Corresponding author: Igor I. Ivanov ( iivanov@ippe.ru ) Academic editor: Yury Kazansky
© 2019 Igor I. Ivanov, Vasily M. Shelemetyev, Radomir Sh. Askhadullin.
This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Citation:
Ivanov II, Shelemetyev VM, Askhadullin RSh (2019) A study on the kinetics of bismuth oxide reduction by hydrogen as applied to the technology of removing hydrogen from circulation circuits with heavy liquid metal coolants. Nuclear Energy and Technology 5(4): 331336. https://doi.org/10.3897/nucet.5.48425

As part of the project on developing methods for removing hydrogen and tritium from the circulation circuits of reactor plants with heavy liquid metal coolants, the authors studied the kinetics of bismuth oxide reduction by hydrogen in the temperature range of 425–500 °C and hydrogen concentrations of 25–100 vol.%. The kinetic characteristics of the test reaction were determined by continuous measurements of the water steam (reaction product) concentration in mixtures of hydrogen with helium that passed through a heated reaction vessel with a sample of bismuth oxide. The water steam concentration was measured by a thermalconductivity detector. The obtained time dependences of the bismuth oxide reduction degree (with varying reaction conditions) were processed by the affine time transformation method. It was also found that the reduction process ran in kinetic mode. The reduction mechanism is the same in the entire temperature range. The limiting reaction stage is the adsorption of hydrogen on the surface of the bismuth oxide sample. The time dependence of the reduction degree is in good agreement with AvramiErofeev equation with n = 1. The reaction activation energy is 92.8 ± 1.9 kJ/mol. The reduction reaction rate is directly proportional to the concentration of hydrogen in its mixture with an inert gas.
Heavy liquid metal coolants (HLMC), nuclear safety, hydrogen, tritium, hydrogen purification of HLMC, hydrogen afterburner, bismuth oxide, reaction kinetics, thermalconductivity analysis, affine time transformation method, AvramiErofeev equation.
In recent decades, civil fast reactor plants with heavy liquid metal coolants (HLMC) based on lead and leadbismuth eutectic (LBE) alloys have been intensely developed. Both lead and leadbismuth alloys have a number of advantages as compared with other coolants for reactor plants, including, first of all, small fast neutron capture cross sections, relatively low melting points and high boiling points, and high thermal conductivity (
However, there are some difficulties associated with their use as coolants. One of the main problems is the interaction of these coolants with oxygen, which can enter the circulation circuit when the coolant is loaded or during operation in the presence of leaks (
To clean the circulation circuit from PbObased slags, a hydrogen regeneration method has been developed, which consists in feeding mixtures of hydrogen with an inert gas to the surface and into the coolant volume (
After hydrogen regeneration, a certain amount of hydrogen remains in the gas circuit. It can also accumulate in the circuit during leaks of the steam generators due to the interaction of incoming water steam with impurities dissolved in the coolant (primarily iron) (
Based on the analysis of various methods for removing hydrogen from gaseous media, the specialists of the SSC RFIPPE proposed purifying the protective gas from hydrogen by passing it through a special device containing heated PbO or Bi_{2}O_{3} (
To select the optimal operating conditions for the gas purifying device (including temperature, gas flow rate through the device, purification time), data are needed on the kinetics of the interaction of PbO and Bi_{2}O_{3} with hydrogen.
The kinetics of PbO reduction by hydrogen was studied in our previous works (
The kinetics of reducing bismuth oxide samples by hydrogen was studied at the facility, the layout of which is shown in Fig.
During the experiments, the temperature in the reaction chamber was controlled by a chromelalumel thermocouple with an accuracy of ± 1 °С. Before the experiments, the thermocouple was calibrated over the entire studied temperature range; the deviation of the thermocouple readings from the true temperature did not exceed 2 °C and was taken into account in the calculations.
