Tritium transport analysis in HCPB DEMO blanket with the FUS-TPC Code

Transcription

1 KIT SCIENTIFIC REPORTS 7642 Tritium transort analysis in HCPB DEMO blanket with the FUS-TPC Code Fabrizio Franza

2

3 Fabrizio Franza Tritium transort analysis in HCPB DEMO blanket with the FUS-TPC Code

4 Karlsruhe Institute of Technology KIT SCIENTIFIC REPORTS 7642

5 Tritium transort analysis in HCPB DEMO blanket with the FUS-TPC Code by Fabrizio Franza

6 Reort-Nr. KIT-SR 7642 Hinweis Die vorliegende wissenschaftliche Kurzdarstellung wurde im Auftrag des Umweltministeriums Baden-Württemberg durchgeführt. Die Verantwortung für den Inhalt dieser Veröffentlichung liegt bei den Autoren. Imressum Karlsruher Institut für Technologie (KIT) KIT Scientific Publishing Straße am Forum 2 D Karlsruhe KIT Universität des Landes Baden-Württemberg und nationales Forschungszentrum in der Helmholtz-Gemeinschaft Diese Veröffentlichung ist im Internet unter folgender Creative Commons-Lizenz ubliziert: htt://creativecommons.org/licenses/by-nc-nd/3.0/de/ KIT Scientific Publishing 2013 Print on Demand ISSN ISBN

7 Abstract In thermonuclear fusion reactors, the fuel is an high temerature deuterium-tritium lasma, in which tritium is bred by lithium isotoes resent inside solid ceramic breeder (e.g. Li-Orthosilicate) or inside liquid eutectic alloys (e.g. Pb-16Li alloy). In the breeding areas a significant fraction of the tritium roduced is extracted out from the Breeding Zone by the He gas urging the breeding ceramic in the Helium Cooled Pebble Bed (HCPB) blanket concet or transorted in solution by the owing alloy in the Helium Cooled Lead Lithium (HCLL) blanket concet. Tritium roduced in the breeding blanket by neutrons interacting with lithium nuclei can enter the metal structures, and can be lost by ermeation to the environment. Tritium in metallic comonents should therefore be ket under close control throughout the fusion reactor lifetime, bearing in mind the risk of accidents and the need for maintenance. In this study the roblem of tritium transort in HCPB DEMO blanket from the generation inside the solid breeder to the release into the environment has been studied and analyzed by means of the comutational code FUS-TPC (Fusion Devoted-Tritium Permeation Code). The code has been originally develoed to study the tritium transort in HCLL blanket and it is a new fusion-devoted version of the fast-fission one called Sodium-Cooled Fast Reactor Tritium Permeation Code (SFR-TPC). The main features of the model inside the code are described. The code has the main goal to estimate the total tritium losses into the environment and the tritium inventories inside the breeder, inside the multilier, inside the urge gas and the main coolant loos and inside the structural materials. Different simulations of the code were erformed by adoting the configuration of the Euroean HCPB blanket for DEMO. Total tritium losses from a generic fusion ower lant, is often considered a key arameter to evaluate the tritium containment caabilities (added to tritium inventories) of a certain nuclear lant. Without any tritium control techniques, ermeation can be quite significant, thus some tritium transort mitigation devices are required. The code is able to model and comute different tritium fluxes exchanged in the overall tritium system. A sensitivity study for the tritium losses and inventories is erformed in this work. I

8

9 Contents Abstract... I Figures... V Tables... VII Acronyms and Abbreviations... IX 1 Introduction Descrition of HCPB DEMO Blanket Descrition of the Model Tritium Fluxes Extracted by TES and CPS Isotoe Exchange Rate Permeation Fluxes Theory on Hydrogen Isotoes Permeation Tritium Permeation Flux through CPs Cooling Channels Tritium Permeation Flux from Imlanted Tritons onto First Wall Tritium Permeation Flux though Steam Generator Tube Walls Tritium Flux Associated to Helium Leaks Tritium Losses and Inventories Tritium Inventories Tritium Losses into the Environment Results and Discussions Material Proerties, Inut Data and Main Assumtions Definition of the Limiting Regime for Tritium Permeation Material Proerties Database Inut Data for the HCPB DEMO Blanket Oerative Conditions Results for the Oerative Blanket Configuration Tritium Concentrations and Partial Pressures Vs. Time III

10 4.2.2 Tritium Inventories Vs. Time Tritium Losses Vs. Time Imact of the Main Assumtions on the Results Oxidized Vs. Clean SG Walls Surfaces Diffusion Vs. Surface-Limited Permeation Regime Presence Vs. Absence of a FW Coating Layer Main Parameters for Tritium Migration in HCPB DEMO Blanket Tritium Losses and Inventories Vs. TES Efficiency Tritium Losses and Inventories Vs. CPS Efficiency Tritium Losses and Inventories Vs. CPS Recirculation Rate Tritium Losses and Inventories Vs. PRF on CPs Tritium Losses and Inventories Vs. PRF on SG Tubes Overall Summary of the Parametric Study Summary and Conclusions References IV

11 Figures Figure 2-1 Basic Layout of HCPB Breeder Blanket... 4 Figure 2-2 Reference Scheme for Tritium Transort in HCPB Blanket... 5 Figure 3-1 H 2 Permeation Vs. Pressure through Ferritic Steel [11] Figure 3-2 Overall Permeation Behavior of Hydrogen Gases through Metals [13] Figure 3-3 Fractional Tritium Release from Neutrons Irradiated Be [21] Figure 4-1 Different Adsortion Constants in MANET Steels Vs. 1000/T Figure 4-2 HT and HTO Concentrations in Purge Gas and Coolant Loos Vs. Time Figure 4-3 HT Partial Pressures in Purge gas and Coolant Loos Vs. Time Figure 4-4 Tritium Inventories Vs. Time Figure 4-5 Tritium Losses Vs. Time Figure 4-6 Tritium Losses Vs. Time for Clean and Oxidized SG Tubes Conditions Figure 4-7 Tritium Inventories Vs. Time for Clean and Oxidized SG Tubes Conditions.. 41 Figure 4-8 Normalized Tritium Losses Vs. Time Vs. Permeation Regime Figure 4-9 Tritium Inventories Vs. Time Vs. Permeation Regimes Figure 4-10 Tritium Losses Vs. Time Vs. Thickness of FW Coating Layer Figure 4-11 Total T Inventories Vs. Time Vs. Thickness of FW Coating Layer Figure 4-12 Steady State T Losses and Inventories Vs. TES Efficiency Figure 4-13 Steady State T Losses and Inventories Vs. CPS Efficiency Figure 4-14 Steady State T Losses and Inventories Vs. CPS Recirculation Rate Figure 4-15 Steady State T losses and Inventories Vs. PRF on CPs Figure 4-16 Steady State T Losses and Inventories Vs. PRF on SG Tubes Figure 4-17 Tritium Losses Vs. α CPS Vs. PRF CP Vs. T k rec. in SG tubes V

