Environ. Sci. Technol. 2000, 34, 4816-4821
Mass Transfer and Warming during Adsorption of High Concentrations of VOCs on an Activated Carbon Bed: Experimental and Theoretical Analysis FRE ´ DE ´ RIC DELAGE, P A S C A L I N E P R EÄ , A N D PIERRE LE CLOIREC* Ecole des Mines de Nantes, De´partement Syste`mes Energe´tiques et Environnement, 4 rue Alfred Kastler, BP 20722, 44307 Nantes Cedex 03, France
An experimental and theoretical study was carried out to predict the warming and the mass-transfer rate during adsorption of high concentrations of volatile organic compounds (VOCs) in an activated carbon bed. A linear driving force (LDF) model is found to provide an acceptable fit to the measured data. An empirical correlation of the mass transfer rate is proposed as a function of the strength of adsorbent-adsorbate interactions and the gas velocity to design the adsorption process without using any adjustable parameter. The model was validated for an adsorption unit with high loadings (up to 100 g.m-3) of seven kinds of VOC and within the velocity range 0.139-0.556 m.s-1. The prediction of the temperature rise inside the adsorber is improved by the use of the differential heat of adsorption instead of the integral heat. A theoretical parameter sensitivity test indicates that the temperature rise is strongly dependent on the molar VOC concentration, the adsorption heat, and the volumetric heat capacity of the carrier gas. The warming of the activated carbon bed can be well predicted from these variables. The relation obtained appears to be a practical means for designing the safety of an adsorber and preventing carbon bed ignition.
Tien (10) provided a review of mass transfer mechanisms, adsorption kinetics, and the existing mathematical models. A considerable amount of work has been done on nonisothermal adsorption (8-25). The simplest model is based on the equilibrium model, neglecting heat and mass transfer resistances (11-14). While the assumption of negligible heat transfer resistance between the gas phase and the solid phase is justified (9), predicting adsorption performance requires the consideration of the mass transfer phenomenon. Mass transfer is usually described by the linear driving force (LDF) expression defined as the difference between the equilibrium surface concentration and the average adsorbed phase concentration because of its simplified mathematical form; the LDF mass-transfer coefficient is generally considered as an adjustable parameter (15-20) although it can be related to diffusion coefficients (9, 10, 15-17). As the dominant intraparticle transport onto activated carbon proves to be surface diffusion when the adsorbed phase layer is appreciable (21), some authors (15-17) have introduced the surface diffusion expression with a fitting parameter in the LDF mass transfer coefficient. But no empirical correlation of this adjustable factor has been proposed, and the use of the model requires experimental and theoretical results to be matched each time. Over the years, most theoretical studies have been validated for limited experimental results where heat effects were not pronounced ( 0 are
mass balance for the solid phase
{
TABLE 1. Properties of Picactif NC 60 and Packing Characteristics
(7)
The set of PDEs was written in dimensionless form. The spatial discretisation is performed using the Keller box scheme, and the method of lines is employed to reduce the PDEs to a system of ordinary differential equations. The resulting
Activated Carbon. The adsorbent used was Picactif NC60 granular carbon (Table 1), manufactured by Pica Co. (Levallois-Perret, France). The average grain size was 0.55 mm for the 20 × 50 mesh size and 1.0 mm for the 14 × 35 mesh size. Heat capacity of the adsorbent is measured by means of differential scanning calorimetry. The material was dried at 105 °C for 24 h and then kept in a dry atmosphere before experiments. The water content is then lower than 1%. Equilibrium Isotherms. The appropriate set of constants qm, bo, and A described in eq 7 are determined from equilibrium isotherms. Measurements of adsorption equilibrium were conducted by batch adsorption method. Heat of Adsorption. Several studies (29, 30) have pointed out that it is essential to use calorimetric methods to obtain accurate data. Differential scanning calorimetry