1.Introduction

Pyroprocessing technology was developed in the United States in the 1960s for treating metal fuels. A new technique for pyroprocessing was designed by adding an oxide reduction process. Given the increased resistance to nuclear proliferation, this new method is considered a promising one for treating and recycling spent oxide fuels, as it involves the use of simple processing equipment and has low processing costs [1-4]. Spent oxide fuel is reduced into a metal by an electrochemical method while using a high-temperature molten salt as the reaction medium. After being subjected to electrorefining and electrowinning processes, the reduced metal fuel can be used in sodiumcooled fast reactors.

The Korea Atomic Energy Research Institute (KAERI) has been developing a pyroprocessing process [5-7]. The vacuum distillation process known as cathode processing, follows the oxide reduction stage and has been developed to remove the residual salt, allowing for clear fuel metal to be supplied for the next step, which is electrorefining.

The equipment used for salt vacuum distillation is operated in a glove box in an argon atmosphere (Fig. 1 (a)). The equipment consists of two sections. These are, an evaporator, which is the lower part and is used to evaporate the molten salt into the vapor state at a high temperature (800–900°C) and vacuum pressure; and a receiver, which is positioned on the upper side and is used to recover the molten salt in powder form. KAERI has manufactured this apparatus in several sizes and has been able to achieve a fuel recovery rate of 95% [8]. However it is very difficult to scale up the equipment. Further, all transport phenomena, including heat transfer and fluid flow, depend on the size and structure of the apparatus used. Therefore, despite the excellent experimental results achieved, an analysis of the characteristics of the salt distillation equipment is necessary. However, such an analysis has not yet been performed. The ideal method for overcoming this issue is nondimensionalization, which allows the characteristic properties of a system to be determined. The advantages of using dimensionless variables are numerous: 1) a decrease in the number of variables and the number of experiments required; 2) the ability to predict the effects of changes in the individual variables by investigating the effects of varying the dimensionless parameter corresponding to the changed variable; 3) the ability to determine the correlation between the heat and fluid flows independent of the size and configuration of the system; and 4) obtaining information essential for the scaling up of the facility by simplifying the apparatus design. It is essential that the calculations be supported by experimental data and the structure size of the equipment used. In this study, the structural characteristics of engineering-scale equipment were evaluated on the basis of successful data records of an M-type apparatus [8] that has been used successfully to recover molten salt in powder form.

2.Strategy

The strategy to compare characteristics of two apparatuses emanates from two approaches: 1) process characteristics of evaporation and sublimation and 2) the structural characteristics of the equipment.

First, the process characteristics are studied, including the phase-transition phenomena and the exothermic and endothermic reactions involved. A salt (LiCl) exists in the molten state due to high operation temperature (800– 900°C) of a vacuum distillation. The molten LiCl salt turns into LiCl vapor through an endothermic process. The resulting salt vapor travels from the evaporation port to the upper sublimation port through the nozzle throat. The LiCl vapor turns into solid LiCl through an exothermic process in the upper port, which is cold. The latent heat from evaporation and sublimation is generated. The heat dissipates within the reactor, changing its internal temperature distribution during cathode processing. As a result, the values of several thermodynamic parameters such as the density, thermal conductivity, and kinetic density of the LiCl, change. The heat balance is modified by process characteristics, applying to the calculation of internal temperature and fluid flow phenomena.

Next, the structural characteristics of the apparatus used are analyzed on the basis of the dimensionless variables related to the heat and fluid flows. Dimensionless variables are essential for elucidating the apparatus characteristics, regardless of the size of the apparatus, and can aid efforts to scale up the distillation process. The representative dimensionless variables used for characterizing the heat and fluid flows using the cathode-processing apparatus are the following: the Reynolds number (Re), the Prandtl number (Pr), the Nusselt number (Nu), and the Stanton number (St). These dimensionless numbers, shown in Table 1, are used because they allow the obtained experimental results to be scaled up under real-world conditions and help prevent round-off errors.

