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Nitrogen, methane, and ethane sorption on activated carbon
Cryogenics 51 (2011) 499–508
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Nitrogen, methane, and ethane sorption on activated carbon N. Tzabar ⇑, G. Grossman Faculty of Mechanical Engineering, Technion, Israel Institute of Technology, Haifa 32000, Israel
a r t i c l e
i n f o
Article history: Received 22 December 2010 Received in revised form 9 June 2011 Accepted 14 June 2011 Available online 24 June 2011 Keywords: A. Adsorbents E. Sorption coolers
a b s t r a c t Joule–Thomson (JT) sorption cryocoolers rely on sorption compressors that provide a continuous flow with predetermined high and low pressures without any vibration emission. These cryocoolers may operate with different fluids, in accordance with the desired cold temperature. Nitrogen, methane, and ethane are prevalent candidate fluids for sorption cryocoolers, providing cold temperatures of about 80 K, 120 K, and 185 K, respectively. In order to develop a sorption compressor it is necessary to know the sorption characteristics of the fluid on the selected adsorbent. In this work we present experimental sorption measurements of the mentioned fluids on a commercial pelleted activated carbon. The Langmuir, Freundlich, and Sips models are fitted to the experimental results and further modified to incorporate the temperature dependence, in order to extend the prediction of sorption properties into wider ranges of temperature and pressure. It appears that each fluid has a different model that best fits its characteristics. Finally, the isosteric heat of adsorption is calculated for the three mentioned fluids as a function of the adsorption coverage and polynomial regressions are obtained for it. Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction A variety of cryocooling technologies are available for cooling from normal room temperature to about 80 K, each with its own advantages and limitations. The only cryocooler for this temperature range with no moving parts (except for valves) is the JT sorption cryocooler; it is therefore characterized by high reliability and no vibration emission. A JT sorption cryocooler includes a sorption compressor that drives a JT cryostat. The choice of working fluid and the operating pressures are determined by the required cooling temperature and the sorption compressor is designed accordingly. The working fluid is determined mainly by the required cold temperature, so as to reach the boiling temperature of the fluid during operation. Many sorption cryocoolers were designed and investigated for cold temperatures of about 80 K using nitrogen [5,12,19,20,26]. Cryocooling to higher temperatures is obtained by using different fluids. Krypton is used for cooling to 125–140 K [2,13]. 130 K was obtained using a sorption cryocooler with methane [3]. A sorption compressor operating with xenon, providing cooling to about 165 K, was suggested by the University of Twente [9,24,25]. Cooling to 170 K is also possible using ethylene [8]. In discussing the fundamentals of adsorption it is useful to distinguish between physical adsorption, involving relatively weak intermolecular forces, and chemisorption which involves the for⇑ Corresponding author. Present address: Cryogenics Group, Rafael Ltd., P.O.B 2250(39), Haifa 31021, Israel. Tel.: +972 4 9906742; fax: +972 4 9906100. E-mail address: [email protected] (N. Tzabar). 0011-2275/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.cryogenics.2011.06.005
mation of a chemical bond between the adsorbate molecule and the surface of the adsorbent. Physical adsorption is the term applied, where no electrons are transferred or shared between the adsorbed molecules and the adsorbent surface [16]. The forces involved in physical adsorption include both van der Waals forces and electrostatic interactions comprising polarization, dipole, and quadrupole interactions. The van der Waals contribution is always present while the electrostatic contributions are significant only in the case of adsorbents such as zeolites which have an ionic structure [21]. Between the two types of adsorption, the physical adsorption is more rapid, is reversible, and has longer range forces enabling multilayer adsorption. Therefore, physical adsorption is preferred for sorption compressors. Fortunately, most of the fluids with boiling temperature between 80 K and 170 K that are in use for JT cryocoolers are physically adsorbed on activated carbon. Therefore, sorption cryocoolers for this range of cooling temperatures usually employ activated carbons as the adsorbents. One of the first steps in developing a sorption compressor for a sorption cryocooler is to characterize the adsorption and desorption of the working fluid on the adsorbent. A convenient form to theoretically analyze experimental data is by adsorption isotherms [1]. There are many adsorption isotherm models in the literature for describing the relationship between the concentration of the adsorbate phase and the state of the gas phase (temperature and pressure). There are models that rely especially on experimental results and fitting parameters, with some parameters derived from the experimental results and others fitted iteratively. In the present work we have performed adsorption measurements of nitrogen, methane, and ethane on a commercial activated
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2. Method of study
the gas weight in the chamber, mgas. The density of the gaseous substance in the void volume, qvoid, is obtained from NISTÒ data base according to p1 and T1. The adsorbent chamber is then located inside a temperature chamber to control its temperature. We have taken measurements of p1, T1, and T2 at constant temperatures between 293.13 and 453.13 K, at 20 K intervals. The concentration of the adsorbed gas at each temperature is calculated as follows:
2.1. Experimental procedure
q¼
A single commercial pelleted activated carbon produced by Chemviron-Carbon is examined in the present work. According to manufacturer data, the pellets are 3 mm in diameter, coal based, activated by high temperature steam. Its BET surface area is 1000 m2/g, the specific heat capacity at 100 °C is 1.0 kJ/(kg K), and the bed density is 450 kg/m3. The experimental apparatus employed in this study is described in Fig. 1. Two k-type thermocouples are installed inside the cell along its central axis, one located near the cell bottom and the other near its top cover. The cover is equipped with a 2 lm filter, a pressure transducer, a valve, and a disconnection fitting. The gas panel includes a high purity nitrogen source, methane source, ethane source, helium source, a pressure regulator, an oil-free vacuum pump, and a vent tube. A 6 kg scale with a resolution of 0.01 g is used to weigh the cell. A climate chamber, not shown in Fig. 1, is used to control the temperature of the cell. Initially, the mass of the empty cell is measured, mcell, and the inner cell volume, Vcell, is determined by filling it with helium and weighing it, knowing the temperature and pressure. After repeating this procedure three times, at different pressures, we found Vcell equals 105 cc. The cell is then filled with 45.28 g of the adsorbent, ms, and evacuated for 24 h at 90 °C. The adsorbent density (calculated from the weight and volume of the pellets introduced into the chamber) is qs = 630 kg/m3, which yields its volume and thus the void volume is found, Vvoid = 33 cc [23]. An attempt to measure the void volume by filling it with helium, assuming helium is not adsorbed on activated carbons at these temperatures, failed since the results were temperature dependent, which means, helium adsorbed on the activated carbon. Each set of measurements starts with vacuum baking of the chamber with the adsorbent for 24 h at 90 °C. Then, the chamber is weighed and connected to the gas panel to fill with the tested gas at a selected pressure at room temperature. After stabilization of the adsorbent temperature, when T1 equals T2, the chamber is disconnected from the gas panel and is weighed again to calculate
where q is measured in grams of adsorbed gas per 1 kg of adsorbent. After completing a set of measurements we added more gas to the chamber, calculated the new mass of gas in the chamber, mgas, and repeated the procedure in the temperature chamber. We have tested the adsorption of nitrogen, methane, and ethane in a few sets of measurements with different amount of gas in the chamber for each substance. More detailed descriptions of the experimental apparatus and procedure are given elsewhere [23].