12

13 Tables Table 2-1 Main Features of HCPB Blanket [8]... 6 Table 3-1 Descrition of Tritium Fluxes in HCPB Blanket... 8 Table 4-1 FUS-TPC Material Proerties...30 Table 4-2 Geometric Inut Data for Tritium Assessment in HCPB Blanket Table 4-3 Main Features of Tritium System in HCPB DEMO Blanket Table 4-4 FUS-TPC Inut Data for FUS-TPC Simulations Table 4-5 Steady State T Concentrations and Partial Pressures Table 4-6 Steady State Tritium Inventories Vs. Time in all the Blanket Locations Table 4-7 Steady State T Losses and Inventories for Clean and Oxidized SG Tubes Table 4-8 Steady State Tritium Losses for all the Permeation Regime Scenarios Table 4-9 Steady State Tritium Inventories for all the Permeation Regime Scenarios Table 4-10 Steady State T Losses and Inventories Vs. Thickness of FW Coating Layer Table 4-11 Summary Results of the Sensitivity Study VII

14

15 Acronyms and Abbreviations BU Breeding Unit CP Cooling Plate CPS Coolant Purification System EOL End Of Life FPP Fusion Power Plant FUS-TPC FUSion devoted-tritium Permeation Code FW First Wall HCLL Helium Cooled Lead-Lithium HCPB Helium Cooled Pebble Bed HCS Helium Coolant System LOCA LOss of Coolant Accident PCS Power Conversion System R&D Research and Develoment PRF Permeation Reduction Factor SFR-TPC Sodium-Cooled Fast Reactor-Tritium Permeation Code SG Steam Generator TBM Test Blanket Module TBR Tritium Breeder Ratio TES Tritium Extraction System IX

16

17 1. Introduction 1 Introduction The management of tritium and the related transort analysis in the overall tritium cycle are key issues for DEMO and future fusion reactors. The most efficient way to rovide tritium in steady state is to roduce it directly inside the fusion reactor and to recover it. In order to achieve this goal, secific breeding blankets are used. Tritium roduction occurs following the reactions: and [1] [1]. The nuclear cross section of the first breeding reaction increases as the neutron energy decreases. Moreover, in a ractical reactor, there are always some unavoidable neutron losses. For these reasons in fusion reactor breeding blanket some neutron multilier and moderator is required (e.g. Beryllium in Helium Cooled Pebble Bed blanket and Lead in Helium Cooled Lead- Lithium blanket) by taking advantage from his interaction with fast neutrons which leads to the neutron multilication reaction, while lithium is needed for tritium breeding inside the fusion reactor. In articular, Beryllium has a great attitude to attenuate fast neutron. Tritium is generated inside the breeder and moves with several mechanisms (e.g. ermeation, adsortion, etc.) and otentially might reach the environment, giving a otential radiological hazard. Thus, the objective of this work is to evaluate the tritium inventories inside several comonents of the tritium management system in blanket (e.g. inside the breeder, inside Beryllium and inside the coolant loo) and the tritium losses into the environment, adoting a DEMO blanket configuration based on a solid breeder (e.g. lithium Orthosilicate Li 4SiO 4); the Helium Cooled Pebble Bed (HCPB) blanket. In this code, it has been adoted a simlified diffusion (or surface)-limited ermeation model, with a series of simlifying and conservative assumtions, in order to solve the mass balance equations of different tritium secies inside different HCPB blanket locations; however, more comlicated models should be foreseen. In order to erform this study, a tritium ermeation analysis code (FUS-TPC) has been used. The code has been firstly develoed in 2011 to analyze tritium transort in the Euroean configuration of the HCLL blanket for DEMO [2]. FUS-TPC is a new simlified fusion-devoted version of the fast-fission one called SFR-TPC [3], develoed to study tritium inventories and losses from Sodium-Cooled Fast Reactors (SFRs). The MATLAB comutational tool was used to develo this code. The FUS-TPC is based on mass -1-

18 1. Introduction balance equation regarding various chemical forms of tritium (i.e., HT and HTO), couled with a variety of tritium sources, sinks, and ermeation models. -2-

