Ind. Eng. Chem. Res. 1994,33, 346-354
346
Measurement and Correlation of the Adsorption Equilibria of Refrigerant Vapors on Activated Carbon John J. Mahle and Leonard C. Buettner US.Army, Edgewood Research, Development and Engineering Center, APG, Maryland 21010-5423 David K. Friday’ Guild Associates, Znc., 5022 Campbell Blvd., Baltimore, Maryland 21236
Adsorption equilibrium data have been measured for four refrigerant vapors (R-113, R-11, R-318, and R-22) on BPL activated carbon at three temperatures over a wide range of partial pressures using an automated isotherm apparatus. Special emphasis is placed on the design and operation of the apparatus to ensure the quality of these data. Isotherm data for each refrigerant vapor are analyzed for correct Henry’s law behavior and correlated using three- and four-parameter functions with specified temperature dependencies. The functions employed in this study include (1)the Langmuir equation, (2) the Dubinin-Astakhov equation, (3)the virial equation, and (4) the modified Antoine equation. The Dubinin-Astakhov equation provides the best (or very comparable) fits, based on the variance, for R-113, R-11, and R-318. However, the Dubinin-Astakhov equation does not correctly describe the behavior of the R-22 data, resulting from its incorrect approach to Henry’s law. Overall results show that, for adsorption of these refrigerants on BPL activated carbon, those correlations with exponents on the adsorbed-phase concentration terms greater than 1generate the smallest variances.
Introduction Adsorption equilibrium data are required to properly design and operate adsorption-based separation or purification systems. The conditions (temperature and partial pressure) where these data need to be measured depend greatly on the specific requirements of the system. For example, for pressure swing adsorption (PSA)separation of air to produce oxygen,isotherm data for key components from 1%to saturation between 280 and 350 K may be required. However, for a temperature swing adsorption (TSA) purification system which removes toxic organic contaminants, isotherm data over 3 or 4 orders of magnitude and temperatures from 298 to 425 K may be required. In both examples, and in general, measured isotherm data must be correlated to facilitate their use in a system-design model. Before correlations can be applied, however, one must have accurate adsorption equilibrium data. Correlations based on limited or inaccurate data are of little value; therefore, a strong emphasis must be placed on the experimental system both to generate data over a wide range of partial pressures and to ensure the quality of the data. This study emphasizes the importance of measuring accurate equilibrium data. An automated experimental isotherm system based on the design of Rudisillet al. (1992) has been developed to reduce potential operator errors and increase reliability. Special care has been given to develop the apparatus and procedures to achieve both accuracy and reproducibility. This system is used to measure single component isotherms for four refrigerant vapors, trichlorotrifluoroethane (R-1131, trichlorofluoromethane (R-111, octofluorocyclobutane (R-318), and chlorodifluoromethane (R-22). Isotherm data for each refrigerant are measured on BPL activated carbon over 4-5 orders of magnitude of partial pressure at three temperatures, 298, 323, and 348 K. Although there is a large amount of data available for vapor adsorption on activated carbons, there are very few references where the measured data span wide ranges of partial pressure and temperatures. In general, available
isotherm data on activated carbon which spans more than 2 or 3 orders of magnitude in partial pressure are limited to very light or permanent gases. Valenzuela and Myers (1989) have compiled a wide selection of adsorption data which includes several systems employingactivated carbon as the adsorbent. Three of these reference works examine several light hydrocarbon vapors measured over 2-3 orders of magnitude of partial pressures on Nuxit carbon (Szepesy and Illes, 1963) and BPL activated carbon (Reich et al., 1980;Walden et al., 1969) . Recently, Rudisill et al. (1992) reported data for n-hexane and acetone on BPL activated carbon covering approximately 5 orders of magnitude in partial pressure and 2 orders of magnitude in loading. Recovery and removal of chlorofluorocarbon (CFC) vapors is of interest from both an environmental and an economic standpoint. Ellington and Meo (1990) present an overview of the implications of atmospheric release of CFC’s. Future policies are likely to result in even more stringent emission requirements placing even more emphasis on recovery processes. One example of an application where adsorption-based systems are used to recycle CFC’s is infoam production where R-11is used as a blowing agent (Knopeck, 1989). There has been some work to characterize the adsorption equilibrium behavior of CFC’s. Recently, R-113adsorption on activated carbon and several other adsorbents was reported by Kodama et al. (1992). The range of concentrations they considered was less than 1 order of magnitude, and some of their data were physically incorrect, demonstrated by intersecting isotherms. Adsorption of several vapors, including R-113 at one concentration and temperature (100 ppm and 298 K), are reported for Columbia type activated carbon by Forsythe et al. (1978).