The aim of this study is to analyze the characteristics of the equipment used for salt vacuum distillation using dimensionless parameters, in order to be able to scale up the distillation process. The first step is to define the standard model. This was taken to be a salt vacuum distillation apparatus already in use (M-type) and exhibiting an efficiency in salt recovery of more than 95%. In the case of the M-type apparatus (Fig. 1(a)), the mass velocity is a critical parameter and is calculated from experimental data. The mass velocity is dependent on 1) the phase transition of the salt from the molten state to the vapor state and from the vapor state to the solid powder state, 2) the temperature and pressure, and 3) the structural properties of the apparatus used. The dimensionless parameters are determined on the basis of the structural properties of the M-type apparatus and the process conditions. The values of these parameters were calculated on the basis of the mass velocity in the target structure. The second step is to analyze the dimensionless parameters on the basis on an analogy between heat transfer and fluid momentum. Several dimensionless parameters corresponding to the system, such as the Reynolds number (Re), the Prandtl number (Pr), the Nusselt number (Nu), and the Stanton number (St), were calculated, owing to forced convection flow. The values of these parameters were calculated at the inlet and outlet points of the nozzle throat between the evaporator and the receiver. An analysis of a P-type apparatus (Fig. 1(b)) was also performed using the same method. A P-type distiller has a similar structure to the M-type but it has a greater evaporator volume to deal with large capacity fuel (50 kg/ batch). Thus, the last step is to compare the characteristics of the P-type apparatus with that of the M-type apparatus. Scale-up facilities can be technically designed by the dimensionless parameters of the standard model.

3.Procedure

3.1.Determination of the Standard Model

The M-type apparatus was selected as the standard model, as this apparatus already exhibits a salt recovery rate of more than 95%. As shown in Fig. 1(a) [8], the apparatus was operated at temperatures of 800–900°C and a pressure of 0.1–1 Torr [8]. At the beginning step the evaporator is heated to the operating temperature. When the temperature of the evaporator reaches the operating temperature, the temperature of the receiver also has plateaued out at a constant temperature (Fig. 2). The vacuum pump turns on and the inner pressure keeps 0.1-1 Torr. After the vacuum operation starts, the temperature of the receiver rises quickly due to the LiCl evaporation. The temperature begins to decrease after reaching its maximum point, at which the evaporation of the LiCl is completed. After some time, the power supplied to the heating furnace and the vacuum pump is cut off, and the apparatus is cooled down to room temperature. The condenser and the receiver are removed to recover the LiCl powder collected in the receiver, and the weight of the recovered LiCl is measured. The recovery of molten LiCl was performed successfully using a 4-kg-scale M-type apparatus. Vapor flow was categorized as being forced convection flow. The oxygen and moisture levels were kept at less than 5 ppm [8]. The results are shown at Fig. 2 [8].

3.2.Heat-Transfer Balance in the M-type Standard Model Based on Phase Transition

We consider a schematic figure as shown in Fig. 3. As soon as LiCl salt in the evaporator converts into vapor, the vapor gets sucked out to the receiver section through a nozzle throat, of which the radius is R cm and the length is L cm. The phase transition rate of evaporation is expressed as mass unit, m' [g/s] and assumed to be equal to the vapor velocity passing through a nozzle throat. The velocity of vapor depends on temperature, pressure and the structure of the nozzle throat such as diameter and length. The target models in this study have the structures in which an inlet diameter of the nozzle throat is smaller than an outlet diameter, as shown in Fig. 3 and Table 2. Hence the inlet velocity of the nozzle throat is different from the outlet velocity and the velocity need to be divided into the inlet velocity and the outlet velocity. At the same time sublimation of LiCl vapor takes place in the upper receiver section and latent heat from phase transition takes place as well. Vapor delivery rate is calculated as a function of the structural design and the operating conditions of the system, and as a function of the thermodynamic properties of the LiCl. The real-time temperature distribution within the evaporator changes the properties of the LiCl vapor locally. The properties of LiCl salt are described with temperature function [9] and thermal conductivity was formulated from experimental data [10].

Heat balance is achieved during cathode processing as follows. The mass delivery rate may be written in the form

where q [cm³/s] is the volumetric flowrate of the vapor passing through the nozzle throat part and ρ [g/cm³] is the vapor mass density.

Assuming that the mass velocity, m' [g/s], through the nozzle throat determines the extent of the phase transition, the heat generated during the phase transition can be calculated using Eq. (2). The heat flux (q_h) is the net heat flux because of the exchange of heat through the reactor wall.

where q_h is the heat flux, h_ext the heat-transfer coefficient, A is the surface area of the reactor, T is the temperature of the reactor wall, T_ar is the temperature of the argon atmosphere, m' is the mass velocity of the material (LiCl), and h is its latent heat from vaporization or its latent heat of sublimation.

