Ind. E n g . Chem. Res. 1991,30, 1032-1039
1032
Ruthven, D.M. Principles of Adsorption and Adsorption Processes. Wiley-Interscience: New York, 1984. Shendalman, L. E.;Mitchell, J. E. A Study of Heatless Adsorption in the Model System C02in He. I. AZChE Symp. Ser. 1972,27, 1449. Skarstrom, C. W. Use of Adsorption Phenomena in Automated Plant-Type Gas Analyzers. Ann. N.Y. Acad. Sci. 1959, 72, 751. Suzuki, M. Adsorption Engineering; Elsevier: Amsterdam, 1990. Tondeur, D.; Wankat, P. C. Gas Purification by Pressure Swing Adsorption. Sep. Purif. Methods 1985, 14, 157. Turk, A. Adsorption. In Air Pollution, 3rd ed.; Stern, A. C., Ed.; Academic Press: New York, 1977;Vol. IV. Wankat, P. C. Large-Scale Adsorption and Chromatography; CRC Press: Boca Raton, FL, 1986;Vol. I and 11.
Weaver, K.; Hamrin, C. E., Jr. Separation of Hydrogen Isotopes by Heatless Adsorption. Chem. Eng. Sci. 1974, 29, 1873. White, D.H. Practical Aspects of Air Purification by Pressure Swing Adsorption. AZChE Symp. Ser. 1988,84, 129. Wilhelm, R. H.; Rice, A. W.; Bendelius, A. R. Parametric Pumping: A Dynamic Principle for Separating Fluid Mixtures. Ind. Eng. Chem. Fundam. 1966,5, 141. Yang,R. T. Gas Separation by Adsorption Processes; Butterworth Boston. 1987.
Received for review June 15, 1990 Revised manuscript received September 10, 1990 Accepted September 25, 1990
Role of Adsorbent Heterogeneity on Mixed Gas Adsorption Shivaji Sircar Air Products and Chemicals, Inc., 7201 Hamilton Boulevard, Allentown, Pennsylvania 18195
A family of simple, analytic, and thermodynamically consistent correlations is developed to describe adsorption of pure and multicomponent gases on heterogeneous adsorbents. The model is based on the assumptions that the adsorbent can be described by the conventional “patchwise homogeneous” framework of heterogeneity with Langmuir adsorption model giving the local equilibria on a patch and that a distribution of Henry’s law constants depict the energetic heterogeneity. A simple site energy matching formula based on coalescence of dimensionless cumulative distribution functions of the Henry’s law constants of different gases is used to connect the pure and mixed gas adsorption. The model is tested by using published experimental data for pure and binary gas adsorption. A parametric study of the model parameters is carried out to demonstrate the very significant role of adsorbent heterogeneity on mixed gas adsorption, including adsorption azeotropy. Introduction Knowledge of multicomponent gas adsorption equilibria is critical for theoretical design of gas separation processes using pressure or thermal swing adsorption technology (Sircar, 1989). The information is needed for the following reasons: (i) It is needed to establish the thermodynamic limits of adsorption of each component of a gas mixture present within an adsorber at the prevailing local conditions of pressure (P), temperature (27, and gas-phase mole fraction ( y i ) of component i. (ii) It is also needed to set up the driving forces for ad(de)sorptive mass transfer of component i from the gas to the adsorbed phase or vice versa at the local conditions within the adsorber. (iii) Finally, it is needed to calculate the isosteric heat of adsorption of component i ( q i ) at the local conditions inside the adsorber which is required to account for local heat generation (consumption) during the ad(de)sorption process. The conditions (P, T, and y i as functions of time and position) within an adsorber, however, may vary substantially during the operation of a cyclic pressure or thermal swing adsorption process. For example the gas-phase composition of a component may change from trace to essentially pure gas, the temperature may change by several tens of degrees, and the pressure can swing between low vacuum to super atmospheric level during a single cycle of operation in a modern pressure swing adsorption process for bulk gas separation (Sircar and Kratz, 1988). Obviously, measurement of multicomponent gas adsorption equilibria over such ranges of conditions is practically impossible. The designer needs mathematical correlations that can be used to generate multicomponent gas adsorption equilibria at the conditions of interest from a
limited source of measured adsorption equilibrium data. The preferred correlations, however, should satisfy the following requirements: (a) They should describe single-component and multicomponent adsorption equilibria over the entire conditions of design interest with reasonable accuracy. (b) They should provide relatively simple (few parameters) and analytical expressions relating the equilibrium amount adsorbed of each component i (ni) as explicit functions of P, T , and yi for both pure and mixed gas systems. (c) They should allow calculation of multicomponent adsorption equilibria using information from pure component adsorption equilibria. (d) Lastly, they must obey all physical constraints and consistency tests set by the physics and thermodynamics of adsorption. The validity of requirement a is most difficult to judge in the absence of representative experimental data covering the conditions of interest. Extensive testing of the correlation may be necessary before it is acceptable for use. Requirements b and c are very desirable to reduce the formidable computation time needed for repeated solution of simultaneous design equations describing the mass, momentum, and heat balances for the steps of the separation processes in order to reach a cyclic steady state operation. Requirement b also simplifies the calculation of isosteric heats of adsorption for the multicomponent systems because they need the knowledge of partial derivatives of ni with respect to P, T, and yi (Sircar, 1985). Requirement d is an absolute must for data interpolation or extrapolation to extreme conditions. A key physical constraint imposed by statistical thermodynamics of adsorption (Hill, 1962) is the existance of Henry’s law region in the adsorption isotherms of both pure gas (np Kip)