19 2. Descrition of HCPB DEMO Blanket 2 Descrition of HCPB DEMO Blanket A detailed descrition of HCPB DEMO blanket design secifications is reorted in Ref. [4]. The helium cooled ebble bed (HCPB) blanket is one of two concets selected in the frame of the Euroean Blanket Programme to be tested during the different ITER exerimental hases. The Helium Cooled Pebble Bed concet has been develoed in Karlsruhe Institute of Technology (KIT, formerly Forschungszentrum Karlsruhe) starting from the nineties. The concet was roosed by M. Dalle Donne [5]; this concet has been successfully imroved by Hermsmeyer in 1999 [6], and comletely revised in 2003 by Hermsmeyer and Malang in the frame of the PPCS studies [7]. The DEMO HCPB Blanket (Hermsmeyer et al.) is derived from the PPCS model B and is the last HCPB DEMO concet validated with neutronic, thermo-hydraulic and structural analyses. The DEMO HCPB general design, is based on a ceramic breeder (lithium orthosilicate or metatitanate) and beryllium neutron multilier in form of flat ebble beds, which are inserted into the blanket modules as a series of breeder units (BUs), searated each other by radial-toroidal and radial-oloidal stiffening lates. The Vacuum Vessel is covered by blanket modules. The blanket thermal ower, around 3000 MW th (DEMO 2003), is extracted by the He rimary coolant flowing at high ressure (8 MPa) through the first wall and blanket cooling lates made in EUROFER 97 martensitic steel. The inlet and outlet temeratures of the rimary coolant are 300 and 500 C. The HCPB Blanket concet is based on the following basic rinciles [4]: Use of a solid breeder in form of a ebble beds. Breeder ternary lithiated comound (Lithium Orthosilicate Li 4SiO 4 or Lithium Metatitanate Li 2TiO 3) have been considered for this function. Use of a neutron multilier: Beryllium (or Be alloy) in form of a ebble bed. Beryllium is essential in this concet to reach Tritium Breeder Ratio (TBR) that are necessary for the self-sufficiently of the fusion reactor. Reduced Activation Ferritic Martensitic steel as structural material (EUROFER is under develoment in EU for the scoe). Using of high ressure (~8 MPa) Helium for the cooling of the blanket. The Helium flows inside small channels realized in the structural material. The ebble beds are cooled indirectly by steel structures. -3-

20 2. Descrition of HCPB DEMO Blanket The extraction of the tritium from the breeder materials is realized by an indeendent low ressure ( MPa) Helium urge flow. The T generated in the ebble bed that can ermeate into the Cooling Loo is considered a arasitic effect (that can have safety relevance for the future Fusion Power Plants FPP) and should be minimized using aroriate design and otimizing mass flow and chemical comosition of the gasses (in both loos). Additional coating as anti-ermeation barriers is not considered necessary for this concet. In any case the demonstration of this oint is an objective of this study and of the ongoing R&D on this concet. Figure 2-1 Basic Layout of HCPB Breeder Blanket A simlified flow-diagram of the main tritium rocessing systems for this blanket concet is shown in Figure 2-2, while the main features of HCPB blanket for DEMO are reorted in Table 2-1. These values are referred to the DEMO 2003 HCPB blanket, which is assumed to be the reference configuration for this study. With reference to Figure 2-2, the first task of TES (Tritium Extraction System) is to extract tritium from the lithium ceramic beds and Be multilier by a low ressure helium stream added with ure hydrogen. Then, TES accomlishes the function of tritium removal in the two main chemical forms, HT and HTO, from He. TES is a key ste in the blanket tritium rocessing and, consequently, all ossible rocess otions to accomlish its function have to be deely studied and comared on the basis of the envisaged oerative conditions, taking into account their erformance, reliability as well as industrial availability. Although in all revious reference designs a He urge stream is added into the blanket modules, with the consequent decrease of the tritium artial ressure in the ebble beds, -4-

21 2. Descrition of HCPB DEMO Blanket however a non-negligible tritium ermeation rate takes lace in direction to the He rimary cooling circuit (HCS, Helium Coolant System). Consequently, an efficient CPS (Coolant Purification System) must be designed in order to carry out the rimary function of tritium removal from He coolant. Figure 2-2 Reference Scheme for Tritium Transort in HCPB Blanket The tritium removal from He coolant has also the beneficial effect to kee low the tritium inventory in HCS, minimising the tritium release into the reactor vault in case of ex-vacuum vessel LOCA and limiting the tritium release (He leaks + tritium ermeation) into the secondary water-steam circuit through the steam generators. The resent work is mainly develoed by combining reference data coming from secifications of HCPB- -5-

22 2. Descrition of HCPB DEMO Blanket DEMO 1995, DEMO 2003 and DEMO model B of PPCS, since the tritium Cycle design remained basically the same. Moreover, the results of this study are also meant to address the R&D efforts toward the right directions and to oint out the most crucial issues related to tritium mobility in blanket comonents. Blanket concet HCPB Fusion Power ~2500 MW Blanket Thermal Power ~3000 MW TBR 1.14 Blanket segmentation Large modules Structural Material RAFM steel (EUROFER) Coolant Helium Breeder Solid Breeder (ebble beds) Li 4SiO 4 (Li 6 enrich. 40%) Coolant Pressure, Temerature in/out 8 MPa, 300/500 C Coolant mass flow rates ~ 2400 kg/s T recovery method Low ressure (1 bar) He urge loo Maximum design temeratures FW (steel) 548 C CP (steel) 544 C Breeder/multilier 917/655 C Table 2-1 Main Features of HCPB Blanket [8] -6-

23 3. Descrition of the Model 3 Descrition of the Model In this section the mathematical structure of the code will be illustrated, analyzing and highlighting the main features. With reference to the tritium fluxes reorted in Figure 2-2, is reorted hereafter the system of differential equations describing the tritium mass balance inside the HCPB blanket, in which the integral balance of total amount of tritium secies i (with i = HT and HTO) inside the j-th Helium loo (with j= urge gas loo, coolant loo) is erformed by means of the mass-averaged concentration where are given by: is the Helium mass inside the loo j. Thus the tritium mass balance equations t t br br dct C G br T v dt res Be dct t Be 1 f G r v dt dc t CP HT t t t HT HTO erm TES dt mhe dc t G t HTO HTO HTO HTO t TES t dt mhe c dcht c dt mhe c c c HTO dc t HT t leak HTO t CPS t HTO, c dt mhe j Ci 0 0, with i T, HT, HTO, j br, Be,, c CP FW SG t t t t c c HT erm im erm HT t leak, HT t CPS t (3.1) where the suerscrits and are related to the urge gas and the Helium Coolant System (HCS) loos resectively, the subscrits br and Be to the breeder and Beryllium ebble beds resectively and the subscrits HT and HTO are related to the tritium hydride (HT) and tritiated water (HTO) resectively. All the tritium fluxes entering in the tritium mass balance of Eq. (3.1) and qualitatively described hereafter, are listed in Table

