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Effects of temperature and pressure on Henry’s law constant for hydrogen in the primary water of a simulated pressurized-water reactor
Annals of Nuclear Energy 106 (2017) 136–142
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Effects of temperature and pressure on Henry’s law constant for hydrogen in the primary water of a simulated pressurized-water reactor Eun-Hee Lee ⇑, Gyeong-Geun Lee, Kyung-Mo Kim Korea Atomic Energy Research Institute, 989-111 Daedeok-daero, Yuseong-gu, Daejeon 34057, Republic of Korea
a r t i c l e
i n f o
Article history: Received 31 July 2015 Received in revised form 30 March 2017 Accepted 2 April 2017 Available online 10 April 2017 Keywords: Henry’s law constant Hydrogen PWR PWSCC Temperature and pressure
a b s t r a c t The measurement of dissolved hydrogen in the primary systems of pressurized water reactors (PWRs) is difficult; hence, hydrogen concentrations are predicted by model equations. An accurate value for the Henry’s law constant for hydrogen is needed if the use of these equations is to be meaningful. The purpose of this study is to develop an empirical correlation for determining the Henry’s law constant for application to nuclear reactors. The effects of temperature and pressure on the Henry’s law constant are investigated using simulated PWR primary-water conditions. The Henry’s law constant was calculated by an in-situ measurement of the partial pressure of hydrogen using a hydrogen sensor based on a Pd–Ag alloy tube. At 20 MPa, the Henry’s law constant decreased by 40% as the temperature increased from 290 to 330 °C. The Henry’s law constant increased by an average of 9% as the pressure increased from 13.8 to 20 MPa at each temperature. Thus, it depends more strongly on the temperature than on the pressure. Based on the experimental data, an empirical correlation for predicting the Henry’s law constant was developed using a linear regression method, which was validated by comparing with results in the literature. The deviation between the Henry’s law constant obtained using our model and that reported in the literature was in the range of 0.5%–10%. The hydrogen fugacity estimated using our model was within 10% of that found in the literature. Thus, the proposed empirical model appears to be more accurate than previously published models. Ó 2017 Elsevier Ltd. All rights reserved.
1. Introduction In pressurized-water reactors (PWRs), hydrogen is added to the reactor coolant system (RCS) to reduce the oxidation of water by radiolysis and to maintain reducing conditions. It is important to maintain the hydrogen concentration within a certain range. This is because this parameter can lead to primary water stress corrosion cracking (PWSCC), general corrosion of the primary structural materials, higher radiation fields, and deposit build-up on fuel rods of a PWR (Fruzetti, 2005). Several researchers have demonstrated that the hydrogen concentration influences the corrosion of structural materials in PWRs (Cassagne et al., 1997; Lee et al., 2002; Ahluwalia, 2007). However, the amount of dissolved hydrogen, which affects the material susceptibility, exhibits a wide scatter. Computational work has suggested that dissolved hydrogen concentrations lower than 15 cc/kg are sufficient to scavenge oxidizing species under normal PWR operating conditions (Fruzetti, 2005). During operation, the concentration of dissolved hydrogen is controlled by varying the hydrogen overpressure in a volume control ⇑ Corresponding author. E-mail address: [email protected] (E.-H. Lee). http://dx.doi.org/10.1016/j.anucene.2017.04.001 0306-4549/Ó 2017 Elsevier Ltd. All rights reserved.
tank (VCT). Since the primary water flows from the VCT into the RCS, the temperature, system pressure, and solution chemistry in the RCS can affect the hydrogen concentration. In addition, hydrogen from the RCS diffuses through the steam generator tubes. To ensure an optimal operating margin, the Electric Power Research Institute (EPRI) PWR primary chemistry guide-lines require hydrogen levels of 25–50 cc/kg as an optimal margin. To mitigate PWSCC, the recent EPRI Hydrogen Management Program for fuel and material reliability focused on plant operations using hydrogen levels of up to 60 cc/kg (Hass et al., 2010). The optimization of the hydrogen concentration in the RCS is regarded as one approach to the management of material integrity and the reduction of radiation sources in the primary circuit. The solubility of gases in water and aqueous solutions is of considerable industrial and theoretical importance. Solubility depends on many factors, including temperature, pressure, association, dissociation, and the type of solvent (Himmelblau, 1960). However, inert gases like the hydrogen that is used in the RCS of PWRs do not react with water or ionize in water, so only the effects of temperature and pressure on the solubility are considered. The amount of hydrogen dissolved in water is directly proportional to the hydrogen fugacity (hydrogen partial pressure) in the gaseous
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phase. Thus, the measured hydrogen fugacity can be used to calculate the Henry’s law constant (Himmelblau, 1960). The Henry’s law constant is important because it is necessary to predict the dissolved hydrogen concentration in a PWR. Using the Henry’s law constant, the amount of dissolved hydrogen at a given temperature and pressure can be calculated. Alternatively, when the dissolved hydrogen concentration is known, the hydrogen fugacity can be determined using the Henry’s law equation. The values obtained for the dissolved hydrogen concentration affect the Ni/NiO phase transition in nickel-based alloys, shifting the Ni/NiO phase boundary up or down. For PWRs, these data can yield erroneous results in the prediction of PWSCC, and hinder the development of a model to fit the hydrogen concentrations (Attanasio and Morton, 2003; Lee et al., 2002; Moss and Was, 2015). Thus, accurate means of measuring and monitoring the hydrogen fugacity in PWRs are needed. In the present study, to measure the hydrogen partial pressure, we fabricated a sensor based on a Pd–Ag (75/25 wt.%) tube. Using this sensor, we measured the hydrogen partial pressure in situ as a function of temperature and pressure in a simulated PWR primary solution containing lithium hydroxide (LiOH) and boric acid (H3BO3). Based on the data collected in our experiments, an empirical correlation for predicting the Henry’s law constant was developed using a linear regression method. It was validated by comparing the obtained results with the values reported in the literature. 2. Theoretical background 2.1. Solubility of hydrogen in water The solubility of hydrogen in water can be determined using the findings of Henry, given by Eq. (1) and known as Henry’s Law (Himmelblau, 1960).
f ¼Hx/
ð1Þ
where f = fugacity of the solute gas in the vapor phase, H = Henry’s law constant, x = mole fraction of the solute gas in the liquid phase, and U = activity coefficient of the solute gas in the liquid phase. For inert gases such as hydrogen, oxygen, and nitrogen, which obey the ideal gas law in the vapor phase above the solution, Eq. (1) can be rewritten to give Eq. (2).
p¼Hx
ð2Þ
where p = partial pressure of hydrogen in the vapor phase and U = 1 for ideal solutions. Himmelblau developed theoretical equations to determine the Henry’s law constant of inert gases at different temperatures using the data reported in the literature. In developing the modified Henry’s law equations, Himmelblau used highpressure data extrapolated to low pressures, and thus considered only the effect of temperature. He then correlated the solubility data with various data plots. The plotted data in the graph are correlated by Eqs. (3)–(5) (Himmelblau, 1960).
logH ¼ 1:142 2:846ð1=TÞ þ 2:486ð1=TÞ2 0:9761ð1=TÞ3 þ 0:2001ð1=TÞ4 H ¼ H=Hmax ð1=TÞ ¼
ð1=TÞ ð1=T c Þ ð1=T max Þ ð1=T c Þ
ð3Þ ð4Þ ð5Þ
where Hmax 104 = 7.54, (1/Tmax) 103 = 3.09, and Tc = critical temperature of water (647 K). However, Himmelblau’s study was limited to the effect of temperature on solubility. In addition, the calculated Henry’s constants
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are for ideal gases and solutions, and are applicable to low pressures only. For hydrogen, the low pressures appear to be 10.3 MPa (1500 psia) at 100 °C and about 13.8 MPa (2000 psia) at 300 °C (Himmelblau, 1960). Many researchers have used the Henry’s law constants determined by Himmelblau’s equations to calculate the hydrogen partial pressures or hydrogen concentrations at different temperatures. However, experimentally measured Henry’s law constants have proven to be quite different from those calculated from Himmelblau’s equations (Lee et al., 2002). This difference arises because his equations assume the concentration of dissolved hydrogen in water to be independent of pressure. This assumption gives rise to the difference between the theoretical and experimental data.