In the steady state model presented here, we assume that the evaporator is at a constant temperature condition. Eq. 1 and Eq.2 can be coupled to yield a single relationship between mass carryover rate, ρq, and the temperature, T. One more equation between ρq and T are required, which are the relationship of flowrate to pressure in the system, and the vapor pressure-temperature relationship with the Antoine equation [10].

For a volumetric flow rate q_v driven by a pressure difference P_vap- P₀, as shown in Fig. 3, the conductance, F, is defined as

Conductance, F, is characteristic of the series of flow elements (tubes, orifices, valves and so on) that connect the evaporator to the downstream pump. P_vap is the vapor pressure of LiCl molten salt and strongly dependent on LiCl temperature, T. P₀ is the downstream pressure. And the volumetric flowrate q_v is evaluated at the pressure P_vap of a compressible fluid. With the assumption of ideal gas behavior,

where P_vap is the vapor pressure of LiCl molten salt and inlet pressure at the entrance of nozzle throat. R_G is the ideal gas constant, and M_w,v is the molecular weight of the vapor LiCl. For the viscous flow of a compressible gas through radius R and length L, conductance F [11] is given by

The vapor pressure-temperature relationship is combined with the Antoine equation of LiCl.

When a compressible fluid with a kinetic density μ goes through a tube of length L and radius R, its mass velocity (m' [g/s]) can be calculated using Eq. (1), Eq. (3), Eq. (4), and Eq.(5)[11].

3.3.Analysis of Heat and Fluid Flows in the M-type Standard Model

In this study, the target volume is considered to be that of the nozzle throat between the lower evaporator and the upper receiver. As per the flow direction, the inlet of the nozzle throat is located in the lower evaporator, while its outlet is located in the upper receiver. The velocity of the LiCl vapor was calculated at eac h point (i.e., the inlet and outlet) using the software program COMSOL, which is employed widely for calculating dimensionless parameters on the basis of the fluid velocity. Governing equations can be of two types: those related to heat transfer (solid part) and those related to non-isothermal flow (salt vapor part). Nonlinear simultaneous equations were solved for each temperature and for the different thermal properties.

The M-type system is operated at low pressures (~ 0.1 Torr). The important dimensionless variables related to forced convection in this system are listed in Table 1. The transport of momentum and the mass and energy exhibit similarities and dimensionless relations with the Reynolds number (Re), the Prandtl number (Pr), the Nusselt number (Nu), and the Stanton number (St). The relationship between these numbers is described by Eq. (7).

Several correlation equations have been reported for turbulent flow. Of these, the Dittus-Boelter equation is applicable in the case of the M-type standard model.

There exists an analogy between various transport phenomena- related parameters, such as momentum, mass, and energy. For instance, the so-called Chilton-Colburn j-factor analogy [Eq. (9)] between heat, mass, and momentum transfer is a widely used one. The unknown transfer coefficient can be predicted using the Chilton-Colburn j-factor analogy, when one of the other coefficients is known. Here, the heat-transfer factor j_h is similar to the friction factor used to describe the drop in pressure within a tube. The j_h value is useful for estimating the heat-transfer coefficients for heat-exchanger tubes and commercial pipes, and is related to the ratio of the length of the pipe to its diameter (L/D), as shown in Fig. 3. It can be described using the Chilton-Colburn analogy, as shown in Eq. (9).

where j_h is the dimensionless heat-transfer factor and μ is the density of the fluid. It is assumed that, for the entire range of turbulent flow, the density of the bulk flow is nearly the same as the density of the fluid on the tube wall. Based on the analogy between heat and momentum, j_h can be used for calculating the dimensionless numbers, the velocity, and the temperature.

Using Eq. (9), one can obtain the temperature of the salt vapor at the nozzle throat; the temperature depends on the nozzle size and the heat and flow distributions within it (Eq. (10)). The temperature and velocity of the fluid passing through the nozzle throat are dependent on its L/D value. The temperature of a turbulent fluid in the pipe is a function of the temperature, the St value, and the length and diameter of the pipe [11].

As shown in Fig. 4, the temperature of the fluid in the pipe changes with the diameter and length of the tube [11].

where T_in is the inlet temperature of the tube, T_out is its outlet temperature, T_w is the wall temperature, D is the diameter of the tube, and L is the length of the tube. When the wall temperature is known, the inlet and outlet temperatures of the nozzle throat can be estimated. The outlet temperature should be higher than the melting point of LiCl (605°C), so that the LiCl can be recovered at the receiver part in powder form.

