Removal of tritiated water molecules by isotope exchange reaction between H₂O vapor and tritium water

Abstract

Developing a cost-effective method for separating and concentrating tritium water (HTO) from light water (H₂O) without consuming additional energy is crucial for achieving reliable and safe nuclear fission and fusion energy technologies. However, this presents a significant challenge because of the difficulties in obtaining basic information, such as the chemical and physical properties of HTO molecules. Here, we investigate the isotope exchange reaction (IER) between HTO molecules in H₂O solution and H₂O vapor in the atmosphere. The reduction and purification rates of HTO-containing water were measured by varying the system conditions, such as temperature (20−50 °C) and humidity (50 %–90 %), under an equilibrium state between the liquid phase (water) and vapor phase (air). Our findings indicate that the concentration of HTO in the solution can be significantly reduced by increasing H₂O vapor in the atmosphere. This result can be quantitatively explained by considering the entropy of mixing between the solution and vapor phases. The results obtained here provide both basic understanding on the exchange process between liquid- and vapor-water molecules and a passive technology for treating HTO-containing water.

Highlights

• •Isotope exchange reaction found as a viable method to purify HTO-containing water.
• •Concentration of HTO can be reduced by increasing H₂O vapor in the atmosphere.
• •Our passive method consumes lower energy and time compared to traditional methods.
• •Airtightness of the storage tank controls HTO concentration reduction rate.

1. Introduction

Tritium is a radioactive isotope of hydrogen that decays by beta emission. It has a physical half-life of 12.3 years [1,2] and a maximum emission energy of 18.6 keV (average energy of 5.7 keV) [3]. Tritium is naturally produced through nuclear reactions caused by cosmic rays in the atmosphere [4,5]. Annual tritium production is approximately 10¹⁶–10¹⁷ Bq [4,6]. The artificial tritium production exceeds natural production and is caused by nuclear fission reactors, nuclear weapons testing, and decommissioning activities, including dismantling and spent fuel reprocessing [[6], [7], [8], [9]]. Large quantities of tritium have been released into rivers, lakes, oceans, and the atmosphere at levels below national legislation limits [10]. However, this amount is expected to increase with new fission reactors and the realization of future fusion energy [[11], [12], [13], [14]].

Various studies have been conducted on technologies to separate and concentrate tritium from contaminated water and/or air, including distillation methods [15,16], Girdler sulfide processing [17], electrolysis methods [18,19], catalytic isotope exchange methods [[20], [21], [22]], and functional nanomaterial usage [23,24]. These technologies are important for solving current and future nuclear power problems and reducing the tritium that is continuously discharged into the natural environment. However, these technologies use high concentrations of tritium, large amounts of energy and/or expensive catalysts or materials; therefore, an economical and efficient separation and concentration method (ecosystem) has yet to be developed. This is because hydrogen isotopes have nearly identical molecular sizes, shapes, and thermodynamic properties [25,26]. Therefore, to separate very low concentration of tritiated water (HTO) molecules from environmental water or air systems, a fundamental understanding of HTO molecules such as chemical and physical properties is required. Specifically, the isotope exchange reaction (IER) between HTO and H₂O molecules must be understood to achieve efficient separation.

The IER considered here is a vapor-liquid exchange process involving evaporation and condensation expressed by the following reaction:

H₂O (liquid) + HTO (vapor) ⇄ H₂O (vapor) + HTO (liquid). (1)

This is known as an isotope exchange reaction between HTO vapor and water [27]. The equilibrium constant κ for this reaction is expressed as

$$\kappa =\exp \left(\frac{37813.2}{T^2}-\frac{136.751}{T}+0.124096\right)\text{,}$$ (2)

and is approximately κ = 1.09 at T = 303 K, as reported by Van Hook [28]. The HTO molecules can be concentrated in H₂O liquid using this low equilibrium constant. However, this low value of κ suggests that the concentration of dilute-HTO vapor into the liquid phase using the reaction from left to right is inefficient, and the concentration requires considerable energy and time.

