Ind. Eng. Chem. Process Des. Dev. 1984, 2 3 , 711-716
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Correlation and Prediction of Adsorption Isotherm Data for Pure and Mixed Gases Bal K. Kaul Exxon Research and Engineering Company, Florham Park, New Jersey 07932
Adsorption isotherm data are required for capacity, selectivity, and breakthrough curve calculations of adsorptive separation processes. Adsorption thermodynamic models available in the literature were evaluated for their ability to correlate single-component isotherms and to predict multicomponent isotherms. Single-component isotherms can be successfully correlated with the modified “Langmuir-Freundlich” model and the “Vacancy Solution”model. Low coverage multicomponent data are successfully predicted from single-component isotherms by both the Ideal Adsorbed Solution model and the Vacancy Solution Model. However, only the Vacancy Solution model successfully provides high coverage multicomponent predlctions if single-component and binary isotherms are available. The experimental isotherm data of gases (e.g., CO, CH, CBHB)used to screen the models cover two different adsorbents, molecular sieve and activated carbon, and a wide range of conditions, 144-301 K and 0.2-4 MPa.
Introduction Adsorption isotherm data for pure components are relatively easy to measure, but measurements for multicomponent systems are more difficult and time consuming. Adsorption measurements for multicomponent systems are a function of the composition of each component, temperature, pressure, and the adsorbent. As the number of components increases, the number of measurements needed to define the adsorption equilibrium in a system increases rapidly. To minimize the experiments, adsorption equilibrium models are useful for correlation and prediction of the equilibrium data. This paper presents the evaluation of the adsorption thermodynamic models available in the literature for their ability to correlate pure component isotherms and to predict mixture data. The correlation of pure component isotherms is important because most of the multicomponent models rely on an accurate representation of pure component isotherms. Adsorption is gaining increased use for bulk separations as well as for removing impurities from process streams. Although not as versatile as distillation, it has greater selectivity for certain classes of compounds and can be much more energy efficient. Some commercially successful adsorption processes are the ENSORB process, developed by Exxon, for separating is0 from normal paraffins in the kerosene range, Pressure Swing Adsorption (PSA) of Union Carbide for the purification of hydrogen, and UOP’s PAREX process for recovering paraxylene from C8aromatics. In future, commercial applications of adsorption are expected to grow even more. Adsorption equilibrium data provide the capacity and the selectivity of an adsorbent needed for the simulation and the design of adsorption processes. Capacity (used to size adsorbent beds) is defined as the number of moles of a component adsorbed per gram of an adsorbent. Selectivity, similar to relative volatility in distillation, governs the feasibility of a separation by adsorption. Both capacity and selectivity depend strongly on the solid surface (adsorbent) used for a separation. Most adsorption processes are cyclic and require the desorption or regeneration of the adsorbent by temperature or pressure swings or by replacement by another species. Calculations for the time required (cycle time) for adsorption and desorption modes of the process also need adsorption equilibrium data in addition to the rate data. 0196-4305/84/1123-0711$01.50/0
There are a number of single-component and multicomponent isotherm models available in the literature. Among the frequently cited single component isotherms are Langmuir isotherm (1916), Freundlich isotherm (1922), vacancy solution model (Suwanyuen and Danner, 1980a), Ruthven’s statistical thermodynamic model (Ruthven et al., 1973), and others (Polanyi, 1932). These single component isotherm models have been also extended to mixtures, but in some cases the extension is strictly empirical. Myers and Prausnitz (1965) have proposed an ideal adsorbed solution model (IASM) for mixtures based on solution thermodynamic principles. Some of these models are evaluated in this paper for their correlative and predictive capabilities of equilibrium data. To establish the correlative and predictive capabilities of the thermodynamic models adsorption equilibrium data are needed. There is an abundance of pure component isotherm data available in the literature but the data for two-component and three-component mixture isotherms are relatively scarce. Some of the data sources (Costa et al., 1981; Dorfman and Danner, 1975; Reich et al., 1980) available in the literature for pure component, binary, and ternary isotherms on the same adsorbent, were used for