Kinetics of Water Vapor Adsorption on Single-Layer Molecular Sieve

Article pubs.acs.org/IECR

Kinetics of Water Vapor Adsorption on Single-Layer Molecular Sieve 3A: Experiments and Modeling Ronghong Lin,† Jiuxu Liu,† Yue Nan,† David W. DePaoli,‡ and Lawrence L. Tavlarides*,† †

Department of Biomedical and Chemical Engineering, Syracuse University, 329 Link Hall, Syracuse, New York 13244, United States Nuclear Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831-6181, United States

‡

ABSTRACT: The objective of the current work was to shorten the gap for fundamental adsorption kinetic data required for the development of advanced adsorption unit-operation models to be incorporated into an overall plant-level model for spent nuclear fuel reprocessing. The kinetics of water-vapor adsorption on molecular sieve 3A was investigated at 25−80 °C and water dew points from −69 to 17 °C. Water uptake curves were fitted with three kinetic models including the linear-driving-force model, the shrinking-core model, and the Langmuir kinetic model. The results suggest that the water-vapor adsorption on molecular sieve 3A under the investigated experimental conditions was controlled by both external film resistance and internal macropore resistance. The contribution of the external film resistance varied from 25% to 50% of the total mass-transfer resistance depending on the adsorption temperature. It was also found that the Langmuir kinetic model fitted individual sets of kinetic data very well, but the Langmuir adsorption constant obtained from curve fitting decreased with increasing adsorption temperature and with increasing water vapor pressure. This result indicates a significant surface heterogeneity of molecular sieve 3A and also implicitly verifies that the Langmuir isotherm model is unable to represent isotherms of water adsorption on molecular sieve 3A.

1. INTRODUCTION The removal and immobilization of tritium (3H) from spent nuclear fuels is a desirable strategy for reducing tritium emissions into the environment. The main options for capturing tritium from spent nuclear fuels include volatilization and adsorption of tritiated water from off-gas streams, isotopic enrichment and collection from liquid streams, and aqueous recycling with removal and solidification of small side streams.1 Voloxidation has been proposed for the removal of tritium from spent fuels prior to dissolution to avoid introducing tritium into the aqueous system.2 The voloxidation process usually takes place at 450−650 °C and releases more than 99.9% of the tritium produced in reactors. The tritium released during voloxidation further reacts with oxygen to form tritiated water, which is released to off-gas systems.2 The state of the art of tritiated water-vapor capture from spent fuel reprocessing offgases is adsorption by solid sorbents.3−10 Over the past four decades, various sorbents have been investigated for the capture of tritiated water vapor including silica gel, molecular sieves (3A, 4A, 5A, 13X), Drierite, and activated alumina. Among these sorbents, molecular sieves, such as molecular sieve 3A, have been the most favorable choice for the removal and temporary storage of tritiated water.11 The U.S. Department of Energy (DOE) Fuel Cycle Research and Development (FCRD) Separations and Waste Form Campaign is currently developing a dynamic plant-level modeling and simulation toolkit to support the development of sustainable nuclear fuel cycles.11 The initial focus of the modeling effort is the development of individual unit-operation models that can be implemented in an overall plant-level model.11 An example of the unit operations for the removal of radioactive species from off-gas streams is a sequence of adsorption beds for the removal of tritium (in the form of tritiated water), krypton, xenon, and iodine.12 The develop© 2014 American Chemical Society

ment of highly efficient dynamic adsorption unit-operation models requires experimental data on adsorption isotherms and kinetics. Although water adsorption on solid sorbents is a relatively mature technology, there is still a data gap in the open literature regarding the kinetics of water adsorption on molecular sieve 3A. The objective of the current work was to shorten this recognized data gap. To serve this purpose, the kinetics of water-vapor adsorption on molecular sieve 3A was investigated at 25−80 °C and water dew points from −69 to 17 °C. Water uptake curves were obtained using a continuous-flow adsorption system developed in this laboratory. Three kinetic models were used to fit water uptake curves including the linear-driving-force model, the shrinking-core model, and the Langmuir kinetic model. The performances of these models were evaluated, and kinetic parameters associated with these models were determined.

2. MATERIALS AND METHODS 2.1. Materials. The molecular sieve 3A used in this work was commercial UOP-type zeolite 3A (CAS no. 308080-99-1, product no. 208582, lot no. MKBH6237V) purchased from Sigma-Aldrich. The chemical composition of the molecular sieve 3A provided by the supplier was K7.2Na4.8(AlO2)12(SiO2)12·xH2O, and its properties and characteristics are listed in Table 1. The sorbents received from the supplier were 8−12-mesh beads. The beads were further sieved with an 8-mesh stainless steel screen to create a narrower pellet size distribution, and the measured average radius of the pellets Received: Revised: Accepted: Published: 16015

June 18, 2014 September 12, 2014 September 16, 2014 September 16, 2014 dx.doi.org/10.1021/ie5024645 | Ind. Eng. Chem. Res. 2014, 53, 16015−16024