In the experiments, bismuth oxide was used in the form of a powder of the “pure for analysis” grade according to GOST 1021675. The particle size ranged from a few micrometers to several tens of micrometers, the crystals had a compact shape. The degree of sample purity and the shape of sample crystals should be taken into account, since the kinetics of heterogeneous reactions very much depends on these parameters (
To determine the dependence of the bismuth oxide reduction rate on the volumetric hydrogen concentration in the gas, mixtures of hydrogen with helium, instead of pure hydrogen, were fed into the reaction chamber. Helium was chosen as an inert “diluent,” since a thermal conductivity detector (built into the chromatograph) was used to analyze the moisture content in the gas passing through the reaction chamber; helium has a thermal conductivity close to that of hydrogen and, therefore, does not significantly affect the sensitivity of the detector and the linear dependence of the detector signal on the moisture content. Gases were supplied from cylinders with a constant flow rate through rotameters, mixed, and the resulting mixture of a required composition was supplied to the reaction vessel and to the reference channel of the thermal conductivity detector. The total gas flow rate through the reaction vessel in each experiment was 50 ml/min. The rotameters were calibrated over the entire range of gas flow rates (0–50 ml/min) against a foam flow meter. The error in determining the gas flow rate was ± 1 ml/min.
The considered reduction reaction of Bi_{2}O_{3} by hydrogen is determined by the equation
${Bi}_{2}{\mathrm{O}}_{3}+3{\mathrm{H}}_{2}=2Bi+3{\mathrm{H}}_{2}\mathrm{O}$. (1)
The main kinetic characteristic of the heterogeneous reaction under consideration is the time dependence of the degree of Bi_{2}O_{3} reduction (kinetic curve). The degree of reduction α is equal to the percentage ratio of the mass of the reacted Βι_{2}O_{3} to the initial mass of Bi_{2}O_{3}:
$\alpha =100\cdot {m}_{{Bi}_{2}{\mathrm{O}}_{3}}/{m}_{{Bi}_{2}{\mathrm{O}}_{3}}^{0}$. (2)
As was already mentioned, the signal recorded from the thermal conductivity detector is directly proportional to the water steam concentration in the gas:
$I=h\cdot {c}_{{\mathrm{H}}_{2}\mathrm{O}}$, (3)
where I is the detector current, mA; c_{H2O} is the mass concentration of water steam, g/l; h is the proportional factor.
Multiplying the concentration of water steam by the gas flow rate through the facility V (l/h), we can obtain the rate of water formation υ_{H20}, g/h:
${v}_{{\mathrm{H}}_{2}\mathrm{O}}=I\cdot V/h$. (4)
The mass of water released at time t can be determined from the ratio
${m}_{{\mathrm{H}}_{2}\mathrm{O}}\left(t\right)={\displaystyle \underset{0}{\overset{t}{\int}}}\genfrac{}{}{0.1ex}{}{V\cdot I\left(t\right)}{h}dt$. (5)
In accordance with the stoichiometry of reaction (1), the mass of the reacted Bi_{2}O_{3} is determined by the ratio
${m}_{{Bi}_{2}{\mathrm{O}}_{3}}\left(t\right)={M}_{{Bi}_{2}{\mathrm{O}}_{3}}\cdot {m}_{{\mathrm{H}}_{2}\mathrm{O}}/(3\cdot {M}_{{\mathrm{H}}_{2}\mathrm{O}})$, (6)
where M _{Bi2O3} and M _{H2O} are the molar masses of Bi_{2}O_{3} and water, respectively. By substituting (5) into (6), and taking into account (2), we can obtain an expression for the time dependence of the Bi_{2}O_{3} reduction degree:
$\alpha \left(t\right)=100\cdot {M}_{{Bi}_{2}{\mathrm{O}}_{3}}\cdot {\displaystyle \underset{0}{\overset{t}{\int}}}\genfrac{}{}{0.1ex}{}{V\cdot I\left(t\right)}{h}dt/(3\cdot {M}_{{\mathrm{H}}_{2}\mathrm{O}}\cdot {m}_{{Bi}_{2}{\mathrm{O}}_{3}}^{0})$. (7)
To compare the shapes of the kinetic curves as well as to determine the reaction activation energy and the dependence of the reaction rate on the partial pressure of hydrogen, the affine time transformation method was used (
${f}_{\alpha}={t}_{1,\alpha}/{t}_{2,\alpha}$, (8)
where α is the reduction degree; t_{i}, is the time during which the reduction degree is achieved in the case of the ith curve.
