Acta Polytechnica CTU Proceedings doi:10.14311/AP.2016.4.0013 Acta Polytechnica CTU Proceedings 4:13–18, 2016 © Czech Technical University in Prague, 2016 available online at http://ojs.cvut.cz/ojs/index.php/app MODELLING OF NUCLEAR FUEL CLADDING TUBES CORROSION Miroslav Cecha, ∗, Martin Seveceka, b a Department of Nuclear Reactors, Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, V Holesovickach 2, Praha 8, Czech Republic b ALVEL a.s., Opletalova 37, Praha 1, Czech Republic ∗ corresponding author: miroslav.cech@post.cz Abstract. This paper describes materials made of zirconium-based alloys used for nuclear fuel cladding fabrication. It is focused on corrosion problems their theoretical description and modeling in nuclear engineering. Keywords: corrosion, zirconium alloys, nuclear fuel, cladding, modelling. 1. Introduction Tubes covering nuclear fuel in current light water reac- tors (LWR) are made of zirconium-based alloys since the very origin of nuclear power utilization. Zirconium- based alloys were first used in nuclear reactors of U.S. nuclear submarines. Later, Zr was adopted by fuel vendors as a suitable material for fuel cladding for commercial reactors around the world. Zirconium has been chosen for its low cross section for neutron absorption, good corrosion resistance, and other out- standing thermomechanical characteristics. Various degradation processes jeopardizing nuclear cladding integrity take place during reactor normal operation such as grid-to-rod fretting, debris-induced failures, crud-induced localized corrosion, waterside corrosion, and hydriding. This article is focused on water corrosion, its quantification, and theoretical description. Corrosion reaction caused mainly by an interaction of nuclear fuel cladding and coolant takes place on an external surface of cladding tubes, less frequently reacts internal cladding surface with oxygen released from pelets. In case of LWRs, metal reacts with water and zirconium oxide arises: Zr + 2 H2O −−→ ZrO2 + 2 H2. (1) Hydrogen released from the reaction described above partly dissolve in coolant water and partly penetrates tubes causing hydriding of zirconium. The fraction of hydrogen released from the reaction that is locally absorbed by the cladding tube is called pickup fraction and in PWR conditions is found to be constant for particular Zr-based alloys [1]. Oxygen diffuses through the zirconium oxide layer and in an interface of metal and oxide causes addi- tional oxidation. The density of the ZrO2 is smaller than zirconium alloy density. The difference in density and different thermal expansion of materilas is the primary cause of tension, internal stresses, and strains in cladding tubes. Moreover, thermal conductivity λ of ZrO2 is much smaller than that of zirconium based alloys causing the Zirconium dioxide layer to decrease the heat transfer from the fuel pellet over the cladding to the coolant and consequently increase maximal temperature in the fuel pellet. The exact physical parameters depend on temperature and models of thermal conductivity of Zirconium dioxide. They are in details described in [2] and [3]. For example, the thermal conductivity of E110 alloy is about 18 W/mK at the temperature of 300 ◦C. The thermal conduc- tivity of the ZrO2 for the same temperature is only about 2 W/mK. The bulk density of the Zircaloy-4 alloy and Zirconium dioxide at the same temperature is 6.5 and 5.6 kg/m3 respectively. When the Zirco- nium dioxide layer thickness exceeds about 100 µm (Zircaloy-4), it might crack and it is washed away by the streaming coolant which can lead to cold spots, additional oxidation, hydridation and later cladding breach [4]. Oxidation takes place also on the internal surface of fuel cladding, where metal reacts with oxygen released from the fuel pellets where fission takes place. When a high burn-up is reached, a bonding layer consisting of ZrO2, UO2, and fission products appears. This layer might be the cause of a firm connection between the fuel cladding and pellets. 