Industrial & Engineering Chemistry Research

Article

controlled by a balance control unit that was connected to a data acquisition system. Water vapor was generated by bubbling water in a controlled manner. Dry air from a gas cylinder was split into two streams, the carrier stream and the makeup stream, controlled by two mass flow controllers. The carrier stream passed through one to three glass tubes containing deionized water. The glass tubes were immersed in a water bath, the temperature of which was controlled at a value between 4 and 20 °C. The carrier stream exiting the glass tubes was then mixed with the makeup stream to generate a mixture of desired water vapor pressure (or dew point). The dew point of the mixture was measured and monitored by a dew-point meter (Easidew Online, Michell Instruments) before the mixture entered into a glass sample tube where adsorption took place. Gas mixtures of desired water vapor pressures were generated by precisely controlling the total gas flow rates, the ratio of the carrier stream to the makeup stream, and the water temperature. The gas mixture was preheated to a desired adsorption temperature by being passed through a glass coil and then entered the sample tube through an inlet located near the bottom of the tube. The integrated unit consisting of the preheating coil and sample tube was placed in a second water bath during the adsorption process. The sample tube was connected to the microbalance head, from which several connected suspension rods hung down to hold a sample pan. Photographs of the adsorption unit and the stainless steel screen pan with sorbents loaded are shown in Figure 2. 2.3. Experimental Conditions and Procedure. Molecular sieve 3A was degassed using an ASAP 2020 Physisorption Analyzer to remove residual water prior to use. Degassing was performed under a vacuum at 230 °C for 8 h to a final pressure of less than 0.5 Pa. All samples were degassed and stored for less than 1 day before use to minimize uncertainty caused by possible water adsorption on the sorbents during storage in the degas tube. The adsorption system was run for several hours to several days to establish desired experimental conditions. The prerunning duration was largely dependent on the desired dew point. After the desired conditions were established, degassed molecular sieve 3A (∼0.27 g) was loaded onto the stainless steel screen pan as shown in Figure 2, and water uptake data were recorded. Adsorption experiments were conducted at 25, 40, 60, and 80 °C over a wide range of dew

Table 1. Properties and Characteristics of Molecular Sieve 3A Used in This Studya

a b

property/characteristic

value

form moisture (%) equilibrium H2O capacity (theory) (%) regeneration temperature (°C) radius of pellets (Rp) (mm) radius of microparticles (crystals) (Rc) (μm) macroporosity (εp) pellet density (ρp) (g/cm3)

beads 1.5 21 175−260 1.18b (8-mesh) 1.5−2.5 0.272b 1.690 ± 0.001b

Data provided by the material supplier, unless otherwise noted. Measured in this study.

was 1.18 mm. The macroporosity and density of the pellets determined by a third party by mercury porosimetry were 0.272 and 1.690 ± 0.001 g/mL, respectively. Molecular sieve beads are composed of microparticles (or crystals) and binder materials. The size of the microparticles of the molecular sieve 3A was 1.5−2.5 μm in radius, assuming spherical particles, as indicated by the supplier. The theoretical equilibrium water adsorption capacities of the molecular sieve 3A powder (without binder material) and beads were 23 and 21 wt %, respectively, as indicated by the supplier. Assuming that the binder material does not adsorb water, the corresponding content of binder material in the molecular sieve 3A was about 9 wt %. 2.2. Experimental Setup. A continuous-flow adsorption system was developed in this work. A brief description of the system was provided previously.13 A schematic diagram of the system is shown in Figure 1. The system was generally composed of three functional units: vapor generation, adsorption, and data acquisition. The core of the system was a microbalance head (model MK2-M5, CI Precision, Salisbury, U.K.) to measure mass gain or loss. The balance head had a loading capacity of 5 g (5 g for sample and 5 g for counterweight), a dynamic weighing range of ±500 mg (weight gain or loss), and a sensitivity of 0.1 μg. The head was maintained at a constant temperature (28 °C) to minimize inaccuracies caused by temperature variations in long-term experiments. The head was purged with nitrogen at a flow rate of less than 50 mL/min to prevent damage of the head from the adsorption carrier gas. The balance was connected to and

Figure 1. Schematic diagram of the continuous-flow water adsorption system used in this work. 16016

dx.doi.org/10.1021/ie5024645 | Ind. Eng. Chem. Res. 2014, 53, 16015−16024


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⎛q − q ⎞ ̅⎟ ln⎜⎜ e ⎟ = −kLDFt q ⎝ ⎠ e

(2)

and the LDF mass-transfer coefficient can then be obtained from a plot of ln[(qe − q)/q ̅ e] versus t. Assuming a linear isotherm, it can be shown that the LDF mass-transfer resistance can be expressed as15 1 kLDF