24 3. Descrition of the Model Tritium is generated inside the breeder in form of atomic tritium with a local roduction rate and it is released into the urge gas with a time lag called tritium residence time (see ); due to the resence of oxygen and water inside the Li orthosilicate, tritium is assumed to be released into the urge gas almost totally in form of tritiated water HTO. A smaller roduction rate is also resent in Beryllium ebble beds, in which large amounts of tritium can be retained and only a little fraction of roduced tritium is released from Be ebbles (see ). The release rate from the breeder and the total tritium release into the urge gas are related by the following relationshi: t br mol CT G HTO t Vbr s (3.2) res where is the total volume of breeder inside the breeding blanket. Once tritium gets into the urge gas loo, due to the resence of swaming hydrogen inside urge Helium (with a swaming ratio fixed to 0.1 %), the chemical equilibrium (see 3.2) takes lace and a certain amount of HTO gets converted into tritium hydride (HT). Flux Descrition Total tritium generation rate inside the breeder Local tritium generation rate inside breeder ebble beds Total tritium generation rate inside Beryllium ebble beds Flux of Tritons from the lasma through the FW cooling channels HT ermeated flux through CP channels HT ermeated flux through SG tubes Flux of tritium form i (i = HT, HTO) extracted by TES Flux of tritium form i (i = HT, HTO) extracted by CPS Losses of tritium form i (i = HT, HTO) with coolant leakages HTO Isotoe exchange rate inside the BU from the urge gas side HT Isotoe exchange rate inside the BU from coolant side Table 3-1 Descrition of Tritium Fluxes in HCPB Blanket In the urge gas loo, tritium is released from the breeder into the urge Helium mainly in form of HTO, and the resence of high hydrogen contents is needed to shift the HTO content into HT, which is much less worrying from the radiological oint of view although is a ermeable secie. The dose coefficients er unit of incororation have been -8-

25 3. Descrition of the Model evaluated at for HT inhalation and for ingested or inhaled HTO [10], thus, for the same ingested or inhaled amount of both secies, the dose rovided by HTO is times higher than the one coming from HT. Since HT is a gaseous (and ermeable) hydrogen secies, a ermeation flux across the Cooling Plates (CPs) laced between Beryllium and breeder ebble beds (see Figure 2-1 and Figure 2-2) occurs as well; this tritium ermeation rate then reaches the rimary coolant system (HCS). Moreover, the tritons coming from the Plasma and imlanted into the First Wall (FW) can ermeate into the HCS by means of the ermeation flux through the FW cooling channels (see 3.3.3). As reorted in the Introduction, tritium is extracted from urge gas in Tritium Extraction System (TES), with a certain removal efficiency (see 3.1) giving a total tritium extraction rate from the urge gas. Following the tritium transort aths, the ermeated tritium fluxes from FW and CPs get into the main coolant loo, in which, due to hydrogen and water addition for the oxidation control, the isotoe exchange rate from HT to HTO takes lace, because of the same chemical equilibrium as considered for. In HCS, the tritium fluxes and are extracted by re-circulating inside the Coolant Purification System (CPS) a certain fraction of total Helium mass flow rate inside the coolant loo in which the tritium fluxes and are extracted with a removal efficiency (see 3.1). Finally, a tritium ermeation fluxes through the Steam Generator (SG) tubes walls gets into the steam circulating into the Power Conversion System (PCS), which is considered to be lost into the environment. As will be shown in the results, this tritium amount constitutes an imortant contribution to the total tritium losses. Finally, a certain amount of tritium released into the environment due to He leakage from seals and material imerfections of the coolant circuit decay and the tritium must be considered. However, the tritium decay generates atoms, which are resonsible also of the nuclear reaction which is a source reaction for tritium and it should comensate losses due to tritons decay. Anyway this nuclear reactions has a relevant influence only at low energy neutrons (in the range of ev [9]), that is quite off from the neutron energy sectrum involved in a breeding blanket (14.1 MeV), tyically around the fast sectrum. Aarently the contribution of this reaction can be neglected and the decay should be considered in the tritium balance. However, tritium decay is usually negligible for short time eriods but on longer time scales, the decay could rovide also some benefits, esecially in terms of T inventory. As a -9-

26 3. Descrition of the Model matter of fact, inside Beryllium Pebbles Beds the fast neutrons are easily slowed down, thus making the nuclear reaction to easily take lace. In conclusion, in order to kee the analysis as much conservative as ossible, the tritium decay is neglected in the system of balance equations reorted in Eq. (3.1). From the mathematical oint of view, the aim of the model is to exress all the tritium fluxes listed above in terms of all the i-th tritium form average concentration (with i = HT, HTO) inside the j-th Helium loo (with j = urge, coolant) and solving this system of differential equations by finding all these time-deendent tritium concentrations which are averaged on their resective total urge and coolant Helium masses, and resectively. As shown hereafter, the differential equations entering in system of Eq. (3.1) can be non-linear, thus only a numerical solution can be found. In the following section all the already described tritium amounts are described from the mathematical oint of view. 3.1 Tritium Fluxes Extracted by TES and CPS The Tritium Extraction System (TES) is aimed to extract the tritium amount released from the solid breeder into the urge gas loo, whilst the Coolant Purification System (CPS) is aimed to urify a certain fraction of rimary coolant mass flow rate from tritium isotoe forms. The aim of this section is to exress as functions of all the concentrations unknowns entering into the tritium mass balance equation of Eq. (3.1) the two following (and imortant) tritium fluxes: Tritium extracted by TES (with i = HT, HTO); Tritium extracted by CPS (with i = HT, HTO). The first term is exressed as a function of the TES efficiency ( ), of the average tritium concentration of the i-th form in urge gas loo and of the urge Helium mass flowrate ( ). The TES efficiency is defined by tritium concentration at the inlet and the outlet of TES system (that is the outlet and the inlet i-th form concentration at the BU, and resectively as shown in Figure 2-2), which are linked to the average concentration in the urge gas loo according to following equations: -10-

