Preliminary analysis of Tritium fuel cycle in Z-pinch driven fusion-fission hybrid reactor

Preliminary analysis of Tritium fuel cycle in Z-pinch driven fusion-fission hybrid reactor 1 first-author 1 1 1 1 1 corresp Corresponding author: zd0823@caep.cn Corresponding author: zd0823@caep.cn zd0823@caep.cn China Academy of Engineering Physics, Institute of Nuclear Physics and Chemistry, Mianyang 621000, China China Academy of Engineering Physics, Institute of Nuclear Physics and Chemistry, Mianyang 621000, China Attaining tritium self-sufficiency is indispensable in a Z-pinch driven fusion-fission hybrid reactor (Z-FFR). In this paper a conceptual design is presented in which the Z-FFR tritium cycle system was divided into eight subsystems. A theoretical analysis of tritium inventory based on the mean residence time was performed to quantitatively obtain the tritium distribution in each subsystem. Tritium self-sufficiency judgment criteria was established using a tritium mass flow analysis method. The dependency relationships between the burning rate, tritium breeding ratio, extraction efficiency, and tritium self-sufficiency were also specified for the steady state. Z-FFR Tritium Self-sufficiency 1. Introduction 1 In the 1950s, the concept of the fusion-fission hybrid reactor was introduced. There are many advantages of this reactor, such as waste management and fuel production [ 1 1 ]. Recently, several different conceptual designs of fusion-fission hybrid reactors have been developed, e.g., magnetic and inertia confinements [ 2 2 - 4 4 2-4 ]. One typical inertia confinement reactor is the In-Zinerator, proposed by the Sandia National Laboratory [ 4 4 - 6 6 4-6 ]. The China Academy of Engineering Physics has also provided a conceptual design of a Z-pinch driven fusion-fission hybrid reactor (Z-FFR) [ 7 7 - 9 9 7-9 ]. In Z-FFR, the main function of the fusion part is to provide high energy neutrons, while the fission zone generates power and the tritium breeding blanket produces tritium. As the important fuel of fusion, tritium is extremely scarce in nature. The problems relating to tritium are similar to those of fusion reactors, such as management, safety issues, and the accountability of tritium [ 10 10 - 13 13 10-13 ]. In order to make efficient use of tritium, achieve tritium self-sufficiency, and evaluate the radiation risks of tritium in a Z-FFR, a detailed analysis of the tritium fuel cycle is essential. Attaining tritium self-sufficiency is also of great importance. In this paper a preliminary analysis of Z-FFR is performed and a tritium mass flow model was established. In particular, the primary subsystems of tritium self-sufficiency were identified. The circulation loop was the key issue in the tritium self-sufficiency analysis. Based on the mean residence time method and design parameters of Z-FFR, the tritium content in subsystems was calculated. In the steady state of the Z-FFR, the tritium inventory of each subsystem based on this model was computed. Then the tritium self-sufficiency judgment and critical conditions were given. Finally, the tritium self-sufficiency conditions were analyzed in a reasonable range for three important parameters, namely the burning rate, tritium breeding ratio (TBR), and extraction efficiency of the isotope separation system. 2. Theory 1 2.1 Calculation model 2 The tritium fuel cycle system of the Z-FFR is shown in Ref [ 14 14 ]. According to the conceptual design, the tritium cycle system was divided into eight subsystems, including the core, which consisted of a fusion core, fission zone, and tritium breeding zone, Z-pinch exhaust processing system (ZEP), tritium extracting system (TES), isotope separation system (ISS), atmosphere detriation system/vent detrition system (ADS/VDS), water detrition system (WDS), tritium storage system (TSS), and target preparation system/R TL handling system (TPS/RHS). The tritium fuel cycle process of our model is shown in Fig. 1 Fig. 1 . In the model, neutrons