R p qeρp 3k f C b

+

R p2 qeρp 15εpDp C b

+

Rc2 15Dc

(3)

where Cb is the bulk gas-phase concentration, Dc is the micropore diffusivity, Dp is the macropore diffusivity, kf is the film mass-transfer coefficient, Rc is the radius of a micropore, Rp is the radius of a pellet, εp is the porosity of the pellets, and ρp is the density of the pellets. The three terms on the right-hand side of eq 3 are, from left to right, the external film resistance, the macropore resistance, and the micropore resistance, respectively. Cb can be calculated from the water vapor pressure assuming ideal gas behavior. 2.3.2. Shrinking-Core Model. The shrinking-core (SC) model is also frequently used in modeling adsorption kinetics. This model simplifies the adsorption process into three sequential steps:15,16 diffusion through an external gas film, diffusion through a saturated shell, and adsorption at the surface of the sorbate-free core. Assuming that the adsorption step occurs sufficiently more rapidly than the two diffusion steps, the sorbate uptake curve can be expressed implicitly by the function t = f(q)̅ as 2/3⎤ ⎡ ⎛ ⎛ q̅ q̅ ⎞ q̅ ⎞ ⎥ ⎢ t = τ1 + ⎢1 + 2⎜⎜1 − ⎟⎟ − 3⎜⎜1 − ⎟⎟ ⎥τ2 qe qe ⎠ qe ⎠ ⎝ ⎝ ⎣ ⎦ (4)

Figure 2. Photographs of the adsorption unit (right) and the stainless steel screen pan with sorbents loaded (left).

points from −69 to 17 °C. The total gas flow rate was set to a value between 0.050 and 1.400 L/min for all runs, and the corresponding gas velocity inside the sample tube was 0.001− 0.033 m/s, considering a tube inner diameter of 0.3 m. 2.3.1. Linear-Driving-Force Model. The linear-driving-force (LDF) model, originally proposed by Gleuckauf and Coates in 1947,14 has been widely used in modeling adsorption kinetics because of its analytical simplicity. According to this model, the average sorbate uptake rate is given by the product of the amount required to reach equilibrium and the so-called LDF mass-transfer coefficient, as in the equation dq ̅ = kLDF(qe − q ̅ ) dt

=

The two parameters τ1 and τ2 are the characteristic diffusion times for diffusion through the external gas film and diffusion through the saturated shell, respectively. They are given by16 R p qeρp τ1 = 3εpk f C b (5)

(1)

τ2 =

Here, q̅ and qe are the transient average sorbate concentration in the sorbent and the equilibrium sorbate concentration in the sorbent, respectively, and kLDF is the LDF mass-transfer coefficient. Integration of eq 1 gives


(6)

This model has been successfully used for the analysis of water uptake curves at or near ambient temperature in molecular sieve adsorbents.15

Figure 3. Determination of τ1 and τ2 in the shrinking-core model. Adsorption temperature = 60 °C; dew point = −44.1 °C. 16017



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Assuming that the external gas film diffusion dominates in the very initial stage (up to 15% weight gain) of the overall adsorption process, τ1 can be determined from a plot of (q/q ̅ e) versus t. τ2 can then be determined from a plot of [1 + 2(1 − q/̅ 2/3 qe) − 3(1 − q/q ̅ e) ] versus [t − (q/q ̅ e)τ1]. Figure 3 illustrates the determination of τ1 and τ2. 2.3.3. Langmuir Kinetic Model. According to the Langmuir kinetic model, the adsorption process is actually a dynamic adsorption and desorption process, and the rate of sorbate uptake is given by the difference between the rate of adsorption and the rate of desorption, expressed as17 dq ̅ = kaC b(qm − q ̅ ) − kdq ̅ dt

where T and P are the dew-point temperature and ambient pressure, respectively. The unit of T is the Kelvin (K), and the unit of pν′ pν, and P is the millibar or hectopascal (hPa). The P value was fixed at 0.1 MPa (1 bar or 1000 hPa) throughout the study. Dew-point temperatures were measured by a dew-point meter.

3. RESULTS AND DISCUSSION 3.1. Effect of Superficial Gas Velocity. Superficial gas velocity influences adsorption kinetics by changing the external gas film resistance. Test adsorption experiments were conducted to demonstrate this effect of superficial gas velocity on the water adsorption kinetics and to determine an optimal superficial gas velocity. Water uptake curves were obtained at two different adsorption temperatures (25 and 40 °C) and three different dew points (5, 10, and 11 °C) and at varying superficial gas velocities. The superficial gas velocity was simply defined as the gas flow rate divided by the cross-sectional area of the sample tube. The gas flow rate was varied from 0.05 to 1.4 L/min, and the corresponding superficial gas velocity varied from 0.001 to 0.033 m/s. Water uptake curves obtained from the test runs were fitted by the LDF model, and the LDF mass-transfer coefficients were determined for different adsorption conditions. The LDF masstransfer resistance, which is the reciprocal of the LDF masstransfer coefficient, is plotted in Figure 4 as a function of the

