clad gap. cg is the total molar concentration of gas in the gap which the ideal gas law can be applied that cg = pt/RTg , Tg is the average gap temperature, and R is the universal gas constant and pt is the total gap pressure. And cgDg is solved by Chapman-Enskog equation shown as equation (28) [65]:

(28) 1 1 √푇 ( + ) 푀퐻2 푀퐻2푂 −3 푐푔퐷푔 = 2.2646 × 10 2 𝜎퐴퐵Ω퐴퐵

where 푀퐻2, 푀퐻2푂 are the molecular weight of H2 and H2O separately, 𝜎퐴퐵 is the average radius of H2 and H2O, Ω퐴퐵 is the e collision integrals between H2 and H2O.

58 3.3 Heat generation and conduction in the fuel and clad

Temperature distribution over the fuel is required to solve all the parameters in equation

(22) to (27) because the oxygen-fuel reaction and mass transport in the fuel are temperature dependent. Typically, for a nuclear fuel pin heat conduction, the heat transfer from the fuel pellet to the gap and the coolant should be considered, as well as the feedback effect result from the thermal conductivity change due to the fuel oxidation in the hyper-stoichiometric fuel [65]. The cladding outside temperature Tso, cladding inner temperature Tsi and surface temperature is from the analysis in [65] for a typically LWR fuel rod. The temperature distribution in the fuel element can be solved by the heat conduction equation (29) [65]:

휕푇 (29) 𝜌 퐶 = 훻⃗ ∙ (푘훻⃗ 푇) + 푄 푠 푝 휕푡 푉

-1 -1 where 𝜌푠 is fuel density, 퐶푝 is the fuel specific heat (J mol K ), 푘 is the fuel thermal conductivity, 푄푉 is the volumetric heat generated in the fuel. The thermal conductivity k depends on the fuel properties, i.e. the oxygen stoichiometry deviation 푥. Besides, the fuel density and fuel specific heat is also temperature dependent. The temperature dependent properties of UO2 is shown as (30) [65]:

59 −3 −2 퐶푝(푥, 푇) = 52.174 + 45.806푥 + (87.951 × 10 − 7.3416 × 10 푥)푇 + (30)

+(1 − 푥){−84.241 × 10−6푇2 + 31.542 × 10−9푇3 − 2.6334 × 10−12푇4} −

−(713910 + 295090푥)푇−2

The fuel density can be expressed as [65] equation (31) and (32):

−6 −10 2 𝜌푠(푇) = 𝜌푠(273퐾) × (0.99734 + 9.802 × 10 푇 − 2.705 × 10 푇 + 4.391(31)

× 10−13푇3)−3,

273퐾 < 푇 < 923퐾

−5 −9 2 𝜌푠(푇) = 𝜌푠(273퐾) × (0.99672 + 1.179 × 10 푇 − 2429 × 10 푇 + 1 .219 (32)

× 10−12푇3)−3, 푇 >> 923퐾

The fuel thermal conductivity of UO2 fuel is affected by many effects, which is shown as

[65]:

푘 = 푘1푑푘1푝푘2푝푘4푟(푘푝ℎ + 푘푒 + 푘푟푎푑) (33)

where 푘푝ℎ the heat transfer coefficient induced by lattice vibration (phonons), 푘푒 accounts for the eletron-hole pair movement, 푘푟푎푑 results from the fuel irradiation thermal effects.

The left four parameters result from the correction of fuel burnup and the fuel porosity: 푘1푑

60 in induced by dissolved fission products in fuel, 푘1푝 results from the fission product precipitation during burnup, 푘4푟 accounts for the radiation damage, and 푘2푝 is due to the fuel porosity correction. For a UO2 fuel, during reactor normal operation process, the influence of radiation thermal effects (푘푟푎푑) is neglected because it contributes very small amount of the overall thermal conductivity, about 0.01%.