the evaluation of the models and cover two different adsorbents, activated carbon and molecular sieve, wide range of temperature (144-301 K), pressure up to 3.8 MPa (550 psia), and number of gases such as methane, propane, carbon monoxide etc. In the next two sections, the results of evaluation of the models with the data available in the literature are discussed in two parts: pure-component isotherms, and mixture isotherm models. Pure Component Isotherms Adsorption isotherms express the equilibrium between the gas phase and the adsorbed phase. There are different types of isotherms, and Brunauer (Sing and Gregg, 1967) has classified them into five common types. Type-I isotherms result in favorable adsorption at relatively low pressures and are of interest for adsorptive separations. Type-I1 isotherms are similar to Type-I isotherms at low pressures, but a t high pressures result in multilayer coverage. The separation factor in the multilayer region approaches that for distillation, and adsorption becomes less attractive. Types 111, IV, and V are of less interest for the adsorption separations because these types are either rare or show hysteresis effects. 0 1984 American Chemical Society
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From an engineering standpoint, we want to know which models will adequately represent the pure component isotherm data of Type-I and what is the minimum number of parameters required for an acceptable fit to the experimental data. A number of isotherm models were considered (discussed below) for evaluation and only few were selected for detailed evaluation. Langmuir Isotherm (2 Parameters). The Langmuir isotherm (1916) is the most widely used and cited isotherm in the literature. This model assumes that there are a fmed number of definite localized adsorption sites, that each site can hold one adsorbate molecule, and that there is no interaction between adsorbed molecules on neighboring sites. The Langmuir isotherm model is as follows
,
140
d
P
51 2
-9
Experimental Data: Oanner & Wsnrel(1969) Langmuir Langmuir.Freundllch Vacancy Solution Model
-c
40
, 200
400
I
i
, BOO
BCQ
1000
Pressure, mmHg
Figure 1. Adsorption isotherm for carbon monoxide on molecular sieve (lox)at 144 K.
where n is the number of moles adsorbed per gram of adsorbent, P is the pressure, and nmand k are the parameters. Both these parameters have a physical significance; k is the slope of the isotherm when P is small and nmis the saturation limit of the isotherm for large values of the pressure. Modified Langmuir-Freundlich Isotherm (3 Parameters). The Freundlich (1922) isotherm is as follows n -=
n"
k(P)"
This isotherm model has three parameters nm,a, and k . A purely empirical combination of the Langmuir and the Freundlich isotherms has been used by some authors and the Langmuir-Freundlich isotherm is as follows n - k P (3) n" l + k P Equation 3 becomes the Langmuir isotherm when a = 1. Vacancy Solution Model (4 Parameters). Suwanayuen and Danner (1980a) have recently developed an alternative model based on treating the adsorbed phase as a mixture of the adsorbed species and the "vacancies". The gas phase which is in equilibrium with the adsorbed phase is also treated as a mixture of the vacancies and the adsorbed species. A "vacancy" is a vacuum entity occupying a space that can be filled by an adsorbate molecule. Then, the equilibrium between the phases is treated as if there is an osmotic equilibrium between the "vacancy" solutions having different composition. The isotherm equations thus derived is as follows:
where subscript 1 refers to the adsorbate (gas) and subscript v refers to the vacancy. nlmis the maximum number of moles adsorbed per gram of adsorbent, 0 is the fraction of the total sites covered with the adsorbate molecules, and P is the gas-phase pressure. The vacancy solution isotherm has four parameters: n*l, bl, Alv, and Avl. All these parameters can be obtained by nonlinear regression if isotherm data are available. Other Isotherm Models. Other isotherm models were considered but were not evaluated in detail because of some limitation of these models. The BET isotherm is known to be applicable only over a limited range of pressure, and mixture predictions by this isotherm are of