2.2. Sensor for measuring hydrogen partial pressure The accuracy of the hydrogen-fugacity measurement was also affected by the hydrogen-sensing materials used. Considerable research has been directed toward developing high-performance hydrogen sensors with high permeability, high selectivity, a fast response time, cost-effective fabrication, and which are easy to use. Among the various hydrogen-sensing materials tested, metallic palladium (Pd) exhibits high permeability and selectivity with hydrogen (Ackerman and Koskinas, 1972; Yang et al., 1998). However, pure Pd undergoes phase transition and hydrogen embrittlement at high temperatures and pressures, leading to fragility after extended use. To avoid these problems, alloying of Pd with group IB metals such as Ag was attempted and an optimal value of hydrogen permeation was attained at an Ag content of 25 wt.% (Knapton, 1977; Foletto et al., 2008). The advantage of using a Pd alloy is that the mechanical strength of the sensor is greater than that of one made from pure Pd. Several researchers have studied the effects of various parameters on the permeation of hydrogen through hydrogen sensors constructed using a Pd–Ag tube, film, and wire (Economy et al., 1987; Wang and Feng, 2007; Foletto et al., 2008).
3. Methods 3.1. Test loop Fig. 1 shows a schematic of the test loop that we used. The hydrogen sensor was mounted in an autoclave with a temperature control precision of ±0.5 °C. Then, 100 l of the test solution was prepared by adding 2 ppm of nuclear-grade lithium (as LiOH) and 1200 ppm of boron (as H3BO3) to purified water produced using an ultrapure water system (18 MOcm). This setup was used to simulate the representative PWR primary water chemistry. The amount of dissolved hydrogen was controlled by fixing the hydrogen overpressure in the feed tank at a temperature of 21 ± 1 °C. The amount of dissolved hydrogen was calculated using the Henry’s law constant for 5.7 kPa (0.826 psia)/(cc/kg) (Himmelblau, 1960). The solution from the feed tank was fed into the autoclave using a high-pressure pump and a double-tube heat exchanger. The outlet solution from the autoclave was cooled to ambient temperature by passing it through a heat-exchanger and a cooler, after which it passed through the sensors for measuring the conductivity and dissolved oxygen content. Finally, the solution was returned to the feed tank. The dissolved oxygen concentration was measured using a DO-32A (TOADKK Co.) and recorded manually. Throughout the experiments, the measured oxygen concentration was less than 1 ppb.
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Fig. 1. Schematic of simulated primary test loop used for measuring hydrogen fugacity in situ.
3.2. Hydrogen sensor The hydrogen sensor was fabricated using a Pd–25 wt.% Ag tube with an active length of 200 mm, an outside diameter of 3.2 mm, and a wall thickness of 0.43 mm (Lee et al., 2002). The inside of the tube was reinforced with a spring-type Inconel wire to prevent the collapse of the Pd–Ag tubing when subjected to a system pressure of 21.4 MPa (3100 psia) in the autoclave. Type 316 stainlesssteel tubing was connected to one end of the Pd–Ag tube while the other end of the tube was connected to the exit of the pressure boundary. The joint between the 316 stainless-steel tubing and the Pd–Ag tubing was gold-brazed. The other extremity of the Pd–Ag tube was sealed with an Inconel plug. The amount of hydrogen permeating from the solution through the Pd–Ag tube wall was measured by an external low-pressure gauge and a vacuum pump. 3.3. Measurement of hydrogen partial pressure The Henry’s law constant was determined by measuring the hydrogen partial pressure in situ at various temperatures (290, 300, 310, 320, and 330 °C) and pressures (13.8/2000, 15.2/2200, 17.9/2600, and 20 /2900 MPa/psia) in an aqueous hydrogenated solution. The system reached thermodynamic equilibrium in 4 to 12 h, depending on the temperature. After 48 h of equilibrium, the measurements were performed. All the measurements were repeated three times to obtain reliable data. The measured hydrogen partial pressure was considered to be the hydrogen fugacity in the autoclave at the given temperature and pressure. The Henry’s law constant was calculated by dividing the measured fugacity by the dissolved hydrogen concentration in the feed water. 4. Results and discussion 4.1. Hydrogen-sensor validation In this study, the hydrogen partial pressure was measured in an aqueous solution of 2 ppm lithium and 1200 ppm boron using the Pd–Ag tube at temperatures ranging from 290 to 330 °C and at 20 MPa. These values decreased linearly as the temperature increased and the determined Henry’s constant was shown in Fig. 2. Lee et al. (2002) measured the hydrogen partial pressure using the same Pd–Ag tube that we used in the present study. The effects of the dissolved hydrogen and lithium/boron-solution concentration on the hydrogen partial pressure were examined. They reported that the hydrogen partial pressure increased linearly
Fig. 2. Comparison of Henry’s law constants obtained from experimental measurements and theoretical calculations at different pressures and temperatures.
with the hydrogen concentration and decreased with increasing temperature. No solution-concentration effect on the hydrogen partial pressure was observed, indicating that the hydrogen partial pressure was the same between water and the aqueous solution within the tested temperature range. These results agree reasonable well with the literature and our data, and confirm the reliability of the Pd–Ag tube for the measurement of the hydrogen partial pressure (Attanasio and Morton, 2003).
4.2. Effects of temperature and pressure on Henry’s law constant Fig. 2 shows the results of the present study and those available in the literature. In the present study, the Henry’s law constant was calculated as a function of the temperature at 20 MPa according to the measured hydrogen fugacity. The Henry’s law constants reported in the literature (Kishima and Sakai, 1984; Moshier and Witt, 2002; Moss and Was, 2015) were also plotted for various pressures, in MPa. These data were determined by the hydrogen fugacity or dissolved hydrogen content, which were measured while the temperature and pressure varied. Himmelblau (1960) and Ziemniak (1992) obtained the Henry’s law constants using theoretical equations inferred by thermodynamic data. As shown in Fig. 2, the Henry’s law constant decreased linearly as the temperature increased and increased with the pressure at any given temperature. However, none of the plotted data can be compared quantitatively, because of the different measuring pressures. A
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substantial deviation between the experimental data and the theoretical estimation can be seen. This is because the assumption involved in most of the theoretical equations (that the Henry’s law constant is independent of the pressure) produced inadequate results. Himmelblau’s study (1960) examined only the effect of the temperature on the solubility of the gases: the effect of the pressure was disregarded. Himmelblau used high-pressure data that were extrapolated to low pressures. Ziemniak (1992) introduced only the effect of the pressure into the thermodynamic calculations of the Henry’s law constant at supercritical temperatures. Fig. 3 shows the results of the present study, in which the Henry’s law constant, as a function of the temperature and pressure, was determined using the measured hydrogen fugacity. The Henry’s law constant decreased linearly as the temperature increased from 290 to 330 °C and increased as the pressure increased from 13.8 to 20 MPa. These temperature and pressure dependences of the Henry’s law constant are consistent with the results of other studies, which are plotted in Fig. 2. When the temperature increased from 290 to 330 °C at 20 MPa, the Henry’s law constant decreased to 40% of its value at 290 °C. The Henry’s law constant increased by an average of 9% as the pressure increased from 13.8 to 20 MPa. It depended more strongly on the temperature than on the pressure. 4.3. Development of empirical model Various theoretical models for estimating the Henry’s law constant can be found in the literature. However, some of these models disregard the effect of the pressure on the Henry’s law constant (Himmelblau, 1960; Ziemniak, 1992), considering only that of the temperature. It may be possible to disregard slight changes in the pressure; however, as shown in Fig. 3, the Henry’s law constant was found to decrease by a maximum of 9% with the pressure in the present study. We developed an empirical model to estimate the Henry’s law constant, considering the effects of the temperature and pressure. The model is based on the experimental data obtained in this study. Because the data shown in Fig. 3 exhibits a linear correlation between the reciprocal temperatures and pressures and the Henry’s law constant, the following multipleregression model can be applied.