In the meantime, the contribution of phonon (푘푝ℎ) in the fuel lattice is a dominant effect on thermal conductivity which will result the lattice defects and phonon self-scattering when fuel temperature is under 3000 K. This factor is a combination of stoichiometry deviation and fuel and the impurity materials in the fuel matrix. To describe 푘푝ℎ, the Ellis-

Porter-Shaw model can be applied when the stoichiometry deviation from 푥 = 0 ~0.2 which is shown as equation (34) [65]:

1 (34) 푘 = kW m−1K−1 푝ℎ 퐴(푥) + 퐵(푥)푇

Where

퐴(푥) = 14 − 10.763√푥 − 2381.4푥 + 12819.86(√푥)3 (35)

61 퐵(푥) = 0.2218 + 0.2562√푥 − 0.64푥 − 3.6764(√푥)3,when 푥 < 0.155 (36)

When 푥 > 0.155, 퐵(푥) = 0

The contribution of electron movement for the thermal conductivity is shown as equation

(37) [65]:

2.024 × 108 16350 (37) 푘 = (0.871 + 2.5 × 10−5푇)−1 × exp (− ) kW m−1K−1 푒 푇2.5 푇

The correction of fuel porosity is using Loeb expression which is shown as equation

(38)[65]:

푘2푝 = (1 − 훽푇푃표푟) (38)

−3 where 훽푇 = 2.6 − 0.5 × 10 푇 (퐾), is result from the temperature effect. The porosity is

calculated from equation (38)[65]:

푃표푟 = (1 − 𝜌푠/𝜌푇퐷)(1 − 퐹퐷) (39)

62 -3 where 𝜌푠 is fuel density, 𝜌푇퐷 is fuel theoretical density of UO2 which is 10.96 g cm .

During the duel burnup, the duel densification effects should be accounted, which can be corrected by (1 − 퐹퐷), where 퐹퐷 is porosity faction change in fuel which is related to temperature T (K) and fuel burnup B (MWh (kgU)-1) shown as equation (40) [65]:

−10 3 −2 퐹푑 = 0.6 − 푒푥푝(−0.506 − 8.67 × 10 푇 ) × [1 − exp (−2.87 × 10 퐵)] (40)

The correction of dissolved fission product in the fuel is given by equation (41) [65], where

β is the burnup in unit of atom fraction (atom %), which can be converted from the burnup

(MWh (kgU)-1): 1 atom % ~ 225 MWh (kgU)-1 :

1.09 0.063 1 (41) 푘 = ( + √푇) × 푎푟푐푡푎푛 ( ) 1푑 훽3.265 1.09 √훽 + (0.0643/√훽)√푇 훽3.265

For the influence of precipitate fission products in the fuel k1p, is described as equation (42)

[65]:

0.019훽 (42) 푘 = 1 + 1푝 (3 − 0.019훽)(1 + 푒푥푝(1(푇 − 1200)/100))

63 Since the impacts of dissolved fission products in fuel is very small which can be neglected when calculating thermal conductivity of fuel. The correction of radiation damage to the thermal conductivity is given by (43) [65]:

0.2 (43) 푘 = 1 − 4푟 (1 + 푒푥푝((푇 − 900)/80))

This model has been verified by the Halden Reseach Project when theoretical density is about 95% of the theoretical density when the burnup is (67 MWd(kgU-1) [65].

3.4 Cesium release from the defective fuel

As discussed previously, the transport of fission products in fuel and bulk are mainly due to the diffusion of fission products in fuel matrix and also in the clad to gap. The fission products diffused to the fuel outer surface will react with water in the fuel-gap water boundary layer, then the dissolved fission product can diffuse through the boundary layer to the cladding outer surface.