unacceptable accuracy (Danner and Wenzel, 1969). Ruthven's Statistical Thermodynamics correlation (Ruthven et al., 1973) is applicable for zeolites only and this limits its application. The virial isotherm equation truncated a t an appropriate point has been used successfully for representing pure gas isotherm data (Barrer, 1978). The predictions of virial isotherms can be improved by adding higher order terms. Including more terms in a virial equation make the equation empirical, thereby creating problems for extrapolation and in the prediction of mixture data. Several authors (Polanyi, 1932; Grant and Manes, 1966)have shown success with the potential theory for hydrocarbons on nonpolar adsorbents such as activated carbon. For polar adsorbents such as molecular sieves, it is reported to have only limited success (Myers, 1981) due to the lack of characterizing the interaction with the solid adsorbent by a suitable parameter. Recently, Myers (1981, 1982) modified the potential theory by taking into account the surface heterogeneity of an adsorbent, but again, it is reported to have limitations for adsorbents such as molecular sieve. Evaluation of the Pure Component Isotherm Models Successful multicomponent adsorption isotherm calculations rely on an accurate representation of the pure component isotherms. The importance of an accurate representation of pure component isotherms is similar to the accurate representation of a vapor pressure for relative volatility calculations in distillation, where error in the estimation of vapor pressure directly results in an error in relative volatility. Three isotherm models discussed above were evaluated to determine how well they represent the pure gas-solid adsorption equilibria. Parameters for the models evaluated in detail are regressed from the experimental isotherm data by using ZXSSQ (International Mathematical and Statistical Library) nonlinear computer regression routine. Figure 1 shows an excellent fit by the Langmuir-Freundlich and the vacancy solution models to experimental isotherm data (Danner and Wenzel, 1969) of carbon monoxide on molecular sieve (1OX) at 144 K and up to 0.14 MPa (20 psia). The Langmuir isotherm shows substantial deviations from the experimental data in comparison to the other models (12% average absolute deviation by the Langmuir model against 10% average absolute deviation) for most of the gases for which data were regressed. The inability of the Langmuir isotherm model to fit the isotherm data is based on some of the assumptions (e.g., no lateral interactions between the adsorbed molecules on the surface) used to derive the model and in reality these assumptions are not valid. Both the Langmuir-Freudlich and the vacancy solution models provide an acceptable overall fit to the isotherm data. Although the Langmuir-Freundlich isotherm provides an acceptable fit to the data, ita extension to mixtures is empirical and in some cases the model violates some of the constraints set by the thermodynamics. The vacancy solution model is based on the solution thermodynamics which makes ita extension to the mixtures straightforward. Prediction of the Mixture Adsorption Equilibrium Data Adsorptive separations involve mixtures and need mixture equilibrium data for the simulation and the design of the adsorbers. In principle, all pure component isotherm models discussed in previous section can be extended to the mixtures. The extension of the Langmuir isotherm to mixtures has met only limited success. Extension of the Langmuir isotherm to mixtures is thermodynamically in-
(5) Where P,O(n)is the equilibrium gas-phase pressure corresponding to the solution temperature and to the solution spreading pressure (n)for the adsorption of pure component i. Spreading pressure is not a measurable quantity but can be derived from macroscopically derived quantities. The isothermal Gibbs adsorption isotherm for pure adsorbate a t low pressures is as follows Adni = niRT d(ln Pi) (6) Integration of eq 6 a t constant temperature yields spreading pressure
where ni(Pi)is the number of moles adsorbed per gram of an adsorbent as a function of pressure (pure component adsorption isotherm). Therefore, for calculation of the spreading pressure, we need pure component isotherms. Equation 7 has been used with the vacancy solution model to obtain spreading pressure for each component in a mixture. The mixture predictions by this model are obtained by carrying out the mixing process a t a constant spreading pressure (ni). "1
=
A2
= Ti
(8)
Multicomponent predictions by IASM are obtained by solving eq 5-8 along with the equations for sum of mole fractions in both phases to be equal to one. IASM was programmed on a computer, and International Mathematical and Statistical Library (IMSL) routines ZXXSQ (nonlinear equation solver) and DCADRE (integration routine) were used to solve the equations. Vacancy Solution Model. Suwanayuen and Danner (1980b) have extended the vacancy solution isotherm to mixtures. The mixture vacancy solution model is general and can be used for any number of components. The
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Ind. Eng. Chem. Process Des. Dev., Vol. 23, No. 4, 1984 1.0
11
I
I
-
I
I
c
Exporlmenlal
-Predicted (VSM and IASM)
0.0
I
0.0
I
0.2
I
1
I 0.4
I
I
Costa et. 11. (1981)
-
Pradlcled
I
I
0.8
0.0
i 1.0
17'
1
0.0 0.0
I
1
I
I
I
0.4
0.2
Adrorbed.Phare Mole Fracllon of Malhane
I
1
I
0.0
i1
I
1.o
0.8
Adsorbed.Phas8 Mole Fractlon of Ethane
Figure 4. Comparison of predicted and experimental data for methane-ethylene on activated carbon (AC-40) at 20 O C and 75 mmHg.