carbon. The experimental results are described and three isotherm models are fitted. The three models are further modified to incorporate the temperature dependence in order to better use them in a wide range of pressures and temperatures. In addition, the isosteric heat of adsorption is determined to complete the calculations required for sorption compressor development.
mgas qv oid V v oid ms
ð1Þ
2.2. Isotherm models Freundlich was one of the few researchers who regarded the process of adsorption as a form of surface condensation. He published his empirical equation, which expresses the amount adsorbed as a function of the equilibrium concentration, in 1907 [22]:
h¼
q ¼ kF p1=n q0
ð2Þ
where p is the pressure, h is the adsorption coverage, q0 is the saturated adsorption concentration, and kF, n are empirical parameters. Eq. (2) may be changed into the following form to allow easier fitting of the parameters:
q ¼ ðq0 kF Þ p1=n
ð3Þ
The Langmuir isotherm model (1918) assumes monolayer adsorption on a homogeneous surface and at low pressure is reduced to Henry’s law. Although the Langmuir isotherm was introduced more than 90 years ago, it still remains the most commonly used adsorption isotherm equation [10]. The Langmuir equation is:
h¼
q bp ¼ q0 1 þ bp
ð4Þ
where b is the Langmuir parameter. In order to derive the value of q0 and b from the experimental results, Eq. (4) has to be changed into the following linear form:
Fig. 1. Experimental apparatus.
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N. Tzabar, G. Grossman / Cryogenics 51 (2011) 499–508 Table 1 Freundlich, Langmuir, and Sips model parameters for nitrogen, methane, and ethane. T (K)
293
313
333
353
373
Freundlich (Eq. (3)) q0KF N2 CH4 C2H6 n N2 CH4 C2H6
393
413
433
453
49.86 58.51 205.2 1.513 1.726 2.860
40.85 47.03 170.1 1.405 1.644 2.674
34.20 38.70 142.3 1.413 1.591 2.589
29.25 32.50 121.9 1.350 1.559 2.494
25.55 27.69 104.7 1.353 1.534 2.391
22.13 23.58 90.56 1.298 1.472 2.295
19.17 20.27 78.38 1.264 1.425 2.203
16.61 17.36 67.03 1.259 1.380 2.080
13.04 13.39 53.74 1.221 1.292 1.835
Langmuir (Eq. (4)) q0 N2 CH4 C2H6 b N2 CH4 C2H6
84.03 73.53 161.3 1.253 2.473 15.50
97.09 77.52 163.9 0.715 1.483 7.625
87.72 78.74 163.9 0.644 1.016 4.692
96.15 80.65 163.9 0.441 0.734 3.050
84.32 83.33 163.9 0.438 0.536 1.968
101.0 84.03 166.7 0.289 0.416 1.364
102.0 86.96 166.7 0.238 0.318 0.952
98.04 92.59 172.4 0.209 0.234 0.644
97.09 105.3 178.6 0.157 0.145 0.415
Sips (Eq. (8)) N2 q0 CH4 C2H6 n N2 CH4 C2H6 a N2 CH4 C2H6
96 94 320 0.85 1.1 1.7 1.08 1.50 2.00
96 94 320 0.85 1.1 1.7 0.80 1.00 1.15
96 94 320 0.85 1.1 1.7 0.60 0.70 0.65
96 94 320 0.85 1.1 1.7 0.50 0.54 0.46
96 94 320 0.85 1.1 1.7 0.42 0.42 0.31
96 94 320 0.85 1.1 1.7 0.35 0.34 0.22
96 94 320 0.85 1.1 1.7 0.30 0.28 0.16
96 94 320 0.85 1.1 1.7 0.25 0.21 0.11
96 94 320 0.85 1.1 1.7 0.19 0.16 0.07
Fig. 2. Experimental results of nitrogen adsorption on Chemviron activated carbon with Freundlich (dotted lines), Langmuir (solid lines), and Sips (dashes lines) isotherms.
1 1 1 1 ¼ þ q q0 bq0 p
ð5Þ
Plotting the experimental results as 1/q versus 1/p provides both parameters and helps determine how well the results fit the Langmuir equation by their linearity. Some generalizations of the Langmuir isotherms are given by Czepirski et al. [10]. Pan et al. [15] have used the Three Process Langmuir Model (TPLM) to correlate their experimental data: 3 X q0;i bi p q¼ ; i ¼ 1; 2; 3 1 þ bi p i¼1
ð6Þ
Bi bi ¼ b0;i expð Þ T
ð7Þ
where q0, i, Bi, and b0, i are correlating parameters.