27 3. Descrition of the Model C C i i TES in, i t W t C inl, i He 2 C C i TES out, i 2 2 out, i 1 t i TES i TES C out, i C i t C t C out, i t inl, i t C inl, i i t 1 C t TES out, i (3.3) Given the above set of equations, the flux of tritium form i extracted by TES is defined as: i TES t W He 2 2 i TES i TES C i t (3.4) The total tritium flux extracted from TES is obtained by summing the HT and HTO contribution. As done for TES, the exression of tritium flux extracted from CPS is develoed using the efficiency (with i=ht,hto) but also considering that only a fraction of the total coolant flow rate (see Figure 2-2) is treated by CPS. Adoting the same aroach used for we have the following set of equations, relating the inlet and the outlet concentration of the i-th form into and from the BU from the coolant side ( and resectively) with the average concentration of the same form into the coolant loo, the CPS efficiency and the fraction of total mass flow rate re-circulated inside CPS. C C C c i t c inl, i c in, i c i c t 1 CPS Cout, i t CPS 1 CPS Cout, i t i 21 t C c inl, i C 2 2 c out, i CPS CPS CPS i CPS C c i t (3.5) Given the above set of equations, the flux of tritium form i extracted by CPS is defined as: i CPS t W c He 2 2 CPS CPS i CPS i CPS C c i t (3.6) As done for TES, the total tritium flux extracted from CPS is obtained by summing the HT and HTO contribution. As shown in the results, the TES and CPS efficiencies have been reresented by a unique arameter for each system (i.e. and ) without distinguishing between HT and HTO removal efficiencies. In general can be different from (as well as -11-

28 3. Descrition of the Model and ) but in this study, since no more detailed values were available, only one efficiency value has been considered for TES and CPS systems. As it can be seen, these arameters affect the tritium losses and inventories assessment in a relevant manner, esecially the CPS recirculation ratio. 3.2 Isotoe Exchange Rate In the urge and coolant He loos, the following chemical equilibriums due to the and addition are assumed to be the most imortant ones: H T 2HT (3.7) 2 HT H 2O H 2 HTO (3.8) Assuming an form exchange rate related to the HT secie for equilibrium 1 and for equilibrium 2 ( and resectively), given the chemical equilibrium constants and the following relationshis can be exressed as [9]: K K eq,1 eq,2 T T 2 HTeq H T 2 eq 2 eq F H 2 HTO eq HT H O eq 2 eq eq eq, H j in, H 2 eq, HT 2 2 eq, T 2 j HT HT 2 F (3.9) in, HT 1 2 HT 1 HT HT j 1 2 F in, T eq, H 2 eq, H eq, HTO eq, H O 2 2 j HT HT j HT Fin, H 1 2 F in, HTO 2 2 HT j 1 HT j HT F F (3.10) in, HT 2 in, H2O 2 2 where, and are the molar concentration at the chemical equilibrium, the artial ressures and the inlet molar flow rate of secies i (i = HT, H 2O, H 2, HTO) resectively inside the j-th He loo (j=urge, coolant) and is the HT isotoe exchange rate of equilibrium k (k=1, 2). This exchange rates must be exressed as functions of tritium concentrations inside the He loos inserted inside the mass balance equation reorted in Eq. (3.1).,,, and and -12-

29 3. Descrition of the Model Tritium molecular secie is usually considered to be a small ortion of all the tritium forms resent inside the system, since all the amount combine with hydrogen and leads to HT secie. In this isotoe exchange model, the resence of is neglected, thus the concentration is immediately given by the chemical equilibrium constant of equilibrium 1 (see Eq. (3.9)) combining the HT concentration (comuted in Eq. (3.1)) and concentration (fixed in this model). Therefore the isotoe rate exchange of equilibrium 1 is considered negligible with resect the one in equilibrium 2. With this simlifying assumtion, the unique tritium isotoe exchange rate considered in the tritium mass balance of Eq. (3.1) will be the one involved in the chemical equilibrium 2 (Eq. (3.8)), that is, which has to be defined both for the urge and the coolant loos. In the urge gas loo, the considered isotoe exchange rate will be the conversion rate from HTO to HT and, that is. Thus, in order to estimate the isotoe exchange rate inside the Breeding Unit (BU) due to the mentioned chemical equilibrium reorted in (3.8), the inlet molar flow rate of all the tritium chemical forms articiating in this chemical equilibrium must be defined. Inside the BU from the urge gas side we find the following conditions: F F F F in, HTO in, H 2 in, HT in, H O 2 W W 0 He HTO He C C HTO, in W HT, in He G C HTO H, in 2 (3.11) where the inlet concentrations in the HCPB blanket of the i-th form are exressed as a function of the average concentration in the urge loo, obtained by averaging between the inlet and the outlet concentrations inside and outside the breeding unit (see 3.1) as reorted in Eq. (3.3), excet for the hydrogen concentration, which is assumed to be at the BU entrance coincident to the one imosed by the swaming ratio (see Table 4-4 for values of swaming ratio in urge loo) in the urge circuit. According to these conditions and the equilibrium constant exression reorted in Eq. (3.10), the isotoe exchange rate in the urge gas loo becomes: HTO mol s K eq,2 F in, HT F iin, H F, 2 in HTO 2 K eq,2 1 2 K eq,2 F in, HT F iin, H F, 4,2 1 2 in HTO Keq 2 K 1 eq,2 F in, HTO F in, H 2 (3.12) -13-

30 3. Descrition of the Model In the coolant loo, considering the feeding hydrogen and water flow rate and fixed by oxidation control with a fixed ratio, a tritiated water inlet flow rate null and all the ermeated tritium flux from HCPB combining with fed hydrogen, we find the following conditions inside the HCPB BU from the coolant side: F F F F c in, HTO c in, H 2 c in, HT c in, H O 2 W W c He c HT c He C c HT C c HTO, in W c He c HT, in W c He C c H, in CP erm, HT C 2 c H O, in 2 (3.13) where the inlet concentrations inside the BU are related to their resective average concentrations inside the coolant loo exressed in the system of differential equations (3.1), according the relationshis defined in Eq.(3.5). According to these conditions, the isotoe rate exchange in the HCPB blanket from the coolant side, is given by: K F F c c c c mol eq in HT ox in HTO,2,, HT c s (3.14) K eq,2 ox The oxidation ration is usually fixed to a certain value and is considered indisensable to roduce an oxidation otential inside the Helium Coolant System caable of maintaining a thin and stable rotective oxide layer on the rimary side of the steam generator walls [16]. 3.3 Permeation Fluxes The tritium ermeation fluxes entering in the total tritium mass balance are given by: Tritium ermeation flux through Cooling Plates channels ; Tritium ermeation flux from imlanted tritons into the First Wall ; Tritium ermeation flux though Steam Generator tube walls Theory on Hydrogen Isotoes Permeation Tritium atoms have an high mobility through high temerature structural materials, and the driving force of the ermeation is characterized by the tritium artial ressure acting on a given material. Deending on the tritium artial ressures involved in the system, two ossible extreme ermeation models are available: -14-