Figure 5. Comparison of predicted and experimental data for ethane-propylene on activated carbon (AC-40)at 20 "C and 75 mmHg.
derivation of the model and calculational procedure is given in their paper, and here only the final equations will be briefly outlined. The equilibrium relation between the ideal gas phase and its nonideal adsorbed phase can be expressed by I
0
I !
The activity coefficients are given by Wilson's model c
'I
n
I
c
-
V I M wllh No Adsorbate. Adsorbate Inlerac.
----iIdeal
The summation for activity coefficient is to be carried out for all values of i including the vacancy
"0
n
0.2
Adaor. Sol. Model
0.8
0.8
0.4
1.0
AdrMb.d.Phmr0 Mole Fraction of O x y w I
Figure 6. Oxygen-carbon monoxide on molecular sieve (lox)at 144 K and 760 mmHg.
where P is the total pressure of the adsorption system, N," is the moles of gas mixture adsorbed per unit weight of adsorbent, Nia,- is the maximum moles of component i adsorbed per unit weight of adsorbent, and bi is the slope of isotherm a t infinite dilution. Aiv and AViare the interactions of component i with the vacancy and these parameters are obtained from the pure component isotherm data regression. hi are always to be taken to unity. Ai;s are the mixture interaction coefficients, and the value of 1 indicates that the interactions are not important. IMSL nonlinear equation solver (ZXSSQ)was used to After NmS is known, y, can be obsolve eq 9-12 for NmB. tained from eq 9. Low Coverage Mixture Data Can Be Predicted from Pure Component Data. Figure 4 shows an excellent agreement between the predicted and the experimental binary isotherm data of Costa et al. (1981) for methane-ethylene on activated carbon (AC-40) at 293 K. The predicted values are by VSM using the pure component data alone. The predictions by IASM are close to the predictions by VSM again using pure component data only. Table I shows excellent agreement between the predicted and the experimental ternary isotherm data for the methane-ethane-ethylene system on activated carbon
!zz
0
-
n
k :
1
V I M wllh No Adrorbate 1
c 0.2
0
Adsorbale intorac.
- - - - Ideal AdsM Sol. Model
-
0.2
0.0
Adsorbed-Phaw Mole Fraction of Nitrogen
1.0
Figure 7. 02-N2-C0 on molecular sieve (10x1 at 144 K and 760 mmHg.
(AC-40) at 293 K. It should be noted that this conclusion is quite contrary to the conclusion published by the authors (Costa et al., 1981) that the IASM cannot predict their mixture isotherms. Figure 5 and Table I1 provide another successful example of predicting low coverage mixture isotherms for the ethylene-ethane-propylene system by
Ind. Eng. Chem. Process Des. Dev., Vol. 23, No. 4, 1984 715 Table 1. Comparison of Experimental and Predicted Gas-Phase Mole Fractions for Methane-Ethane-Ethylene on Activated Carbon (AC-40)at 20 OC Mole Fraction of Methane predicteda exptl VSM IASM 0.95 0.92 0.90 0.79 0.68 0.71 0.63
exDtl 0.035 0.033 0.085 0.113 0.250 0.138 0.230
0.93 0.89 0.88 0.77 0.67 0.69 0.62
-
-
-
0.93 0.89 0.88 0.80 0.70 0.72 0.65
-
0.038 0.039 0.081 0.114 0.213 0.110 0.193
-
Fitted VSM with Adsorbate Adaorbete Intaractlon
Mole Fraction of Ethane predicteda VSM IASM 0.040 0.034 0.089 0.112 0.240 0.122 0.215
-
Urperlmental Danner & Wenzel (lOS9)
0.2
0.0
0.4
1.o
0.6
0.6
Adsorbed-Phase Mole Fractlon of Oxygen
Figure 8. Oxygen-carbon monoxide on molecular sieve (lox)at 144 K and 760 mmHg.
Predictions entirely based on pure component data. Mole fraction of ethylene = 1- y m e h e- y e h e .