Sips (1948) proposed the following isotherm, which is a combination of the Langmuir and Freundlich equations. Koble and Corrigan (1952) have found that the Sips model is superior to either of the Langmuir or Freundlich equations:
h¼
q ðapÞ1=n ¼ q0 1 þ ðapÞ1=n
ð8Þ
where q0 and n are constants independent of temperature, while ‘a’ is a parameter that depends on the temperature [6]. A similar model is used by Balathanigaimani et al. [4], referred to as the Langmuir– Freundlich isotherm. Unlike the models mentioned above, the Dubinin model, usually used for sorption compressor calculations, is based on the potential theory of adsorption, originally developed by Polanyi (1932). Although Dubinin has modified the model at least twice
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Fig. 3. Experimental results of methane adsorption on Chemviron activated carbon with Freundlich (dotted lines), Langmuir (solid lines), and Sips (dashes lines) isotherms.
Fig. 4. Experimental results of ethane adsorption on Chemviron activated carbon with Freundlich (dotted lines), Langmuir (solid lines), and Sips (dashes lines) isotherms.
(Dubinin–Radushkhevich and Dubinin–Astakhov), the following classical equation is widely in use [17]:
q¼
Ma expðc xÞ b
ð9Þ
where M is the molecular weight, b is the molecular volume in the van der Waals equation of state, and x is the adsorption potential. a and c are correlating parameters that can be calculated from the experimental data. The best technique to calculate them is by drawing a straight line through experimental results on a ln (q) versus x plot [18], where a is determined by the intercept and c is determined by the slope. There are several ways to calculate x, however,
since we deal with cases above the critical point the following equation is used [12]:
" # 2 RT p T x¼ ln c b p Tc
ð10Þ
where b is the affinity coefficient, R is the universal ideal gas constant, pc and Tc are the critical pressure and temperature, respectively. There are adsorption models that rely on the intermolecular interaction between the adsorbed molecules based on the Lenard-Jones potential [14], for example, the Jensen–Seaton equa-
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N. Tzabar, G. Grossman / Cryogenics 51 (2011) 499–508 Table 2 Modified Freundlich, modified Langmuir, and modified Sips model constants for nitrogen, methane, and ethane. N2
CH4
C2H6
Modified Freundlich (Eq. (13)) a1 491.83 a2 0.0079 0 b1 b2 0.0009 b3 0.4139
734.22 0.0088 0 0.0011 0.2572
2116.2 0.0080 5E-06 0.0024 0.6676
Modified Langmuir (Eq. (14)) 0 c1 c2 0.0738 c3 66.625 1e + 11 d1 d2 4.4365
0.0011 0.6580 174.75 2E + 15 6.0759
0.0009 0.5743 255.63 6E + 20 7.9673
Modified Sips (Eq. (15)) e1 1.85e + 9 e2 3.7462
2E + 12 4.9024
3E + 18 7.3791
qiso ¼
R @ lnðpÞ M @ð1=TÞ
ð12Þ q
where R is the universal ideal gas constant. Eq. (12) may be employed to determine qiso by plotting ln (p) versus 1/T for the adsorption isotherms at different temperatures and at constant loading. The linearity of this plot is an indication of the adsorbent surface homogeneity. Usually, activated carbons have nonlinear isosters that indicate their heterogeneous characteristics [4]. Other reasons for nonlinearity of the isosters are described in detail by Bulow et al. [7]. He et al. [11] give a comparison between calorimetric measurements and isotherm-based calculations of isosteric heat of adsorption. Pan et al. [15] have studied the isosteric heat of adsorption by numerical differentiation of Nonlocal Density Functional Theory (NDFT) isotherms. In the current study we used Eq. (12) for calculating the heat of adsorption. 3. Results and discussion 3.1. Isotherm models
tion that allows for the compressibility of the adsorbed phase and gives an accurate fit to experimental data at high pressures [11]:
" q¼Kp 1þ
Kp
t #1=t
að1 þ j pÞ
ð11Þ
where K, a, and t are parameters and j is the isothermal compressibility. A totally different model is suggested by Basu et al. using Artificial Neural Networks (ANN) that are highly parallel flexible mathematical constructs that have been inspired by the workings of the biological nervous system [6]. ANNs have a natural propensity for storing experimental knowledge and making it available for use. 2.3. Isosteric heat of adsorption The isosteric heat of adsorption, qiso, can be determined either from adsorption isotherms or directly by calorimetric measurements. The heat of adsorption is usually calculated by using the Clausius–Clapeyron equation:
In a previous study [23] we found that the Freundlich, Langmuir, and Sips models are in better agreement with experimental results for nitrogen than the Dubinin model, that is usually employed by many sorption cooler developers [12,20]. Therefore, in this work we considered only the Freundlich, Langmuir, and Sips models for reduction of our experimental data. Table 1 lists the parameters of the three models for nitrogen, methane, and ethane, where the pressure, p, is in MPa and the loading, q, is in ggas/kgs. The three isotherms with the experimental results are shown in Figs. 2–4 for nitrogen, methane, and ethane, respectively. One might notice that the loadings of methane and nitrogen are similar while the loadings of ethane are much higher. He et al. [11] have observed the same trend, and explain it by ethane being a nonspherical molecule that can assume different orientations with respect to the surface. All three models show a direct dependence of q on the pressure and indirect dependence on the temperature through their parameters. While designing sorption compressors it is necessary to incorporate the temperature in the models in order to
Fig. 5. Experimental results of nitrogen adsorption on Chemviron activated carbon with modified Freundlich (dotted lines), modified Langmuir (solid lines), and modified Sips (dashes lines) isotherms.
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Fig. 6. Experimental results of methane adsorption on Chemviron activated carbon with modified Freundlich (dotted lines), modified Langmuir (solid lines), and modified Sips (dashes lines) isotherms.