The values of the affine transformation coefficients for different reduction degrees may slightly differ, for example, due to the measurement error when the signal from the detector is recorded. It is possible to calculate the average value of the affine transformation coefficient for the two kinetic curves used in this paper:
$f={\displaystyle \underset{0}{\overset{100}{\int}}}\genfrac{}{}{0.1ex}{}{{t}_{1}\left(\alpha \right)}{{t}_{2}\left(\alpha \right)}d\alpha /100$. (9)
The Gibbs energy of reaction (1) is determined by the relation
$\Delta {G}_{m}^{0}=3\Delta {G}_{m,{\mathrm{H}}_{2}\mathrm{O}}^{0}\Delta {G}_{m,{\mathrm{B}}_{2}{\mathrm{O}}_{3}}^{0}+3\cdot R\cdot T\cdot \mathrm{ln}({p}_{{\mathrm{H}}_{2}\mathrm{O}}/{\mathrm{p}}_{{\mathrm{H}}_{2}})$, (10)
where Т is the temperature (in kelvins). According to (
$\Delta {G}_{m}^{0},kJ\cdot {mol}^{1}=886.40.1278\cdot T+3\cdot R\cdot T\cdot \mathrm{ln}({p}_{{\mathrm{H}}_{2}\mathrm{O}}/{p}_{{\mathrm{H}}_{2}})$. (11)
The criterion for establishing the thermodynamic equilibrium in the system is the equality of the Gibbs energy of the reaction to zero. Hence, using (11), we can obtain the criterion for establishing the equilibrium of reaction (1):
${p}_{{\mathrm{H}}_{2}\mathrm{O}}/{p}_{{\mathrm{H}}_{2}}=\mathrm{exp}\left[(886.4+0.1278T)\right]/(3\cdot R\cdot T)$. (12)
According to equation (12), the equilibrium ratio of partial pressures of water steam and hydrogen for reaction (1) is 2.23 × 10^{24} at a temperature of 425 °C and 1.59 × 10^{22} at 500 °C. At lower values of this ratio, the Gibbs energy of reaction (1) takes a negative value and the reaction proceeds spontaneously. This is true for the experimental conditions of this work, since the maximum recorded partial pressure of the water steam formed during Bi_{2}O_{3} reduction did not exceed 0.1 atm (at 500 °C and a hydrogen partial pressure of 1 atm at the initial moment of reduction), while the minimum created partial pressure of hydrogen was 0.26 atm. The Bi_{2}O_{3} reduction process should be complete, which is confirmed by direct measurement of the weight of the samples before and after the reduction reaction with an accuracy of ± 0.005 g; the measurement showed that bismuth oxide was completely reduced to metallic bismuth in all experiments.
First, it is necessary to consider the effect of the reduced Bi_{2}O_{3} powder layer thickness and sample heating during the reduction reaction on the reaction rate. It was found that the powder layer thickness in the alundum boat does not affect the kinetics of the reduction process. Thus, a change in the sample weight from 0.25 to 1 g, while the length and width of the powder layer is maintained (1.5 and 1.0 cm, respectively), did not affect the shape of the time dependence of the reduction degree at a temperature of 500 °C; therefore, it can be assumed that the stage of diffusion of the reagents (reaction products) through the powder layer does not limit the reaction rate (
To determine the thermal effect of the reduction reaction on the sample temperature, 1 g of Bi_{2}O_{3} was reduced by hydrogen at 500 °C, and a thermocouple was placed in the center of the sample in a thinwalled alundum sheath. No deviations of the sample temperature from the furnace operating temperature were recorded, which allows us to consider the heatrelease effect on the reaction rate to be negligible.
Figure
Time dependences of the Bi_{2}O_{3} reduction degree obtained at various temperatures and combined by an affine time transformation with the dependence obtained at 425 °C. The solid line is the approximation of the obtained dependences by the exponential function (R^{2} is the approximation confidence coefficient).