Experiments A. Apparatus. Shown in Figure 1 is a schematic of the apparatus used to measure the adsorption phase equilibrium of the four vapors on BPL carbon. The operation is similar to that used by Rudisill et al. (1992) to measure single-component and multicomponent ad-
0888-588519412633-0346$04.50/0 @ 1994 American Chemical Society
Ind. Eng. Chem. Res., Vol. 33, No. 2,1994 347
I l7
I
f&b 5
4
1
i
/u/
7
1. Carrler Gas 2. Gas Chromatograph 3. Gaa Sample Loop 4. Six Port Sample Valve 5. Bed Thermocouple 6 . Adsorbent Samnle 7 . Constant Temperature B a t h 8. Bellow8 Pump 9. Rcgulatlng Valve
f 10. Bed Bypass Valve 11. Six Port InJection Valve 12. B a l l a s t Tank 13. Vapor/Llquld InJectlon Loop 14. Chemlcal Feed Reservolr 15. Chcmlcal Collectlon Reservolr 16. Flow Meter 17. Pressure Transducer 18. S y s t e m Purge Valve
Figure 1. Schematic of the adsorption equilibria apparatus.
sorption equilibria of hydrocarbons and water on BPL activated carbon. The configuration of the apparatus, particularly the adsorbent bed temperature control, is similar to the system of Kaul (1987). There are three subsystems which comprise the apparatus, namely, (1) the main loop circulation system, (2) the chemical injection system, and (3) the vapor phase analysis system. The operation and sequencing of each subsystem is automated using a computer-controlled system. The main circulation loop consists of two four-way valves with Teflon seats, a mass-flow meter (0-50 L(STP)/min), a circulation pump, a 4-L ballast tank, an adsorbentsample-holding unit, and a constant-temperature bath. The adsorbent-sample-holding unit consists of a metal cup with a 15-pm frit a t the bottom and a glass-wooland-spring assembly to hold the adsorbent in place. The two four-way valves, one just above the water bath (element 10) and one on the bottom right (element 18)of Figure 1 are used to direct flows. In the positions shown in Figure 1, the system is operating in a closed-loop mode with flow over the adsorbent. If the position of the four-way valve above the water bath (element 10) is changed, the system is in the bypass mode. If the position of the other fourway valve (element 18) is changed, the system becomes open-loop and purge air from a PSA drier enters the system through this valve, flows around the main circulation loop, and exits through the same valve. The chemical injection subsystem consists of three, sixport ValCo valves connected in series. Each valve is equipped with a sample loop varying in volume from 1pL to 10 mL. The loop volume is selected to achieve the desired range of injected quantities for the adsorbing vapor. The method of filling the sample loops is determined by the chemical under study. For chemicals which are liquids at ambient temperature and pressures below about 45 psig (R-113, R-11, and R-3181, the sample loops are filled with liquid using an air cylinder as an upstream pressure source. For these chemicals, the smaller loop sizes are used. Chemicals which are gases a t pressures above about 45 psig (R-22 1, are charged into the sample injection system as saturated vapor and larger loop sizes are employed. There are two positions for each valve: (1)injection, where the sample loop is in the flow path of a portion of the main circulation system vapor, and (2) fill, where the sample
loop is in the path of liquid or gas fill stream. The position of each of the chemical injection valves is computercontrolled. A flow restrictor is used generate a low-pressure region at the outlet of the injection system to more quickly move the chemical from the selected sample loop into the main circulation loop. The vapor analysis subsystem consists of an HP-5880A gas chromatograph (GC), equipped with a six-port automatic gas sampling valve with a 1-mL sample loop, a flame ionization detector (FID) and an HP-5880 integrator. A small amount of the main circulation vapor is diverted to the six-port GC injection valve using the flow restrictor. There are two positions for the GC injection valve, inject and fill. In the fill mode, vapor flows from the main circulation system through the sample loop and back into the system. In the inject mode, the GC carrier gas flows through the sample loop sweeping the sample onto the GC column. The vapor in the main circulation loop flows through the GC injection valve, but bypasses the sample loop. When the controlling computer program requires a measurement of the vapor-phase concentration, the integrator is started and 10 s later the GC injection valve is switched from the sample mode to the inject mode. After a specified amount of time, the integrator is stopped and the peak summary report is sent to the computer over an RS-232 communications link. The peak area for the chemical of interest and the