Fig. 7. Experimental results of ethane adsorption on Chemviron activated carbon with modified Freundlich (dotted lines), modified Langmuir (solid lines), and modified Sips (dashes lines) isotherms.
develop a numerical simulation and to extrapolate the results to temperatures even higher or lower than measured. Several trend line functions were examined to describe the dependence of the model parameters on temperature and the best fitted function was adopted for each parameter. For the following three equations the loading, q, is in ggas/kgs, the pressure, p, is in MPa, and the temperature, T , is in Kelvin. The modified Freundlich isotherm is:
q ¼ a1 expða2 TÞ pðb1 T
2
þb2 Tþb3 Þ
ð13Þ
where a1, a2, b1, b2, and b3 are constants listed in Table 2. The modified Langmuir isotherm is:
q ¼ ðc1 T 2 þ c2 T þ c3 Þ
ðd1 T d2 Þ p 1 þ ðd1 T d2 Þ p
ð14Þ
where c1, c2, c3, d1, and d2 are constants listed in Table 2. The modified Sips isotherm is:
q ¼ q0
ðe1 T e2 pÞ1=n 1 þ ðe1 T e2 pÞ1=n
ð15Þ
where e1 and e2 are constants listed in Table 2. q0 and n are constants given in Table 1. The isotherms calculated with the three modified models are presented in Figs. 5, 6, and 7 for nitrogen, methane, and ethane, respectively.
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Fig. 8. The mean absolute error for nitrogen. The solid lines and full markers represent the original three models, while the dashed lines and empty markers represent the modified versions of the models.
Fig. 9. The mean absolute error for methane. The solid lines and full markers represent the original three models, while the dashed lines and empty markers represent the modified versions of the models.
Fig. 10. The mean absolute error for ethane. The solid lines and full markers represent the original three models, while the dashed lines and empty markers represent the modified versions of the models.
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Fig. 11. Nitrogen experimental results as ln (p) versus 1/T for calculating the isosteric heat of adsorption.
Fig. 12. Methane experimental results as ln (p) versus 1/T for calculating the isosteric heat of adsorption.
Fig. 13. Ethane experimental results as ln (p) versus 1/T for calculating the isosteric heat of adsorption.
N. Tzabar, G. Grossman / Cryogenics 51 (2011) 499–508 Table 3 Constants for calculating the isosteric heat of adsorption with equation (17).
N2 CH4 C2H6
A1
A2
A3
A4
0.0031 0.0004 0.00004
0.347 0.1743 0.0254
9.6804 5.1088 6.1146
396.58 978.3 1156
In order to determine which isotherm has the best agreement with the experimental results, the mean absolute error, E, is calculated as follows:
N 100 X qi;exp erimental qi;predicted E¼ N qi;exp erimental i1
ð16Þ
E is calculated for each temperature, and N is the number of measurements at the particular temperature. The results are shown in Figs. 8, 9, and 10, for nitrogen, methane, and ethane, respectively. Fig. 8 shows that the Freundlich isotherm has the best agreement with the nitrogen experimental results among the original models as well as the modified versions. Methane shows a different behavior. The original isotherms show almost the same agreement with the experimental results with a minor advantage to the Langmuir isotherm. On the other hand, there is a significant difference among the modified versions. While both modified Langmuir and modified Sips show significant deviations from their original models, the modified Freundlich exhibits almost the same results as its original form. Thus, the modified Freundlich model is clearly the preferred one among the modified models for methane. Ethane shows a different behavior than both nitrogen and methane. Here again, the original isotherms exhibit almost the same agreement with the experimental results with a minor advantage to the Sips model at low temperatures and a minor advantage to the Langmuir model at high temperatures. The modified Freundlich isotherm, in this case, shows major deviations from the original model, while both Langmuir and Sips models are very close to their original forms. This means that the Sips model is preferred at low temperatures and the Langmuir model is preferred at high temperatures. 3.2. Isosteric heat of adsorption The isosteric heat of adsorption is the heat released during adsorption at constant loading. This value is calculated from the
507
experimental results, according to Eq. (12), at constant q for different temperatures. We have plotted the results of the three gases as ln (p) versus 1/T, drew linear curves through the constant loading points and found their slopes. The plots are shown in Figs. 11, 12, and 13, for nitrogen, methane, and ethane, respectively. All results show good linearity of the isosters. According to these plots, the isosteric heat of adsorption is calculated using Eq. (12) for each loading value and a correlation between the loading and the isosteric heat of adsorption is found in the following form:
qiso ¼ A1 q3 þ A2 q2 þ A3 q þ A4
ð17Þ
while q is the loading in ggas/kgs, qiso is the isosteric heat of adsorption in kJ/kg, and A1, A2, A3, A4 are constants listed in Table 3. The polynomial plots of nitrogen, methane, and ethane that present the isosteric heat of adsorption are shown in Fig. 14. The isosteric heat of adsorptions of nitrogen is about half that of methane, while ethane has almost the same values as methane for low loadings. 4. Conclusions A method for measuring the adsorption isotherm of pure gases is described, and the results for nitrogen, methane, and ethane are presented. The results were correlated with three well known adsorption models (Freundlich, Langmuir, and Sips). Different gases show best correlation with different models. Nitrogen adsorption is best described by Freundlich isotherms, methane is best described by Langmuir isotherms, and ethane is best described by the Sips model for low temperatures and Langmuir model for higher temperatures. In order to make better use of the models for developing sorption compressors, the original models were modified to incorporate the temperature dependence. In this case, the modified Freundlich model shows the best agreement with nitrogen and methane experimental results, while for ethane the modified Sips model is best fitted at low temperature and the modified Langmuir model is best fitted at higher temperatures. The isosteric heat of adsorption is calculated using the best fitting model for each gas. A formula is proposed for calculating the isosteric heat of adsorption as a function of the loading only. The data obtained from the present work help develop and design a sorption compressor for the three mentioned gases by simulating the compressor cycles relying on the results presented here.
Fig. 14. Isosteric heat of adsorption for nitrogen, methane, and ethane on Chemviron activated carbon.