(7)

where ka and kd are temperature-dependent adsorption and desorption constants, respectively, and qm is the maximum sorbate concentration in the sorbent. In this work, qm equals 21 wt % (dry sorbents). Although the Langmuir model was developed on the basis of the surface reaction mechanism18 and might not be applicable to water adsorption on zeolites, which is controlled by mass diffusion,13 this model was considered for kinetic data analysis in this work because the Langmuir isotherm model has been widely used for modeling the isotherms of gas adsorption on zeolites. The current analysis and discussion will provide new insight into the application of this model to gas−solid adsorption systems. 2.4. Calculation of Water-Vapor Partial Pressure. The water-vapor partial pressure in moist air was calculated by a method described by Buck.19 According to this method, the water-vapor partial pressure in moist air (p′ν) is the pure-water vapor pressure (pν) multiplied by an enhancement factor ( f) pv′ = pv f

(8)

The pure-water vapor pressure can be obtained with Wexler’s most accurate formulations19−21 pv = 0.01 exp( −2991.2729T −2 − 6017.0128T −1 + 18.87643854 − 0.028354721T + 0.17838301 × 10−4T 2 − 0.84150417 × 10−9T 3 + 0.44412543 × 10−12T 4 + 2.858487 ln T )

for T > 273.15 K (9a)

pv = 0.01 exp( −5865.3696T −1 + 22.241033

Figure 4. Effect of the superficial gas velocity on the LDF masstransfer resistance. Adsorption temperature = 25 or 40 °C; dew point = 5, 10, or 11 °C.

−4 2

+ 0.013749042T − 0.34031775 × 10 T

+ 0.26967687 × 10−7T 3 + 0.6918651 ln T ) for T ≤ 273.15 K

(9b)

superficial gas velocity. It was found that the LDF mass-transfer resistance generally decreased as the superficial gas velocity increased to a transitional point, beyond which the LDF masstransfer resistance slightly increased. This transitional superficial gas velocity varied from 0.014 m/s (0.6 L/min) to 0.028 m/s (1.2 L/min) depending on the adsorption temperature and water dew point, as shown in Figure 4. The results also suggested that the dew point played a more important role than the adsorption temperature did and that a higher dew point led to a lower mass-transfer resistance. One single superficial gas velocity was applied throughout the remaining experiments, namely, 0.024 m/s (1 L/min).

The enhancement factor can be fitted by the expressions f = 1 + 4.1 × 10−4 + P[3.48 × 10−6 + 7.4 × 10−10(T − 242.55 − 3.8 × 10−2P)2 ] T > 273.15 K

(10a)

f = 1 + 4.8 × 10−4 + P[3.47 × 10−6 + 5.9 × 10−10(T − 249.35 − 3.1 × 10−2P)2 ] T ≤ 273.15 K

(10b) 16018



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Figure 5. Water uptake curves at 25, 40, 60, and 80 °C.

Figure 6. Curve fitting of a water uptake curve by the linear-driving-force, shrinking-core, and Langmuir kinetic models. Adsorption temperature = 60 °C; dew point = −44.1 °C.

17.0 °C. The results plotted in Figure 5 show that, as the water dew point decreased, the equilibrium water uptake capacity (maximum weight gain) decreased and the time required to

3.2. Water Uptake Curves and General Comparison of Kinetic Models. Water uptake curves were obtained at 25, 40, 60, and 80 °C and at water dew points varying from −68.9 to 16019



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Table 2. Experimental Results and Model Parameters for the Linear-Driving-Force (LDF), Shrinking-Core (SC), and Langmuir Models at 25, 40, 60, and 80 °C LDF DP (°C)

P (kPa)

−68.9 −64.9 −60.2 −50.0 −39.9 −30.0 −20.6 −5.2 5.1 10.1 average

3.105 5.530 1.060 3.963 1.306 3.821 9.791 3.966 8.820 1.241

× × × × × × × × ×

10−4 10−4 10−3 10−3 10−2 10−2 10−2 10−1 10−1

−66.1 −60.7 −53.4 −47.5 −42.7 −35.8 −30.5 −22.9 −15.0 −0.1 9.9 average

4.661 9.905 2.588 5.377 9.484 2.060 3.627 7.829 1.660 6.086 1.225

× × × × × × × × × ×

10−4 10−4 10−3 10−3 10−3 10−2 10−2 10−2 10−1 10−1

−59.6 −52.4 −44.1 −39.5 −32.1 −25.1 −17.2 −5.9 3.0 9.2 average

1.150 2.938 8.057 1.367 3.065 6.296 1.353 3.734 7.610 1.168

× × × × × × × × ×

10−3 10−3 10−3 10−2 10−2 10−2 10−1 10−1 10−1

−51.2 −39.8 −28.3 −22.5 −16.6 5.1 17 average

3.415 1.321 4.554 8.142 1.431 8.820 1.945

× × × × × ×

10−3 10−2 10−2 10−2 10−1 10−1

qe (g/g)

kLDF (h−1)