When the cladding is defected, water will ingress into the gap, which may cause a bulk velocity in the gap region, which may force a convective transport of fission product in the bulk and enhance the dissolve process and transport of fission product to the cladding outer surface. Previous study show that, when the fuel element linear power is about 50 kW/m, when the bulk temperature is about 700 K with a average pressure of 10MPa, the bulk velocity flow velocity is estimated about 푣 = 1.37 × 10−7 푚/푠 by Hagen-Poiseuille flow

64 law, the corresponding bulk steam viscosity of 휇 = 2.67 × 10−5 푘푔/(푚 ∙ 푠), and the

Reynold’s number is calculated as 푅푒 = 3.6 × 10−6, which indicate that the bulk flow in the gap is laminar flow[61]. Since the gap flow velocity is very small and also the laminar flow, the fission product transport by convective flow can be neglected, therefore, the diffusion process will dominant the fission product release to the coolant. The diffusion coefficient of the fission product in the gap steam-fluid mixture is given by equation (44)

[61]:

(44) −7 3 푚1 + 푚2 1.8583 × 10 √푇 ( 푚 푚 ) 퐷 = 1 2 푃𝜎2

2 where D is the diffusion coefficient in the gap (m /s), m1 and m2 are the molecular weight of H2O and fission product (g/mol), P is the average gap pressure about 10 MPa, T is the average gap temperature about 700K, 𝜎 is the molecular potential energy parameter =

3.2 Å, therefore, use equation (44), the diffusion coefficient of the fission product in the gap water mixture can be calculated about 8.6 × 10−7 m2/s [61].

The fission products diffusion in the fuel is shown as equation (45)[61]:

휕푛 (45) = 푞(푟, 푡) − 휆푛(푟, 푡) − 훻⃗ ∙ 퐽 (푟, 푡) 휕푡

65 where n is the atomic concentration (atoms m-3)of a fission product in the fuel, q(r, t) is the production rate of fission product in time t point r, λ is the decay constant for fission product species, J(r, t) is the fission product flux through a unit area [61]. Since the convective contribution to fission product transport is neglected, the fission product flux [61]:

퐽 (푟, 푡) = −퐷훻⃗ 푛 (46)

The fission product birth rate q(r, t) can be regard as a constant during the fuel burnup.

During fuel burn up, cesium mainly has three fission product isotopes: Cs-135, Cs-133,

Cs-137. Cs-137 The fission yield of three cesium isotope is shown in Table 7 [104],since the half-life of Cs-135 is about 2.3 million years, the other cesium fission product isotope

Cs-137 has with the half-life of 30.05 years, Cs-133 is a stable nuclide which will not contribute to the radioactive decay. Therefore the decay constant of Cs can be estimated as

휆 ≈ 3.58 × 10−10 푠−1.

Table 7 Relative and absolute fission yield of cesium isotopes occurring in the thermal neutron fission of U235 [107]

Relative Absolute fission yield Isotope yield Experimental value Katcoff and Rubinson Cs133 1.072 6.59 6.62 Cs135 1.043 6.41 6.40 Cs137 1.000 6.15 6.07

66 The fission product flux[61]:

J(r, t) = −D훻⃗ n

where D is the diffusion coefficient of cesium in fuel matrix. The diffusion coefficient of cesium is a function of temperature T (K) and stoichiometry deviation x, is shown in the following expression in equation (47) [105] which is called Booth diffusion model:

퐷 = 퐷(푇) + 퐷(푥, 푇) (47)

where D(T) is intrinsic diffusion coefficient given by equation (48) [61]:

−7.0 × 10−4 (48) 퐷(푇) = 7.6 × 10−10푒푥푝 { } 푅푇

D(x,t ) is the enhanced uranium vacancy production term, shown as equation (49)(47) [61]:

−푄 퐷(푥, 푇) = 퐷 푥2푒푥푝 { } for 푥2 ≫ 4퐹 (49) 0 푅푇 0

4 where 퐹0 = 푒푥푝{−7.13 × 10 /푅푇} which is corresponding to Schottky and Frenkel defect

−11 2 −1 [105]. D0 is binary diffusion coefficient is about 퐷0 = 6.1 × 10 푚 ∙ 푠 , Q is the

67 activation energy about 7.13 × 104 J mol-1 [59].Therefore the diffusion of cesium in fuel can be described as [61]:

휕푛 (50) = 푞(푟, 푡) − 휆푛(푟, 푡) − 훻⃗ ∙ (퐷 ∙ 훻푛) 휕푡

When the cesium fission product on the fuel surface contact with water, it will dissolves in the water very quickly, then the cesium will diffusion through the boundary layer to the coolant side, the cesium diffusion out of the fuel outer surface will diffuse to the bulk coolant, therefore, the diffusion of cesium in the bulk flow in the gap is shown as equation:

휕푛(푟,푡) = 퐷훻2푛(푟, 푡) (51) 휕푡

The boundary condition is given by 푛(푅, 0) = 푛0, which means the cesium on the fuel surface will diffuse to the coolant.