produced by the deuterium-tritium (DT) fusion reaction in the fusion core are introduced into the tritium breeding zone to breed tritium. After DT ignition, the ZEP recycles the unburned tritium, while the TES extracts tritium from the tritium breeding blanket, and WDS the handles the tritiated water. Afterwards, the impure tritium is introduced into ISS for isotope separation and the separated tritium is stored in TSS. The target preparation and equipment of the tritium fuel are obtained by TPS and RHS, respectively. Then it ultimately produces a tritium cycle. In Fig. 1 Fig. 1 , the solid line represents the main circulation loop leading to tritium self-sufficiency. Since the tritium recovery had a certain time lag from the start of reactor, the analysis below was computed under the assumption of steady tritium self-sufficiency. 2.2 Calculation method 2 Based on the principle of mass conservation and the mean residence time method [ 15 15 - 17 17 15-17 ], we established a theoretical analysis equation of the tritium cycle system to simplify the calculation. Tritium losses of the TPS/RHS and TSS were not considered. 2.2.1 Tritium flow analysis 3 In the consumption and proliferation of tritium, tritium loss by transmission (tritium that is retained in materials and diffused into environment) and tritium loss by decay ( T 1/2 =12.3 yrs) should be taken into consideration [ 16 16 ]. The tritium entering the environment can be estimated backwards from the safety limits. However, compared with the retention, this part is negligible. Tritium loss in the waste is relatively difficult to estimate. In our description equations of the model, the tritium flow was divided into four directions: ① the effective tritium transferring between subsystems; ② the consumption tritium in fusion and breeding tritium; ③ the radioactive-loss tritium; and ④ the nonradioactive-loss tritium. Therefore, the tritium mass flow of each subsystem was obtained. Effective tritium is the tritium that can be totally introduced into the next subsystem. The separate tritium loss in each subsystem was taken into consideration. The parameters in our calculations are listed in the following Table 1 Table 1 . 1 1 Parameters 1 1 Definition 1 1 Λ 1 1 Tritium breeding ratio 1 1 N 1 1 Tritium burning amount per day 1 1 I i 1 1 Effective tritium 1 1 L i 1 1 Effective tritium mass flow 1 1 T i 1 1 Mean residence time 1 1 E i 1 1 Nonradioactive loss fraction 1 1 β 1 1 Burning rate 1 1 η 1 1 Fueling efficiency 1 1 λ 1 1 Radioactive loss fraction 1 1 μ 1 1 Target preparing efficiency 1 1 W 0 1 1 Fraction of tritium from Core to WDS 1 1 W 2 1 1 Fraction of tritium from TES to WDS 1 1 a 1 1 1 Fraction of tritium from ZEP to ADS/VDS Based on the theory mentioned above, the tritium mass flow equations for each subsystem given in Eqs. 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stretchy="false">)</mo><mi>μ</mi><mfrac><mrow><msub><mi>I</mi><mn>5</mn></msub></mrow><mrow><msub><mi>T</mi><mn>5</mn></msub></mrow></mfrac><mo>−</mo><mo stretchy="false">(</mo><mn>1</mn><mo>+</mo><msub><mi>E</mi><mrow><mn>52</mn></mrow></msub><mo stretchy="false">)</mo><mo stretchy="false">(</mo><mn>1</mn><mo>−</mo><mi>μ</mi><mo stretchy="false">)</mo><mfrac><mrow><msub><mi>I</mi><mn>5</mn></msub></mrow><mrow><msub><mi>T</mi><mn>5</mn></msub></mrow></mfrac><mo>−</mo><mi>λ</mi><msub><mi>I</mi><mn>5</mn></msub><mo>,</mo></mrow></math> <math display="block" id="M8"><mrow><mfrac><mrow><mtext>d</mtext><msub><mi>I</mi><mn>6</mn></msub></mrow><mrow><mtext>d</mtext><mi>t</mi></mrow></mfrac><mo>=</mo><msub><mi>a</mi><mn>1</mn></msub><msub><mi>I</mi><mn>1</mn></msub><mo>−</mo><mo stretchy="false">(</mo><mn>1</mn><mo>+</mo><msub><mi>E</mi><mn>6</mn></msub><mo stretchy="false">)</mo><mfrac><mrow><msub><mi>I</mi><mn>6</mn></msub></mrow><mrow><msub><mi>T</mi><mn>6</mn></msub></mrow></mfrac><mo>−</mo><mi>λ</mi><msub><mi>I</mi><mn>6</mn></msub><mo>,</mo></mrow></math> <math