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Cryogenics journal homepage: www.elsevier.com/locate/cryogenics
Nitrogen, methane, and ethane sorption on activated carbon N. Tzabar ⇑, G. Grossman Faculty of Mechanical Engineering, Technion, Israel Institute of Technology, Haifa 32000, Israel
a r t i c l e
i n f o
Article history: Received 22 December 2010 Received in revised form 9 June 2011 Accepted 14 June 2011 Available online 24 June 2011 Keywords: A. Adsorbents E. Sorption coolers
a b s t r a c t Joule–Thomson (JT) sorption cryocoolers rely on sorption compressors that provide a continuous flow with predetermined high and low pressures without any vibration emission. These cryocoolers may operate with different fluids, in accordance with the desired cold temperature. Nitrogen, methane, and ethane are prevalent candidate fluids for sorption cryocoolers, providing cold temperatures of about 80 K, 120 K, and 185 K, respectively. In order to develop a sorption compressor it is necessary to know the sorption characteristics of the fluid on the selected adsorbent. In this work we present experimental sorption measurements of the mentioned fluids on a commercial pelleted activated carbon. The Langmuir, Freundlich, and Sips models are fitted to the experimental results and further modified to incorporate the temperature dependence, in order to extend the prediction of sorption properties into wider ranges of temperature and pressure. It appears that each fluid has a different model that best fits its characteristics. Finally, the isosteric heat of adsorption is calculated for the three mentioned fluids as a function of the adsorption coverage and polynomial regressions are obtained for it. Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction A variety of cryocooling technologies are available for cooling from normal room temperature to about 80 K, each with its own advantages and limitations. The only cryocooler for this temperature range with no moving parts (except for valves) is the JT sorption cryocooler; it is therefore characterized by high reliability and no vibration emission. A JT sorption cryocooler includes a sorption compressor that drives a JT cryostat. The choice of working fluid and the operating pressures are determined by the required cooling temperature and the sorption compressor is designed accordingly. The working fluid is determined mainly by the required cold temperature, so as to reach the boiling temperature of the fluid during operation. Many sorption cryocoolers were designed and investigated for cold temperatures of about 80 K using nitrogen [5,12,19,20,26]. Cryocooling to higher temperatures is obtained by using different fluids. Krypton is used for cooling to 125–140 K [2,13]. 130 K was obtained using a sorption cryocooler with methane [3]. A sorption compressor operating with xenon, providing cooling to about 165 K, was suggested by the University of Twente [9,24,25]. Cooling to 170 K is also possible using ethylene [8]. In discussing the fundamentals of adsorption it is useful to distinguish between physical adsorption, involving relatively weak intermolecular forces, and chemisorption which involves the for⇑ Corresponding author. Present address: Cryogenics Group, Rafael Ltd., P.O.B 2250(39), Haifa 31021, Israel. Tel.: +972 4 9906742; fax: +972 4 9906100. E-mail address: [email protected] (N. Tzabar). 0011-2275/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.cryogenics.2011.06.005
mation of a chemical bond between the adsorbate molecule and the surface of the adsorbent. Physical adsorption is the term applied, where no electrons are transferred or shared between the adsorbed molecules and the adsorbent surface [16]. The forces involved in physical adsorption include both van der Waals forces and electrostatic interactions comprising polarization, dipole, and quadrupole interactions. The van der Waals contribution is always present while the electrostatic contributions are significant only in the case of adsorbents such as zeolites which have an ionic structure [21]. Between the two types of adsorption, the physical adsorption is more rapid, is reversible, and has longer range forces enabling multilayer adsorption. Therefore, physical adsorption is preferred for sorption compressors. Fortunately, most of the fluids with boiling temperature between 80 K and 170 K that are in use for JT cryocoolers are physically adsorbed on activated carbon. Therefore, sorption cryocoolers for this range of cooling temperatures usually employ activated carbons as the adsorbents. One of the first steps in developing a sorption compressor for a sorption cryocooler is to characterize the adsorption and desorption of the working fluid on the adsorbent. A convenient form to theoretically analyze experimental data is by adsorption isotherms [1]. There are many adsorption isotherm models in the literature for describing the relationship between the concentration of the adsorbate phase and the state of the gas phase (temperature and pressure). There are models that rely especially on experimental results and fitting parameters, with some parameters derived from the experimental results and others fitted iteratively. In the present work we have performed adsorption measurements of nitrogen, methane, and ethane on a commercial activated
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2. Method of study
the gas weight in the chamber, mgas. The density of the gaseous substance in the void volume, qvoid, is obtained from NISTÒ data base according to p1 and T1. The adsorbent chamber is then located inside a temperature chamber to control its temperature. We have taken measurements of p1, T1, and T2 at constant temperatures between 293.13 and 453.13 K, at 20 K intervals. The concentration of the adsorbed gas at each temperature is calculated as follows:
2.1. Experimental procedure
q¼
A single commercial pelleted activated carbon produced by Chemviron-Carbon is examined in the present work. According to manufacturer data, the pellets are 3 mm in diameter, coal based, activated by high temperature steam. Its BET surface area is 1000 m2/g, the specific heat capacity at 100 °C is 1.0 kJ/(kg K), and the bed density is 450 kg/m3. The experimental apparatus employed in this study is described in Fig. 1. Two k-type thermocouples are installed inside the cell along its central axis, one located near the cell bottom and the other near its top cover. The cover is equipped with a 2 lm filter, a pressure transducer, a valve, and a disconnection fitting. The gas panel includes a high purity nitrogen source, methane source, ethane source, helium source, a pressure regulator, an oil-free vacuum pump, and a vent tube. A 6 kg scale with a resolution of 0.01 g is used to weigh the cell. A climate chamber, not shown in Fig. 1, is used to control the temperature of the cell. Initially, the mass of the empty cell is measured, mcell, and the inner cell volume, Vcell, is determined by filling it with helium and weighing it, knowing the temperature and pressure. After repeating this procedure three times, at different pressures, we found Vcell equals 105 cc. The cell is then filled with 45.28 g of the adsorbent, ms, and evacuated for 24 h at 90 °C. The adsorbent density (calculated from the weight and volume of the pellets introduced into the chamber) is qs = 630 kg/m3, which yields its volume and thus the void volume is found, Vvoid = 33 cc [23]. An attempt to measure the void volume by filling it with helium, assuming helium is not adsorbed on activated carbons at these temperatures, failed since the results were temperature dependent, which means, helium adsorbed on the activated carbon. Each set of measurements starts with vacuum baking of the chamber with the adsorbent for 24 h at 90 °C. Then, the chamber is weighed and connected to the gas panel to fill with the tested gas at a selected pressure at room temperature. After stabilization of the adsorbent temperature, when T1 equals T2, the chamber is disconnected from the gas panel and is weighed again to calculate
where q is measured in grams of adsorbed gas per 1 kg of adsorbent. After completing a set of measurements we added more gas to the chamber, calculated the new mass of gas in the chamber, mgas, and repeated the procedure in the temperature chamber. We have tested the adsorption of nitrogen, methane, and ethane in a few sets of measurements with different amount of gas in the chamber for each substance. More detailed descriptions of the experimental apparatus and procedure are given elsewhere [23].