0.0277 0.0500 0.1050 0.1440 0.1565 0.1665 0.1750 0.1920 0.1960 0.2040

7.400 5.100 5.700 2.170 6.880 1.635 3.655 1.091 1.872 3.462

× × × × × × ×

0.0270 0.0370 0.0650 0.0990 0.1225 0.1390 0.1505 0.1555 0.1650 0.1800 0.1880

5.200 1.030 1.430 1.910 3.050 7.630 1.052 2.163 3.846 1.328 3.233

× × × × × × × × ×

0.0200 0.0307 0.0500 0.0843 0.1142 0.1385 0.1510 0.1636 0.1678 0.1810

1.420 2.920 4.990 6.800 1.208 2.427 3.740 1.214 1.974 3.458

× × × × × × ×

0.0187 0.0355 0.0730 0.1055 0.1160 0.1495 0.1550

4.920 1.288 2.296 3.294 4.853 1.939 3.751

× × × × ×

10−3 10−3 10−3 10−2 10−2 10−1 10−1

10−3 10−2 10−2 10−2 10−2 10−2 10−1 10−1 10−1

10−2 10−2 10−2 10−2 10−1 10−1 10−1

10−2 10−1 10−1 10−1 10−1

SC error (%)

τ1 (h)

kd (h−1)

error (%)

4.537 3.597 4.014 1.080 3.425 1.441 6.072 2.151 1.129 7.606

× × × × × ×

3.7 6.5 1.3 1.6 0.6 1.0 1.4 0.8 1.0 2.2 2.0

4.161 2.882 3.607 5.024 5.165 4.570 4.122 3.304 2.717 3.973

× × × × × × × × × ×

105 105 105 105 105 105 105 105 105 105

5.862 3.043 2.524 5.943 1.421 2.904 5.032 7.566 8.136 1.363

× × × × × × × × × ×

10−3 10−3 10−3 10−3 10−2 10−2 10−2 10−2 10−2 10−1

5.4 5.5 2.6 2.8 1.8 1.8 2.1 1.6 1.7 2.2 2.8

3.890 1.436 1.786 1.316 7.692 3.003 2.208 1.129 5.855 1.744 7.699

× × × × × × × ×

6.0 2.7 1.6 1.7 1.0 1.0 0.7 0.7 0.6 1.0 0.9 1.6

2.039 2.469 2.456 2.445 2.749 3.452 2.882 2.866 2.469 2.575 3.247

× × × × × × × × × × ×

105 105 105 105 105 105 105 105 105 105 105

3.743 7.310 9.305 1.001 1.238 2.385 2.664 5.047 6.105 1.501 2.905

× × × × × × × × × × ×

10−3 10−3 10−3 10−2 10−2 10−2 10−2 10−2 10−2 10−1 10−1

4.9 3.8 3.1 1.9 1.5 1.5 1.6 2.0 1.6 1.6 2.2 2.3

× × × × ×

× 10−1 × 10−1 × 10−1

1.509 8.000 4.587 3.937 2.033 9.407 6.365 1.853 1.218 7.678

4.7 2.0 2.1 2.0 1.4 1.1 2.0 1.5 1.7 1.5 2.0

2.059 2.242 2.338 3.275 3.314 3.971 3.110 3.800 3.177 3.796

× × × × × × × × × ×

105 105 105 105 105 105 105 105 105 105

1.746 2.482 3.946 4.421 5.450 7.993 1.181 2.676 4.039 4.678

× × × × × × × × × ×

10−2 10−2 10−2 10−2 10−2 10−2 10−1 10−1 10−1 10−1

2.2 1.8 0.7 1.7 1.3 1.6 2.1 1.4 1.5 1.8 1.6

80 °C 1.905 × 101 6.892 3.994 2.698 1.973 5.234 × 10−1 2.638 × 10−1

4.739 1.873 1.009 7.348 4.801 1.054 5.504

× 101 × 101 × 101

1.9 2.3 2.6 1.7 1.4 1.2 1.3 1.8

2.093 2.797 3.004 3.387 3.056 2.498 2.308

× × × × × × ×

105 105 105 105 105 105 105

4.442 1.127 1.598 1.690 2.167 5.026 9.244

× × × × × × ×

10−2 10−1 10−1 10−1 10−1 10−1 10−1

1.3 1.0 0.9 0.8 0.9 1.4 1.4 1.1

25 °C × 101 × 102 × 102 × 101 × 101

6.5 3.9 3.5 3.3 2.8 2.4 1.6 1.8 2.4 2.4 3.0

9.901 2.079 1.598 4.065 1.357 5.705 2.699 8.638 × 10−1 5.077 × 10−1 2.372 × 10−1

4.5 4.9 3.8 2.2 2.2 1.9 2.1 2.4 2.8 2.2 1.9 2.8

1.858 1.152 5.952 4.608 2.907 1.271 9.074 4.141 2.551 7.214 2.703

5.0 2.0 0.8 1.6 1.6 2.3 1.5 1.5 1.5 1.6 1.9

6.579 3.268 1.852 1.179 7.457 3.712 2.510 8.165 4.678 2.330

1.6 1.2 1.1 0.9 0.9 2.0 1.6 1.3

Langmuir ka (cm3g−1h−1)