31 3. Descrition of the Model Diffusion-limited model; Surface-limited model. In the ast many authors studied this net distinction between the two ermeation regimes (e.g. Refs. [11], [12] and [13]) and they stated that for low tritium artial ressures the ermeation is governed by surface limited model, whilst for high values the diffusion rules the mobility thought structural materials. In rincile, according to grahs reorted in Figure 3-1 and Figure 3-2, when the system is characterized by low artial ressures, the diffusive model (roortional to ) overestimates the ermeated flux through a given wall, characterized by certain high and low ressures acting on it and a given temerature, with resective to the one estimated with surfacelimited model (roortional to ). On the other hand, when the system is characterized by relatively high artial ressures (i.e. underlying the right lines of Figure 3-1), a surface limited ermeation model would overestimate the ermeation flux through the same membrane at the same oerative conditions. Figure 3-1 H 2 Permeation Vs. Pressure through Ferritic Steel [11] The threshold value dividing the low and the high ressure areas robably deends on the oerative conditions (e.g. structural materials, temerature, gas comositions, etc.) and, after a literature review, any consistent formulations or criteria have been found to establish this artial ressure. For examle according to Ref. [12] this value has been stated to be around 10 Pa, while in Ref. [11] (as shown in Figure 3-1, this value is included between 10-3 and 10-2 bar (i.e. between 100 and 1000 Pa). -15-

32 3. Descrition of the Model In case of diffusive ermeation model (at relatively high ressures) hydrogen migration through the metal membrane is limited rimarily by hydrogen diffusion in the metal lattice while the surface rocesses (hydrogen adsortion, desortion) are considerably faster [14]. On the other hand, when a surface limited model is assumed, the diffusion through the membrane occurs fast enough, so that any concentration gradient is cancelled by diffusion. Figure 3-2 Overall Permeation Behavior of Hydrogen Gases through Metals [13] Assuming a membrane of a certain material, with a given thickness, an high artial ressure and a low artial ressure acting on each side resectively, the ermeated flux through the membrane for the two limiting models are reorted in Eqs. (3.15) and (3.16). J J diff erm surf erm mol 1 D T m s PRF K S T P T 2 h l h l (3.15) mol k1 2 m s 2 x T k T K T h l 2 2 S 2 x h l (3.16) where: is the tritium diffusivity in the membrane; is solubility (or Sieverts) constant of tritium inside the membrane; is the tritium ermeability of the membrane (Richardson s law); is the adsortion constants of tritium of the membrane surface; -16-

33 3. Descrition of the Model is the surface roughness factor, defined as the ratio of the real area to the geometric area of the surface; is the recombination constant of hydrogen onto the surface of the membrane; is the Permeation Reduction Factor. Coating the membrane with an additional metallic layer (barrier) results in the reduced ermeation if diffusion remains the rate limiting rocess [14]. This is why the PRF is not included in the exression defining the ermeation flux through a membrane driven by surfacelimiting rate. The exerimental roof of the barrier efficiency is a relative reduction of the steady ermeation flux measured at the identical conditions (, T). Its definition is the ratio of the steady flux through the uncoated membrane versus the flux through the coated membrane. From Eq. (3.16) can be derived the following relationshi between Sieverts constant, recombination and adsortion constant, defined as: k 2 T T T k1 krec T 2 (3.17) K S From the tritium analysis oint of view, it would be interesting to carry out the study by considering both models for ermeation and check the influence of the adoted ermeation regime on the results. As shown in the results the differences in terms of tritium losses and inventories are quite remarkable. As it will be seen in the next aragrah, the tye of ermeation regime (i.e. the assumed value of the adsortion constant) has a strong imact on the calculated tritium ermeation rate into the HCS loo. In the following aragrahs the tritium ermeation fluxes listed above will be mathematically described either using diffusion and surface limited models. As assumed by [15], the effect of H 2 swaming in the urge stream as well as in the rimary cooling circuit on the tritium ermeation rate can be neglected, thus considering the HT artial ressure as the driving force of ermeation and not the artial ressure coming from the chemical equilibrium between H 2 and T 2 (see equilibrium reaction (3.7)) Tritium Permeation Flux through CPs Cooling Channels The tritium ermeation flux through the CP cooling channel walls given a secified CPs ermeation area, a wall thickness, a tritium ermeability (defined at the CP wall average temerature ), a ermeation reduction factor (PRF), an adsortion constant on the CP channel surface, -17-

34 3. Descrition of the Model the tritium artial ressure in the urge loo and a tritium artial ressure inside coolant loo is given by: CP erm CP erm mol s mol s diff surf 1 PRF k CP 2 CP P CP CP CP T av, w Aerm c HT HT x CP CP CP CP T K T av, w S 2 av, w 2 A CP erm HT c HT (3.18) (3.19) The HT artial ressure in the j-th loo concentrations (j = urge, coolant) and the corresonding T are related by means of Dalton s law for each, since tritium and Helium can be seen as a mixture of gaseous secies. The Dalton s law describing the relationshi between the i-th tritium form concentration and ressure (with i = HT, HTO) inside the j-th Helium loo (with j = urge, coolant) is defined as: C j i mol 1 kg He M He j i j He (3.20) where is the He atomic weight, and is the total Helium ressure in the j- th loo. Eq. (3.20) is derived considering that the molar fraction (then also the concentration) of a gaseous secies inside a gaseous mixture is roortional to its artial ressure in it. Combining Eqs. (3.18)/(3.19) with (3.20) the ermeation flux through the CP cooling channel can be exressed as a function of HT concentrations in urge and coolant loos equations in Eq. (3.1). and resectively, and ut inside the tritium mass balance Tritium Permeation Flux from Imlanted Tritons onto First Wall The contribution to the tritium ermeation rate into HCS coming from ion imlantation from the lasma into the first wall with the subsequent tritium diffusion towards the cooling channels of the first wall is often neglected (e.g. [15], [16]). In fact, taking into account the foreseen resence of tungsten as coating of the first wall (assumed to be equal to 2 mm [15], [16]), this second contribution to the tritium ermeation into the coolant is negligible. Tungsten is used as a 2 mm coating at the DEMO FW. Tritium (and Deuterium) coming from lasma imlant into the reactor FW. A fraction of the imlanted DT flux recycles back into lasma (recycling) at FW surfaces. The balancing art of the flux diffuses into the cooling circuit and/or builds-u a tritium a D-T inventory (solved and traed) at the DEMO FW structure. -18-