Y ¼ A þ Bð1=TÞ þ CðPÞ;
ð6Þ
where Y is the predicted Henry’s law constant, which is expressed in units of atm/(cc(STP)/kg-water); T is the temperature in Kelvin; P is the system pressure in psia (1 psia = 6.9 kPa); and A is the regres-
Fig. 3. Henry’s law constants calculated using the hydrogen fugacity, measured as a function of the temperature and pressure in an aqueous solution containing 2 ppm lithium and 1200 ppm boron.
139
Fig. 4. Comparison of Henry’s law constants obtained using the present model with experimental data as a function of the reciprocal temperature.
sion constant. The regression coefficients B and C represent the independent contributions of each independent variable to the prediction of the dependent variable. The regression analysis indicates that A, B, and C have values of 0.06568, 42.219, and 1.12 106, respectively. Eq. (6) can be rewritten as follows:
Y ¼ 0:06568 þ 42:219 T 1 þ 1:12 106 P
ð7Þ
The coefficient of determination (R2) used to statistically evaluate the model fit is 0.999232. This model equation can be used to estimate the Henry’s law constant if no data are available for a temperature range of 290–330 °C and a pressure range of 13.8– 20 MPa. With the calculated Henry’s law constant, the concentration of the dissolved hydrogen or the hydrogen fugacity in an aqueous solution can be obtained using Henry’s law equation (Himmelblau, 1960). 4.4. Model validation Fig. 4 compares the Henry’s law constant calculated using the present model with the experimental data obtained in the present study. There is excellent agreement between the linear fit and experimental data. At 13.8 MPa and at 330 °C, no experimental data were obtained, because of problems with the apparatus. Thus, the value for this temperature and pressure was estimated using Eq. (7) and then extrapolated to fit the experimental results, as shown in Fig. 4. This estimated value also agrees well with the trend of the experimental data. Table 1 shows that both the Henry’s law constants reported in the literature and those calculated using the present model agree well with the data in the literature (Himmelblau, 1960; Kishima and Sakai, 1984; Lee et al., 2002; Moss and Was, 2015; Attanasio and Morton, 2003; Ziemniak, 1992; Moshier and Witt, 2002). Here, the large deviations in the Henry’s law constant may arise from experimental errors or differences in the modeling equation, sensor used to measure the hydrogen fugacity, and the experimental environment. The Henry’s law constants obtained using Lee et al. (2002) and Attanasio’s models (2003), as well as those obtained using the present model were found to agree to within 4% at 20 MPa. As the temperature increased, the deviation also increased. This indicates that the effect of the pressure increased with the temperature. Their model disregards the dependence of the pressure on the Henry’s law constant, even though the experimental data obtained at different temperatures and pressures were used in the development of the model. This oversight led to large errors in the estimated results for the Henry’s law constant when varying the pressure. In the present study, as shown in
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Table 1 Henry’s law constants from the literature and calculated using the present model. Ref.
Himmelblau (1960), Ziemniak (1992), Lee et al. (2002), and Attanasio and Morton (2003)
Kishima and Sakai (1984)
Moshier and Witt (2002)
Moss and Was (2015)
Autoclave conditions
Henry’s law constant (atm/(cc/kg)
T (°C)
P (MPa/psia)
Reference data
Estimated using present model
290 300 310 320 330 296 326 356 260 288 316 333 360 320 360
20/2900 20/2900 20/2900 20/2900 20/2900 9.8/1421 14.5/2102 19.8/2871 6.9/1000 10.3/1500 20.7/3000 20.7/3000 22.1/3200 24.83/3600 24.81/3597
0.01244 0.0113 0.01016 0.00902 0.00788 0.0102 0.0072 0.00439 0.0160 0.0122 0.0101 0.0072 0.0049 0.01033 0.00563
0.01256 0.01125 0.00999 0.00876 0.00758 0.01011 0.00716 0.00466 0.01465 0.01126 0.00936 0.00678 0.00460 0.00955 0.00505
Fig. 3, the Henry’s law constant increased by an average of 9% as the pressure increased from 13.8 to 20 MPa at each temperature. The Henry’s law constants reported by Kishima and Sakai (1984) at 9.8 MPa (1421 psia) and 14.5 MPa (2102 psia) are in good agreement with the constants calculated using the present model. However, the difference between Kishima’s and our data increased rapidly at 356 °C, even though the pressure was similar in both studies. The temperature in Kishima’s study (1984) was well in excess of the present upper temperature of 330 °C, leading to a large deviation. These results confirm that the Henry’s law constant is more dependent on the temperature than on the pressure. The deviations between Moshier and Witt (2002) data and the present data are greater than those between the present data and the data reported in the literature. None of the pressure ranges were consistent with those in the present study, yielding a deviation of 10%. Moshier and Witt (2002) developed a Henry’s law correlation with the hydrogen fugacity, which was measured according to the temperature and system pressure. They improved the Henry’s law correlation by fitting the hydrogen-fugacity data using Krichevsky and Kasarnovsky’s equations (1935). However, their thermodynamic equations were verified at pressures of up to 100 MPa (14,500 psia) and at temperatures ranging from 0 to 100 °C. The data obtained using Krichevsky and Kasarnovsky’s equations were in good agreement with the experimental data obtained at the aforementioned temperature and pressure. However, it is uncertain whether their equations fit well above 100 °C. There is a large difference between our data and that obtained by Moss and Was (2015). They used Pd–20wt.% Ag tube with a length of 25.4 mm, an outer diameter of 3.2 mm, and an inner diameter of 1.6 mm. In the literature, the hydrogen permeability was affected by the Ag content and the thickness of the Pd–Ag tube (Nguyen et al., 2009). The large deviation in the Henry’s law constant may arise from the hydrogen-sensing material and type. Fig. 5 shows the experimental data reported in the literature and the fitting with the data obtained with the present model (Lee et al., 2002; Attanasio and Morton, 2003; Economy and Pement, 1989). The filled symbols indicate the hydrogen-fugacity data calculated using the present model, while the open symbols represent the experimental data obtained from the literature. First, the Henry’s law constant was calculated using Eq. (7) at the same temperature and pressure as were reported in the literature. Second, the hydrogen fugacity was calculated by multiplying the calculated Henry’s law constant by the dissolved hydrogen content. The estimated hydrogen-fugacity data for dissolved hydrogen
Error (%)
1 0.5 1.7 3 4 0.9 0.6 5.8 9.2 8.4 7.9 6.2 6.5 8.2 11.6
Fig. 5. Comparison of hydrogen fugacity calculated using the present model with experimental data obtained from the literature.
contents of 50 and 17 cc/kg at 20 MPa was in good agreement with the experimental data obtained by Lee et al. (2002). These results confirm the accuracy of the hydrogen-fugacity measuring sensor, the experimental data, and the present empirical model. The errors between the experimental data obtained by Economy et al. and our estimated data were greater than 17%, and the deviation increased slightly with the temperature. Economy and Pement (1989) used a Pd–25 wt.% Ag tube, but adopted a measurement system that was different from ours. Furthermore, they measured the hydrogen partial pressure at a low temperature (100–110 °C). In the present study, the hydrogen fugacity was measured in situ at given temperatures and pressures, and these data were used to develop the empirical model. This was because the hydrogen fugacity was affected by both the system temperature and pressure, as shown in Fig. 4. The experimental result obtained by Attanasio and Morton (2003) at 316 °C agrees reasonable well with the result obtained using the present model.