τ2 (h)

40 °C × 102 × 102 × 101 × 101 × 101 × 101

× 10−1 × 10−1 60 °C × 101 × 101 × 101 × 101

reach equilibrium significantly increased. For example, at 25 °C, adsorption equilibrium was reached in less than 1 h at a dew point of 10.1 °C. At the same adsorption temperature, however, more than 500 h was required to reach equilibrium when the dew point was reduced to −68.9 °C. Figure 6 shows an example of curve fitting of water uptake curves by the LDF model, the SC model and the Langmuir kinetic model, which suggests that all three models were able to fit the data very well. Model parameters obtained from curve fitting of all sets of kinetic data are presented in Table 2. The curve-fitting error was estimated as

102 102 102 102 101 101

× 10−1

102 102 102 102 101 101 101 101

× 10−1

102 101 101 101 101

× 10−1

× 10−1

n

error (%) =

∑ i=1

yiexp − yimodel yiexp

error (%)

× 100 (11)

where the subscript i indicates the ith data point, n represents the total data points, and the superscripts exp and model indicate experimental data and model predictions, respectively. Table 2 shows that the average curve-fitting errors for all three models for all conditions were 3.0% or less, indicating very good curve fitting. 16020



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3.3. Linear-Driving-Force Model. Water uptake curves were fitted with the LDF model, and kLDF values were determined (Table 2). The overall mass-transfer resistances (1/ kLDF) were then determined to be on the order of 10−1−102 h. According to eq 3, the overall mass-transfer resistance is a combination of the external film resistance, the macropore resistance, and the micropore resistance. The micropore diffusivity (Dc) in zeolites is usually on the order of 10−8 cm2/s.15 The corresponding micropore resistance is on the order of 10−4−10−5 h−1, which is much smaller than the overall mass-transfer resistance and can thus be neglected. Accordingly, eq 3 can be simplified to 1 kLDF

=

R p qeρp 3k f C b

+


Figure 7. Average curve-fitting errors of the LDF model using predicted and curve-fitted kLDF values.

(12)

The film mass-transfer coefficient (kf) can be estimated by the Ranz and Marshall correlation22 Sh = 2 + 0.6Sc1/3Re 0.5

model is capable of predicting the water adsorption kinetics in this system. Finally, both the external film resistance and the macropore resistance included in eq 12 can be estimated. Figure 8 indicates

(13)

where Sh, Sc, and Re are the dimensionless Sherwood, Schmidt, and Reynolds numbers, respectively. It should be pointed out that eq 13 is for mass transfer to unobstructed spheres, and the presence of a support screen might affect the kf value. However, this issue is beyond the scope of this discussion. The water molecular diffusivity required for this calculation can be estimated by the correlation of Fuller et al.23 DAB =

0.00143T1.75 PMAB1/2[(∑ ν)A1/3 + (∑ ν)B1/3 ]2

(14)

Here, the subscripts A and B indicate water and air, respectively; P is the pressure in bar, MAB is the average molecular weight, defined as MAB = 2/(1/MA + 1/MB); and ν is the atomic diffusion volume. For the current system, P = 1 bar, MAB = 22.21 g/mol, (∑ν)A = 13.1, and (∑ν)B = 19.7.23 The density and viscosity of air needed for estimating the external mass-transfer coefficient were estimated by REFPROP24 and are listed in Table 3. Also included in Table 3 are the calculated

Figure 8. Distribution of mass-transfer resistances.

that the film resistance contributed 25−50% of the overall mass-transfer resistance during the course of water adsorption on zeolite 3A and that the percentage contribution generally decreased as the adsorption temperature was increased. Therefore, it can be concluded that water adsorption on zeolite 3A under the current experimental conditions was controlled by both external film resistance and macropore resistance. It should be pointed out that the above analysis was done assuming isothermal adsorption, that is, that the water uptake was entirely controlled by mass transfer. The isothermal LDF model is a special case of the general nonisothermal LDF model,25 which accounts for both heat- and mass-transfer resistances. As shown previously,25 for isothermal adsorption, the solution of the general nonisothermal LDF equation reduces to eq 2, and a plot of ln[(qe − q)/q ̅ e] versus t is linear with a slope of −kLDF and an intercept of 0 at t = 0. Indeed, the ln[(qe − q)/q ̅ e]−t plots of the water uptake curves obtained in this work showed very good linearity. Also, water adsorption occurred very slowly under the current experimental conditions and required hours to hundreds of hours to reach equilibrium, indicating that the adsorbate uptake was actually controlled by mass transfer rather than external heat transfer or both. In addition, Figure 6, as an example, shows nearly perfect curve fitting of the experimental water uptake data by the isothermal LDF model. Therefore, isothermal adsorption is a valid