3.5 BISON Kernel development.

To use MOOSE/BIOSN to develop the kernels needed to solve the above coupled PDES, first, using the JFNK method to form a “weighted residual” or “variational statement” or

“weak form”. A weak form is what is needed to input into MOOSE in order to solve the problem. The following steps are summarized for generating a weak form [76].

(1) Write down the strong form (original PDE form) of PDEs.

(2) Rearrange terms so that zero is on the right of the equals sign.

68 (3) Multiply the rearranged equation by a “test” function (ψ).

(4) Integrate the whole equation over the domain (Ω).

(5) Integrate the whole equation by part, which typically will involve the divergence

theorem to get the desired derivative order on the functions and simultaneously

get the boundary integrals.

(6) MOOSE depends on C++, therefore, code the above integrated functions, after

testing the correctness of the kernels, the input file can be generated by following

certain patterns using a script editor or “peacock” in MOOSE. Then run the input

file on MOOSE or BISON to get the modeling result.

To specify the kernel development of MOOSE/BISON in detail, the development process of the fuel oxidation governing equation (22) is discussed in detail.

By following the kernel development steps shown above, firstly, write down the strong form of equation (22) which is just equation (22). Rearrange the terms of equation (22) and multiply the test function ψ and then integral the equation over domain Ω shown as:

휕푥 푄 (52) 푐 − 푐 훻⃗ ∙ (퐷 (훻푥 + 푥 훻푇)) − 𝜎 푅푟푒푎푐푡 = 0 푈 휕푡 푈 푅푇2 푓 푓

multiply the test function 휓 to each term, yield:

휕푥 푄 (53) 푐 ∙ 휓 − 푐 훻⃗ ∙ (퐷 (훻푥 + 푥 훻푇)) ∙ 휓 − 𝜎 푅푟푒푎푐푡 ∙ 휓 푈 휕푡 푈 푅푇2 푓 푓

= 0

69 Integrate the equation over domain Ω, yields:

휕푥 푄 (54) ∫ 푐 ∙ 휓 − ∫ 푐 훻⃗ ∙ (퐷 (훻푥 + 푥 훻푇)) ∙ 휓 − ∫ 𝜎 푅푟푒푎푐푡 ∙ 휓 = 0 푈 휕푡 푈 푅푇2 푓 푓

Apply the divergence theorem to the second term in equation (54)

푄 (55) ∫ 푐 훻⃗ ∙ (퐷 (훻푥 + 푥 훻푇)) ∙ 휓 푈 푅푇2

푄 = ∫ 푐 훻⃗ ∙ (퐷훻푥) ∙ 휓 + ∫ 푐 훻⃗ ∙ (퐷 ∙ 푥 훻푇) ∙ 휓 푈 푈 푅푇2

Using the divergence theorem, yields,

푄 (56) ∫ 푐 훻⃗ ∙ (퐷훻푥) ∙ 휓 + ∫ 푐 훻⃗ ∙ (퐷 ∙ 푥 훻푇) ∙ 휓 푈 푈 푅푇2

= 푐푈 ∫ 훻⃗ ∙ (휓 ∙ 퐷훻푥) − 푐푈 ∫ 훻⃗ 휓 ∙ (퐷훻푥) +

푄 푄 푐 ∫ 훻⃗ ∙ (휓 ∙ 퐷 ∙ 푥 훻푇) − 푐 ∫ 훻⃗ 휓 ∙ 퐷 ∙ 푥 훻푇 푈 푅푇2 푈 푅푇2

equation (56) will yields,

70 푄 ⏟〈휓 , 푐 퐷훻푥 ∙ 푛⃗ 〉 + ⏟(− 훻휓 , 푐 퐷훻푥 ) + 〈휓, 푐 퐷푥 훻푇 ∙ 푛⃗ 〉 푈 푈 ⏟ 푈 푅 푇 2 퐵표푢푛푑푎푟푦 푐표푛푑𝑖푡𝑖표푛 푘푒푟푛푒푙 퐵표푢푛푑푎푟푦 푐표푛푑𝑖푡𝑖표푛 (57)