previously determined calibration parameters are used to calculate the chemical concentration in the circulating vapor. Each of the three subsystems is controlled using an IBMAT compatible computer. Hardware used to control flow path, temperature, chemical injection, and concentration measurements includes (1) a 24-channel DPDT relay output board, (2) an analog and digital interface board, (3) thermocouple modules, and (4) 10- and 24-V power supplies. B. Materials. The adsorbate chemicals used in this study were (1) trichlorotrifluoroethane (R-113) from Matheson Gas products, 99.8% pure, by weight; (2) trichlorofluoromethane (R-ll), from Matheson Gas Products, 98.9% pure, by weight; (3) octofluorocyclobutane (R-318) from Matheson Gas Products, 99.2% pure, by weight; and (4) chlorodiiuoromethane (R-221,from Matheson Gas Products, 99.1% pure, by weight. Each was used as received from the manufacturer without further purification. The adsorbent used in these experiments was 12 X 30 mesh, type BPL activated carbon, Lot No. 7816V, made by Calgon Corporation. C. Procedure. The carbon is dried overnight in an oven a t 423 K, then removed from the oven and placed in a desiccator and allowed to cool to room temperature. A sample of dry carbon, between 0.2 and 1.2 g depending on the chemical vapor to be measured, is weighed, placed in the sample holder, and inserted into the main circulation loop. The system is leak-tested prior to the start of each experiment by pressurizing the system to about 1300Torr and waiting approximately 1/2 h for any measurable change in pressure (0.1Torr). The four-way valves are positioned such that air from the PSA drier is introduced into the system through the purge line and directed over the bed at about 10 L/min for about 1 h to remove any water adsorbed during the weighing process. Both four-way valves are changed to bypass the adsorbent and put the system in a closed-loop orientation. The main loop circulation flow is set at about 7 L/min by adjusting the flow restrictor valve. A computer program controls all of the required steps to measure isotherm data. Operational parameters such
348 Ind. Eng. Chem. Res., Vol. 33, No. 2, 1994
as isotherm temperature(s), the desired amount of material to be injected into the system (target mass) for each equilibrium point, and the number of equilibrium points desired for the system are selected by the operator and saved in a setup file used by the computer control program. Other critical parameters saved in the setup file which are required to control the system and perform required calculations include (1) FID calibration parameters, (2) nominal mass of chemical contained within each injection loop, (3) all wait (delay) times and interval times, (4) equilibration criteria parameters, and (5) the mass of adsorbent. The water bath is set a t the first selected temperature using the 0-10-V power supply under computer control. Once the bath temperature has stabilized, the program injects chemical into the main circulation loop in samplebypass mode to obtain the first selected target mass. Nominal mass values for each injection loop are used to calculate the required number of injections of each loop in order to reach the target mass. After the appropriate number of injections have been made, the program waits a user-specified amount of time for the material to equilibrate in the main loop, typically between 2 and 10 min. Samples of the vapor phase are then taken at regular intervals (defined in the setup file) until the vapor-phase concentration is stable. The actual amount of material injected can be calculated on the basis of the net change in concentration. If the actual mass injected is more than 75% of the target mass, then the adsorption equilibrium phase is initiated. If the actual mass is less than 75% of the target mass, then another series of injections is performed to achieve the desired target mass. Once it has been verified that the desired mass of chemical has been injected, the four-way valve is switched to direct flow over the adsorbent. A user-defined, adsorption equilibrium wait (delay) time is used prior to starting the vapor-phase analysis. Following the equilibrium delay, vapor-phase samples are taken at regular time intervals to determine if equilibrium has been established. The equilibration criterion is that the difference between two successive concentration values is close to the signal-to-noise level of the detector-integrator (corresponding to about 2 area counts on the integrator) or 0.575, whichever is less. After the system has equilibrated, an isotherm point is established using the measured vapor-phase equilibrium concentration and calculating the adsorbed-phase concentration by taking the difference between the