This study investigates the following IER process from right to left: the exchange reaction between HTO molecules in an H₂O solution and H₂O vapor in the atmosphere. The equilibrium constant in this direction is approximately 1 at room temperature and using H₂O vapor in the atmosphere minimizes the partial pressure of the HTO vapor. Here we investigate the fundamental aspects of this IER process and try to explore the possibility of purifying a large quantity of dilute HTO solution using atmospheric humidity. To attain this possibility, the reduction and purification rates of HTO-containing water were measured by varying the system conditions, such as temperature (20−50 °C) and humidity (50 %–90 %), under an equilibrium state between the liquid phase (water) and vapor phase (air). A quantitative explanation for this result is based on the entropy of mixing between the solution and vapor phases. According to the thermodynamic analysis, the IER process can be controlled by varying the amount of H₂O vapor injected into the system. Consequently, the results obtained here provide a fundamental understanding of the exchange processes between liquid and vapor water molecules using HTO. Furthermore, we consider that the IER process elucidated here leads to a safe and efficient passive technology for treating HTO-containing water discharged from a nuclear power plant and collecting future nuclear fusion resources.

2. Materials and methods

2.1. Model of the exchange reaction between H₂O and HTO molecules at the interface of water

The surface level of the water does not change under saturated vapor pressure because the condensation and evaporation processes between the vapor and liquid phases are in equilibrium. However, the dynamic motion of H₂O molecules at the interface on the order of picoseconds to nanoseconds shows frequent exchange reactions between the liquid and vapor. For instance, at 300 K, approximately 250 mol of water vapor molecules collide with 1 m² of water surface per second [29,30]. Although most of these molecules are reflected, some are absorbed by the water surface. This exchange reaction occurs in H₂O molecules and its isotope molecules, such as HTO, as shown in Fig. 1. By successively introducing clear water vapor onto the surface of the HTO-containing water, the number of HTO molecules in the HTO-containing water is reduced; thus, purifying the solution (see Supplemental information V1). The degree of purification of HTO-containing water can be quantitatively explained by considering the entropy of mixing between the liquid and vapor phases, as shown in the following thermodynamic analysis.

Fig. 1.

Model for exchange reaction. (a) H₂O molecules (vapor) entering the water surface. Most of them are reflected, while some are absorbed. (b) Exchange reaction between H₂O and HTO at the water surface. The number of HTO molecules in the HTO-containing water is reduced and purification occurs.

2.2. Formulation of HTO and H₂O exchange reactions: Thermal equilibrium state model

We consider the vapor-liquid interface to be in thermal equilibrium. In this case, the number of H₂O and HTO molecules in the vapor-liquid system as a function of duration t can be described as

$$N_1\left(t\right)=N_{1\text{v}}\left(t\right)+N_{1l}\left(t\right)\text{,}$$ (3)

$$N_2=N_{2\text{v}}\left(t\right)+N_{2l}\left(t\right)\text{,}$$ (4)

where subscripts 1, 2, l, and $\text{v}$ denote H₂O molecules, HTO molecules, liquid phase, and vapor phase, respectively, N₁(t) and N₂ are the total number of H₂O and HTO molecules, respectively, and N₂ takes a constant value. (We do not consider the physical half-life of 12.3 years during the experiments.) When the system is in equilibrium, the vapor pressure P can be described by the equation of state for an ideal gas as follows:

$$P_{1}V=N_{1\text{v}}{k}_{B}T\text{,}$$ (5)

$$P_{2}V=N_{2\text{v}}{k}_{B}T\text{,}$$ (6)

where k_B is Boltzmann constant, V (cm³) is the volume, and T (K) is the temperature of the system. By applying Raoult's law for H₂O liquid and Henry's law for liquid HTO, the equilibrium vapor pressure can be described as

$$P_1=P_1^0\frac{N_{1l}}{N_{1l}+N_{2l}}\text{,}$$ (7)

$$P_2=P_2^0{\gamma }_{12}\frac{N_{2l}}{N_{1l}+N_{2l}}\text{,}$$ (8)

where $P_1^0$ and $P_2^0$ are the equilibrium vapor pressures of pure H₂O and HTO, respectively, and γ₁₂ is a constant calculated from the chemical potentials and interaction energy between the H₂O and HTO molecules in the liquid. Referring to the equilibrium constant in Ref. 28, we assume

$$\frac{|P_1^0-P_2^0{\gamma }_{12}|}{P_1^0}«1\text{.}$$ (9)