푄 + (−훻휓, 푐 퐷푥 훻푇) ⏟ 푈 푅 푇 2 퐾푒푟푛푒푙

Therefore, the overall weak form of equation (22) is shown as:

휕푥 푄 (−휓, 푐 ) − ⏟〈휓 , 푐 퐷훻푥 ∙ 푛⃗ 〉 − ⏟(− 훻휓 , 푐 퐷훻푥 ) − 〈휓, 푐 퐷푥 훻푇 ∙ 푛⃗ 〉 ⏟ 푈 휕푡 푈 푈 ⏟ 푈 푅 푇 2 퐵표푢푛푑푎푟푦 푐표푛푑𝑖푡𝑖표푛 푘푒푟푛푒푙 푘푒푟푛푒푙 퐵표푢푛푑푎푟푦 푐표푛푑𝑖푡𝑖표푛 (58)

푄 − (−훻휓, 푐 퐷푥 훻푇) − (휓, 𝜎 푅 푟푒푎푐푡) = 0 ⏟ 푈 푅 푇 2 ⏟ 푓 푓 푘푒푟푛푒푙 퐾푒푟푛푒푙

Four kernels in total is derived from equation (22), the same deriving method can be applied to the rest three PDEs.

3.6 Model validation and cesium release result

The cesium release model is developed using MOOSE/BISON, to validate the applicable of the code, model validation is conducted to verify the self-developed kernels and also the

MOOSE/BISON code. Since the cesium release model is based on the fuel oxidation model developed by B. Lewis and J. Higgs [49], [61], [62], [65], [101], [106]–[110], the same fuel boundary conditions in [65] is used in this work to validate the model result. Ten fuel elements with different linear power and defect size located in different position is examined in [65], the fuel centerline temperature (maximum temperature) is compared

71 with the results in [65], the comparison is shown in Table 8. The temperature distribution from MOOSE/BIOSN results for fuel element K31 is shown in Figure 9.

Figure 9 Fuel radial temperature distribution for fuel element K31 of the model (radial cross-section view)

72 Table 8 Comparison of fuel centerline temperature between MOOSE/BISON results and reference work Maximum Maximum Fuel Centerline Centerline error(%) element temperature (K) temperature (K)[65] (This work) K31 1164 1151 1.12 K22 1387 1426 2.81 A18 2004 2088 4.19 X4 1816 1818 0.11 X5 1879 1697 9.69 M6 1584 1656 4.55 M14a 1652 1606 2.78 M14b 1905 1656 13.07 M11 1745 1811 3.78 M15 1848 1777 3.84

The results from MOOSE/BISON model show good consistent with the result in Ref. [65], however, since Ref. [65] only provide one set of the boundary condition during the simulation, the results from this work has some different with that in Ref. [65], Table 8 shows the largest different is about 13.07% for fuel element M14b, and 9.69% for fuel element X5, the smallest different is for fuel element K31 and X4, which the difference is about 1.12% and 0.11%. Though some results shows a relatively large difference, it still acceptable for engineering acceptable discrepancy. Figure 9 shows the temperature distribution of the cross section of fuel element K31 which is reasonable and the out surface temperature is 645 K which agrees with the result in Ref. [65] very well.

73 Besides, the temperature distribution, the stoichiometry deviation of fuel element K31 is also compared with the result in Ref. [65], shown as Figure 11 [65]. The oxygen to fuel metal ratio distribution of K31 is shown as Figure 10, the simulation result agrees with the result in Ref. [65], the center of the fuel has the largest oxygen stoichiometry deviation because the highest temperature in the center, and the near of defect site let more efficient for oxygen diffuse into the fuel. The average stoichiometry deviation of the fuel after 16 days with about 0.5 mm × 2mm defect size is shown as Figure 12. From the result, the fuel oxidation continue increasing over the time which is reasonable because more and more oxygen diffuse into the fuel matrix.