4.5. Ni/NiO phase transition Fig. 6 shows the calculated and measured hydrogen-fugacity data corresponding to the Ni/NiO phase transition (Attanasio and Morton, 2003; Moss and Was, 2015) at different pressures and hydrogen concentrations. The hydrogen fugacity was calculated
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alloys occurred in the proximity of the Ni/NiO phase boundary. Therefore, both the temperature and pressure are important for determining the location of the Ni/NiO phase boundary. Many researchers have determined the hydrogen fugacity by using Henry’s law constants obtained from their thermodynamic models, experimental data, or the literature. The present model was obtained by a linear regression analysis of the experimental data, as discussed in this study. Thus, more accurate data can be obtained using the present model, relative to other models. 5. Conclusion
Fig. 6. Measured and calculated hydrogen-fugacity data corresponding to Ni/NiO phase transition.
by multiplying the Henry’s law constant by the dissolved hydrogen concentration. The hydrogen fugacity is a direct measure of the thermodynamic stability of nickel and exhibits a good correlation with the free energy of nickel oxidation (Moss and Was, 2015). As the temperature increased, the calculated hydrogen fugacity exhibited a trend similar to that reported by Attanasio and Morton (2003) and Moss and Was (2015) The filled square symbols indicate the hydrogen fugacity of the Ni/NiO phase transition reported by Attanasio and Morton (2003) at various pressures (6.9, 10.3, 20.7, 20.7, and 22.1 MPa) and concentrations (2, 4, 7.5, 13.8, and 25 cc/kg), respectively. The open-triangle symbols represent the hydrogen fugacity calculated using the present model under the same conditions as those used by Attanasio and Morton (2003). The calculated data were found to be within 8% of the experimental data obtained by Attanasio et al. over a temperature range of 260 to 360 °C. The discrepancies between the two sets of data are explained as follows. Attanasio and Morton (2003) determined the hydrogen fugacity using the hydrogen concentration that was experimentally obtained from exposure tests and using the Henry’s law correlation reported by Moshier and Witt (2002). Moshier and Witt (2002) used the thermodynamic equations of Krichevsky and Kasarnovsky (1935) to improve the Henry’s law correlation. These results indicate that the hydrogenfugacity data reported by Attanasio and Morton (2003) accurately reflected the thermodynamic properties. However, the present model was developed using only experimental data. Therefore, the present data are more reasonable than those reported by Attanasio and Morton (2003). Fig. 6 shows that the present model can be extrapolated to temperatures and pressures ranging from 260 to 360 °C and 7 to 22 MPa, respectively. The filled circles represent the data obtained by Moss and Was (2015), which were generated at 320 °C (6 cc/kg H2) and 330 °C (8 cc/kg H2) at 25 MPa; these circles are located in the NiO regime. Using the present model, their data were recalculated under the same conditions; the recalculated values are indicated by the open circles. These data points are also located in the NiO regime, according to the literature (Attanasio and Morton, 2003; Moss and Was, 2015). In the study by Moss et al., when the dissolved hydrogen content increased from 6 to 8.5 cc/kg at 320 °C and at 25 MPa, this data point moved into the Ni regime. In this case, a change in the pressure from 25 to 20 MPa shifted the hydrogen fugacity calculated using the present model downward; this value is denoted by an open diamond. As the pressure decreased, the hydrogen fugacity also decreased, which may have caused a crossing of the Ni/NiO phase boundary. In PWRs, the maximum PWSCC susceptibility of
A hydrogen sensor made using a Pd–25 wt.% Ag tube was used to indirectly determine the Henry’s law constant for hydrogen in an aqueous solution containing lithium and boron. Using this sensor, in-situ measurements of the hydrogen fugacity were performed for temperature and pressure ranges of 290–330 °C and 13.8–20 MPa, respectively. The Henry’s law constant was calculated by dividing the measured hydrogen fugacity by the dissolved hydrogen concentration. The Henry’s law constant decreased linearly as the temperature increased and the pressure decreased. The Henry’s law constant was found to be more strongly dependent on the temperature than on the pressure. When the temperature increased from 290 to 330 °C at 20 MPa, the Henry’s law constant decreased to 40% of its initial value at 290 °C. However, the Henry’s law constant increased by a maximum of 9% as the pressure increased at each given temperature. An empirical model that uses the experimental data was developed to estimate the simultaneous effects of the temperature and pressure on the Henry’s law constant. The deviations in the Henry’s law constants obtained using the present model and those indicated in the literature were in a range of approximately 0.5%–10%. The hydrogen fugacity calculated using the Henry’s law constant estimated using the present model was found to agree reasonably well with that reported in the literature. The deviations in the hydrogen fugacity data corresponding to the Ni/NiO phase transition were within 10% of the values in the literature, indicating that the Ni/NiO phase transition can be traversed by decreasing the pressure. Using the hydrogen sensor and the present model, the dissolved hydrogen concentration and hydrogen fugacity can be determined. The ability to calculate these values will be useful for applications in nuclear reactors and other fields. Acknowledgements This work was financially supported by the Korean Nuclear R&D Program organized by the National Research Foundation of Korea grant funded by the Ministry of Science, ICT & Future Planning (2017M2A8A4015155) and was carried out as a part of the R&D Program supported by Korea Atomic Energy Research Institute. References Ackerman, F.J., Koskinas, G.J., 1972. Permeation of hydrogen and deuterium through palladium-silver alloys. J. Chem. Eng. Data 17, 51–55. Ahluwalia, K., 2007. Materials reliability program: mitigation of PWSCC in nickelbase alloys by optimizing hydrogen in the primary water (MRP-213). EPRI Report no. 1015288. Attanasio, S.A., Morton, D.S., 2003. Measurement of the nickel/nickel oxide transition in Ni-Cr-Fe alloys and updated data and correlations to quantify the effect of aqueous hydrogen on primary water SCC. In: Proceedings 11th International Conference on Environmental Degradation of Materials in Nuclear Systems. Stevenson, WA, USA, pp. 143–154. Cassagne, T., Fleury, B., Vaillant, F., Bouvier, O., Combrade, P., 1997. An update on the influence of hydrogen on the PWSCC of nickel base alloys in high temperature water. In: Proceedings 8th International Conference on Environmental Degradation of Materials in Nuclear Power System – Water Reactors. TMS, Amelia Island, Florida, USA, pp. 307–315.