Using Eq. (9), the following equation can be obtained under the equilibrium conditions:

$$\frac{N_{2l}\left(t\right)}{N_{1l}\left(t\right)}=\frac{N_{2\text{v}}\left(t\right)}{N_{1\text{v}}\left(t\right)}=\frac{N_{2l}\left(t\right)+N_{2\text{v}}\left(t\right)}{N_{1l}\left(t\right)+N_{1\text{v}}\left(t\right)}=\frac{N_2}{N_1\left(t\right)}\text{.}$$ (10)

Therefore, we can purify the HTO-containing water (decrease the rate of $N_{2l}/N_{1l}$) by increasing the amount of H₂O vapor (increase the molar number of $N_{1\text{v}}$). To quantitatively evaluate $N_{1\text{v}}$, we consider the H₂O-vapor-injection model described in Fig. 2. We increase the volume of the vapor phase (represented by the light-gray-colored cylinder) with a velocity of $v^{\left(T\right)}$ while maintaining thermal equilibrium at temperature T (K). The increase in volume results in the introduction of H₂O vapor from the reservoir (that is, H₂O vapor enters from outside the system). When the temperature of the system is T (K), the amount of H₂O vapor in the volume $N_{1\text{v}}\left(t\right)$, can be calculated by multiplying the saturated vapor density ρ^(T) (mol/cm³), relative humidity Φ, HTO-containing-water-surface area S (cm²), velocity $v^{\left(T\right)}$ (cm/h), and duration t (h) as follows:

$$N_{1\text{v}}\left(t\right)=\mathit{\Phi }{\rho }^{\left(T\right)}S{v}^{\left(T\right)}t\text{.}$$ (11)

Substituting Eq. (11) into Eq. (10), the normalized reduction rate of HTO-containing water as a function of the duration η(t) can be expressed as

$$\eta \left(t\right)=\left(\frac{N_{2l}\left(t\right)}{N_{1l}\left(t\right)}\right)/\left(\frac{N_{2l}\left(0\right)}{N_{1l}\left(0\right)}\right)=\frac{1}{1+\mathit{\Phi }{\rho }^{\left(T\right)}S{v}^{\left(T\right)}t/N_1\left(0\right)}\text{,}$$ (12)

where N₁(0) is the initial number of H₂O molecules in water. Eq. (12) represents that HTO-containing water can be purified by the amount of injected water vapor expressed by Eq. (11). We note here that the same result of Eq. (12) can be obtained based on the reaction rate analysis described in Eq. (1). To determine the IER velocities $v^{\left(T\right)}$ as a function of temperature, as in Eq. (11), we performed experiments by varying the system temperature from 20 to 50 °C. After experimentally determining the velocities, we conducted S- and Φ-dependence measurements to confirm the validity of Eq. (12).

Fig. 2.