Figure 10 Fuel oxygen to metal ratio distribution of fuel element K31

Figure 11 Model predictions and O/M measurements for element K31 [65].

The fuel oxygen-to-metal ratio from the fuel centerline to the out surface from the

MOOSE/BISON model is shown in Figure 13, and the result in Ref. [65] is shown as Figure

11. The results of the fuel oxygen-to-metal ratio agrees with that in Ref. [65]. From all the results of temperature comparison, fuel oxygen to meatal ratio comparison and the fuel oxygen to metal distribution across the plane, results show the MOOSE/BISON model development is effective and validate.

75 Stoichiometry deviation after 16 days of 0.5 mm ×2 mm defect size 0.003

0.0025

0.002

0.0015

0.001

0.0005 Stoichiometry Stoichiometry deviation x 0 0 5 10 15 20 Time (day)

Figure 12 Average stoichiometry deviation of the fuel after 16 days with about 0.5 mm

×2 mm defect size

Fuel Oxygen To Metal Ratio 2.045 2.04 2.035 2.03 2.025 2.02

2.015 O/U Ratio O/U 2.01 2.005 2 0 1 2 3 4 5 6 mm from surface Fuel out surface Point on fuel

Figure 13 Result for MOOSE/BISON simulation of fuel oxygen to metal ratio radial distribution for K31 after the defect formed after 28 days

76 Based on the previous analysis, cesium transport model is coupled in with the previous fuel interaction with water model BISON/MOOSE. This model is based on Booth model, which has been already applied to the ASTEC (Accident source term evaluation code) in IRSN and CROSOR code. The modeling work has extend the MOOSE/BIOSN code in the field of defective fuel oxidation and fission products release.

When the fuel cladding defected, the coolant water will contact with fuel surface and result in the release of fission product in water. For cesium, the average escape of the fission product to water after the contact of fuel and water is about 9.88 × 10−4 푚표푙 푠−1 푚−3

[61], from Table 1 , the fission yield of Cs for U-235 is about 901 g/ t U after 1 year, by considering the UO2 fuel density and reactor core size, the fission product produce rate is about 2.236 × 10−9 푚표푙 푠−1 푚−3. Since the cladding defect will not appear on the cladding very soon after operation, the appearance of defects after 1 year is considered.

The fission product Cesium retention in the fuel after 1 year operation is about

63.85 푚표푙 푚−3. The fuel linear power is about 26 kW/m, result a fuel maximum temperature about 1050K.

Due to the pressure difference between fuel gap and system coolant pressure, and the fuel swelling may lead to the contact between fuel and cladding which all the factors will decrease the contact area of water and fuel after fuel defects appeared. Therefore, different water-fuel contact areas are examined to obtain the fission product retention/release to the coolant system, the contact areas of: zero contact, 1.25%, 2.5%, 5%, 12.5%, 25%, 50% and

100% (full contact) are modelled. Cesium molar concentration variation after water-fuel contact is shown as Figure 14. The Cs concentration distribution after 15 days when the

77 contact area for 12.5 % contact area and 100% fuel-water contact area is shown in Figure

15 and Figure 16. Based on the simulation, we can obtain the specific activity of Cs released to the coolant. The average decay constant of Cs isotopes is 휆 ≈ 3.58 × 10−10 푠−1. The cesium activity (Ci per kg UO2) releasing to the coolant is shown in Figure 17.