display="block" id="M9"><mrow><mfrac><mrow><mtext>d</mtext><msub><mi>I</mi><mn>7</mn></msub></mrow><mrow><mtext>d</mtext><mi>t</mi></mrow></mfrac><mo>=</mo><msub><mi>W</mi><mn>0</mn></msub><msub><mi>I</mi><mn>0</mn></msub><mo>+</mo><msub><mi>W</mi><mn>2</mn></msub><msubsup><mi>I</mi><mn>2</mn><mrow/></msubsup><mo>+</mo><mfrac><mrow><msub><mi>I</mi><mn>6</mn></msub></mrow><mrow><msub><mi>T</mi><mn>6</mn></msub></mrow></mfrac><mo>−</mo><mo stretchy="false">(</mo><mn>1</mn><mo>+</mo><msub><mi>E</mi><mn>7</mn></msub><mo stretchy="false">)</mo><mfrac><mrow><msub><mi>I</mi><mn>7</mn></msub></mrow><mrow><msub><mi>T</mi><mn>7</mn></msub></mrow></mfrac><mo>−</mo><mi>λ</mi><msub><mi>I</mi><mn>7</mn></msub><mo>.</mo></mrow></math> 2.2.2 Tritium self-sufficiency judgment method 3 The fusion power of the Z-FFR stays constant in steady state. Tritium self-sufficiency is a prerequisite for long-term operations. Therefore, the amount of recovery and breeding tritium is required to be higher than the normal supply of TPS / RHS. Therefore, the tritium self-sufficiency is determined by; <math display="block" id="M10"><mrow><mfrac><mrow><msub><mi>I</mi><mn>3</mn></msub></mrow><mrow><msub><mi>T</mi><mn>3</mn></msub></mrow></mfrac><mo>></mo><mfrac><mrow><msub><mi>I</mi><mi>b</mi></msub></mrow><mi>β</mi></mfrac><mo>×</mo><mfrac><mn>1</mn><mi>a</mi></mfrac><mo>×</mo><mfrac><mn>1</mn><mi>η</mi></mfrac><mo>,</mo></mrow></math> where I b and a are the tritium combustion of the core and tritium injection efficiency, respectively. The initial tritium is stored in the TSS. When the hybrid reactor starts to work, tritium in the TSS is gradually reduced to a minimum amount that can maintain the normal operation of the TPS/RHS and core. At the same time, the breeding and recycling tritium provide the consumption. Therefore, in the steady state, it is reasonable to determine the tritium self-sufficiency by comparing the tritium flow of the ISS with the consumption of the TPS/RHS. 2.3 Parameters 2 As the tritium processing system in the Z-FFR is similar to a pure fusion reactor, some parameters of the tritium systems test assembly (TSTA) were applied in our calculations. The input parameters are listed in Table 2 Table 2 - 3 3 by referring to Ref. [ 14 14 , 18 18 - 21 21 18-21 ]. As the fission zone in the Z-FFR produces extra neutrons, it is relatively easier to make the TBR reach 1.15 comparing with international thermonuclear experimental reactor (ITER). Generally, the operation temperature of the ISS is very low and nonradioactive loss can be ignored. 1 1 System 1 1 Tritium mean residence time (T/day) 1 1 Percentage of nonradioactive loss (%) 1 1 Z-pinch exhaust processing system 1 1 1 1 1 0.1 1 1 Tritium extraction system 1 1 1 1 1 0.1 1 1 Isotope separation system 1 1 0.1 1 1 0 1 1 Tritium storage system 1 1 / 1 1 0.01 1 1 Water detriation system 1 1 0.5 1 1 0.0001 1 1 Fusion power 1 1 150MW 1 1 Tritium fueling into the core through TPS/RHS 1 1 79.78g/day 1 1 Burning rate 1 1 30% 1 1 Tritium breeding ratio 1 1 1.15 1 1 Tritium efficiency of ZEP entering ISS 1 1 95% 1 1 Tritium efficiency of TES entering ISS 1 1 95% 1 1 Tritium efficiency of WDS entering ISS 1 1 90% 1 1 TPS/RHS targeting efficiency 1 1 99% 3. Results and discussion 1 3.1 Tritium in subsystems 2 The total tritium of each subsystem consisted of tritium loss and effective tritium. Therefore, it was expected that the tritium handling capacity of each subsystem should be marginally higher than the effective tritium mass flow. The effective tritium mass and effective tritium mass flows are listed in Table 4 Table 4 , which can be used as a reference for the Z-FFR design. 