35 3. Descrition of the Model In the literature diverse tritium tracking calculations at the DEMO FW can be found. It is commonly noticed the large uncertainty of ermeation rates. For DEMO -95 secifications values ranging from 6 to 60 g/d are usual (FW MANET). Main sources of uncertainty come from emirical arameters in the equations: value of sticking coefficient (or surface roughness factor already reorted in Eq. (3.16)). On the FW, tritium ermeation and inventory assessment in the W- coating/eurofer/coolant should be derived from a comlete D-T recyclingermeation analysis for nearly steady-state lasma conditions (DEMO) or cyclic ion wallloading (case of ITER-TBM). From DEMO95 study, a tritium transort assessments on the FW (bare MANET) [16] estimated tritium into the HCS at FW ~ 18 g/d (with an uncertainties range of 2-60 g/d). Permeation assessment with 2 mm W-coating reduce such value below 0.1 g/d, and even below if recycling at W surface would be roerly considered. From this literature review, it can be ointed out that tritons imlantation into the FW constitutes a roblem from the ermeated flux into the HCS only if no FW coating is foreseen. In this study, a simlified estimation of the ermeated flux is erformed, in order to determine the influence of the FW on the total tritium losses. Assuming to have the FW characterized by a certain coating membrane facing the lasma defined by a thickness and a ermeability, and the main FW, defined by its thickness (searating the coating and the coolant channels) and its ermeability, the effective FW ermeability can be defined (assuming diffusion to be the rate limiting rocess for FW) as [14]: x x coat FW Peff FW x P coat coat x P FW FW (3.21) Such membrane has been modeled as a membrane comosed of two homogeneous layers. Effective ermeability is based on the sum of ermeation resistances for each layer, analogous to the electrical resistors in series. In the results section a arametric study of tritium losses is carried out by varying the coating thickness, in order to show its influences on the tritium analysis (see 4.3.3). Assuming, then an effective ermeability, the tritium ermeation flux through the FW cooling channel is given by: FW im mol s 1 PRF CP FW Peff T x coat FW av A x FW erm FW J 2 k FW im coat 1 FW HT Tav c (3.22) -19-

36 3. Descrition of the Model where is incident T ion flux from the lasma into the first wall, is the adsortion constant of coating membrane and is the ermeation area onto the FW. The resence of a FW coating barrier is necessary in order to avoid large amount of imlanted tritons into the main coolant but also to rotect the FW from neutrons damages. The PRF on FW channels aearing in Eq. (3.22) is assumed to be coincident to the one on CPs because it is obtained from a formation of an oxidation layer by means of hydrogen and water addition with a certain molar ratio to the coolant circuit. Thus, excet for neutrons and temerature influences on this coating layer, the assumtion is that this PRF is maintained in all the blanket-side coolant loo (i.e. not in SG, where we have different temeratures and structural materials). As reorted in the results, the differences in terms of tritium losses are quite remarkable with and without coating barriers Tritium Permeation Flux though Steam Generator Tube Walls The tritium flux through SG tube walls is obtained considering that the tritium concentration in water is negligible with resect to that in He. Therefore, considering for the SG a ermeation area, a tubes thickness, a ermeability of SG tube material (defined at the SG average tube walls temerature ) and a ermeation reduction factor inside SG heat exchange walls ( ), the tritium ermeation flux through SG tubes (in diffusion and surface limited model otions) is given by: SG erm SG erm mol s mol s diff surf 1 PRF k SG SG 2 P SG SG SG T av, w Aerm c x SG HT SG SG SG 2 SG T av, w K S T av, w Aerm c 2 HT (3.23) (3.24) where is SG the ermeation area, is the SG wall thickness, is the tritium ermeability of SG tubes (defined at the SG tubes walls average temerature ), is the ermeation reduction factor (PRF) due to SG wall oxide layer, is the adsortion constant of SG tubes surface and is the HT artial ressure inside the coolant loo. On SG tubes walls, is usually alied an oxidation layer aimed to kee the corrosion under control, thus reducing the tritium ermeation of a certain. If ermeation is dominated by surface henomena, the reduction in terms of ermeated tritium amounts -20-

37 3. Descrition of the Model results in terms of a reduced adsortion constant for oxidized SG tubes surfaces, which might be several order of magnitudes lower [16]. 3.4 Tritium Flux Associated to Helium Leaks Helium leakages from urge and coolant circuit can occur because of the resence of seals and material imerfections. In this study are considered only the leakages from the coolant circuit since the urge gas system it is assumed to be in a controlled and monitored environment, so the related to the leaked urge Helium has not to be considered and accounted in the tritium losses. Moreover, it is a relatively low ressure system, so the He leakages from this circuit are suosed to be negligible to ones found in the coolant loo. For the evaluation of He leakage in the coolant circuit leakage data are reorted in Gas Cooled Reactors field and they are taken as a reference for out uroses. Estimates of the rate of relenishment necessary to evaluate He leakage vary between 0.1% of total He inventory er day (0.1% inv./d) and one comlete relenishment er year (100 % inv./yr.) [11], [16]. In this study, it is assumed that the leakage rate is the 0.1% of the He inventory inside the coolant loo er day. However, these leakage values seem to be too essimistic (22.6 kg/d are assumed to be lost considering an Helium inventory of order of 22.6 ton [16]), thus for the comutation of the tritium losses related to helium leakage are assumed other values ( coming from more focused analysis on Helium circuit for breeding blankets [17]. Thus, the losses of i-th tritium form due to Helium leakage is deduced from the helium leak flowrate defined as the released Helium flowrate and the i-th form concentration (i = HT, HTO) inside the coolant ; it is defined as: c leak mol c i t W, leak Ci t s (3.25) The total tritium losses due to Helium leakage is obtained by summing the HT and HTO contribution. 3.5 Tritium Losses and Inventories Tritium inventories and tritium losses are the key arameters in a tritium transort analysis. Tritium inventories in this work are characterized by; tritium inventory inside the urge Helium ; -21-