Figure 14 and Figure 17 indicate that, the larger the water-fuel contact area, the more releasing of Cs into the coolant. Since the diffusion coefficient of Cs in the fuel matrix is very small which is about 10−13 푚2 /푠. During the accident situation, when the fuel largely contact with steam atmosphere, Cs diffusion coefficient will be enhanced to several order of magnitude [11], which Cs will release to the coolant much quickly. Different diffusion coefficients are applied to the model to examine the Cs release during a diffusion enhanced environment. Cs diffusion coefficient in fuel in increased by 10 time, 20 times, 100 times,

1000 times are simulated for different fuel-water contact areas. The Cs retention in the fuel when increasing Cs diffusion coefficient and the fuel-water contact area is 12.5% is shown in Figure 18.

78 69 Cs retention in the fuel for different fuel-water

) 0 contact 3 67 contact area 1.25% contact 65 2.5% contact 63 5% contact 12.5% contact 61 25% contact 59 50% contact 100% conatct Cs Cs concentration in fuel (mol/ m 57

55 0 5 10 15 20 Time (Days)

Figure 14 Cs retention concentration in the fuel for different fuel-water contact area

3D view of 1/4 of the fuel pin 2D radial cross-section view of the ¼ fuel pin 3D view of 1/4 of the fuel pin in

Figure 15 Cs concentration distribution in the fuel after 16 days for fuel-water contact area 12.5% (Left: ¼ fuel, right: cross section view of the fuel)

79 3D view of 1/4 of the fuel pin 2D radial cross-section view of the ¼ fuel pin

Figure 16 Cs concentration distribution in the fuel after 16 days for fuel-water contact area 100% (Left: ¼ fuel, right: cross section view of the fuel)

Cs activity released to the coolant for different contact aera 5 ) 1.25% contact 2 4.5 4 2.5% contact 3.5 5% contact 3 12.5% contact 2.5 2 25% contact 1.5 50% contact 1 100% conatct 0.5 0 0 5 10 15 20 Time (day)

Activity Activity releasedthe tocoolant (Ci/kg (UO

Figure 17 Released Cs activity to coolant for different fuel-water contact area (Ci/ kg UO2)

80 Figure 19 shows that when increasing the diffusion coefficient to 100 times, Cs releasing to the coolant will the largely increased. The increasing of Cs diffusion coefficient is possible for high steam environment or the fuel melt to debris, which the contact area of fuel and coolant will largely increase, the releasing of Cs into the coolant could be very significant.

Cs retension in the fuel with different diffusion

70 coefficient ) 3 65

50 Diffusion Coefficient × 1 Diffusion Coefficient × 10 45 Diffusion Coefficient × 100 40 Diffusion Coefficient × 1000

35 Cs concentration (mol/ m fuel in Csconcentration 30 0 5 10 15 20 Time (day)

Figure 18 Cs retention concentration in the fuel for different diffusion coefficient

81 18 Cs activity released to the coolant for different 16 diffusion coefficient 14

12 Diffusion Coefficient × 1 ) 2 10 Diffusion Coefficient × 10

(UO 8 Diffusion Coefficient × 100 6 Diffusion Coefficient × 1000 4

2 (Activity released to the coolant (Ci/kg (Ci/kg coolantthe to released (Activity 0 0 2 4 6 8 10 12 14 16 18 Time (Day)

Figure 19 Released Cs activity to coolant for different Cs diffusion coefficient (Ci/ kg UO2)

From the above simulation results, Cs release model is developed based on a fuel-water interaction. Results indicate the model developed by MOOSE/BIOSN can is reasonable.

When the fuel defected, the contact of fuel and water will result a significant release of Cs to the coolant when the contact area is 5%. And the increasing of diffusivity will also result a significant increase releasing of Cs into the coolant.

82 Chapter 4. Summary

LWR is the most widely applied nuclear power plant type all over the world, reactor safety is the priority consideration of nuclear reactor energy development. When reactor accident happens, the reactor source term will be a radiological hazard if releasing to the containment building or even out of the containment building. However, during normal reactor operation, fuel defects can also occurred due to the fuel-pellet mechanical interaction, the hydriding of the Zr clad, the grid fritting from the assembly support, the warp wire fritting with the clad and also the stress corrosion cracking (SCC). When fuel cladding defects forms, water will ingress to the gap and react with nuclear fuel and the cladding inner surface, which will affect the fuel thermal properties and deteriorate the cladding hydride. The change of fuel thermal properties will decrease the thermal conductivity, lead the decrease of heat transfer coefficient which may increase the fuel melt risks. And the volatile fission products and fission gas will release to the coolant through cladding defects and increase the coolant activity and will be a radioactivity source term.