1 1 subsystem name 1 1   1 1 Effective tritium (g) 1 1 Effective tritium mass flow (g/day) 1 1 Core 1 1 I 0 1 1 / 1 1 77.50 1 1 ZEP 1 1 I 1 1 1 52.30 1 1 52.30 1 1 TES 1 1 I 2 1 1 25.40 1 1 25.40 1 1 ISS 1 1 I 3 1 1 8.13 1 1 81.30 1 1 TSS 1 1 I 4 1 1 / 1 1 80.59 1 1 WDS 1 1 I 7 1 1 1.80 1 1 3.60 3.2 Critical requirement of tritium self-sufficiency 2 In the design of the Z-FFR [ 14 14 ], the burning rate was estimated at 30%, while TBR and extraction efficiency were set to 1.15 and 95%, respectively, to meet the requirements of tritium self-sufficiency. In our model and calculation, the limited condition for every parameter was calculated. The results showed that the burning rate or extraction efficiency must be greater than 23.9% and 87%, respectively. As the burning rate is supposed to reach 40%, it is not possible for the extraction efficiency to be 100%. The burning rate changed from 23.9% to 40% and the extraction efficiency changed from 87% to 99%. The critical requirements of the extraction efficiency, burning rate, and TBR are shown in Figs. 2 Figs. 2 , 3 3 , and 4 4 . As shown in Figs. 2 Figs. 2 , 3 3 , and 4 4 , the three crucial parameters of the Z-FFR were considered under the assumption of tritium self-sufficiency. The results indicated that the design leaves a certain margin for tritium self-sufficiency. As the fusion power stayed constant, the general principle that a higher burning rate is better was calculated quantitatively. The increase in the burning rate led to a decrease of tritium that was needed for injection into the core, and managed in the subsystems. The goal of the TBR is to attain tritium self-sufficiency. A higher TBR can be used to lower the requirements of the other parameters, or it can produce more tritium than is needed for self-sufficiency and further used to supply another reactor. However, improvements of the tritium treatment capacity of subsystems are also required. The security risk of the Z-FFR will increase due to excessive tritium over the entirety of the tritium cycle. In the analysis, the radioactive and nonradioactive losses of subsystems were taken into account, except for the TSS and TPS/RHS. There are still uncertainties caused by the model description and other differences in specific details. The unknown parameters of the TSS and TPS/RHS in the Z-FFR still need to be addressed in the future. Since the TBR of the Z-FFR can be relatively high, the calculations and complementary relationship of tritium self-sufficiency shown in Figs. 2 Figs. 2 - 4 4 provide good references for Z-FFR design. 4. Conclusion 1 The preliminary analysis model of the Z-FFR tritium cycle system based on the mean residence time method was established, making it available for calculations of the effective tritium and tritium mass flow in the steady state. The tritium self-sufficiency was also determined to analyze the critical requirements for the Z-FFR. The calculation of the tritium fuel cycle in Z-FFR was completed. The effective tritium and tritium mass flow of some subsystems were obtained by employing the design parameters in steady state. It was found that the ZEP contained the most effective tritium among the subsystems, followed by the TES, ISS, and WDS. However, the effective tritium mass flow of ISS was the highest, followed by the TSS, core, ZEP, TES, and WDS. There are three crucial parameters for the tritium self-sufficiency, the burning rate, extraction efficiency, and TBR. 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Des . 106 , 17 - 20 ( 2016 ). doi: 10.1016/j.fusengdes.2016.02.100 http://doi.org/10.1016/j.fusengdes.2016.02.100 Tritium fuel cycle modeling and tritium breeding analysis for CFETR 10.1007/s41365-018-0441-x This work was supported by the National Natural Science Foundation of China (No. 11505165) 2017-04-18 2017-06-21 2017-06-27 2018-05-30 2018-07-01 2021-04-11 © China Science Publishing & Media Ltd. (Science Press), Shanghai Institute of Applied Physics, the Chinese Academy of Sciences, ChineseNuclear Society and Springer Nature Singapore Pte Ltd. 2018 This is a post-peer-review, pre-copyedit version of an article published in Nuclear Science and Techniques. The final authenticated version is available online at: http://dx.doi.org/10.1007/s41365-018-0441-x http://dx.doi.org/10.1007/s41365-018-0441-x . 2018 Nuclear Science and Techniques 07 29