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Lee, D.H., Choi, M.S., Kim, U.C., 2002. The effect of the hydrogen on the stress corrosion cracking of Alloy 600 in simulated PWR primary water at 330°C. In: Proceedings 10th International Conference on Environmental Degradation of Materials in Nuclear Power System – Water Reactors, TMS, Lake Tohoe, Nevada, USA. Moshier, W.C., Witt, R.C., 2002. Unpublished data. Moss, T., Was, G.S., 2015. Determination of the nickel/nickel oxide phase transition and Henry’s constant in hydrogenated subcritical and supercritical water. J. Electrochem. Soc. 162 (1), C35–C41. Nguyen, T.H., Mori, S., Suzuki, M., 2009. Hydrogen permeance and the effect of H2O and CO on the permeability of Pd0.75-Ag0.25 membranes under gas-driven permeation and plasma-driven permeation. Chem. Eng. J. 155, 55–61. Wang, M., Feng, Y., 2007. Palladium-silver thin film for hydrogen sensing. Sensors Actuat. B Chem 123, 101–106. Yang, L., Sun, X., Steward, F.R., Morris, D.R., 1998. Measurements of Henry’s law constant for hydrogen in water utilizing a palladium differential resistance sensor. Phys. Chem. 102, 708–785. Ziemniak, S.E., 1992. Metal oxide solubility behavior in high temperature aqueous solutions. J. Solution Chem. 21, 745–760.
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Effects of temperature and pressure on Henry’s law constant for hydrogen in the primary water of a simulated pressurized-water reactor Eun-Hee Lee ⇑, Gyeong-Geun Lee, Kyung-Mo Kim Korea Atomic Energy Research Institute, 989-111 Daedeok-daero, Yuseong-gu, Daejeon 34057, Republic of Korea
a r t i c l e
i n f o
Article history: Received 31 July 2015 Received in revised form 30 March 2017 Accepted 2 April 2017 Available online 10 April 2017 Keywords: Henry’s law constant Hydrogen PWR PWSCC Temperature and pressure
a b s t r a c t The measurement of dissolved hydrogen in the primary systems of pressurized water reactors (PWRs) is difficult; hence, hydrogen concentrations are predicted by model equations. An accurate value for the Henry’s law constant for hydrogen is needed if the use of these equations is to be meaningful. The purpose of this study is to develop an empirical correlation for determining the Henry’s law constant for application to nuclear reactors. The effects of temperature and pressure on the Henry’s law constant are investigated using simulated PWR primary-water conditions. The Henry’s law constant was calculated by an in-situ measurement of the partial pressure of hydrogen using a hydrogen sensor based on a Pd–Ag alloy tube. At 20 MPa, the Henry’s law constant decreased by 40% as the temperature increased from 290 to 330 °C. The Henry’s law constant increased by an average of 9% as the pressure increased from 13.8 to 20 MPa at each temperature. Thus, it depends more strongly on the temperature than on the pressure. Based on the experimental data, an empirical correlation for predicting the Henry’s law constant was developed using a linear regression method, which was validated by comparing with results in the literature. The deviation between the Henry’s law constant obtained using our model and that reported in the literature was in the range of 0.5%–10%. The hydrogen fugacity estimated using our model was within 10% of that found in the literature. Thus, the proposed empirical model appears to be more accurate than previously published models. Ó 2017 Elsevier Ltd. All rights reserved.
1. Introduction In pressurized-water reactors (PWRs), hydrogen is added to the reactor coolant system (RCS) to reduce the oxidation of water by radiolysis and to maintain reducing conditions. It is important to maintain the hydrogen concentration within a certain range. This is because this parameter can lead to primary water stress corrosion cracking (PWSCC), general corrosion of the primary structural materials, higher radiation fields, and deposit build-up on fuel rods of a PWR (Fruzetti, 2005). Several researchers have demonstrated that the hydrogen concentration influences the corrosion of structural materials in PWRs (Cassagne et al., 1997; Lee et al., 2002; Ahluwalia, 2007). However, the amount of dissolved hydrogen, which affects the material susceptibility, exhibits a wide scatter. Computational work has suggested that dissolved hydrogen concentrations lower than 15 cc/kg are sufficient to scavenge oxidizing species under normal PWR operating conditions (Fruzetti, 2005). During operation, the concentration of dissolved hydrogen is controlled by varying the hydrogen overpressure in a volume control ⇑ Corresponding author. E-mail address: [email protected] (E.-H. Lee). http://dx.doi.org/10.1016/j.anucene.2017.04.001 0306-4549/Ó 2017 Elsevier Ltd. All rights reserved.
tank (VCT). Since the primary water flows from the VCT into the RCS, the temperature, system pressure, and solution chemistry in the RCS can affect the hydrogen concentration. In addition, hydrogen from the RCS diffuses through the steam generator tubes. To ensure an optimal operating margin, the Electric Power Research Institute (EPRI) PWR primary chemistry guide-lines require hydrogen levels of 25–50 cc/kg as an optimal margin. To mitigate PWSCC, the recent EPRI Hydrogen Management Program for fuel and material reliability focused on plant operations using hydrogen levels of up to 60 cc/kg (Hass et al., 2010). The optimization of the hydrogen concentration in the RCS is regarded as one approach to the management of material integrity and the reduction of radiation sources in the primary circuit. The solubility of gases in water and aqueous solutions is of considerable industrial and theoretical importance. Solubility depends on many factors, including temperature, pressure, association, dissociation, and the type of solvent (Himmelblau, 1960). However, inert gases like the hydrogen that is used in the RCS of PWRs do not react with water or ionize in water, so only the effects of temperature and pressure on the solubility are considered. The amount of hydrogen dissolved in water is directly proportional to the hydrogen fugacity (hydrogen partial pressure) in the gaseous
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phase. Thus, the measured hydrogen fugacity can be used to calculate the Henry’s law constant (Himmelblau, 1960). The Henry’s law constant is important because it is necessary to predict the dissolved hydrogen concentration in a PWR. Using the Henry’s law constant, the amount of dissolved hydrogen at a given temperature and pressure can be calculated. Alternatively, when the dissolved hydrogen concentration is known, the hydrogen fugacity can be determined using the Henry’s law equation. The values obtained for the dissolved hydrogen concentration affect the Ni/NiO phase transition in nickel-based alloys, shifting the Ni/NiO phase boundary up or down. For PWRs, these data can yield erroneous results in the prediction of PWSCC, and hinder the development of a model to fit the hydrogen concentrations (Attanasio and Morton, 2003; Lee et al., 2002; Moss and Was, 2015). Thus, accurate means of measuring and monitoring the hydrogen fugacity in PWRs are needed. In the present study, to measure the hydrogen partial pressure, we fabricated a sensor based on a Pd–Ag (75/25 wt.%) tube. Using this sensor, we measured the hydrogen partial pressure in situ as a function of temperature and pressure in a simulated PWR primary solution containing lithium hydroxide (LiOH) and boric acid (H3BO3). Based on the data collected in our experiments, an empirical correlation for predicting the Henry’s law constant was developed using a linear regression method. It was validated by comparing the obtained results with the values reported in the literature. 2. Theoretical background 2.1. Solubility of hydrogen in water The solubility of hydrogen in water can be determined using the findings of Henry, given by Eq. (1) and known as Henry’s Law (Himmelblau, 1960).
f ¼Hx/
ð1Þ
where f = fugacity of the solute gas in the vapor phase, H = Henry’s law constant, x = mole fraction of the solute gas in the liquid phase, and U = activity coefficient of the solute gas in the liquid phase. For inert gases such as hydrogen, oxygen, and nitrogen, which obey the ideal gas law in the vapor phase above the solution, Eq. (1) can be rewritten to give Eq. (2).
p¼Hx
ð2Þ
where p = partial pressure of hydrogen in the vapor phase and U = 1 for ideal solutions. Himmelblau developed theoretical equations to determine the Henry’s law constant of inert gases at different temperatures using the data reported in the literature. In developing the modified Henry’s law equations, Himmelblau used highpressure data extrapolated to low pressures, and thus considered only the effect of temperature. He then correlated the solubility data with various data plots. The plotted data in the graph are correlated by Eqs. (3)–(5) (Himmelblau, 1960).