Theoretical model to calculate isotope exchange reaction (IER) using H₂O vapor injection. Red and black circles represent HTO and H₂O molecules, respectively. Volume of the vapor phase (light-gray-color cylinder) is increased with velocity $v^{\left(T\right)}$ while maintaining thermal equilibrium. When the temperature of the system is T (K) and initial H₂O liquid molar number of N₁(0), the amount of H₂O vapor can be calculated as the product of the saturated vapor density ρ (mol/cm³), relative humidity Φ, surface area S (cm²), velocity $v^{\left(T\right)}$, and duration t (h). (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)

2.3. Experimental setup for HTO and H₂O exchange reactions

Fig. 3 shows the experimental setup for the HTO and H₂O IER measurements. Water containing HTO at a concentration of 18.5 GBq/mL (ART0194; American Radiolabeled Chemicals, Inc. St. Louis, Missouri, USA) was diluted with purified water with resistivity above 18 MΩcm (Milli-Q Advantage, Merck KGaA, Darmstadt, Germany) to obtain 250 mL of HTO-containing water at a concentration of 1.67 MBq/L. HTO-containing water was placed in a constant-temperature and constant-humidity chamber (STC-V, SANPLATEC Corp. Osaka, Japan). We varied the temperature and humidity inside the chamber from 20 to 50 °C and 50 %–90 %, respectively. We also varied the surface area of HTO-containing water using beakers of different sizes ranging from 80 to 160 mm in diameter to confirm the assumption described in Eq. (11). To provide clear H₂O vapor to the HTO-containing-water surface, the HTO-containing vapor was removed through an exhaust hood using a dry scroll pump (IDP-3, Varian-Agilent Technologies Corp. California, USA). A flow controller (FS-25 N₂, YAMATO SANGYO Corp. Osaka, Japan) was used to control the evacuation flow rate and maintain thermal equilibrium. The HTO-containing vapor was cooled into water liquid. A Graham condenser (COG-031525, AS ONE Corp. Osaka, Japan) was used to evaluate the amount of water vapor injected into the system. The HTO concentration in the HTO-containing water (high- and low-concentration beakers in Fig. 3) was measured by collecting 100 μL of the solution from the water and then dissolving it in a 5 mL liquid scintillation cocktail (Monofluor LS-191-2, National Diagnostics, Georgia, USA). The mixture was then placed in a low-diffusion polyethylene vial (6000477, PerkinElmer, Connecticut, USA). A liquid scintillation counter (LSC-6000; Nippon RayTech Co., Ltd. Tokyo, Japan) was used for the measurements. The accuracy of the experimental system such as temperature is ±1.0 °C and that of humidity is ±3.0 %. All experiments were performed at least three times independently and all data were expressed as the mean ± standard deviation. All experiments were performed with permission (#23–426) from the Isotope Research Laboratory of Nagoya City University.

Fig. 3.

Experimental setup for HTO and H₂O exchange reaction measurements.

3. Results

3.1. Temperature dependence of IER velocity measurements (Φ = 90 % and S = 200 cm²)

The temperature dependence of IER velocity ($v^{\left(T\right)}$) measurements was performed between 20 and 50 °C at a humidity of 90 %, and surface area of 200 cm². Fig. 4(a) shows the normalized reduction rate of HTO in HTO-containing water as a function of exchange time under the above conditions. The blue, green, brown, and red circles represent the experimentally observed reduction rates at 20, 30, 40, and 50 °C, respectively. The reduction rate increases with increasing temperature. The solid lines represent the theoretically fitted curves, as described by Eq. (12), with IER velocity of $v^{\left(20°C\right)}=3530$ (cm/h), $v^{\left(30°C\right)}=5120$ (cm/h), $v^{\left(40°C\right)}=7609$ (cm/h), and $v^{\left(50°C\right)}=10718$ (cm/h). The IER reaction velocity becomes larger as the temperature increases. The values of IER velocities and saturated vapor pressures [29,31] are provided in Supplemental information (Table S1). The fitted curves described the experimental results well, indicating the validity of Eq. (12). The magnitude of the exchange reaction obtained using this system is interesting. For example, at 30 °C [$v^{\left(30°C\right)}=5120$ (cm/h), ${\rho }^{\left(30°C\right)}=1.69\times {10}^{-6}$ (mol/cm³), humidity Φ = 90 %, and surface area S = 200 cm²], after 100 h, approximately 155 mol of H₂O vapor will be absorbed into the liquid and the same amount of HTO-containing H₂O water molecules will evaporate from the liquid.