coupled to a thermobalance (model Setaram TG-DSC 111) was used for the determination of the differential heat of adsorption. The gas flow through the DSC cell consisted of pure helium (5 L.h-1). Prior to the experiment, the sample was heated to 120 °C at a rate of 5 K.min-1 so as to minimize the water content of the activated carbon. The sample was then cooled to the adsorption temperature (20 °C). Several adsorption steps of VOC vapor (concentration about 50 g.m-3) were carried out. Each increment produced a thermal response due to the adsorption. The accompanying exothermic response was recorded as a function of time, and the differential heat of adsorption was then determined by integrating the heat flux signal corresponding to the amount adsorbed. The integral heat of adsorption is defined as the integration of the differential heat curve. Experimental Setup. The experimental setup is shown in Figure 1. The VOC vapor was produced by bubbling the air through a vessel filled with the organic liquid. The adsorber is a glass column of 46 mm inner diameter and 200 mm in height. The column is insulated to approach adiabatic conditions. Heat loss was evaluated by simulating air heating data as described by Schork and Fair (15). The value retained for ho coefficient corresponds to the best fit to experimental data and is equal to 4 W.m-2.K-1. The temperature of the inlet gas was approximately laboratory temperature (20 ( 2 °C). The temperature was measured by means of type K thermocouples placed along the central axis of the column at intervals of 40 mm. The breakthrough time noted tp10% is when the time of the exit concentration becomes equal to 10% of the inlet concentration. The gas phase concentration was continuously VOL. 34, NO. 22, 2000 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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TABLE 3. Constants for Langmuir Isotherm Equation compound
qm (mol.kg-1)
b (m3.mol-1)
A (J.mol-1)
acetone 1,2-dichloroethane ethyl acetate ethyl alcohol methylethyldioxolane methyl ethyl ketone toluene
5.921 5.322 4.411 8.462 3.578 5.060 4.609
2.28 × 10-5 1.63 × 10-7 1.36 × 10-5 5.98 × 10-5 2.79 × 10-7 1.27 × 10-6 4.06 × 10-7
31.4 × 103 47.5 × 103 60.6 × 103 28.7 × 103 45.2 × 103 42.7 × 103 45.5 × 103
FIGURE 1. Schematic diagram of the experimental setup.
TABLE 2. Operating Conditions of Adsorption Experiments VOC acetone acetone acetone acetone acetone toluene ethyl alcohol methyl ethyl ketone methyl ethyl ketone methyl ethyl ketone methyl ethyl ketone methyl ethyl ketone methylethyldioxolane 1,2-dichloroethane ethyl acetate
C0 (g.m-3)
U0 (m.s-1)
25 33 50 75 100 25-51-6275-99 22-37-4758-73-100 27 48 55 85 100 50 51-102 52-100
0.139-0.278-0.556 0.139 0.139-0.278-0.556 0.139-0.278-0.556 0.139 0.139 0.139 0.139-0.278-0.556 0.139 0.139-0.278-0.556 0.139-0.278-0.556 0.139 0.139 0.139 0.139
FIGURE 3. Differential heat of adsorption on Picactif NC 60. concentrations, the adsorption mechanism looks like a volume-filling of micropores rather than monolayer adsorption. Besides adsorbate/adsorbate interactions can occur (27). We must then focus on the predictive ability of the isotherm equation rather than on the meaning of the equation parameters. The set of constants of the Langmuir equation is given in Table 3. Heat of Adsorption. The differential heat of adsorption determined by TG-DSC apparatus is presented in Figure 3 for several VOCs. The drop in the adsorption energy with loading is typical of heterogeneous adsorbents (27). At low loadings, the adsorbates occupy the most energetically favorable positions and adsorbent-adsorbate interactions dominate. At higher loadings, multilayer adsorption takes place and adsorbate-adsorbate interactions, which are less energetic, become more important. The difference in the adsorption heat between these two extremes is around 10 kJ.mol-1. Variations of the adsorption heat with surface coverage are introduced in the model by fitting a polynomial equation to experimental data for each VOC:
-∆Hd ) eo + e1q + e2q2 FIGURE 2. Measured and modeled results for ethyl alcohol adsorption onto Pica NC 60 using the Langmuir equation. measured by a flame ionization detector (Cosma 355) at several heights (intervals of 40 mm). Operating conditions corresponding to 38 adsorption experiments are summarized in Table 2.