logH ¼ 1:142 2:846ð1=TÞ þ 2:486ð1=TÞ2 0:9761ð1=TÞ3 þ 0:2001ð1=TÞ4 H ¼ H=Hmax ð1=TÞ ¼
ð1=TÞ ð1=T c Þ ð1=T max Þ ð1=T c Þ
ð3Þ ð4Þ ð5Þ
where Hmax 104 = 7.54, (1/Tmax) 103 = 3.09, and Tc = critical temperature of water (647 K). However, Himmelblau’s study was limited to the effect of temperature on solubility. In addition, the calculated Henry’s constants
137
are for ideal gases and solutions, and are applicable to low pressures only. For hydrogen, the low pressures appear to be 10.3 MPa (1500 psia) at 100 °C and about 13.8 MPa (2000 psia) at 300 °C (Himmelblau, 1960). Many researchers have used the Henry’s law constants determined by Himmelblau’s equations to calculate the hydrogen partial pressures or hydrogen concentrations at different temperatures. However, experimentally measured Henry’s law constants have proven to be quite different from those calculated from Himmelblau’s equations (Lee et al., 2002). This difference arises because his equations assume the concentration of dissolved hydrogen in water to be independent of pressure. This assumption gives rise to the difference between the theoretical and experimental data.
2.2. Sensor for measuring hydrogen partial pressure The accuracy of the hydrogen-fugacity measurement was also affected by the hydrogen-sensing materials used. Considerable research has been directed toward developing high-performance hydrogen sensors with high permeability, high selectivity, a fast response time, cost-effective fabrication, and which are easy to use. Among the various hydrogen-sensing materials tested, metallic palladium (Pd) exhibits high permeability and selectivity with hydrogen (Ackerman and Koskinas, 1972; Yang et al., 1998). However, pure Pd undergoes phase transition and hydrogen embrittlement at high temperatures and pressures, leading to fragility after extended use. To avoid these problems, alloying of Pd with group IB metals such as Ag was attempted and an optimal value of hydrogen permeation was attained at an Ag content of 25 wt.% (Knapton, 1977; Foletto et al., 2008). The advantage of using a Pd alloy is that the mechanical strength of the sensor is greater than that of one made from pure Pd. Several researchers have studied the effects of various parameters on the permeation of hydrogen through hydrogen sensors constructed using a Pd–Ag tube, film, and wire (Economy et al., 1987; Wang and Feng, 2007; Foletto et al., 2008).
3. Methods 3.1. Test loop Fig. 1 shows a schematic of the test loop that we used. The hydrogen sensor was mounted in an autoclave with a temperature control precision of ±0.5 °C. Then, 100 l of the test solution was prepared by adding 2 ppm of nuclear-grade lithium (as LiOH) and 1200 ppm of boron (as H3BO3) to purified water produced using an ultrapure water system (18 MOcm). This setup was used to simulate the representative PWR primary water chemistry. The amount of dissolved hydrogen was controlled by fixing the hydrogen overpressure in the feed tank at a temperature of 21 ± 1 °C. The amount of dissolved hydrogen was calculated using the Henry’s law constant for 5.7 kPa (0.826 psia)/(cc/kg) (Himmelblau, 1960). The solution from the feed tank was fed into the autoclave using a high-pressure pump and a double-tube heat exchanger. The outlet solution from the autoclave was cooled to ambient temperature by passing it through a heat-exchanger and a cooler, after which it passed through the sensors for measuring the conductivity and dissolved oxygen content. Finally, the solution was returned to the feed tank. The dissolved oxygen concentration was measured using a DO-32A (TOADKK Co.) and recorded manually. Throughout the experiments, the measured oxygen concentration was less than 1 ppb.
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Fig. 1. Schematic of simulated primary test loop used for measuring hydrogen fugacity in situ.
3.2. Hydrogen sensor The hydrogen sensor was fabricated using a Pd–25 wt.% Ag tube with an active length of 200 mm, an outside diameter of 3.2 mm, and a wall thickness of 0.43 mm (Lee et al., 2002). The inside of the tube was reinforced with a spring-type Inconel wire to prevent the collapse of the Pd–Ag tubing when subjected to a system pressure of 21.4 MPa (3100 psia) in the autoclave. Type 316 stainlesssteel tubing was connected to one end of the Pd–Ag tube while the other end of the tube was connected to the exit of the pressure boundary. The joint between the 316 stainless-steel tubing and the Pd–Ag tubing was gold-brazed. The other extremity of the Pd–Ag tube was sealed with an Inconel plug. The amount of hydrogen permeating from the solution through the Pd–Ag tube wall was measured by an external low-pressure gauge and a vacuum pump. 3.3. Measurement of hydrogen partial pressure The Henry’s law constant was determined by measuring the hydrogen partial pressure in situ at various temperatures (290, 300, 310, 320, and 330 °C) and pressures (13.8/2000, 15.2/2200, 17.9/2600, and 20 /2900 MPa/psia) in an aqueous hydrogenated solution. The system reached thermodynamic equilibrium in 4 to 12 h, depending on the temperature. After 48 h of equilibrium, the measurements were performed. All the measurements were repeated three times to obtain reliable data. The measured hydrogen partial pressure was considered to be the hydrogen fugacity in the autoclave at the given temperature and pressure. The Henry’s law constant was calculated by dividing the measured fugacity by the dissolved hydrogen concentration in the feed water. 4. Results and discussion 4.1. Hydrogen-sensor validation In this study, the hydrogen partial pressure was measured in an aqueous solution of 2 ppm lithium and 1200 ppm boron using the Pd–Ag tube at temperatures ranging from 290 to 330 °C and at 20 MPa. These values decreased linearly as the temperature increased and the determined Henry’s constant was shown in Fig. 2. Lee et al. (2002) measured the hydrogen partial pressure using the same Pd–Ag tube that we used in the present study. The effects of the dissolved hydrogen and lithium/boron-solution concentration on the hydrogen partial pressure were examined. They reported that the hydrogen partial pressure increased linearly
Fig. 2. Comparison of Henry’s law constants obtained from experimental measurements and theoretical calculations at different pressures and temperatures.
with the hydrogen concentration and decreased with increasing temperature. No solution-concentration effect on the hydrogen partial pressure was observed, indicating that the hydrogen partial pressure was the same between water and the aqueous solution within the tested temperature range. These results agree reasonable well with the literature and our data, and confirm the reliability of the Pd–Ag tube for the measurement of the hydrogen partial pressure (Attanasio and Morton, 2003).