Fig. 4.

Time-dependent reduction rates of HTO in HTO-containing water versus (a) temperature: 20 °C (blue circles), 30 °C (green circles), 40 °C (brown circles) and 50 °C (red circles); (b) surface area: 50 cm² (blue circles), 100 cm² (green circles), and 200 cm² (red circles); and (c) humidity: 50 % (blue circles), 70 % (green circles), and 90 % (red circles). (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)

3.2. Surface area dependence measurements (T = 30 °C and Φ = 90 %)

Surface area dependence measurements were performed by using polypropylene beakers with diameters of 80 mm (S₁: 50 cm²), 112 mm (S₂: 100 cm²), and 160 mm (S₃: 200 cm²) at 30 °C and a humidity of 90 %. Fig. 4(b) shows the normalized reduction rate as a function of exchange time at the surface area of S₁ (blue circles), S₂ (green circles), and S₃ (red circles). The reduction rate increases with increasing the surface area. The solid lines represent the theoretically fitted curves described in Eq. (12) for the three surface areas. All these curves were fitted by the unique parameter determined by the previous temperature dependence experiments, with $v^{\left(30°C\right)}=5120$ (cm/h), ${\rho }^{\left(30°C\right)}=1.69\times {10}^{-6}$ (mol/cm³), Φ = 0.9, and N₁(0) = 13.9 mol. The fitted curves accurately describe the experimental results. The agreement between the experimental results and theoretical curves shows a strong correlation between the reduction rates and surface area.

3.3. Humidity dependence measurements (T = 30 °C and S = 50 cm²)

Humidity dependence measurements were performed by changing the humidity level from 50 % to 90 % at 30 °C and a surface area of 50 cm². Fig. 4(c) shows the normalized reduction rate as a function of exchange time at relative humidity levels of 50 % (blue circles), 70 % (green circles), and 90 % (red circles). The reduction rate increases with increasing humidity. The solid lines represent the theoretically fitted curves described in Eq. (12) for each humidity level (Φ = 0.5, 0.7, or 0.9) with $v^{\left(30°C\right)}=5120$ (cm/h), ${\rho }^{\left(30°C\right)}=1.69\times {10}^{-6}$ (mol/cm³), N₁(0) = 13.9 mol, and surface area S = 50 cm². The fitted curves accurately describe the experimental results. The agreement between the experimental results and theoretical curves shows a strong correlation between the reduction rates and humidity.

3.4. Supply rate plots

We performed temperature-, surface area-, and humidity-dependence experiments. The experimental results indicate that the reduction rates are accurately described by Eq. (12). Here, to describe these experimental results in a unified manner, we introduce the variable ξ, which represent the supply rate of the water vapor introduced into the liquid system as

$$\xi =\frac{1}{N_1\left(0\right)}\mathit{\Phi }{\rho }^{\left(T\right)}S{v}^{\left(T\right)}t\text{.}$$ (13)

Using Eq. (13), Eq. (12) can be simplified to η(ξ) = 1/(1+ξ), and each reduction rate obtained from the previous experiments (Sections 1, 2, 3) can be fitted by a single curve. Fig. 5 shows all the plots of reduction rates η as a function of ξ, where ξ was calculated by putting the experimental conditions of N₁(0), $v^{\left(T\right)}$, ${\rho }^{\left(T\right)}$, S, Φ, and t, into Eq. (13). The solid circles, squares, and rhombus represent the points obtained from the temperature-dependence- (Section 3.1), surface-area- (Section 3.2), and humidity-dependence-experiments (Section 3.3), respectively. The plots of reduction rates as a function of ξ align completely with the theoretical curve of η(ξ) = 1/(1+ξ) over a wide range of regions from small (0≦ξ≦20; as shown in the inset) to large (0≦ξ≦100) values. This alignment strongly suggests that the purification of HTO-containing water is governed by the IER between liquid- and vapor-water molecules and that the magnitude of reduction increases at large ξ.