Table 3. Properties and Model Parameters for the LDF Model (P = 0.1 MPa) T (°C)

density24 (kg/m3)

viscosity24 (10−6 m2/s)

DAB (cm2/s)

kf (m/s)

Dp (cm2/s)

25 40 60 80

1.1688 1.1127 1.0458 0.9865

18.448 19.165 20.099 21.009

0.254 0.276 0.308 0.341

0.0318 0.0342 0.0375 0.0409

0.295 0.140 0.158 0.124

water molecular diffusivity, external mass-transfer coefficient, and macropore diffusivity. The results indicate that both molecular diffusivity and the external mass-transfer coefficient increased as the temperature was increased. The macropore diffusivity of water in molecular sieve 3A generally decreased as the temperature was increased, except from 40 to 60 °C, where the macropore diffusivity increased slightly, which could be explained by experimental uncertainties. When kf and Dp have been determined, kLDF can be calculated according to eq 12. Consequently, the water uptake curves can be predicted by eq 2 using the calculated kLDF values. Figure 7 shows that, using the predicted kLDF, the average errors were below 9%, somewhat higher than those obtained with the curve-fitted kLDF values. This result suggests that the LDF 16021



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Figure 9. Plots of adsorption time versus water vapor pressure.

Figure 10. Comparison of external mass-transfer coefficients and macropore diffusion coefficients obtained by the LDF and SC models.

adsorption temperature was increased from 25 to 40 °C, and it remained nearly constant when the temperature was further increased to 80 °C. At 25 °C, the kf value obtained using the SC model was nearly twice that obtained with the LDF model by the Ranz and Marshall empirical correlation, whereas at 40−80 °C, the kf values of the two models agreed very well. The Dp values obtained with the SC model were comparable to but smaller than those obtained with the LDF model. Also, it was found that, considering experimental uncertainties, Dp generally decreased as the temperature was increased. This analysis further confirms that water adsorption on molecular sieve 3A under the current experimental conditions was controlled by both external film resistance and macropore resistance. 3.5. Langmuir Kinetic Model. From the linear plots of dq/dt versus q,̅ the kinetic parameters ka and kd were ̅ determined. The results are also included in Table 2. The curve-fitting errors of less than 3.0% indicate that the Langmuir kinetic model fit the individual experimental water uptake curves very well. Let θ = qe/qm and α = ka/kd. At equilibrium, when dq/dt ̅ = 0, eq 7 becomes the well-known Langmuir adsorption isotherm

assumption for current experimental conditions. For very rapid adsorption in which adsorbate uptake might be controlled by both heat and mass transfer, the nonisothermal LDF model25 should be applied to determine kinetic parameters for both the heat- and mass-transfer equations. 3.4. Shrinking-Core Model. Following the method described in section 2.3.2, parameters for the SC model, namely, τ1 and τ2, were obtained and are reported in Table 2. As also shown in Table 2, the average curve-fitting error ranged between 1.6% and 2.0% for adsorption temperatures from 25 to 80 °C, with an average value somewhat lower than that of the LDF model (1.85% vs 2.25%). This result suggests that the SC model has a very good capability of describing the kinetics of water adsorption on molecular sieve 3A and that it worked slightly better than the LDF model for the current application. Plots of τ1 and τ1 + τ2 versus water vapor pressure on a log−log scale, as shown in Figure 9, indicate that the adsorption time (time to reach adsorption equilibrium) increased significantly as the water vapor pressure was reduced. According to eqs 5 and 6, kf and Dp can be obtained from the slopes of linear plots of τ1 versus qeρp/Cb and τ2 versus qeρp/Cb, respectively. Figure 10 provides a comparison of the kf and Dp values obtained using the LDF and SC models. The kf value obtained with the SC model decreased significantly when the

θ= 16022

αC b 1 + αC b

(15)



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where θ is the fractional coverage of the surface and α is the Langmuir adsorption constant. Figure 11 shows that the

molecular sieve 3A under the investigated experimental conditions was controlled by both external film resistance and macropore resistance. The external film resistance contributed 25−50% of the total mass-transfer resistance depending on the adsorption temperature. The results from curve fitting with the Langmuir kinetic model showed that the Langmuir adsorption constant decreased with an increase in adsorption temperature and with an increase in water vapor pressure, which can be explained by Langmuir adsorption theory. This result suggests that significant surface heterogeneity might exist on molecular sieve 3A and implicitly verifies that the Langmuir isotherm model is unable to describe isotherms of water adsorption on molecular sieve 3A if α remains constant over the entire watervapor-pressure range of interest.

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AUTHOR INFORMATION

Corresponding Author

*Tel.: 1-315-443-1883. Fax: 1-315-443-9175. E-mail: lltavlar@ syr.edu.