Results Equilibrium isotherms and adsorption energies must be determined prior to solving the theoretical model. Then, experimental and numerical data are compared before investigating the expression of the mass-transfer coefficient, and the significance of parameters on the temperature rise. Adsorption Data. Typical isotherm data of ethyl alcohol are presented in Figure 2. The temperature-dependent form of the Langmuir isotherm equation proves to describe the adsorption data well. The Langmuir model assumes monolayer coverage and homogeneous surface energy. However these basic assumptions are probably not fulfilled. The volume of ethyl alcohol adsorbed at high concentration is about 0.47 cm3.g-1 and is close to the pore volume. At these 4818
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(8)
Constants of the eq 8 and integral heat of adsorption values are described in Table 4. Comparison of Experimental and Modeling Results. Heat and mass tranfer zones resulting from the dynamic adsorption of organic vapor present in air on a granular activated carbon bed have already been discussed in a previous publication (1). Experimental temperature and concentration profiles are compared with the theoretical curves obtained from the mathematical model in the case of ethyl alcohol adsorption on Picactif NC 60 (Figures 4 and 5). The model provides a good prediction of the experimental results obtained for each location. Regarding the breakthrough curve, a slight difference in the later stage of uptake is noticed. The model slightly overestimates the measured adsorption capacity as gas analysis is carried out near the column wall where the porosity is greater than at the bed center. This deviation might also be explained by the adsorbate concentration dependence of the diffusion coefficient which is not considered in eq 6. The temperature rise predicted during the first minutes is higher than experimental data; the main source of error is likely to be due to the simplified expression of heat loss. But this difference is not of great importance since attention should be paid to the maximum temperature
TABLE 4. Heat of Adsorption Values differential heat of adsorption (-∆Hd ) eo + e1 q + e2q2) compound
e0 (kJ.mol-1)
e1 (kJ.kg.mol-2)
e2 (kJ.kg2.mol-3)
R2
heat of adsorption -∆Hint (kJ.mol-1)
acetone 1,2-dichloroethane ethyl acetate ethyl alcohol methylethyldioxolane methylethyl ketone toluene
53.794 55.386 67.769 54.761 81.359 63.887 78.788
-1.249 -0.557 -3.825 -1.867 -6.892 -4.469 -6.699
0.048 -0.028 0.317 0.108 0.841 0.443 0.795
0.976 0.978 0.998 0.962 0.989 0.981 0.979
50.6 53.2 61.2 48.6 72.4 58.0 67.6
FIGURE 4. Breakthrough data and simulation of ethyl alcohol adsorption on Picactif NC 60 (C0 ) 47 g.m-3; U0 ) 0.139 m.s-1).
FIGURE 5. Temperature data and simulation of ethyl alcohol adsorption on Picactif NC 60 (C0 ) 47 g.m-3; U0 ) 0.139 m.s-1).
FIGURE 6. Comparison of the calculated and observed maximum temperature rise. rise to design the safety of an adsorber, and a good prediction is obtained for the thermal amplitude. Figures 6 and 7 show the predictive ability of the model for the high loading of VOCs listed in Table 2. Student t-statistics prove that the slope of the regression is not significantly different from the perfect agreement for a 95% confidence interval. If the heat of adsorption is considered constant in the heat balance (eq 3) as in previous published studies (16-25), the following regression between the calculated and measured thermal amplitude is obtained:
∆Tm calc ) 0.945 ∆Tm meas 2
r ) 0.957
sb ) 0.022
(9)
FIGURE 7. Comparison of the calculated and observed breakthrough time.
FIGURE 8. Comparison between adjusted mass-transfer coefficient and values calculated from eq 10. This regression demonstrates significant deviation from the perfect agreement. The use of a differential heat of adsorption is then required to improve the prediction of the warming inside an adsorber (Figure 5). No effects are found concerning the breakthrough time. Prediction of the Mass-Transfer Coefficient. The LDF model with surface diffusion as the dominant mass-transfer mechanism is used to describe the adsorption kinetics. It means that equilibrium is established at the exterior surface of the adsorbent and the transport into the particle is by surface diffusion. The migration of adsorbed molecules may be considered as involving a hopping mechanism from site to site. The R parameter (eq 6) is found by fitting the model with the experimental breakthrough curve. This parameter proves to be independent of the inlet concentration C0 and proportional to the linear gas velocity U0 for each compound. In addition, a linear relation is found between ln(R) and the integral heat of adsorption for constant gas velocity. The applicability of the model is then improved by relating the R parameter to operating conditions and adsorbate/ adsorbent properties through the following relationship:
R ) 1.23 × 10-9 U0 exp(-1.694 × 10-4 ∆Hint) (10) A comparison between the adjusted values and the data calculated from eq 10 is shown in Figure 8. Equation 10 provides a reasonably accurate prediction of the massVOL. 34, NO. 22, 2000 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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FIGURE 9. Significance of parameters on the warming of an adsorber. transfer coefficient for all operating conditions described in Table 2. R values are found in the range 7 × 10-7-3.2 × 10-5 m.s-2; deviation from adjusted values stands between 0.5% and 13% and proves to have no significant effect on the breakthrough time, the maximum temperature rise, and the shape of the concentration and thermal waves. Combining eqs 4, 6, and 10, the mass transfer coefficient k can be calculated as follows:
k)
7.38 × 10-8 U0 0.45 - 1.694 × 10-4 exp ∆Hint 2 RT dp
[
(
)]
(11)
The connection between Ds and U0 can appear astonishing as U0 is rather related to the external film mass transfer. But the mass transfer coefficient k is a lumped quantity owing to the simplified formulation of the LDF model. Equation 11 should then be considered as an expression combining external mass transfer and surface diffusion. Yun et al. (31) found also a direct relation between the LDF mass-transfer coefficient and the gas velocity. The gas velocity affects accumulation of adsorbate at the exterior surface of the adsorbent particle and thus the solid-phase concentration gradient. The inlet VOC concentration C0 has no immediate effect on Ds as the driving force is the solid-phase concentration gradient. But C0 influences greatly the warming of the carbon bed (1); consequently C0 is implicitly contained in the temperature term. The relation between R and the integral heat of adsorption means that the diffusional activation energy is smaller than the 0.45 coefficient retained by Sladek et al. (28) (eq 5). Do and Hu (32) reported activation energy values ranging from 0.3 to 0.8 of the adsorption energy. But the use of an expression such as c∆Hint/RT with c as an adjustable parameter replacing the 0.45 coefficient shows no good results, and the relation described by eq 11 is then preferred. This empirical correlation enables the present adsorption process to be designed without using any adjustable parameter provided that surface diffusion is the rate-limiting step for adsorption. Parameter Sensitivity. A parameter sensitivity test has to be made to determine the operating conditions which may induce carbon bed combustion. The sensitivity test is performed from the measurements of the thermal waves shown in Figure 5. The thermal waves are predicted with the parameter values identical to those used in the computation except for the parameter to be tested for sensitivity. C0, -∆H, and FgCg appear to be the most sensitive parameters, and other factors are not very sensitive. The volumetric heat capacity of the carrier gas is constant from one experiment to another, and its value is known with good accuracy from thermodynamic tables. Using the integral adsorption heat and the molar VOC concentration, a good correlation is found with the maximum temperature rise measured (Figure 10). Besides the operating conditions listed in Table 2, experimental data obtained for adsorption of other VOCs are included in Figure 10: hexane, cyclohexane, isopropylic ether, 4820
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FIGURE 10. Prediction of the warming of an activated carbon bed from the inlet VOC concentration and the integral heat of adsorption. triethylamine, isobutyl vinyl ether, methyl isobutyl ketone, tetrahydrofuran, chloroform. Some experimental results tend to deviate from the perfect agreement above a temperature rise of 60 °C. The maximum temperature rise is then underestimated with a maximum error of 20%. Oxidizing reactions might occur at temperatures greater than 60 °C especially for ketone-like compounds (3, 4, 33) and could explain this deviation which is observed mainly for methyl ethyl ketone. One other possible cause could be the use of the average heat of adsorption which does not take into account the most energetic adsorption sites. However this correlation provides a simple means of estimating the temperature rise in an adsorber. This relation can also be used for VOC adsorption in a humid air stream since the moisture content of the air (in the range 0-95%) is not a prominent factor affecting neither the adsorption capacity nor the warming of a dry carbon bed at high VOC concentration (1). As bed combustion is initiated either by oxidation of the solvent or by oxidation of the adsorbent, knowledge of these temperatures enables the determination of the maximum VOC concentration which must not be exceeded to avoid a fire hazard.
Acknowledgments The financial support provided by ADEME (Agence de l’Environnement et de la Maıˆtrise de l’Energie, France) under contract no. 9774100 is gratefully acknowledged. The authors wish also to thank Pica Co. and G. Dagois, the Managing Director, for the supply of activated carbon.