total mass injected and the mass in the vapor phase and dividing by the adsorbent mass. The temperature of the water bath is changed to the next selected value and allowed to stabilize. Following the adsorption equilibrium delay, the vapor phase is again sampled at regular intervals to determine if and when equilibrium has been achieved. The equilibrium loading is determined and the next temperature is selected. After equilibrium points for all of the selected temperatures have been measured, the four-way valve is changed to bypass the adsorbent, and the next desired mass is injected into the circulation loop. Equilibrium values at each selected temperature are measured with the increased amount of chemical in the system. To save time, the temperature is not changed back to the initial temperature for the next injection, Le., if 298, 323, and 348 K are the selected temperatures, then the second mass injection would be performed with the water bath at 348 K. This procedure is repeated until each mass injected has been allowed to establish equilibrium at each selected temperature.
Correlations Three of the most common approaches used to correlate adsorption equilibria for type I behavior are (1) the Langmuir approach, (2) the Gibbs approach, and (3) the potential theory (pore-filling) approach (Yang, 1987). In order to limit the scope of the analysis, only those correlations with a defined temperature dependence are considered. For example, the Toth equation used by Valenzuela and Myers (1989) will not be considered since one must correlate each isotherm separately and then build the temperature dependence between the fit parameters. In this study, all three isotherms for each chemical will be fit using three- and four-parameter functions from each common approach. Following LeVan and Hacskaylo (1985), correlation parameters will be obtained by minimizing the variance as given in equation 1 to give equal weight to the low concentrations. 1 Nm
var = Npts
[(ln P),,,
- (In P ) ~ , I ~
(1)
1
A. Langmuir Approach. The Langmuir isotherm may be written as
where 0 is the fractional saturation loading, q/qBLLt.The temperature dependence of K may be expressed as
K = K, e x p [ s
(3)
where AH and KO are fit parameters. The Langmuir approach has been extended to four parameters by Sips (1950). (4)
B. Gibbs Approach. The virial equation (VE) results from the assumption of smooth two-dimensional surface interactions (Zhang et al., 1991). As such, the VE does not have the correct saturation limit since eq 5 does not require that W equal the total pore saturation value when p equals psat.The VE is expressed as a series expansion of the following form,
n
“z + ?a
...Iw2 + ... . . I
(5)
where Ki’s are the Henry’s law terms. The above form does suggest a means by which terms can be added to reduce the correlation variance. For the correlations considered here, the three-parameter version virial equation will use KO,K1,and B1, while the four-parameter correlations will add either a B2 or a C1 term to the threeparameter version. C. Pore-Filling Approach. Models using the porefilling approach have the advantage over the other two approaches in that they become the vapor-liquid equilibrium expression when the adsorbent is saturated. The most widely recognized three-parameter function derived using a pore-filling approach is the Dubinin-Astakhov equation (DAE),
where BE , n, and qsatare the fit parameters (Dubinin,
Ind. Eng. Chem. Res., Vol. 33, No. 2,1994 349 1979). When m = 2, eq 6 reduces to the two-parameter Dubinin-Radushkevitch equation (DRE)(Dubinin, 1979). However, both of these relationships give rise to an unbounded heat of adsorption as the loading approaches zero. There is no four-parameter form based on the Polanyi potential theory which meets the criteria for use in this work. Ozawa et al. (1976) proposed a series expansion for the DAE, but the result is an expression which results in a maximum in loading prior to the saturation vapor pressure. A more rigorous approach was taken by Kapoor et al. (1989) to extend the DRE to include four parameters and a correct Henry’s law limit. However, their expression cannot be written as In@) = f ( q )and there is a significant temperature dependence in the correlation parameters not specified in their model. A second pore-filling approach was first published by LeVan and Friday (1982) and subsequently discussed in detail by Hacskaylo and LeVan (1985). It is based on the Antoine vapor pressure function where loading dependencies are introduced into each Antoine parameter. The general form proposed by Hacskaylo and LeVan correctly approaches both the saturation and Henry’s law limits. Their form, called the modified Antoine equation (MAE), will be used in this work and is given below.