Fig. 5.

Reduction rate of HTO plotted against supply rate ξ. Solid circles are points from the temperature dependence experiments, where blue, green, brown, and red circles represent 20, 30, 40, and 50 °C, respectively. Solid squares are points from the surface area dependence experiments, where blue, green, and red squares represent 50, 100, and 200 cm², respectively. Solid rhombus are points from the humidity dependence experiments, where blue, green, and red rhombus represent 50 %, 70 %, and 90 %, respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)

4. Discussion

The exchange reaction described in this paper likely occurs continuously in the HTO storage tanks at the Fukushima nuclear power plant. Here we quantitatively evaluate the IER velocities in the Fukushima HTO storage tank, $v_F^{\left(T\right)}$, based on the IER model. We use the following equation, considering a physical half-life of τ = 12.3 years:

$${\eta }_F\left(t\right)=\frac{{\left(1/2\right)}^{t/\tau }}{1+\mathit{\Phi }{\rho }^{\left(T\right)}S{v_F}^{\left(T\right)}t/N_F\left(0\right)}\text{,}$$ (14)

where ${\eta }_F\left(t\right)$ is the normalized reduction rate of the HTO-containing water in the Fukushima HTO storage tank, N_F(0) is the initial number of H₂O molecules in the tank, and t is the time elapsed between HTO concentration measurements. Using Eq. (14) and the reported concentration values of 6.19 × 10⁵ Bq/L in Ref. [32] and 5.38 × 10⁵ Bq/L in Refs. [33,34], we calculate the velocity $v_F^{\left(13.4°C\right)}$ as 200 cm/h. This calculation assumed an average temperature of T = 13.4 °C [35], $\mathit{\rho }$ = 6.47 × 10⁻⁷ mol/cm³ [31], Φ = 69 % [35], S = 1 × 10⁶ cm² [36], $N_F\left(0\right)$ = 5.6 × 10⁷ mol [36], and t = 17520 h (2 years from 2021 to 2023) [[32], [33], [34]]. This velocity shows that although the tanks are well sealed, achieving a perfect seal, such as a vacuum vessel, is challenging, and that IERs occur over an extended period at the low reaction velocity. There is a minimal air exchange between the interior and exterior atmospheres of the tank, possibly reducing the concentration of HTO in the storage tank to 1/10 in 34 years as shown by the red curve in Fig. 6. The reduction rates for various IER velocities are also shown in Fig. 6; for example, $v_F^{\left(13.4°C\right)}$ as 0 cm/h (perfect seal), the rate is shown by the blue line, 200 cm/h by the red line, 2000 cm/h by the green line, 10000 cm/h by the pink line, and 20000 cm/h by the brown line. The velocity of $v_F^{\left(13.4°C\right)}=200\text{cm/h}$ was obtained from the IER experiments conducted here and the average values of temperature and humidity recorded throughout the year. However, it is important to note that temperature and humidity levels can vary significantly depending on the season and location. Therefore, we consider that on-site evaluation is necessary to accurately determine this velocity.

Fig. 6.

HTO concentration reduction rates as a function of adjusting the airtightness. $v_F^{\left(13.4°C\right)}$ as 0 cm/h (perfect seal), the rate is shown by blue line, 200 cm/h by red line, 2000 cm/h by green line, 10000 cm/h by pink line, and 20000 cm/h by brown line. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)

A comparison of the energy savings achievable through the proposed method with those achievable through the conventional evaporation method is required. Based on the values reported in Refs. [37] and [38], it is assumed that each nuclear power plant evaporates 10⁴ m³ of tritiated water per year with a concentration of 10⁶ Bq/L. In this case, the total amount of energy required to evaporate is approximately 10¹³ J. (It requires 1 J to treat 1 Bq tritium.) When we assume the environmental conditions of T = 13.4 °C, Φ = 69 %, and $v_F^{\left(13.4°\mathrm{C}\right)}=20000\text{cm/h}$ discussed above, and that we can prepare S = 1 × 10⁸ cm², the concentration of 10⁶ Bq/L can be reduced to 6 × 10⁴ Bq/L after one year by the IER. In environments with higher temperature, humidity, and wind speed, the purification velocity increases, allowing for the treatment of a smaller area. To implement the IER method described here, it is necessary to consider various aspects, including meteorological conditions, the required treatment time, and cost-effectiveness.