carbon. The experimental results are described and three isotherm models are fitted. The three models are further modified to incorporate the temperature dependence in order to better use them in a wide range of pressures and temperatures. In addition, the isosteric heat of adsorption is determined to complete the calculations required for sorption compressor development.
mgas qv oid V v oid ms
ð1Þ
2.2. Isotherm models Freundlich was one of the few researchers who regarded the process of adsorption as a form of surface condensation. He published his empirical equation, which expresses the amount adsorbed as a function of the equilibrium concentration, in 1907 [22]:
h¼
q ¼ kF p1=n q0
ð2Þ
where p is the pressure, h is the adsorption coverage, q0 is the saturated adsorption concentration, and kF, n are empirical parameters. Eq. (2) may be changed into the following form to allow easier fitting of the parameters:
q ¼ ðq0 kF Þ p1=n
ð3Þ
The Langmuir isotherm model (1918) assumes monolayer adsorption on a homogeneous surface and at low pressure is reduced to Henry’s law. Although the Langmuir isotherm was introduced more than 90 years ago, it still remains the most commonly used adsorption isotherm equation [10]. The Langmuir equation is:
h¼
q bp ¼ q0 1 þ bp
ð4Þ
where b is the Langmuir parameter. In order to derive the value of q0 and b from the experimental results, Eq. (4) has to be changed into the following linear form:
Fig. 1. Experimental apparatus.
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N. Tzabar, G. Grossman / Cryogenics 51 (2011) 499–508 Table 1 Freundlich, Langmuir, and Sips model parameters for nitrogen, methane, and ethane. T (K)
293
313
333
353
373
Freundlich (Eq. (3)) q0KF N2 CH4 C2H6 n N2 CH4 C2H6
393
413
433
453
49.86 58.51 205.2 1.513 1.726 2.860
40.85 47.03 170.1 1.405 1.644 2.674
34.20 38.70 142.3 1.413 1.591 2.589
29.25 32.50 121.9 1.350 1.559 2.494
25.55 27.69 104.7 1.353 1.534 2.391
22.13 23.58 90.56 1.298 1.472 2.295
19.17 20.27 78.38 1.264 1.425 2.203
16.61 17.36 67.03 1.259 1.380 2.080
13.04 13.39 53.74 1.221 1.292 1.835
Langmuir (Eq. (4)) q0 N2 CH4 C2H6 b N2 CH4 C2H6
84.03 73.53 161.3 1.253 2.473 15.50
97.09 77.52 163.9 0.715 1.483 7.625
87.72 78.74 163.9 0.644 1.016 4.692
96.15 80.65 163.9 0.441 0.734 3.050
84.32 83.33 163.9 0.438 0.536 1.968
101.0 84.03 166.7 0.289 0.416 1.364
102.0 86.96 166.7 0.238 0.318 0.952
98.04 92.59 172.4 0.209 0.234 0.644
97.09 105.3 178.6 0.157 0.145 0.415
Sips (Eq. (8)) N2 q0 CH4 C2H6 n N2 CH4 C2H6 a N2 CH4 C2H6
96 94 320 0.85 1.1 1.7 1.08 1.50 2.00
96 94 320 0.85 1.1 1.7 0.80 1.00 1.15
96 94 320 0.85 1.1 1.7 0.60 0.70 0.65
96 94 320 0.85 1.1 1.7 0.50 0.54 0.46
96 94 320 0.85 1.1 1.7 0.42 0.42 0.31
96 94 320 0.85 1.1 1.7 0.35 0.34 0.22
96 94 320 0.85 1.1 1.7 0.30 0.28 0.16
96 94 320 0.85 1.1 1.7 0.25 0.21 0.11
96 94 320 0.85 1.1 1.7 0.19 0.16 0.07
Fig. 2. Experimental results of nitrogen adsorption on Chemviron activated carbon with Freundlich (dotted lines), Langmuir (solid lines), and Sips (dashes lines) isotherms.
1 1 1 1 ¼ þ q q0 bq0 p
ð5Þ
Plotting the experimental results as 1/q versus 1/p provides both parameters and helps determine how well the results fit the Langmuir equation by their linearity. Some generalizations of the Langmuir isotherms are given by Czepirski et al. [10]. Pan et al. [15] have used the Three Process Langmuir Model (TPLM) to correlate their experimental data: 3 X q0;i bi p q¼ ; i ¼ 1; 2; 3 1 þ bi p i¼1
ð6Þ
Bi bi ¼ b0;i expð Þ T
ð7Þ
where q0, i, Bi, and b0, i are correlating parameters.