38 3. Descrition of the Model tritium inventory inside the rimary coolant ; tritium inventories inside structural steels (Cooling lates, FW and SG tubes) ; tritium inventory inside the breeder ; tritium inventory inside Beryllium ebbles. Tritium losses are simly given by: Tritium ermeation rate through Steam Generator tubes into the steam line ; Total tritium losses due to Helium leakage with i =HT, HTO Tritium Inventories Tritium Inventories inside Purge and Coolant Loos The first two terms are exressed by means of the average concentrations in urge loo I, and are defined as: g C t C t and the total average concentrations in the coolant loo HT HTO mhe M T (3.26) I c c HT HTO mhe M T c c g C t C t (3.27) where and are the total Helium inventories inside the urge and the coolant loos resectively and is the atomic weight of tritium Tritium Inventory in Steels Tritium inventories inside steels are characterized by the sum of inventories inside structural materials of the breeder (e.g. Cooling lates and First Wall) and those inside the SG tubes. These contributions are evaluated considering the average concentrations and the volume of the k comonent steels (with k = FW, CP, or SG) and the total tritium inventory inside steels is given by: I steel g C V M (3.28) k k steel k steel T The average concentration is calculated averaging the concentrations acting on the m side of the k steel (with m = high or low tritium artial ressure side), which are evaluated by means of Sievert s law as follows: C k,m steel mol = K 3 m k S,steel k m T av,wall k (3.29) -22-

39 3. Descrition of the Model where the is the tritium artial ressure acting on the m side of the k steels (derived from Dalton s laws reorted in Eq. (3.20) using the HT concentrations ) and is the Sievert s constant of tritium inside the k steels evaluated at k steels average temerature values). and (see Table 4-1 and Table 4-4 for When we deal with CPs the high and the low tritium artial ressure are characterized by the one inside urge gas loo and that inside the coolant resectively, when k = FW, are resectively the equivalent imlanted tritons artial ressure (see 3.3.3) and the coolant artial ressure and finally when k = SG the high and the low tritium artial ressures are and the inside steam/water loo resectively. This last artial ressure was assumed to be negligible with resect to and therefore to Tritium Inventory in Breeder Pebble Beds The tritium concentration inside the breeder is obtained by solving the first equation of system of ODEs written in Eq. (3.1), which is uncouled from the other equations and it can be easily integrated in time, giving the following analytical solution: C br T t v res av 1 ex br res T (3.30) av br br t G T where is the tritium residence time inside the breeder and it is strongly deendent on breeder temerature (see Table 4-4 for values). The tritium inventory inside the breeder is simly derived multilying the concentration inside it (see Eq. (3.30)) by the total volume of breeder, and it is defined as: I br br BU mod g CT V br N BU N mod M T (3.31) where, and are the volume of breeder inside the Breeding Unit (BU), the number of BU inside a blanket module and the total number of modules (see Table 4-4 for values). Although this model aears to be accurate and intuitive, since the temerature rofiles into breeder ebbles bed are very imortant for tritium release another aroach is adoted for tritium inventory inside the breeder. In fact, as reorted in Table 4-1, the tritium residence into Li-Orthosilicate has an Arrhenius form, in which it is exonentially decreasing with the 1/T ower of temerature. Therefore, if we have large temerature variations along the breeder rofiles, assuming an average breeder temerature (as done for the model of Eq. (3.31) with ) might give high uncertainties to this imortant -23-

40 3. Descrition of the Model arameter. Thus, assuming to define the breeder volume with the coordinate and the temerature distribution on this domain, the total tritium inventory inside the breeder material can be defined as [18]: I g m( r) res T ( r br ) dv (3.32) where is the local tritium roduction rate and is the breeder volume. From this relation, a simler formula has been derived and it is defined as follows: I br g T br max G T br min br min T br max T res T dt (3.33) where is geometry factor ( for DEMO geometry), is the total tritium roduction rate (see Eq. (3.2)) and and are the maximum and the minimum temeratures in breeder material resectively. As it can be seen, in this way it is ossible to calculate the tritium inventory inside the breeder by taking into account of the oerative temerature ranges Tritium Inventory in Beryllium Pebble Beds The tritium inventory inside Beryllium ebbles is a crucial oint for a tritium assessment of breeding blanket. As far as the beryllium is concerned, since 1999 the reference material grade has been considered the 1-mm ebbles roduced by NGK with electrode rotating methods. The major design issue connected with the use of Be is its behavior under irradiation, mainly swelling and tritium inventory [19]. Lack in the database and in the modeling give large uncertainties in the design calculation of the EOL tritium inventory in Be in FPP conditions. In site of the rogress made to better understanding the hysic of the henomena [20], the goal of roducing a reliable code to suort the designer in these choices, has not been achieved yet. An irradiation camaign to obtain data of Be at 3000 am of helium in 2006 and 6000 am helium in 2008 with temeratures in the range C has started in Petten in the frame of HIDOBE task. With these data the modeling should be imroved and comlementary an emirical extraolation to the DEMO condition ( am) could be attemted. A detailed analysis with irradiated Beryllium has been carried out in FZK [21], in which exerimental data were suorted by theoretical model imlemented into the comutational code ANFIBE, firstly develoed in the years [22]. In this study more imroved models for tritium and helium kinetics in Beryllium were imlemented in order to udate the ANFIBE code from the version 0 to version 1 (see Figure 3-3). -24-