To understand the fuel behavior for a defective fuel pin, experimental and model development are applied to study the high volatile fission products release and transport into the coolant. The experimental part focus on the dissolution test of rare earth fission products in simulated LWR coolant chemistry and the diffusion coefficient measurement of cesium iodide in simulated LWR coolant chemistry. Though rare earth fission products

83 species are categorized as the low-volatile fission products, however, the changing of oxygen potential in the fuel will enhance the release of low-volatile fission products, besides, rare earth fission products significantly contribute the residual heat and large quantity of radioactivity after the core shut down or in severe accident, however, their dissolution kinetic parameters in LWR coolant is rare to find.

1. The solubility test of rare earth fission product species (La2O3, Nd2O3 and CeO2)

in simulate LWR coolant water (1000 ppm H3BO3 and 2 ppm LiOH) under different

temperatures (room temperature 23 oC, 40 oC, 60 oC and 80 oC), results show that

Neodymium oxide has the largest solubility in boric acid water and cerium oxide

has the lowest solubility, the addition of boric acid will significantly increase the

solubility of rare earth oxide in boric acid water.

2. The self-diffusion coefficient of cesium iodide in boric acid water is measured

using Nuclear Magnetic Resonance (NMR) technique, an average value about 3.04

× 10-11 m2/s is obtained which is about 100 times smaller than Cs+ in free water, the

large difference of Cs+ value from reference work can be caused by various reasons:

different solution composition, temperature difference, pH difference and also the

measurement method difference.

3. The long lived fission product cesium is considered for the modeling part because

their high volatility and relative fission yield also the high radioactivity. The cesium

transport and diffusion through the fuel matrix and release to the gap and coolant

is modelled based on a fuel oxidation model. MOOSE/BISON code developed by

Idaho National Laboratory is used to develop the cesium release model, the

84 oxidation model results from MOOSE/BIOSN agree with the results in reference

very well which validate the model development using MOOSE/BISON. The

cesium release model shows the time dependent cesium release after fuel defects

reside on the fuel cladding, the radioactivity release to the coolant will be

significant in the long term operation.

Also the simulation results indicate that, when the fuel-water contact area increases,

the releasing of Cs to the coolant will increase, when the contact area is about 5%,

the reactivity release to the coolant will significantly increase. When the diffusion

coefficient of cesium in fuel matrix is increasing, the releasing of Cs to the coolant

is also increase significantly, because the diffusion of Cs to the fuel out surface will

be faster. In reactor operation, the increase of cesium diffusion coefficient is very

possible due to the fuel crack, the porous structure of fuel will let more water

contact with fuel, can result an increasing the cesium to the coolant. When the

contact area is 100% percent, the activity releasing to coolant is about 4.4 Ci per kg

of UO2.

There are also some limitation in this work which could be done in the future:

1. High temperature and high pressure solubility test should be done to make a more

comprehensive solubility data base.

2. High temperature and high pressure Cs+ diffusion coefficient cannot be measured

from NMR DOSY technique, other methods should be used.

85 3. The Cs release model needs consider other volatile fission products release for

defective fuel, such as Iodine.

4. Chemical reaction model with fission product between Zr cladding could be

developed to evaluate Zr corrosion using BISON/MOOSE.

MOOSE/BISON are powerful tools to study nuclear fuel behavior during normal operation and accident situation. A more comprehensive fuel-water interaction model could be developed using MOOSE/BISON by combination of the fuel phase field model after the residence of defects on the fuel pin and the release of more volatile fission products such as iodine, tellurium, strontium and chemical reaction among fuel, water and fission products. Besides, the high temperature solubility and diffusion coefficient data of fission products in LWR coolant are very important in prediction fission products releasing of defective fuel or in reactor accident situation.

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