2. Zirconium Based Alloys Zirconium-based alloys has been used as the nuclear fuel cladding since 1950s [6]. There were originally two main groups of Zr-based alloys developed: (1.) Zirconium-Tin and Iron-based alloys (originally developed in the U.S.) (2.) Zirconium-Niobium based alloys (originally de- veloped in former USSR) During the evolution of the nuclear fuel, fuel ven- dors and research organizations developed dozens of concepts of fuel cladding alloys. However, the two main groups remained as can be seen in Figure 1. Different cladding concepts can be based on the figure 13 http://dx.doi.org/10.14311/AP.2016.4.0013 http://ojs.cvut.cz/ojs/index.php/app Miroslav Cech, Martin Sevecek Acta Polytechnica CTU Proceedings Figure 1. Nuclear fuel cladding alloys developed for usage in PWR reactors [5]. There were two main groups of cladding alloys developed: Zr-Sn (right branch) and Zr-Nb (left branch) based alloys with dozens other concepts depending on the alloying ele- ments introduced around the world. divided into four development directions depending on their composition and development history. Each al- loy has a different corrosion characteristics depending on the alloying elements but also on manufacturing process and reactor type. 2.1. Zirconium-Tin Alloys A well-known family of alloys called Zircaloy was developed under a Westinghouse-led program. An alloy first developed is called Zircaloy-1. This alloy was replaced by the innovative Zircaloy-2, which is still in use in the BWR reactors. After abandoning of the Zircaloy-3 alloy development and utilization due to metallurgical processing issues, concerns with the high hydrogen pickup fraction exhibited by the Zircaloy-2 alloy led to the development of the Zircaloy- 4 alloy. Nickel was substituted by iron in this alloy and it was used from the 1950s to 1990s. 2.2. Zirconium-Niobium Alloys An alloy called E110 has been used by the Russian nu- clear industry for nuclear fuel cladding fabrication for VVER reactors fuels. Similar alloys made of zirconium-doped by niobium were used from the origin of the nuclear power utilization in the USSR. Recently, Westinghouse replaced Zircaloy-4 alloy in most of their nuclear fuel for PWRs by the ZIRLO alloy. In BWR reactors, Zircaloy-2 is still in use. ZIRLO is doped with niobium and is similar to the Russian alloy called E635. French alloy called M5 is a zirconium-based alloy containing 1 % of niobium with oxygen. The M5 alloy is produced by the French company Areva since 1990s. Generally, alloys doped with niobium such as E110, M5, and ZIRLO have a higher corrosion resistance than alloys from the Zircaloy family. Summary of composition of currently widely employed alloys is presented in Table 1 [7]. 3. Corrosion Models The growth and development of the cladding corro- sion layer for each zirconium-based alloy is usually expressed by corrosion models. 3.1. Garzarolli models Models developed by Garzarolli et al. [8] are adopted for describing the thickness of the corrosion layer of cladding tubes made of Zircaloy-4 , M5, and ZIRLO alloys under PWR conditions. These models generally based on Arrhenius law divide a growth of corrosion layer into two phases: (1.) The first phase continues until a transition thick- ness of oxide layer str is reached. The rate of corro- sion layer growth is expressed by the cubic rate law – Equation (2) (original units and the temperature of oxide-metal interface is used) [2, 3]. (2.) After reaching an alloy-specific transition thick- ness of oxide layer str, second phase quantified by a linear differential Equation (3) taking into account also fast neutron flux Φ is adopted. There are other transition points observed during the corrosion process. However, only the first transition is significant for the general progress of the corro- sion kinetics. For modelling purposes the use of only one transition is satisfactory. Model is defined for temperature range of 250–400 ◦C. ds3 dt = A s2 exp ( − Q1 RT ) , (2) ds dt = (C0 + U(MΦ)P ) exp ( − Q2 RT ) , (3) where s . . . Oxide layer thickness [µm], T . . . Temperature [◦C], Φ . . . Neutron flux [neutrons/m2s], A = 6.3 × 109 m3/day, R = 1.98 cal/mol K, C0 = 8.04 × 107 µm/day, M = 7.46 × 10−15 cm2s/n, P = 0.24, U = 2.59 × 108 µm/day. Values of constants Q1, Q2 and transition thickness of oxide layer str are alloy-dependent and are summa- rized in Table 2 for four widely used alloys which were subject to many studies. In literature, there were modifications of correlation models (2) and (3) defined. Modified models differ by values of constants and consider other physical phenomena neglected in the presented models. These models are implemented for example in FEMAXI and FRAPCON fuel performance codes. 