$\alpha \left(t\right)=100\cdot (1\mathrm{exp}[k\cdot t])$, (13)
where k is the coefficient depending on the temperature, partial pressure of hydrogen, and qualitative characteristics of the Bi_{2}O_{3} sample (specific surface, crystal surface structure).
Expression (13) formally corresponds to AvramiErofeev equation for the exponent n = 1 (
$\alpha \left(t\right)=100\cdot (1\mathrm{exp}[k\cdot {t}^{n}])$. (14)
It was noted in (
The rate of the heterogeneous chemical reaction is directly proportional to the first time derivative of the reduction degree (
${v}_{{Bi}_{2}{\mathrm{O}}_{3}}\left(t\right)={m}_{{Bi}_{2}{\mathrm{O}}_{3}}^{0}\cdot k\cdot \mathrm{exp}[k\cdot t]$, (15)
where υ_{Βι}_{2O3} (t) is the Bi_{2}O_{3} reduction rate, g/h. Thus, the Bi_{2}O_{3} reduction rate and, in accordance with reaction equation (1), the rate of hydrogen removal from the protective gas decreases exponentially with time. The k coefficient value for these reduction conditions can be determined by mathematical processing of the data, plotting the dependence dα/dt (α). The slope of the obtained linear relationship is equal to the desired k value.
A satisfactory combination of the kinetic curves during the affine time transformation suggests that the Bi_{2}O_{3} reduction mechanism is the same in the entire studied temperature range (
The logarithmic dependence of the affine transformation coefficient on the inverse temperature is shown in Fig.
$k\left(T\right)=b\cdot \mathrm{exp}[92800/(R\cdot T)]$, (16)
where b is the coefficient depending on the partial pressure of hydrogen in the gas, the specific surface area of the sample and the surface structure; R is the universal gas constant; T is the temperature (in kelvins).
To determine the dependence of the bismuth oxide reduction rate on the hydrogen concentration in the gas, Bi_{2}O_{3} was reduced by heliumhydrogen mixtures with a volumetric hydrogen content of 26, 52, 76, and 100 %. The obtained time dependences of the reduction degree are satisfactorily combined with an affine time transformation.
The dependence of the reduction rate (i.e., the affine transformation coefficient proportional to it) on the volume concentration of hydrogen is well described by a straight line passing through the origin of coordinates (Fig.
$b=c\cdot {p}_{{\mathrm{H}}_{2}}$, (17)
where c is the constant for a given Bi_{2}O_{3} sample, depending on its specific surface and surface structure; it can be determined by calculating the k coefficient for an arbitrary dependence dα/dt (α) obtained at a temperature Т and a partial pressure of hydrogen p_{H2}, and using relations (16) and (17). Thus, using the value of k = 1.87 ∙ 10^{–4} s ^{–1} found for Bi_{2}O_{3} at a temperature of 425 °C and p_{H2} = 100 kPa, we find c = 0.0164 s^{–1}Pa ^{–1}.
A dependence similar to equation (17) was found in (
The authors studied the kinetics of bismuth oxide reduction by hydrogen. The activation energy of the reduction process is 92.8 ± 1.9 kJ/mol, i.e., the reaction rate is highly dependent on temperature. Due to this, it is advisable to purify the gas of the circulation circuit from hydrogen at an elevated temperature of about 500 °C. The time dependence of the bismuth oxide reduction degree is described by AvramiErofeev equation with a power factor n = 1. The reduction rate linearly depends on the partial pressure of hydrogen in the gas. The resulting kinetic equation obtained by generalizing relations (13), (16) and (17) has the following form:
$\alpha (t,T,{p}_{{\mathrm{H}}_{2}})=100\{1\mathrm{exp}[c\cdot {p}_{{\mathrm{H}}_{2}}\cdot \mathrm{exp}(92800/(R\cdot T\left)\right)\cdot t]\}$. (18)
The obtained kinetic equation will be further used to calculate and optimize the device for purifying gas from hydrogen in a circulation circuit with heavy liquid metal coolants.