Sips (1948) proposed the following isotherm, which is a combination of the Langmuir and Freundlich equations. Koble and Corrigan (1952) have found that the Sips model is superior to either of the Langmuir or Freundlich equations:
h¼
q ðapÞ1=n ¼ q0 1 þ ðapÞ1=n
ð8Þ
where q0 and n are constants independent of temperature, while ‘a’ is a parameter that depends on the temperature [6]. A similar model is used by Balathanigaimani et al. [4], referred to as the Langmuir– Freundlich isotherm. Unlike the models mentioned above, the Dubinin model, usually used for sorption compressor calculations, is based on the potential theory of adsorption, originally developed by Polanyi (1932). Although Dubinin has modified the model at least twice
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Fig. 3. Experimental results of methane adsorption on Chemviron activated carbon with Freundlich (dotted lines), Langmuir (solid lines), and Sips (dashes lines) isotherms.
Fig. 4. Experimental results of ethane adsorption on Chemviron activated carbon with Freundlich (dotted lines), Langmuir (solid lines), and Sips (dashes lines) isotherms.
(Dubinin–Radushkhevich and Dubinin–Astakhov), the following classical equation is widely in use [17]:
q¼
Ma expðc xÞ b
ð9Þ
where M is the molecular weight, b is the molecular volume in the van der Waals equation of state, and x is the adsorption potential. a and c are correlating parameters that can be calculated from the experimental data. The best technique to calculate them is by drawing a straight line through experimental results on a ln (q) versus x plot [18], where a is determined by the intercept and c is determined by the slope. There are several ways to calculate x, however,
since we deal with cases above the critical point the following equation is used [12]:
" # 2 RT p T x¼ ln c b p Tc
ð10Þ
where b is the affinity coefficient, R is the universal ideal gas constant, pc and Tc are the critical pressure and temperature, respectively. There are adsorption models that rely on the intermolecular interaction between the adsorbed molecules based on the Lenard-Jones potential [14], for example, the Jensen–Seaton equa-
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N. Tzabar, G. Grossman / Cryogenics 51 (2011) 499–508 Table 2 Modified Freundlich, modified Langmuir, and modified Sips model constants for nitrogen, methane, and ethane. N2
CH4
C2H6
Modified Freundlich (Eq. (13)) a1 491.83 a2 0.0079 0 b1 b2 0.0009 b3 0.4139
734.22 0.0088 0 0.0011 0.2572
2116.2 0.0080 5E-06 0.0024 0.6676
Modified Langmuir (Eq. (14)) 0 c1 c2 0.0738 c3 66.625 1e + 11 d1 d2 4.4365
0.0011 0.6580 174.75 2E + 15 6.0759
0.0009 0.5743 255.63 6E + 20 7.9673
Modified Sips (Eq. (15)) e1 1.85e + 9 e2 3.7462
2E + 12 4.9024
3E + 18 7.3791
qiso ¼
R @ lnðpÞ M @ð1=TÞ
ð12Þ q
where R is the universal ideal gas constant. Eq. (12) may be employed to determine qiso by plotting ln (p) versus 1/T for the adsorption isotherms at different temperatures and at constant loading. The linearity of this plot is an indication of the adsorbent surface homogeneity. Usually, activated carbons have nonlinear isosters that indicate their heterogeneous characteristics [4]. Other reasons for nonlinearity of the isosters are described in detail by Bulow et al. [7]. He et al. [11] give a comparison between calorimetric measurements and isotherm-based calculations of isosteric heat of adsorption. Pan et al. [15] have studied the isosteric heat of adsorption by numerical differentiation of Nonlocal Density Functional Theory (NDFT) isotherms. In the current study we used Eq. (12) for calculating the heat of adsorption. 3. Results and discussion 3.1. Isotherm models
tion that allows for the compressibility of the adsorbed phase and gives an accurate fit to experimental data at high pressures [11]:
" q¼Kp 1þ
Kp
t #1=t
að1 þ j pÞ
ð11Þ
where K, a, and t are parameters and j is the isothermal compressibility. A totally different model is suggested by Basu et al. using Artificial Neural Networks (ANN) that are highly parallel flexible mathematical constructs that have been inspired by the workings of the biological nervous system [6]. ANNs have a natural propensity for storing experimental knowledge and making it available for use. 2.3. Isosteric heat of adsorption The isosteric heat of adsorption, qiso, can be determined either from adsorption isotherms or directly by calorimetric measurements. The heat of adsorption is usually calculated by using the Clausius–Clapeyron equation:
In a previous study [23] we found that the Freundlich, Langmuir, and Sips models are in better agreement with experimental results for nitrogen than the Dubinin model, that is usually employed by many sorption cooler developers [12,20]. Therefore, in this work we considered only the Freundlich, Langmuir, and Sips models for reduction of our experimental data. Table 1 lists the parameters of the three models for nitrogen, methane, and ethane, where the pressure, p, is in MPa and the loading, q, is in ggas/kgs. The three isotherms with the experimental results are shown in Figs. 2–4 for nitrogen, methane, and ethane, respectively. One might notice that the loadings of methane and nitrogen are similar while the loadings of ethane are much higher. He et al. [11] have observed the same trend, and explain it by ethane being a nonspherical molecule that can assume different orientations with respect to the surface. All three models show a direct dependence of q on the pressure and indirect dependence on the temperature through their parameters. While designing sorption compressors it is necessary to incorporate the temperature in the models in order to
Fig. 5. Experimental results of nitrogen adsorption on Chemviron activated carbon with modified Freundlich (dotted lines), modified Langmuir (solid lines), and modified Sips (dashes lines) isotherms.
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Fig. 6. Experimental results of methane adsorption on Chemviron activated carbon with modified Freundlich (dotted lines), modified Langmuir (solid lines), and modified Sips (dashes lines) isotherms.