14 vol. 4/2016 Modelling of Cladding Tubes Corrosion Alloying element Zircaloy-4 ZIRLO M5 E-110 E-635 Sn 1.2–1.7 % 0.96–0.98 % 1.25–1.30 % Fe 0.18–0.24 % 0.094–0.105 % <500 ppm 0.30–0.35 % Cr 0.07–0.13 % 79–83 ppm <200 ppm Nb 1.02–1.04 % 0.8–1.2 % 0.9–1.1 % 1.0 % Ni 0.01 % N <65 ppm 22–30 ppm <60 ppm 30–40 ppm C 150–400 ppm 60–80 ppm <200 ppm < 200 ppm O 900–1400 ppm 900–1200 ppm 0.11–0.17 % <1000 ppm 0.07 % Table 1. Composition of zirconium-based alloys widely used around the world in PWRs as materials for cladding tubes fabrication [7]. Q1[cal/mol] Q2[cal/mol] str Zircaloy-4 32289 27354 2 µm M5 27446 29816 7 µm ZIRLO 32289 27080 2 µm Opt.ZIRLO 32289 27354 2 µm Table 2. Values of corrosion model’s constants used in corrosion models (2) and (3) as defined by [3]. Figure 2. Zirconium dioxide layer development from the point of reaching first transition thickness str corre- sponding to the transition time ttr. Axis x represents time in days after the moment, when transition thick- ness was reached. The temperature of 320 ◦C and neutron flux of 1 × 1015 neutrons/m2s were chosen in this model situation. 3.2. Three-phase model Another model for describing of Zircaloy-4 corrosion layer thickness in PWR conditions divides its evolu- tion into three phases instead of two. The purpose is a faster oxide thickness growth after the second transition thickness is reached [7]. The model was developed by experimental data fitting and is more precise for higher values of oxide thickness than model developed by Garzarolli et al. [8]. Oxide layer growth during the first phase can be calculated by the follow- ing expression [6] ds3 dt = 2.187 × 10−13 exp ( − 135188 RT ) . (4) The first transition thickness is the same as in the previous model – 2 µm for Zircaloy-4. Afterward, different formula is used instead of Equation (3) ds dt = ( 9.31 × 10−4 + 2.75 × 10−3 ( Φ 5.24 × 1018 )0.24) · exp ( − 114526 RT ) . (5) After reaching the second transition thickness – 35 µm, following equation is used ds dt = ( 9.31 × 10−4 + 2.75 × 10−3 ( Φ 5.24 · 1018 )0.24 ) · 1.8 exp ( − 114526 RT ) . (6) 3.3. E110 corrosion model A model describing the corrosion layer growth of E110 alloy in VVER conditions was developed by fitting experimental data at the Russian A.A. Bochvar High- technology Scientific Research Institute for Inorganic Materials. For the E110 alloy following relation was derived [9] ds dt = 40 exp ( − 5147 T ) . (7) Model was derived byl data base on experiments, which took place in temperature range of 320–360 ◦C. This model considers only one phase of corrosion layer development, transition thickness is disregarded. Com- parison between corrosion layer growth of Zircaloy-4 and E110 is plotted in Figure 3. Figure 3. Comparison of the zirconium oxide layer thickness of Zircaloy-4 and E110 alloys in conditions of 320 ◦C and neutron flux of 1E15 neutrons/m2s. The corrosion growth of E110 is considerably lower in comparison with the Zircaloy-4 alloy. Accelerating 15 Miroslav Cech, Martin Sevecek Acta Polytechnica CTU Proceedings growth can be seen for the Zircaloy-4 three-phase model which is not the case for the E110 alloy. For that reason, the neglecting of transitions in case of E110 is justified. If the behavior of nuclear fuel during LOCA, RIA or other design basis accidents is calculated by fuel perfor- mance codes like FRAPTRAN or TRANSURANUS, the thickness of oxide layer is an initial condition which strongly influences a progress of the accident and its consequences. 4. Corrosion in LOCA Conditions Large Break Loss of Coolant Accident (LBLOCA) is the maximal design basis accident of PWRs of second and third generation. During this accident, a temper- ature of the whole fuel rod including pellets quickly rises due to limited cooling conditions. The high temperature of fuel pellets leads to high-temperature gradients, stresses, and cracking of pellets. Rapid release of fission gases from the fuel can be observed and the internal pressure of filling gas rises. The high temperature of cladding together with the high internal pressure can be a cause of a deformation, ballooning, or bursting of the cladding. This geometry changes can limit the coolant