3.4.Comparison of M-type and P-type Cathode- Processing Apparatuses

Table 2 lists the differences in the diameters and lengths of the nozzle throats of the M-type and P-type apparatuses. Compared to the M-type, the P-type apparatus has a very similar structure but is larger than M-type due to the large capacity (Fig. 1(a) and (b)). The ratio of the inlet diameter to the outlet diameter of the P-type apparatus (2.84) is slightly higher than that of the M-type (2) apparatus. Further, the L/D value of the P-type apparatus (10) is higher than that of the M-type one. The dimensionless parameters for the P-type apparatus were calculated in the same manner as that used for the M-type apparatus.

4.Results and Discussion

4.1.Velocity Distribution in the Nozzle Throat

It is assumed that the molten salt (LiCl) is completely vaporized when heated to a temperature higher than its melting point (605°C). The heat generated during this phase transition has an irreversible effect on the inner temperature of the apparatus. Experiments of M type were conducted at each operating temperature (i.e., at 800, 850, and 900°C) [8] and inlet and outlet velocities of the nozzle throat were calculated with the previous method as in section 3.3. Both pieces of equipment, M type and P type, have the same nozzle structure in that the diameter of the entrance is smaller than that of the outlet. The path width of vapor expands at the end part of the nozzle throat into a receiver section. Hence, the velocity of vapor should be calculated at each point (inlet and outlet).

Table 3 shows the inlet and outlet velocities for both cathode-processing apparatuses. For both apparatuses, the velocities exhibit similar trends at 800, 850, and 900°C. In the case of the M-type apparatus, the velocity of the salt is the highest near the entrance of the nozzle throat: maximum of 0.3049 m/s at 800°C, maximum of 0.3285 m/s at 850°C, and maximum of 0.332 m/s at 900°C. As the velocity in the evaporation section is higher, the salt vapor passes more quickly through the nozzle throat. The velocity at the outlet decreases, as the diameter of the outlet is twice that of the inlet. The same trend was observed in the velocity data for the P-type apparatus. The velocities at the inlet and outlets of the nozzle throat play a very important role in determining the salt recovery rate during cathode processing. The LiCl salt vapor flows through the nozzle throat and is sublimated into a powder form at the upper low-temperature receiver. When the vapor velocity is low, the vapor can cool and undergo condensation before reaching the upper receiver, thus clogging the nozzle throat. On the other hand, when the vapor velocity is high, the vapor can get sucked into the vacuum pump trap before it is sublimated. Hence, for a given set of operating conditions, the heat balance and momentum balance should be coupled highly effectively, in order to improve recovery performance.

4.2.Evaluation of Dimensionless Parameters for M-type and P-Type Apparatuses

As mentioned above, the dimensionless parameters were derived from the inlet and outlet velocities. The Reynolds number (Re) for each inlet and outlet point was calculated from the corresponding velocity, as shown in Fig. 5 and Fig. 6. Here, "M" and "P" in the x-axis denote the M-type and P-type apparatuses, respectively, while the numbers (800, 850, and 900) represent the operating temperatures. Finally, the letters "I" and "O" indicate inlet and outlet, respectively. In both apparatuses, the fluid flow was in the turbulence range (Re > 4000). The Re number at the outlet was higher than that of the inlet point because the radius of the outlet is broader, and as a result, the fluid velocity at the outlet point was lower. In the case of the M-type apparatus, the Re number at the outlet was 1.1 times that at the inlet. On the other hand, the difference in the Re numbers for the P-type apparatus was almost 1.3 times. The reason is that the P-type apparatus had a relatively broader outlet, and the compressed vapor from the inlet expanded rapidly at the outlet. As the diameter of the outlet was greater, the effect of the turbulent flow was large. Further, despite the vapor velocity in the P-type apparatus being lower, most of the Re numbers corresponding to the P-type apparatus were larger than those of the M-type apparatus. This was because the length of the nozzle tube in the P-type apparatus was greater than that in the M-type one. Thus, the difference in the Re numbers of the inlet and outlet was greater in the case of the P-type apparatus than in the M-type one.