1.
’.,
,
W1 01
l
ID
P.rn.1
B‘ C’ + T
(7)
..
Figure 2. Henry’s law plot for R-113adsorbed on BPL activated carbon.
..
.
9.
In@) = A ’ - -
,000
100
P n u u n (Pa)
L
2o(K 321K W K
1-
. . 0.
Nb
ill
(10) Figure 3. Henry’s law plot for R-11adsorbed on BPL activated carbon.
w= dPa&
(12)
Several different three-parameter and four-parameter versions of the MAE using various combinations of ai’s, bi’s,and ci)s will be correlated with the measured isotherm data.
Results A. Refrigerant IsothermData. Measured adsorption equilibria for R-113, R-11, R-318, and R-22 on BPL activated carbon at three temperatures 298,323, and 348 K are given in tabular form in Appendix A. These data are analyzed for the correct Henry’s law behavior by plotting the results as q / p versus p . Shown in Figures 2-5 are the Henry’s law plots for each refrigerant vapor. Data are shown on a log-log scale in order to accommodate the wide range of partial pressures and loadings. Duplicate experiments are performed for each adsorbate using a different sample of BPL carbon for each experiment. These data, in particular the R-113 results, demonstrate the reproducibility of the experimental system. Figure 2 shows that Henry’s law is not reached for R-113 at the partial pressures measured in this study as evidenced by the increasing value of q / p with decreasing pressure for all temperatures. Even the 348 K isotherm data indicate that q l p is still increasing at the lowest partial
t .
..
.. 0s..
. 0
0
.. .. .
00-
no
Figure 4. Henry’s law plot for R-318adsorbed on BPL activated carbon. pressures. The results for R-11 are shown in Figure 3, and
they also indicate that Henry’s law has not been attained a t any temperature. However, the data measured at 348 K demonstrate that R-11 is much closer to Henry’s law at
350 Ind. Eng. Chem. Res., Vol. 33, No. 2, 1994
Table 2. Variances for Three-Parameter Fits of Refrigerant Isotherm Data
. rn
ZOK
Langmuir DAE virial MAE (ai,~ MAE ( b l , ~
323K 348X
1 )
1 )
MAE (ai,bl) MAE ( b l , bi) pL = p,[l
R-22 0.0992 0.1825 0.0587 0.0572 0.0623 0.0597 0.0572
+ 0.85(1-
R-318 0.9304 0.0519 0.2156 0.1860 0.2077 0.2149 0.1686
R-11 0.6797 0.0204 0.0814 0.0665 0.0742 0.0841 0.0643
R-113 1.1009 0.0207 0.0925 0.0676 0.0758 0.0996 0.0928
R-22(mod) 0.0844 0.1904 0.0427 0.0436 0.0416 0.0472 0.0416
T/T,) + (1.6916 + 0.98460)(1T/Tc)”sl (13)
wo1
Parun1 Prnssurn (Pal
Figure 5. Henry’s law plot for R-22 adsorbed on BPL activated carbon.
