Ind. Eng. Chem. Res. 1997, 36, 3993-3994
3993
Gas Adsorption Isotherm for Dealuminated Zeolites Dieter Bathen,* Henner Schmidt-Traub, and Marcus Simon Department of Chemical Engineering, University of Dortmund, 44221 Dortmund, Germany
A new equation for complex adsorption isotherms was developed by using a mathematical method well-known in control engineering. On the basis of this analogy, it is possible to describe the transitional region between Langmuir isotherms and isotherms following Henry’s law. Development and verification of the equation are based on experimental data of the system zeolite DAYethanol-air. Introduction Adsorption is a current technique to remove volatile organic compounds from process gas streams. In industrial applications hydrophobic dealuminated zeolites are often used as adsorbents, because of their specific advantages in comparison to activated carbon or polar zeolites. Until today design and simulation of such processes is very difficult, because there does not exist a single equation to describe the complex adsorption equilibrium over the whole temperature range. The use of different equations for each temperature section is inconvenient for the application in software programs for dynamic simulation and optimization. Consequently an equation which sufficiently describes experimental data was developed during a scientific research project on microwave-enhanced desorption carried out by Bathen et al. (1996). Measurement of Isotherms During the investigation isotherms were measured by using the desorptive method: The column filled with the adsorbent is loaded until maximum capacity of the adsorbent is reached and subsequently the gas phase concentration is reduced step by step. This method well-known and described by Kast (1988) and Yang (1987) is therefore not discussed in detail here. The use of this technique leads to the acquisition of desorption isotherms. Consequently an adsorptiondesorption-hysteresis needs to be considered if one wishes to transfer the resulting isotherms to adsorption processes. The system investigated in this study consists of the three compounds (dealuminated) “zeolite DAY” as adsorbent (DEGUSSA, 1994), ethanol as the adsorptive, and air as the carrier gas. The data obtained in the performed experiments can be classified into three different types of isotherms (Figure 1): In the low-temperature region (21 °C) the isotherms are of typical Langmuir type changing into an s-formed shape with rising temperature (60 °C). At high temperatures (82 °C) isotherms following Henry’s law can be found. In literature this type of isotherms is described for a lot of systems containing hydrophobic zeolites, e.g. Otten et al. (1992), who investigated combinations like zeolite DAY-toluol-air. Furthermore, it must be stated that * Author to whom correspondence should be addressed. Tel.: ++49/231-755-2541. Fax: ++49/231-755-2341. E-mail:
[email protected]. S0888-5885(97)00197-8 CCC: $14.00
Figure 1. Measured isotherms for the system zeolite DAYethanol-air.
the zeolite DAY-ethanol-air isotherm for 20 °C, measured but not yet published by this group, fits to our experimental results. Development of Equation In general, experimental data has to be correlated empirically to a special type of function. In the present case it is not possible to use a single type of isotherm known from literature to describe the obtained data. Consequently a new kind of equation based on an analogy to control engineering was developed. In detail a function called time-cycle-operation second order (PT-2) was introduced. In the following the development of this equation is briefly presented: 1. Formulation of the common transmission function of a time-cycle-operation second order in the Laplace range:
G(s) )
KR (1 + sc*)(1 + sbc*)
(1)
2. Determination of c* using the method of secant gradient. In the present case c* was found to be equal to 0.013 for the experimental data at 21 °C. 3. Determination of the parameters KR and b by correlating the measured data under the following assumptions: (a) c* is constant, and (b) KR and b only depend on temperature and not on concentration. 4. Regression of KR and b as functions of temperature. 5. Transformation of the equation into the time range. Following these instructions the following equation was obtained: © 1997 American Chemical Society
3994 Ind. Eng. Chem. Res., Vol. 36, No. 9, 1997
Figure 2. Calculated isotherms for the system zeolite DAYethanol-air (eqs 2-4).
X(c,T) ) KR(T) +
( )
KR(T) c exp + c* b(T) - 1 KR(T)b(T) c exp (2) 1 - b(T) c*b(T)
(
)
The temperature dependance of KR is expressed with an equation to the power of 5:
KR(T) [kg/m3]
) -3.8145 × 10
4 T5 -7 T + 1.3399 × 10 [K5] [K4]
-10
-1.6972 × 10-5
3
2
T T + 9.3541 × 10-4 2 3 [K ] [K ] -2 T + 0.38654 (3) 2.3497 × 10 [K]
Figure 3. Comparison between calculated and measured isotherms.
°C isotherm shows a systematic deviation: The experimental load is lower than the calculated one. The other measured data scatter around the calculated loads and are in sufficient accordance. Acknowledgment The authors acknowledge the support of DEGUSSA AG, Max-Buchner-Foundation, and DECHEMA e.V. Nomenclature b ) isotherm parameter c ) gas phase concentration (kg/m3) c* ) isotherm parameter (kg/m3) KR ) isotherm parameter (kg/kg) T ) temperature (°C) X ) load (kg/kg)
The parameter b follows a straight line equation:
b(T) ) 0.0889
T - 1.7632 [K]
Literature Cited
(4)
The developed equations are consistent on SI units; consequently temperature has to be converted into [°C] and concentration into [kg/m3] to calculate the load in [kg of ethanol/kg of zeolite]. In the temperature range between 21 °C and 120 °C and the concentration range between 0 and 100 g/m3 at a pressure of 10130 Pa the obtained equation fits well to the experimental data. As can be seen in Figure 2 the equation leads to a Langmuir type at lower temperatures, s-shaped forms at medium temperatures, and Henry isotherms in the high-temperature region. In comparison with the experimental data the obtained equation describes the isothermal equilibrium sufficiently for technical applications. Only the T ) 73
Bathen, D.; Schmidt-Traub, H. Untersuchungen zur Desorption durch Mikrowellenenergie. Chem. Ing. Tech. 1996, 68 (4), 434. DEGUSSA AG (Frankfurt/Main). Technical Informations Wessalith DAY, no. 4307.0, 1994. Kast, W. Adsorption aus der Gasphase; VCH: Weinheim, 1988. Otten, W.; Gail, E.; Frey, T. Einsatzmo¨glichkeiten hydrophober Zeolithe in der Adsorptionstechnik. Chem. Ing. Tech. 1992, 64 (10), 914. Yang, R. T. Gas Separation by Adsorption Processes; Butterworths Publishers: Boston, 1987.
Received for review March 7, 1997 Revised manuscript received May 12, 1997 Accepted May 21, 1997X IE970197C X Abstract published in Advance ACS Abstracts, July 1, 1997.