Table 11. Comparison of Experimental and Predicted Mole Fractions for Ethylene-Ethane-Propylene on Activated Carbon (AC-40)at 20 "C Mole Fraction of Ethylene Dredicted" exptl VSM IASM 0.889 0.865 0.810 0.734 0.604 0.573 0.394 0.332
0.860 0.830 0.780 0.700 0.550 0.540 0.384 0.300
0.860 0.827 0.780 0.697
0.550 0.537 0.386 0.302
q 105
I
I
0.2
I
0.4
I
0.8
,
I
0.8
1 1.O
Mole Fractlon of Oxygen In the Adsorbed.Phase
Figure 9. Total volume adsorbed vs. mole fraction for oxygencarbon monoxide at 144 K and 760 mmHg.
H
L
i c
Mole Fraction of Propylene predictedn exptl VSM IASM 0.001 0.011 0.014 0.021 0.009 0.039 0.022 0.012
0.001 0.011 0.012 0.020 0.100 0.038 0.022 0.017
0.001 0.013 0.013 0.023 0.100 0.038 0.026 0.019
t
c n
t >"
Dotiman & Damar
Adsorbed-Phase Mole Fractlon of Nltrogen
aPredictions entirely based on pure component data. Mole fraction of ethane = 1 - yethylene - ypmwleneene; surface coverage less than 25%.
Figure 10. 02-N2-C0 mixture on molecular sieve (lox)at 144 K and 760 mmHg.
using VSM and IASM and pure component isotherms data. Therefore, VSM and IASM can predict low coverage binary and ternary isotherm data by using pure component isotherm data alone. High Coverage Mixture Data Predictions Also Need Binary Data. Figures 6 and 7 show poor predictions for the oxygen-carbon monoxide and the nitrogenoxygen-carbon monoxide systems on molecular sieve 1OX adsorbent a t 144 K (Danner and Wenzel, 1969; Dorfman and Danner, 1975). The predicted values are those for VSM and IASM and using pure component isotherm data only. The reason for the predicted values to show substantial deviations with the experimental data is because the mixture isotherm data for this system are for high
surface coverage. For such high coverages, it appears that the binary interactions between the adsorbate molecules cannot be ignored, and as a result, the mixture predictions from pure component data alone are not successful. However, it binary isotherm data are used, then ternary isotherms can be successfully predicted. VSM can incorporate these binary interactions (&is) in the model, but for IASM there is no framework available to incorporate such effects. Therefore use of the IASM for high coverage data needs further development. Figures 8 and 9 show an excellent fit to the binary isotherm for the oxygen-carbon monoxide system after adjusting for the adsorbate-adsorbate interactions. For the pure component isotherms and adsorbateadsorbate interactions obtained from the
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Ind. Eng. Chem. Process Des. Dev., Vol. 23, No. 4, 1984
binary isotherms, successful ternary predictions are obtained as shown in Figure 10. Figure 10 provides a convenient way of representing the ternary data. The table comparing the predictions with the experimental data is deposited as Supplementary Material. (See paragraph at end of article regarding this material.) The vacancy solution model also predicts the adsorption azeotrope qualitatively for an ethylene-isobutane mixture on molecular sieve 1OX using only the pure component isotherms as reported by Hyan and Danner (1980). However, good quantitative agreement is obtained only by fitting the binary mixture data. Loughlin et al. (1976) have reported an adsorption azeotrope for ethylene-cyclopropane on molecular sieve @A). Besides these mixtures the number of other systems having an azeotropic behavior is still limited. It will be interesting to establish the predictive capabilities of the vacancy solution model for such mixtures as more data become available. Such prediction will be particularly of interest for ternary mixtures having a t least one binary adsorption azeotrope. The ideal adsorbed solution model will not hold for such systems because this model cannot predict the azeotropes. Therefore, for low coverages both IASM and VSM provide reasonable multicomponent predictions from the pure component isotherms alone. VSM is successful for predicting ternary data for high surface coverages using the pure component and the binary data. Conclusions