flow and further reduce the heat transfer from the fuel rods to the coolant. Construction of reactor, design of the nuclear fuel and its properties must ensure that acceptance limits for LOCA accidents will not be violated: (1.) A peak cladding temperature can nowhere exceed 1204 ◦C (2.) Sufficient fuel rod strength upon quench taking into account an additional mechanical load (main- tain post-quench ductility) (3.) Fraction of zirconium reacted into oxide cannot exceed 1 % (due to hydrogen production) (4.) Melting temperature of fuel can not be reached in any place of the reactor core 4.1. Corrosion Models in LOCA Conditions To develop corrosion models in LOCA conditions, it is necessary to measure experimental data in similar conditions. Experiments are done at high-temperature steam (800–1200 ◦C). Experiments with as-received cladding tubes and as well as with cladding tubes with corrosion layer has been performed. Preoxidation of experimental samples ensures that simulation will be performed in conditions which are similar to the real LOCA accident conditions with operating fuel. A model of high-temperature corrosion of sponge based E110 alloy was developed at the UJP in the Czech Republic and is based on its experimental data [10]. Experiments cover a wide range of con- ditions (temperature 600–1300 ◦C and 0–480 minute long exposition). These wide conditions enable to use the model in various conditions and for various scenario for E110 alloy. No. T [◦C] Process 1 600–750 Phases α + β transformation 2 750–950 Formation of β phase 3 950–1100 Delated transformation, tetrag- onal oxide 4 1100–1300 Tetragonal oxide Table 3. Physical processes taking place in zirconium E110 alloy in different temperature intervals during LOCA accident conditions. This model describes a mass growth of oxide as defined in [10] ∆G = A exp ( E T ) tn = ktn, (8) where ∆G . . . mass growth [mg/dm2], A,E,k . . . fitting parameters, t . . . time [s], n . . . kinetic constant. Figure 4. Development of the parameter n with temperature as defined by [10]. Figure 5. Development of the parameter k with temperature as defined by [10]. For n and k parameters were derived following for- mulas n = 0.4 for T < 768.4 ◦C (9) n = 2.609 − 4.898 × 10−3(T − 273.15) + 2.633 × 10−6(T − 273.15)2 for T < 960.3 ◦C (10) n = 1.202 × 10−3(T − 273.15) − 0.8208 for T < 1098.9 ◦C (11) n = 0.5 for T > 1098.9 ◦C (12) 16 vol. 4/2016 Modelling of Cladding Tubes Corrosion Figure 6. Power history of rods BSM-25 and BK365. Figure 7. Oxide layer thickness of BSM-25 and BK365 rods. k = 85265.6 exp ( − 9875.59 T ) for T < 934.1 ◦C (13) k = 1072.21 exp ( − 4592.6 T ) for T < 1054.5 ◦C (14) k = 33.33 for T < 1098.0 ◦C (15) k = 96482.3 exp ( − 10913.1 T ) for T > 1098.0 ◦C (16) Temperature intervals of equations (9)–(16) approx- imately correspond to physical processes, which take place in the cladding material during LOCA accident. These processes are described in Table 3. This model well describes a corrosion kinetic for all ranges of temperature covered by experiment. The value of parameter n is 1/2 for high-temperature cor- rosion and 1/3 for middle-temperature corrosion [7]. These values are the same as in other used models. Another model for n also very well describes the n temperature reliance. Constant k equals approximately equals to 0 and increase with temperature to about 90 at 1300 ◦C. Di- viding model into four ranges where different formulas are used brings a good agreement of the model with experimental data. A comparison between this model and data can be found in [10]. 5. Model of Corrosion in FEMAXI A calculation of oxide layer development in the FEMAXI-6 code has been performed for two fuel rods: BSM-25, and BK365. These rods were irra- diated in the BR-3 reactor and reached burn-up of 66 and 52 MWd/kgHM. Rods were irradiated within the High Burnup Effect Program in the BR-3 reactor, cladding was made of Zircaloy-4 alloy, coolant inlet temperature was 255 ◦C. A model originally developed by Garzarolli et al. [8] (Equations (2) and (3)) was used for the Zircaloy-4 al- loy corrosion modeling. The two power histories used as a model input are plotted in Figure 6. Correspond- ing oxide layer thickness growth is shown in Figure 7. For both tested fuel rods, an average thickness and the maximal oxide layer