The enrichment of HTO is an open question. To solve this problem, the diverse functionalities within metal hydrides and nanomaterials make them promising candidates for separating and storing tritium [23,24]. In particular, the surface of hydrogen-terminated nanocrystalline silicon (n-SiH) has been investigated to separate deuterium efficiently [39]. Based on the previous results [[39], [40], [41]], we can expect the efficient exchange reaction occurring between the surface of n-SiH and HTO vapor, such as n-SiH (Solid) + HTO (Vapor) ⇄ n-SiT (Solid) + H₂O (Vapor). The rate of this reaction from left to right was theoretically calculated to be larger than that from right to left by more than one order of magnitude [[39], [40], [41]]. Therefore, this simple exchange process on the n-SiH surface, which is based on the second most abundant element in the Earth, may provide a more sustainable, economical, and environmentally friendly method for tritium enrichment. This protocol, using n-Si, is currently under investigation and will be reported elsewhere.

Interphase mass transfer at the liquid-vapor interface of water is a fundamental process that impacts many areas of physical science, engineering, and biology [42]. However, despite intensive research, the reported evaporation and condensation coefficients [43] differ three order of magnitude [44,45] and there is currently no consensus as to the rate. Based on our results by using HTO molecules, the evaporation coefficient, ε_E [42,43], can be estimated as ε_E = 1 × 10⁻⁴ at 30 °C, which is approximately the same value as that is previously observed [44,45]. To determine the coefficients correctly, we are currently planning a closed system experiment; for example, HTO transfer measurement between a HTO containing water and a purified water in a closed system. Furthermore, we are currently investigating the use of Hofmeister ions [46,47] on the effect of IER. Because the evaporation and condensation process can be controlled by the Hofmeister ions. For example, NaI shows the largest evaporation rate and Na₂HPO₄ shows the smallest evaporation rate [46,47]. Both the determination of the coefficients and the effects of Hofmeister ions on the IER by using HTO molecules are under investigation and will be reported elsewhere.

5. Conclusion

This study determined IER velocities between HTO in H₂O solvent and atmospheric water vapor under various environmental conditions. The results obtained here were quantitatively analyzed by the IER mechanism using thermodynamic calculations. Introducing H₂O vapor onto the surface of HTO-containing water can purify the water without consuming significant energy or time compared to generally used water evaporation discharging. The method presented here offers energy saving approach for treating HTO-containing water discharged from a nuclear power plant and for developing future nuclear fusion technology. The low-temperature treating process compared to the high-temperature vapor discharges may facilitate the handling of tritium-containing water and mitigates corrosion deterioration of nuclear equipment; for example the deterioration of Zr alloys caused by high temperature and humidity conditions [48,49]. Furthermore, we consider that the results obtained in this study may provide fundamental information on the simulation of global circulation of HTO between the ocean and the atmosphere [4,9,50].

Data availability statement

Data will be made available on request.

CRediT authorship contribution statement

Takahiro Matsumoto: Writing – review & editing, Writing – original draft, Project administration, Funding acquisition, Conceptualization. Chiyori Sakuragawa: Visualization, Resources, Investigation, Data curation. Tong Mu: Software, Resources, Methodology, Data curation. Koki Tachibana: Methodology, Investigation, Data curation. Masashi Ishihara: Resources, Methodology, Conceptualization. Makoto Tomita: Writing – review & editing, Supervision, Formal analysis. Hidehiko Sugimoto: Writing – review & editing, Supervision, Formal analysis, Conceptualization.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Appendix B. Supplementary data

The following are the Supplementary data to this article.