4.2. Effects of temperature and pressure on Henry’s law constant Fig. 2 shows the results of the present study and those available in the literature. In the present study, the Henry’s law constant was calculated as a function of the temperature at 20 MPa according to the measured hydrogen fugacity. The Henry’s law constants reported in the literature (Kishima and Sakai, 1984; Moshier and Witt, 2002; Moss and Was, 2015) were also plotted for various pressures, in MPa. These data were determined by the hydrogen fugacity or dissolved hydrogen content, which were measured while the temperature and pressure varied. Himmelblau (1960) and Ziemniak (1992) obtained the Henry’s law constants using theoretical equations inferred by thermodynamic data. As shown in Fig. 2, the Henry’s law constant decreased linearly as the temperature increased and increased with the pressure at any given temperature. However, none of the plotted data can be compared quantitatively, because of the different measuring pressures. A
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substantial deviation between the experimental data and the theoretical estimation can be seen. This is because the assumption involved in most of the theoretical equations (that the Henry’s law constant is independent of the pressure) produced inadequate results. Himmelblau’s study (1960) examined only the effect of the temperature on the solubility of the gases: the effect of the pressure was disregarded. Himmelblau used high-pressure data that were extrapolated to low pressures. Ziemniak (1992) introduced only the effect of the pressure into the thermodynamic calculations of the Henry’s law constant at supercritical temperatures. Fig. 3 shows the results of the present study, in which the Henry’s law constant, as a function of the temperature and pressure, was determined using the measured hydrogen fugacity. The Henry’s law constant decreased linearly as the temperature increased from 290 to 330 °C and increased as the pressure increased from 13.8 to 20 MPa. These temperature and pressure dependences of the Henry’s law constant are consistent with the results of other studies, which are plotted in Fig. 2. When the temperature increased from 290 to 330 °C at 20 MPa, the Henry’s law constant decreased to 40% of its value at 290 °C. The Henry’s law constant increased by an average of 9% as the pressure increased from 13.8 to 20 MPa. It depended more strongly on the temperature than on the pressure. 4.3. Development of empirical model Various theoretical models for estimating the Henry’s law constant can be found in the literature. However, some of these models disregard the effect of the pressure on the Henry’s law constant (Himmelblau, 1960; Ziemniak, 1992), considering only that of the temperature. It may be possible to disregard slight changes in the pressure; however, as shown in Fig. 3, the Henry’s law constant was found to decrease by a maximum of 9% with the pressure in the present study. We developed an empirical model to estimate the Henry’s law constant, considering the effects of the temperature and pressure. The model is based on the experimental data obtained in this study. Because the data shown in Fig. 3 exhibits a linear correlation between the reciprocal temperatures and pressures and the Henry’s law constant, the following multipleregression model can be applied.
Y ¼ A þ Bð1=TÞ þ CðPÞ;
ð6Þ
where Y is the predicted Henry’s law constant, which is expressed in units of atm/(cc(STP)/kg-water); T is the temperature in Kelvin; P is the system pressure in psia (1 psia = 6.9 kPa); and A is the regres-
Fig. 3. Henry’s law constants calculated using the hydrogen fugacity, measured as a function of the temperature and pressure in an aqueous solution containing 2 ppm lithium and 1200 ppm boron.
139
Fig. 4. Comparison of Henry’s law constants obtained using the present model with experimental data as a function of the reciprocal temperature.
sion constant. The regression coefficients B and C represent the independent contributions of each independent variable to the prediction of the dependent variable. The regression analysis indicates that A, B, and C have values of 0.06568, 42.219, and 1.12 106, respectively. Eq. (6) can be rewritten as follows:
Y ¼ 0:06568 þ 42:219 T 1 þ 1:12 106 P
ð7Þ
The coefficient of determination (R2) used to statistically evaluate the model fit is 0.999232. This model equation can be used to estimate the Henry’s law constant if no data are available for a temperature range of 290–330 °C and a pressure range of 13.8– 20 MPa. With the calculated Henry’s law constant, the concentration of the dissolved hydrogen or the hydrogen fugacity in an aqueous solution can be obtained using Henry’s law equation (Himmelblau, 1960). 4.4. Model validation Fig. 4 compares the Henry’s law constant calculated using the present model with the experimental data obtained in the present study. There is excellent agreement between the linear fit and experimental data. At 13.8 MPa and at 330 °C, no experimental data were obtained, because of problems with the apparatus. Thus, the value for this temperature and pressure was estimated using Eq. (7) and then extrapolated to fit the experimental results, as shown in Fig. 4. This estimated value also agrees well with the trend of the experimental data. Table 1 shows that both the Henry’s law constants reported in the literature and those calculated using the present model agree well with the data in the literature (Himmelblau, 1960; Kishima and Sakai, 1984; Lee et al., 2002; Moss and Was, 2015; Attanasio and Morton, 2003; Ziemniak, 1992; Moshier and Witt, 2002). Here, the large deviations in the Henry’s law constant may arise from experimental errors or differences in the modeling equation, sensor used to measure the hydrogen fugacity, and the experimental environment. The Henry’s law constants obtained using Lee et al. (2002) and Attanasio’s models (2003), as well as those obtained using the present model were found to agree to within 4% at 20 MPa. As the temperature increased, the deviation also increased. This indicates that the effect of the pressure increased with the temperature. Their model disregards the dependence of the pressure on the Henry’s law constant, even though the experimental data obtained at different temperatures and pressures were used in the development of the model. This oversight led to large errors in the estimated results for the Henry’s law constant when varying the pressure. In the present study, as shown in
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Table 1 Henry’s law constants from the literature and calculated using the present model. Ref.
Himmelblau (1960), Ziemniak (1992), Lee et al. (2002), and Attanasio and Morton (2003)
Kishima and Sakai (1984)
Moshier and Witt (2002)
Moss and Was (2015)
Autoclave conditions
Henry’s law constant (atm/(cc/kg)
T (°C)
P (MPa/psia)
Reference data
Estimated using present model
290 300 310 320 330 296 326 356 260 288 316 333 360 320 360
20/2900 20/2900 20/2900 20/2900 20/2900 9.8/1421 14.5/2102 19.8/2871 6.9/1000 10.3/1500 20.7/3000 20.7/3000 22.1/3200 24.83/3600 24.81/3597
0.01244 0.0113 0.01016 0.00902 0.00788 0.0102 0.0072 0.00439 0.0160 0.0122 0.0101 0.0072 0.0049 0.01033 0.00563
0.01256 0.01125 0.00999 0.00876 0.00758 0.01011 0.00716 0.00466 0.01465 0.01126 0.00936 0.00678 0.00460 0.00955 0.00505
Fig. 3, the Henry’s law constant increased by an average of 9% as the pressure increased from 13.8 to 20 MPa at each temperature. The Henry’s law constants reported by Kishima and Sakai (1984) at 9.8 MPa (1421 psia) and 14.5 MPa (2102 psia) are in good agreement with the constants calculated using the present model. However, the difference between Kishima’s and our data increased rapidly at 356 °C, even though the pressure was similar in both studies. The temperature in Kishima’s study (1984) was well in excess of the present upper temperature of 330 °C, leading to a large deviation. These results confirm that the Henry’s law constant is more dependent on the temperature than on the pressure. The deviations between Moshier and Witt (2002) data and the present data are greater than those between the present data and the data reported in the literature. None of the pressure ranges were consistent with those in the present study, yielding a deviation of 10%. Moshier and Witt (2002) developed a Henry’s law correlation with the hydrogen fugacity, which was measured according to the temperature and system pressure. They improved the Henry’s law correlation by fitting the hydrogen-fugacity data using Krichevsky and Kasarnovsky’s equations (1935). However, their thermodynamic equations were verified at pressures of up to 100 MPa (14,500 psia) and at temperatures ranging from 0 to 100 °C. The data obtained using Krichevsky and Kasarnovsky’s equations were in good agreement with the experimental data obtained at the aforementioned temperature and pressure. However, it is uncertain whether their equations fit well above 100 °C. There is a large difference between our data and that obtained by Moss and Was (2015). They used Pd–20wt.% Ag tube with a length of 25.4 mm, an outer diameter of 3.2 mm, and an inner diameter of 1.6 mm. In the literature, the hydrogen permeability was affected by the Ag content and the thickness of the Pd–Ag tube (Nguyen et al., 2009). The large deviation in the Henry’s law constant may arise from the hydrogen-sensing material and type. Fig. 5 shows the experimental data reported in the literature and the fitting with the data obtained with the present model (Lee et al., 2002; Attanasio and Morton, 2003; Economy and Pement, 1989). The filled symbols indicate the hydrogen-fugacity data calculated using the present model, while the open symbols represent the experimental data obtained from the literature. First, the Henry’s law constant was calculated using Eq. (7) at the same temperature and pressure as were reported in the literature. Second, the hydrogen fugacity was calculated by multiplying the calculated Henry’s law constant by the dissolved hydrogen content. The estimated hydrogen-fugacity data for dissolved hydrogen
Error (%)
1 0.5 1.7 3 4 0.9 0.6 5.8 9.2 8.4 7.9 6.2 6.5 8.2 11.6
Fig. 5. Comparison of hydrogen fugacity calculated using the present model with experimental data obtained from the literature.