Table 1. Physical Parameters for Each Refrigerant Vapor chemical w pc Tc A B C MW R-22 R-318 R-11 R-113
0.215 0.361 0.188 0.252
6069 3095 4032 3074
369 388 471 487
21.329 2051.5 21.265 2278 20.974 2508.2 20.954 2648.1
-23.244 -33.783 -31.554 -39.905
86.5 200 137.4 187.4
low partial pressures than the R-113 data. One can see from Figure 4 and Figure 5 for R-318 and R-22, respectively, that data for the lower partial pressures are in the Henry’s law regime. The results for R-22 also indicate that three points may be in error, p = 3.556 Pa and p = 2.365 Pa at 348 K, and p = 0.3036 at 298 K. With these three data points removed from the full R-22 data set, a new data set identified as R-22 (mod) was used to establish a different set of correlation parameters and variances. The measurement errors for the R-22 experiments can be explained on the basis of the procedure. For the two points at 348 K, the loadings are very small, 0.001 55 and 0.000 93 mol/kg, respectively. Recall that the loading is calculated on the basis of the difference in the vaporphase concentrations in the bed bypass mode and after equilibration with the adsorbent. For these two points, the difference in the vapor-phase concentrations is near the detection limit of the FID (using a 1.0-mL sample loop). For the point at 298 K, the partial pressure of 0.3036 Pa is also near the detection limits. B. Correlation of Measured Data. A commercial software package, MINSQ by Micromath, Inc., was used to determine the best fit correlation parameters for each chemical vapor data set. Initial parameter estimates were refined using a simplex search. Optimum parameter values were then obtained using a nonlinear least squares algorithm to minimize the variance. Physical parameters required to evaluate the four correlation functions are provided in Table 1. Values for Pitzer’s acentric factor, w , for R-22, R-11, and R-113 were obtained from Appendix Aof Reid at al. (1977). For R-318, w was calculated using eq 2-3.3 from Reid et al. (1977). Critical properties and vapor pressure data for each chemical were obtained from Braker and Mossman (1980). The Antoine parameters A , B, and C were obtained from a least squares best fit of the vapor pressure data. For all correlation results, the adsorbed-phase density is assumed to be the liquid-phase density at the temperature of interest. The liquid densities as a function of temperature for each chemical species were calculated using eq 13 (Campbell and Thodos, 1984).
Isotherm data for each chemical were correlated using the four three-parameter functions given in the previous section. The variances calculated for each three-parameter fit are shown in Table 2. The R-22 (mod) column reflects the results with the three points identified in Figure 5 not included. On the basis of variances, the best fit for the more strongly adsorbed vapors, R-318, R-11, and R-113 is obtained using the DAE equation (eq 3). The Langmuir equation (LE) given in eq 1results in the poorest fit of the data for every chemical except R-22. For the most strongly adsorbed gas, R-113, the LE is more than an order of magnitude worse (based on the variance) than any of the other three-parameter equations. The MAE and VE have approximately 3-4 times the variances of the DAE for R-318, R-11, and R-113. For R-22, the best fit for both the full and modified data sets is obtained using the MAE with bl and bz. The variances for the VE are slightly larger than the variances for the best MAE fits; however they are smaller than two of the four MAE versions. Note also that, for both R-22 data sets, the variance for the DAE is twice as large as the variance for the LE. It is interesting that Hacskaylo and LeVan (1985) found that the MAE with a bl and c1 correlated isotherm data consistently better than the DAE. However, the highest boiling vapor they considered was butane (bp = 272 K), and their correlations were performed using an independently determined value for the adsorbent saturation capacity, WO;i.e., W Owas not a correlated parameter. In addition, a close inspection of the variances from their work shows that the differences in the variances for DAE and MAE become smaller as the adsorbing gas becomes more strongly adsorbed. This trend for the MAE to describe the behavior of the less strongly adsorbed gases is confirmed with these results. The fact that the VE and LE, which possess the correct Henry’s law behavior, give better fits for R-22 than the DAE may be an indication that the problems with the DAE in the Henry’s law regime are significant only for gases as weakly adsorbed as R-22. The inadequacies of the DAE in the Henry’s law region are illustrated in Figure 6, where R-22 data are compared to the best fit results for the DAE and the MAE using a1 and c1. The MAE shows the correct behavior in the Henry’s law regime, while the DAE shows a maximum in the value of q / p ,particularly evident in the 348 K results at a partial pressure of about 50 Pa. In addition, it is clear from these results that the DAE cannot accurately describe the heat of adsorption for R-22. This is demonstrated by the large spread in the DAE model isotherms relative to the data. There has been some speculation in previous works about the capability of the DAE to accurately characterize adsorption behavior at low loadings. For example, Kapoor et al. (1989) refer to Dubinin (1975) and suggest that the DRE begins to break down below 8 = 0.2. Consider the
Ind. Eng. Chem. Res., Vol. 33, No. 2, 1994 361
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