The prediction of mixture adsorption equilibrium data relies strongly on the representation of single-component isotherms, and a minimum of three parameters are needed to represent the data. The Langmuir-Freundlich and the vacancy solution models provide adequate representation of the Type-I isotherms. Both the ideal adsorbed solution and the vacancy solution models can successfully predict low coverage multicomponent data from pure component data alone. The vacancy solution model is also successful in predicting high coverage multicomponent data if pure and binary data are used. The ideal adsorbed solution model needs further developments for its use in successfully predicting high surface coverage data. It should be noted that the evaluations of the models presented here are based on the data for nonpolar or slightly polar gas mixtures due to the lack of mixture data for strongly polar systems. Acknowledgment The author is grateful to Exxon Research and Engineering Company for permission to publish this work. The author is also grateful to N. H. Sweed and C. Tsonopoulos of Exxon Research and Engineering Company for helpful discussions. Nomenclature 6,= partial molar surface area of i A = surface area of adsorbent b, = Henry's law constant of i N,B = number of moles of component i in adsorbed phase per unit mass of adsorbent N,"," = maximum number of moles of i in adsorbed phase
NmB = total number of moles of mixture in adsorbed phase Nm8rm = maximum total number of moles of mixture in adsorbed phase Pi0 = pressure of pure gas in equilibrium with its adsorbed phase P = total pressure of mixture in equilibrium with its adsorbed phase T = adsolute temperature xi = mole fraction of i in the adsorbed phase yi = mole fraction of i in the vapor phase Greek Letters y? = activity coefficient of i
in adsorbed-phase vacancy solution % = fractional coverage (N?/Np") hi,!Aji = Wilson's parameters for interaction between molecule I and molecule j CL = chemical potential P = spreading pressure Superscripts s = surface phase value
= value at maximum adsorption limit
Subscripts i , j , k = components i, j , k m = mixture n = total number of components in a mixture v = vacancy
Literature Cited Barrer, R. M. "Zeolites and Clay Minerals as Sorbents and Molecular Slews", 1st ed.;Academic Press: New York, 1978; p 31. Costa, E.; Sotelo, J. L.; Calleja, 0.;Marron, C. AIChE J. 1981, 2 7 , 5. Danner, R. P.; Wenzel, L. A. AICh€ J. 1969, 15, 515. Dorfman. L. R.; Danner, R. P. AIChE Syny. Ser. 1975, 7 7 , 30. Freundllch, H. "Colloid and Capillary Chemistry", 3rd ed.; Translated from German by Hatfield, H. S.;E. P. Dutton and Company: New York, 1922; p 111. Grant, R. J., Manes, M. Ind. Eng. Chem. Fundam. 1966, 5 , 490. Hyun, S. H.; Danner, R. P. J. Cham. Eng. Data 1982, 2 7 , 196. Langmuir, 1. J. Am. Chem. SOC. 1916, 38, 2221. Loughiin, K. F.; Holborow, K. A.; Ruthven, D. M. AIChESym. Ser. 1976, 7 1 , 24. Myers, A. L.; Prausnltz, J. M. A I C E J . 1965, 7 1 , 1216. Myers, A. L. University of Pennsylvania, Philadelphia, PA, personal communication, 1981. Myers, A. L. National Meeting of American Institute of Chemical Engineers, Orlando, FL, Feb 1982. Polanyi, M. Trans. FaradaySoc. 1832, 28, 316. Reich, R.; Ziegler, W.T.; Rogers, K. A. Ind. €ng. Chem. Process Des. D e v . 1980. 19. 336. Ruthven; D. M.; Loughlln, K. F.; Holborow, K. A. Chem. Eng. Sci. 1973, 28, 7016. Sing, K. S.W.; Gregg, S.J. "Adsorption, Surface Area and Porosity", Academic Press: New York, 1967; p 7. Suwanayuen, S.;Danner, R. P. AIChE J . 198Oa, 26, 68. Suwanayuen, S.;Danner, R. P. AICh€ J. 1980b. 26, 76. Van Ness. H. C. Ind. Eng. Chem. Fundam. 1969, 8 , 464.
Receiued for reuiew January 13, 1983 Revised manuscript received December 7 , 1983 Accepted January 17, 1984
Presented at the AIChE Annual Meeting, Los Angeles, CA, Nov 1982. Supplementary Material Available: Tabular comparison of predicted and experimental data for oxygen-nitrogen-carbon monoxide on molecular sieve (lox)at 144 K and 101 kPa (2 pages). Ordering information is given on any current masthead page.