contents of 50 and 17 cc/kg at 20 MPa was in good agreement with the experimental data obtained by Lee et al. (2002). These results confirm the accuracy of the hydrogen-fugacity measuring sensor, the experimental data, and the present empirical model. The errors between the experimental data obtained by Economy et al. and our estimated data were greater than 17%, and the deviation increased slightly with the temperature. Economy and Pement (1989) used a Pd–25 wt.% Ag tube, but adopted a measurement system that was different from ours. Furthermore, they measured the hydrogen partial pressure at a low temperature (100–110 °C). In the present study, the hydrogen fugacity was measured in situ at given temperatures and pressures, and these data were used to develop the empirical model. This was because the hydrogen fugacity was affected by both the system temperature and pressure, as shown in Fig. 4. The experimental result obtained by Attanasio and Morton (2003) at 316 °C agrees reasonable well with the result obtained using the present model.
4.5. Ni/NiO phase transition Fig. 6 shows the calculated and measured hydrogen-fugacity data corresponding to the Ni/NiO phase transition (Attanasio and Morton, 2003; Moss and Was, 2015) at different pressures and hydrogen concentrations. The hydrogen fugacity was calculated
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alloys occurred in the proximity of the Ni/NiO phase boundary. Therefore, both the temperature and pressure are important for determining the location of the Ni/NiO phase boundary. Many researchers have determined the hydrogen fugacity by using Henry’s law constants obtained from their thermodynamic models, experimental data, or the literature. The present model was obtained by a linear regression analysis of the experimental data, as discussed in this study. Thus, more accurate data can be obtained using the present model, relative to other models. 5. Conclusion
Fig. 6. Measured and calculated hydrogen-fugacity data corresponding to Ni/NiO phase transition.
by multiplying the Henry’s law constant by the dissolved hydrogen concentration. The hydrogen fugacity is a direct measure of the thermodynamic stability of nickel and exhibits a good correlation with the free energy of nickel oxidation (Moss and Was, 2015). As the temperature increased, the calculated hydrogen fugacity exhibited a trend similar to that reported by Attanasio and Morton (2003) and Moss and Was (2015) The filled square symbols indicate the hydrogen fugacity of the Ni/NiO phase transition reported by Attanasio and Morton (2003) at various pressures (6.9, 10.3, 20.7, 20.7, and 22.1 MPa) and concentrations (2, 4, 7.5, 13.8, and 25 cc/kg), respectively. The open-triangle symbols represent the hydrogen fugacity calculated using the present model under the same conditions as those used by Attanasio and Morton (2003). The calculated data were found to be within 8% of the experimental data obtained by Attanasio et al. over a temperature range of 260 to 360 °C. The discrepancies between the two sets of data are explained as follows. Attanasio and Morton (2003) determined the hydrogen fugacity using the hydrogen concentration that was experimentally obtained from exposure tests and using the Henry’s law correlation reported by Moshier and Witt (2002). Moshier and Witt (2002) used the thermodynamic equations of Krichevsky and Kasarnovsky (1935) to improve the Henry’s law correlation. These results indicate that the hydrogenfugacity data reported by Attanasio and Morton (2003) accurately reflected the thermodynamic properties. However, the present model was developed using only experimental data. Therefore, the present data are more reasonable than those reported by Attanasio and Morton (2003). Fig. 6 shows that the present model can be extrapolated to temperatures and pressures ranging from 260 to 360 °C and 7 to 22 MPa, respectively. The filled circles represent the data obtained by Moss and Was (2015), which were generated at 320 °C (6 cc/kg H2) and 330 °C (8 cc/kg H2) at 25 MPa; these circles are located in the NiO regime. Using the present model, their data were recalculated under the same conditions; the recalculated values are indicated by the open circles. These data points are also located in the NiO regime, according to the literature (Attanasio and Morton, 2003; Moss and Was, 2015). In the study by Moss et al., when the dissolved hydrogen content increased from 6 to 8.5 cc/kg at 320 °C and at 25 MPa, this data point moved into the Ni regime. In this case, a change in the pressure from 25 to 20 MPa shifted the hydrogen fugacity calculated using the present model downward; this value is denoted by an open diamond. As the pressure decreased, the hydrogen fugacity also decreased, which may have caused a crossing of the Ni/NiO phase boundary. In PWRs, the maximum PWSCC susceptibility of
A hydrogen sensor made using a Pd–25 wt.% Ag tube was used to indirectly determine the Henry’s law constant for hydrogen in an aqueous solution containing lithium and boron. Using this sensor, in-situ measurements of the hydrogen fugacity were performed for temperature and pressure ranges of 290–330 °C and 13.8–20 MPa, respectively. The Henry’s law constant was calculated by dividing the measured hydrogen fugacity by the dissolved hydrogen concentration. The Henry’s law constant decreased linearly as the temperature increased and the pressure decreased. The Henry’s law constant was found to be more strongly dependent on the temperature than on the pressure. When the temperature increased from 290 to 330 °C at 20 MPa, the Henry’s law constant decreased to 40% of its initial value at 290 °C. However, the Henry’s law constant increased by a maximum of 9% as the pressure increased at each given temperature. An empirical model that uses the experimental data was developed to estimate the simultaneous effects of the temperature and pressure on the Henry’s law constant. The deviations in the Henry’s law constants obtained using the present model and those indicated in the literature were in a range of approximately 0.5%–10%. The hydrogen fugacity calculated using the Henry’s law constant estimated using the present model was found to agree reasonably well with that reported in the literature. The deviations in the hydrogen fugacity data corresponding to the Ni/NiO phase transition were within 10% of the values in the literature, indicating that the Ni/NiO phase transition can be traversed by decreasing the pressure. Using the hydrogen sensor and the present model, the dissolved hydrogen concentration and hydrogen fugacity can be determined. The ability to calculate these values will be useful for applications in nuclear reactors and other fields. Acknowledgements This work was financially supported by the Korean Nuclear R&D Program organized by the National Research Foundation of Korea grant funded by the Ministry of Science, ICT & Future Planning (2017M2A8A4015155) and was carried out as a part of the R&D Program supported by Korea Atomic Energy Research Institute. References Ackerman, F.J., Koskinas, G.J., 1972. Permeation of hydrogen and deuterium through palladium-silver alloys. J. Chem. Eng. Data 17, 51–55. Ahluwalia, K., 2007. Materials reliability program: mitigation of PWSCC in nickelbase alloys by optimizing hydrogen in the primary water (MRP-213). EPRI Report no. 1015288. Attanasio, S.A., Morton, D.S., 2003. Measurement of the nickel/nickel oxide transition in Ni-Cr-Fe alloys and updated data and correlations to quantify the effect of aqueous hydrogen on primary water SCC. In: Proceedings 11th International Conference on Environmental Degradation of Materials in Nuclear Systems. Stevenson, WA, USA, pp. 143–154. Cassagne, T., Fleury, B., Vaillant, F., Bouvier, O., Combrade, P., 1997. An update on the influence of hydrogen on the PWSCC of nickel base alloys in high temperature water. In: Proceedings 8th International Conference on Environmental Degradation of Materials in Nuclear Power System – Water Reactors. TMS, Amelia Island, Florida, USA, pp. 307–315.
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