Figure 11. Effects of adsorption temperature and water vapor pressure on the Langmuir adsorption constant.

Notes

The authors declare no competing financial interest.

■

constant α decreased with an increase in adsorption temperature and with an increase in water vapor pressure. This result can be explained by Langmuir adsorption theory. 18,26 According to Langmuir adsorption theory, the constant α can be expressed as26 α = β(2πMRT )−1/2 exp(Q /RT )

ACKNOWLEDGMENTS This research was performed using funding received from the U.S. DOE Office of Nuclear Energy’s Nuclear Energy University Programs (Grant NFE-12-03822).

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(16)

where β is a constant, M is the molecular weight, Q is the heat of adsorption, and R is the ideal gas constant. Because adsorption is an exothermic process and, thus, the heat of adsorption is positive,26 according to eq 16, the constant α should decrease with increasing temperature. Furthermore, previous studies have shown that the heats of adsorption of water vapor on zeolites generally decrease with an increase in the quantity adsorbed.27,28 That is, as the water vapor pressure increases, the quantity of water adsorbed on molecular sieve 3A increases, and the heat of adsorption decreases, and as a result, the adsorption constant α decreases. This result implicitly verifies that the Langmuir isotherm model is unable to represent isotherms of water adsorption on molecular sieve 3A if α remains constant over the entire water-vapor-pressure range, which is in agreement with a previous study.29 This result also indicates that significant surface heterogeneity might exist on molecular sieve 3A. Therefore, adsorption isotherm equations that take into consideration surface heterogeneity effects should be used for modeling isotherms of water adsorption on molecular sieve 3A.

REFERENCES

(1) Zabaluev, Y. V. Management of radionuclides from reprocessing plant gaseous effluents. IAEA Bull. 1979, 21, 23−31. (2) Jubin, R. Spent Fuel Reprocessing. Presented at the Introduction to Nuclear Chemistry and Fuel Cycle Separations Course, Nashville, TN, Dec 16, 2008; available at http://www.cresp.org/education/courses/ shortcourse/. (3) Filss, P. Sampling and counting tritiated water vapour from radioactive off-gas streams by adsorption of silica gel. Radiochem. Radioanal. Lett. 1973, 15, 213−223. (4) Burger, L. L.; Ryan, J. L. The Technology of Tritium Fixation and Storage; Technical Report BNWL-1807; Battelle Pacific Northwest Laboratories: Richland, WA. 1973. (5) Good, J. H.; Baybarz, R. D.; Clinton, S. D.; Farrar, L. G.; Fitzgerald, C. L.; Haire, R. G.; Tennery, V. J.; Vaughen, V. C. A.; Watson, C. D. Voloxidation: Removal of Volatile Fission Products from Spent LMFBR Fuels; Technical Report ORNL-TM-3723; Oak Ridge National Laboratories: Oak Ridge, TN, 1973. (6) Tanaka, S.; Yamamoto, Y. Removal of tritiated water vapor by adsorption. J. Nucl. Sci. Technol. 1976, 13, 251−259. (7) Holland, W. D.; Shah, A. H.; Kaiser, A. F.; McGee, J. C. Experimental Studies Concerning the Drying of Voloxidizer Off-Gases; Technical Report ORNL/SUB-7164/1; Tennessee Technological University: Cookeville, TN, 1981. (8) Nakashima, M.; Tachikawa, E.; Saeki, M.; Aratono, Y. Removal mechanism of tritium by variously pretreated silica gel. J. Inorg. Nucl. Chem. 1981, 43, 369−373. (9) Nakashima, M.; Tachikawa, E. Removal of tritiated water vapor by molecular sieves 5A and 13X, silica-gel and activated alumina. J. Nucl. Sci. Technol. 1982, 19, 571−577. (10) Tanaka, S.; Ono, F.; Takahashi, Y.; Kiyose, R. Removal of tritiated water vapor by adsorption on molecular sieves: Effect of coexisting H2O. Fusion Technol. 1985, 8, 2196−2201. (11) Haefner, D.; Law, J.; Tranter, T. System Design Description and Requirements for Modeling the Off-Gas Systems for Fuel Recycling Facilities; Technical Report INL/EXT-10-18845; Idaho National Laboratory: Idaho Falls, ID, 2010.

4. CONCLUSIONS A continuous-flow adsorption system was developed to gather accurate adsorption equilibrium and adsorption kinetic data for applications in the design and simulation of processes for offgas treatment from spent nuclear fuel reprocessing plants. The kinetics of water-vapor adsorption on molecular sieve 3A was investigated at adsorption temperatures of 25−80 °C and water dew points from −69 to 17 °C. Water uptake curves were fitted with three kinetic models including the linear-driving-force model, the shrinking-core model, and the Langmuir kinetic model. It was found from curve fitting with the linear-drivingforce and shrinking-core models that water adsorption on 16023



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Kinetics of Water Vapor Adsorption on Single-Layer Molecular Sieve

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