Nomenclature Ca
heat capacity of the adsorbate (J.mol-1.K-1)
Cg
heat capacity of the gas (J.kg-1.K-1)
Cs
heat capacity of the adsorbent (J.kg-1.K-1)
C
gas concentration (mol.m-3)
C0
inlet VOC concentration (mol.m-3)
D
column diameter (m)
dp
adsorbent diameter (m)
Ds
diffusion coefficient (m2.s-1)
e0, e1, e2 constants of the equation fitting the differential heat of adsorption (eq 8) ho
overall heat transfer coefficient (W.m-2.K-1)
k
mass-transfer coefficient (s-1)
q
adsorbed phase concentration (mol.kg-1)
qe
equilibrium adsorbate concentration (mol.kg-1)
qm, bo, A constants of the Langmuir equation (eq 7) R
gas constant (8.314 J.mol-1.K-1)
r2
coefficient of determination
sb
standard deviation of the slope of the linear regression
t
time (s)
tp10%
breakthrough time (s)
T
temperature (K or °C)
(10)
T0
room temperature; temperature of the fluid flowing into the bed (K or °C)
(11)
U0
linear gas velocity (m.s-1)
z
axial position (m)
Greek Symbols R
adjustable parameter (m.s-2)
porosity
-∆Hd
differential heat of adsorption (J.mol-1)
-∆Hint
integral heat of adsorption (J.mol-1)
∆T
temperature increase (K or °C)
∆Tm
maximum temperature rise (K or °C)
Fb
bed density (kg.m-3)
Fg
gas density (kg.m-3)
τ
tortuosity
(8) (9)
(12) (13) (14) (15) (16) (17) (18) (19) (20) (21) (22) (23) (24) (25) (26) (27)
Literature Cited (1) Delage, F.; Pre´, P.; Le Cloirec, P. J. Envir. Eng. 1999, 125(12), 1160-1167. (2) Wildman, J. Proceedings, Carbon’88; University of Newcastle Upon Tyne, United Kingdom, Sept 1988, 185-187. (3) Naujokas, A. A. Loss Prev., CEP Technol. Man. 1979, 12, 128135. (4) Naujokas, A. A. Plant Operation Prog. 1985, 4(2), 120-126. (5) Chapman, M. J.; Field, D. L. Loss Prev., CEP Technol. Man. 1979, 12, 136-141. (6) Harrell, W. A.; Sewall, J. O.; Walsh, T. J. Loss Prev., CEP Technol. Man. 1979, 12, 124-127. (7) Chemical safety alert; EPA-550-F-97-002e; U.S. Environmental Protection Agency, Chemical Emergency Preparedness and
(28) (29) (30) (31) (32) (33)
Prevention Office, U.S. Government Printing Office: Washington, DC, 1997. Suzuki, M. Adsorption Engineering; Kodansha, Ed., Elsevier: 1990; Chapter 8, pp 187-203. Ruthven, D. M. Principles of adsorption and adsorption processes; John Wiley & Sons: New York, 1984. Tien, C. Adsorption calculations and modeling; ButterworthHeinemann Series in Chemical Engineering: 1994. Pan, C.-Y.; Basmadjian, D. Chem. Eng. Sci. 1970, 25, 16531664. Pan, C.-Y.; Basmadjian, D. Chem. Eng. Sci. 1971, 26, 45-57. Basmadjian, D.; Dan Ha, K.; Pan, C.-Y. Ind. Eng. Chem., Process Des. Dev. 1975, 14(3), 328-340. Jacob, P.; Tondeur, D. Chem. Eng. J. 1983, 26, 41-50. Schork, J.-M.; Fair, J.-R. Ind. Eng. Chem. Res. 1988, 27(3), 457469. Huang, C.-C.; Fair, J.-R. AIChE J. 1988, 34(11), 1861-1877. Huang, C.-C.; Hwu, T.-L.; Hsia, Y.-S. J. Chem. Eng. Jpn. 1993, 26(1), 21-27. Ozil, P.; Bonnetain, L. Chem. Eng. Sci. 1978, 33, 1233-1237. Meunier, F.; Sun, L. M.; Kraehenbuehl, F.; Stoeckli, F. J. Chem. Soc., Faraday T. 1988, 84(6), 1973-1983. Yoshida, H.; Ruthven, D. Chem. Eng. Sci. 1983, 38(6), 877-884. Costa, E.; Calleja, G.; Domingo, F. AIChE J. 1985, 31(6), 982988. Meyer, O. A.; Weber, T. W. AIChE J. 1967, 13(3), 457-465. Kaguei, S.; Yu, Q.; Wakao, N. Chem. Eng. Sci. 1985, 40(7), 10691076. Farooq, S.; Ruthven, D. M. Ind. Eng. Chem. Res. 1990, 29, 10761090. Ruthven, D. M.; Garg, D. R.; Crawford, R. M. Chem. Eng. Sci. 1975, 30, 803-810. Matsumoto, A.; Zhao, J.-X. Langmuir 1997, 13, 496-501. Pan, H.; Ritter, A.; Balbuena, P. B. Ind. Eng. Chem. Res. 1998, 37, 1159-1166. Sladek, K. J.; Gilliland, E. R.; Baddour, R. F. Ind. Eng. Chem. Fundam. 1974, 13(2), 100-105. Rychlicki, G.; Terzyk, A. P. J. Therm. Anal. 1995, 45, 961-965. Berlier, K.; Fre`re, M. J. Chem. Eng. Data, 1996, 41, 1144-1148. Yun, J. H.; Choi, D. K.; Kim, S. H. Ind. Eng. Chem. Res. 1998, 37, 1422-1427. Akubuiro, E. C. Ind. Eng. Chem. Res. 1993, 32, 2960-2968. Do, D. D.; Hu, X. Chem. Eng. Sci. 1993, 48, 2119-2127.
Received for review April 17, 2000. Revised manuscript received August 11, 2000. Accepted August 17, 2000. ES001187X
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