thickness are shown. Maximal thickness of the corrosion layer is about two times higher than the average value. Maximal thickness was reached in the middle of the fuel rod which does 17 Miroslav Cech, Martin Sevecek Acta Polytechnica CTU Proceedings not correspond to the case in commercial power reac- tors. The oxide layer growth is strongly dependent on the temperature, the higher the temperature is the faster the growth. Therefore, the maximal thickness of the zirconium oxide layer in commercial power re- actors is at the top of the fuel rod where the coolant temperature is highest. Figure 7 shows, that higher linear heat rate causes faster oxide layer creation. The graph also shows that the first phase of oxide layer growth is independent of fast neutron flux. Small differences are caused by higher temperature. In the later phase of fuel rod’s irradiation, there is a clear dependance of corrosion layer thickness on fast neutron flux and linear heat rate. When BSM-25 rod was operating in high heat rate condition, layer growth was much faster than in the case of smaller heat rate of the second fuel rod. Higher heat rate (and corresponding tempera- ture) causes the bigger corrosion layer, even when the burnup of the BSM-25 rod is lower. 6. Conclusion This article describes models quantifying corrosion of nuclear fuel cladding tubes made of zirconium-based alloys widely used in nuclear industry in nominal con- ditions and LOCA accident conditions. Models used for calculating of an oxide layer thickness in normal op- eration conditions for the widely used alloys Zircaloy-4, ZIRLO, M5 and E110 are presented and compared. A model for corrosion and high-temperature oxida- tion in LOCA conditions is described and reliance of particular parameters used in models are shown in graphs. A corrosion model for nominal conditions was applied in the FEMAXI-6 code to calculate corrosion of fuel rods BK363 and BSM-25 tested in the BR-3 reactor. The relations of burnup, linear heat rate, and corrosion layer thickness growth is illustrated in the example. Results show faster oxide growth in case of BSM-25 rod after reaching the transition thickness for Zircaloy-4 alloy, because this rod was operated at higher linear heat rate. Acknowledgements This work was supported by the Grant Agency of the Czech Technical University in Prague, grant No. SGS OHK4-008/16. References [1] K. Geelhood, W. Luscher. Frapcon-3.5: Integral assessment. Progress in Nuclear Energy 2014. [2] M. Suzuki, H. Saitou, N. G. K. K. Kikō. Light Water Reactor Fuel Analysis Code: FEMAXI-6 (Ver. 1): Detailed Structure and User’s Manual. Japan Atomic Energy Research Institute, 1997. [3] W. G. Luscher, K. J. Geelhood, et al. Material property correlations: comparisons between FRAPCON-3.4, FRAPTRAN 1.4, and MATPRO. US Nuclear Regulatory Commission, Office of Nuclear Regulatory Research, 2011. [4] P. Billot, B. Cox, K. Ishigure, et al. Corrosion of zirconium alloys in nuclear power plants. In TECDOC- 684. International Atomic Energy Agency (IAEA), 1993. [5] L. Hallstadius, S. Johnson, E. Lahoda. Cladding for high performance fuel. Progress in Nuclear Energy 57:71–76, 2012. [6] A. T. Motta, A. Couet, R. J. Comstock. Corrosion of zirconium alloys used for nuclear fuel cladding. Annual Review of Materials Research 45:311–343, 2015. [7] D. Kobylka. Termofyzikální vlastnosti pokrytí nových typů paliva, jejich implementace v kódu FEMAXI-6 a testování. Tech. Rep. 14117/2012/02Kob, ÚJV Řež, a.s., 2012. [8] F. Garzarolli, D. Jorde, R. Manzel, et al. Review of PWR fuel rod waterside corrosion behavior. Tech. rep., Kraftwerk Union AG, Erlangen (Germany, FR); Combustion Engineering, Inc., Windsor, CT (USA), 1980. [9] V. Konkov, M. Sablin, T. Khokhunova, et al. Assessment of E110 and E635 alloy corrosion behavior in VVER-1200 reactors. JSC VNIINM 2009. [10] J. Krejčí. Oxidace palivového pokrytí během havárie LOCA. Bezpečnost jaderné energie 45:311–343, 2015. 18 Acta Polytechnica CTU Proceedings 4:13–18, 2016 1 Introduction 2 Zirconium Based Alloys 2.1 Zirconium-Tin Alloys 2.2 Zirconium-Niobium Alloys 3 Corrosion Models 3.1 Garzarolli models 3.2 Three-phase model 3.3 E110 corrosion model 4 Corrosion in LOCA Conditions 4.1 Corrosion Models in LOCA Conditions 5 Model of Corrosion in FEMAXI 6 Conclusion Acknowledgements References