The values of the heat-transfer factor ( j_h ) and the Stanton number (St) for the different positions and operating temperatures are shown in Fig. 7 and Fig. 8. The heattransfer factor ( j_h) values of the M-type and P-type apparatuses were 0.002–0.003 over the range of Re values (≅ 1.0 to 2.0 × 10⁵) [12]. This means that the heat-transfer behavior of the nozzle was similar to that of a commercial tube. Even though the sizes of the two apparatuses were different, their heat-transfer behaviors against fluid flow were very similar. The Stanton number is closely related to the heat-transfer coefficient, which can be obtained from Eq. (5). As shown in Fig. 7, the M-type apparatus had a slightly higher St number than that of the P-type apparatus (Fig. 8), meaning that the M-type apparatus exhibited a greater heat-transfer force against the heat and flow velocities for the same operating temperature. The St numbers for all the locations at the outlet were slightly lower than those measured at the inlet. This meant that the degree of heat transfer at the outlet was lower. Further, compared to the M-type apparatus, the P-type exhibited a greater deviation in the j_h factor and St number values corresponding to the inlet and outlet. This indicates that, in the P-type apparatus, the fluid velocity at the outlet was lower and so was the amount of heat transferred to the wall, because the nozzle of the P-type apparatus had a higher L/D ratio. The longer the pathway for the fluid, the lower will be its velocity.

Figure 9 shows a plot of the heat-transfer factor versus the Reynolds number (Re). According to Kern [13], the modified heat-transfer factor ( j_H) can be defined as follows:

The modified heat-transfer factor corresponds to the rectangular area between Re and the heat-transfer factor ( j_h) and reflects the effects of fluid flow. The M-type apparatus exhibited a modified heat-transfer factor ( j_H) value of 220–270, whereas the P-type one had a value of 250–361. This shows that, regardless of the equipment size, the proposed method can be a suitable one for the comparison and scale-up of the distillation process.

4.3.Temperature and Vapor Flow Distributions of P-type apparatus

The results of calculations show that, in the M-type apparatus, the vapor temperature reaches at least 788.35 °C. Hence, the successful recovery of the molten salt is attributable to a perfect balance between the geometrical structure and the heat and fluid flows. On the other hand, the vapor temperature in the P-type apparatus reached at least 738°C, 782°C, and 826°C for operating temperatures of 800°C, 850°C, and 900°C, respectively. The vaportemperature and vapor-flow distributions were calculated using the commercial computational software program COMSOL; the results are shown in Fig. 10 and Fig. 11. The changes in the vapor temperature of the P-type apparatus during cathode processing can be seen in Fig. 10. During cathode processing, the hot salt vapor rises vertically through the nozzle throat, resulting in an increase in the temperature at the end of nozzle to a value higher than the melting point (605°C) of LiCl salt. When the hot salt vapor enters the cold receiver, it undergoes sublimation. The temperature at the top point of the evaporator was nearly the same as the operating temperature. This was confirmed through experimental measurements. On the other hand, the temperature of the receiver above the insulation layer increased to 350–400°C, owing to the hot salt vapor. This, too, was confirmed through experimental measurements [8], as shown in Fig. 2. The temperature of the vapor in the nozzle throat is of great importance, because if the vapor temperature is close to the melting point of LiCl, the vapor can stick to the wall of the inner nozzle, blocking the nozzle tube and lowering the recovery rate. The distribution of the vapor flow rate is shown in Fig. 11. The vapor velocity at the nozzle inlet was the highest, in keeping with the calculation results. Fluid velocity was visualized with color. Its velocity (red color) in the nozzle throat indicates higher velocity, and vapor passes quickly through the nozzle throat.

5.Conclusions

A new method for scaling up salt vacuum distillation based on an analysis of the dimensionless characteristics of the cathode-processing equipment was proposed. A comparison of the dimensionless variables corresponding to the M-type and P-type apparatuses performed on the basis of phase-transition phenomena, as well as the results of the above-mentioned analysis, elucidated the differences between the two apparatuses. It also means that the structure of the nozzle throat can be one of the several factors in recovery performance. First, the standard model (i.e., the M-type apparatus) was analyzed using dimensionless parameters. The characteristics of this apparatus were the following: 1) the diameter of the outlet of the nozzle throat was twice that of the inlet; 2) the ratio of the length to the diameter (L/D) was 8; and 3) the modified heat-transfer factor was 220–270. Next, the target model (i.e., the P-type apparatus) was analyzed using the same method. Most of the dimensionless parameters corresponding to the P type apparatus were similar to those for the M-type apparatus. However, for the P-type apparatus, the modified heat-transfer factor for all the operating temperatures was 250–361, and exhibited a wider distribution. This indicates that the distribution of the modified heat-transfer factor can be a criteria for designing apparatuses regardless of their size. Future studies should investigate the suitability of the approach used in this study for scaling up salt vacuum distillation under real-world conditions.