Fig. 7. Experimental results of ethane adsorption on Chemviron activated carbon with modified Freundlich (dotted lines), modified Langmuir (solid lines), and modified Sips (dashes lines) isotherms.
develop a numerical simulation and to extrapolate the results to temperatures even higher or lower than measured. Several trend line functions were examined to describe the dependence of the model parameters on temperature and the best fitted function was adopted for each parameter. For the following three equations the loading, q, is in ggas/kgs, the pressure, p, is in MPa, and the temperature, T , is in Kelvin. The modified Freundlich isotherm is:
q ¼ a1 expða2 TÞ pðb1 T
2
þb2 Tþb3 Þ
ð13Þ
where a1, a2, b1, b2, and b3 are constants listed in Table 2. The modified Langmuir isotherm is:
q ¼ ðc1 T 2 þ c2 T þ c3 Þ
ðd1 T d2 Þ p 1 þ ðd1 T d2 Þ p
ð14Þ
where c1, c2, c3, d1, and d2 are constants listed in Table 2. The modified Sips isotherm is:
q ¼ q0
ðe1 T e2 pÞ1=n 1 þ ðe1 T e2 pÞ1=n
ð15Þ
where e1 and e2 are constants listed in Table 2. q0 and n are constants given in Table 1. The isotherms calculated with the three modified models are presented in Figs. 5, 6, and 7 for nitrogen, methane, and ethane, respectively.
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Fig. 8. The mean absolute error for nitrogen. The solid lines and full markers represent the original three models, while the dashed lines and empty markers represent the modified versions of the models.
Fig. 9. The mean absolute error for methane. The solid lines and full markers represent the original three models, while the dashed lines and empty markers represent the modified versions of the models.
Fig. 10. The mean absolute error for ethane. The solid lines and full markers represent the original three models, while the dashed lines and empty markers represent the modified versions of the models.
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Fig. 11. Nitrogen experimental results as ln (p) versus 1/T for calculating the isosteric heat of adsorption.
Fig. 12. Methane experimental results as ln (p) versus 1/T for calculating the isosteric heat of adsorption.
Fig. 13. Ethane experimental results as ln (p) versus 1/T for calculating the isosteric heat of adsorption.
N. Tzabar, G. Grossman / Cryogenics 51 (2011) 499–508 Table 3 Constants for calculating the isosteric heat of adsorption with equation (17).
N2 CH4 C2H6
A1
A2
A3
A4
0.0031 0.0004 0.00004
0.347 0.1743 0.0254
9.6804 5.1088 6.1146
396.58 978.3 1156
In order to determine which isotherm has the best agreement with the experimental results, the mean absolute error, E, is calculated as follows:
N 100 X qi;exp erimental qi;predicted E¼ N qi;exp erimental i1
ð16Þ
E is calculated for each temperature, and N is the number of measurements at the particular temperature. The results are shown in Figs. 8, 9, and 10, for nitrogen, methane, and ethane, respectively. Fig. 8 shows that the Freundlich isotherm has the best agreement with the nitrogen experimental results among the original models as well as the modified versions. Methane shows a different behavior. The original isotherms show almost the same agreement with the experimental results with a minor advantage to the Langmuir isotherm. On the other hand, there is a significant difference among the modified versions. While both modified Langmuir and modified Sips show significant deviations from their original models, the modified Freundlich exhibits almost the same results as its original form. Thus, the modified Freundlich model is clearly the preferred one among the modified models for methane. Ethane shows a different behavior than both nitrogen and methane. Here again, the original isotherms exhibit almost the same agreement with the experimental results with a minor advantage to the Sips model at low temperatures and a minor advantage to the Langmuir model at high temperatures. The modified Freundlich isotherm, in this case, shows major deviations from the original model, while both Langmuir and Sips models are very close to their original forms. This means that the Sips model is preferred at low temperatures and the Langmuir model is preferred at high temperatures. 3.2. Isosteric heat of adsorption The isosteric heat of adsorption is the heat released during adsorption at constant loading. This value is calculated from the
507
experimental results, according to Eq. (12), at constant q for different temperatures. We have plotted the results of the three gases as ln (p) versus 1/T, drew linear curves through the constant loading points and found their slopes. The plots are shown in Figs. 11, 12, and 13, for nitrogen, methane, and ethane, respectively. All results show good linearity of the isosters. According to these plots, the isosteric heat of adsorption is calculated using Eq. (12) for each loading value and a correlation between the loading and the isosteric heat of adsorption is found in the following form:
qiso ¼ A1 q3 þ A2 q2 þ A3 q þ A4
ð17Þ
while q is the loading in ggas/kgs, qiso is the isosteric heat of adsorption in kJ/kg, and A1, A2, A3, A4 are constants listed in Table 3. The polynomial plots of nitrogen, methane, and ethane that present the isosteric heat of adsorption are shown in Fig. 14. The isosteric heat of adsorptions of nitrogen is about half that of methane, while ethane has almost the same values as methane for low loadings. 4. Conclusions A method for measuring the adsorption isotherm of pure gases is described, and the results for nitrogen, methane, and ethane are presented. The results were correlated with three well known adsorption models (Freundlich, Langmuir, and Sips). Different gases show best correlation with different models. Nitrogen adsorption is best described by Freundlich isotherms, methane is best described by Langmuir isotherms, and ethane is best described by the Sips model for low temperatures and Langmuir model for higher temperatures. In order to make better use of the models for developing sorption compressors, the original models were modified to incorporate the temperature dependence. In this case, the modified Freundlich model shows the best agreement with nitrogen and methane experimental results, while for ethane the modified Sips model is best fitted at low temperature and the modified Langmuir model is best fitted at higher temperatures. The isosteric heat of adsorption is calculated using the best fitting model for each gas. A formula is proposed for calculating the isosteric heat of adsorption as a function of the loading only. The data obtained from the present work help develop and design a sorption compressor for the three mentioned gases by simulating the compressor cycles relying on the results presented here.
Fig. 14. Isosteric heat of adsorption for nitrogen, methane, and ethane on Chemviron activated carbon.
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