0888-588519112630-1032$02.50/0 0 1991 American Chemical Society
-
-
Ind. Eng. Chem. Res., Vol. 30, No. 5, 1991 1033
-
and gas mixtures (ni KiPyi) a t the limit of P 0 at constant T.Ki is the Henry’s law constant for adsorption of pure component i. The superscript o represents pure gas adsorption. Physics also dictates that the isosteric heat of adsorption of a pure gas i (qp) at the limit of P 0 be finite. The key thermodynamic consistency test to be satisfied is the binary isobaric-isothermal integral test which relates binary constant pressure adsorption equilibria with the adsorption isotherms of the pure gases (Sircar, 1985). The adsorption equilibria of a single gas on an adsorbent is considered to be the minimum source of information needed to define the interactions between the gas-solid pair. Numerous efforts have been made in the past 30 years to develop techniques for prediction of multicomponent adsorption equilibria from the pure gas adsorption equilibria of the components. The most notable works in this area are the ideal adsorbed solution theory (IAST), vacancy solution model, adsorption potential model, simplified statistical thermodynamic model, Dubinin-Raduskevich mixed gas model, etc. Several publications (Sircar and Myers, 1973; Ruthven, 1984; Valenzuela and Myers, 1984; Yang, 1987) provide excellent reviews of these theories. Some of these models satisfy requirements b-d and some do not. The predictions of multicomponent equilibria by these models are very good for some systems, but they are unacceptable for others (Valenzuela and Myers, 1984). Consequently, the state of the art does not allow a priori selection of one of the above methods over the others without extensively testing the model using experimental data for the system of interest. This obviously defeats the purpose. Clearly, much more work is necessary in this area to alleviate a very practical problem. The situation is further impeded by the lack of a sufficient quantity of published multicomponent gas mixture adsorption data over a large range of conditions (Valenzuela and Myers, 1989). In particular, mixture data for ternary systems and beyond are rare. This prevents serious testing of these adsorption models which has been initiated only recently (Valenzuela and Myers, 1984).
q, (Kcal/Mole) COz ON Na-Mordenite (b) CH4 ON BPL CARBON (c) CO2 ON Nax ZEOLITE (d) CsHs ON SILICA GEL
-
Nature of the Problem The problem at hand is by no means simple. The adsorbents of practical use such as activated carbons, aluminas, silica gels, and zeolites are very heterogeneous microporous solids. The first three types of adsorbents contain intricate networks of interconnected micro- and mesopores of various shapes and sizes that give rise to a nonuniform distribution of gas-solid and gas-gas interaction fields within the adsorbent mass. Heterogeneity, in these adsorbents, is also caused by differences in the chemical nature of the surfaces at different parts of the adsorbent mass. The pore structures of the zeolites may be ideally well-defined and uniform, but energetic heterogeneity for adsorption is introduced by lattice defects, presence of hydrated and nonhydrated ion species of one or more kinds at different locations within the framework, presence of trace moisture within the pore structure, nonuniform hydrolysis of zeolite framework during regeneration, existence of distributed Si/Al ordering of the framework, etc. The most direct proof of adsorbent heterogeneity is manifested by the decrease of isosteric heat of adsorption with increasing amount adsorbed for pure gas adsorption. Figure 1 shows some examples of this phenomenon that were estimated from the data reported in various publications (Barrer and Coughlan, 1968; Maslan and Abereth, 1972; Reich et al., 1980). The ratios of isosteric heat of
11.4
(a)
0.2
4.3
14.0 11.7
4 I
I
I
1
I
0
2
3
I
1
4
5
no(mmoles/g 4)
Figure 1. Isosteric heat of adsorption as a function of surface coverage.
adsorption at a finite adsorbate loading (no)to that at the limit of zero coverage are plotted as functions of no. The highest energy adsorption sites are predominantly filled at the lowest gas pressure followed by progressive filling of the lower energy sites of the heterogeneous adsorbent as the gas pressure is increased. An energetically homogeneous adsorbent would not exhibit any variation of isosteric heat of adsorption with coverage (plot a in Figure 1). A constant isosteric heat of adsorption, however, does not guarantee that the adsorbent is homogeneous (Golden and Sircar, 1991). It is apparent that realistic estimation of single-component or multicomponent gas-solid or gas-gas interactions within such distributed energy fields inside the adsorbent pores (which remains unknown) will not be easy if not impossible. Even the current experimental methods to characterize the pore structures of real heterogeneous microporous solids are very crude and full of uncertainty. Despite these complexities, some progress has been made to calculate gas-solid and gas-gas interactions for adsorption of simple pure gases within well-defined zeolitic frameworks using Monte Carlo simulations (Monson and Finn, 1988). The method is also being extended to calculate binary gas-solid interactions (Razmus and Hall, 1991). Although these methods provide interesting insights of gas-solid interactions within zeolite pores, they consume enormous computational time and are too far removed to be practical or predictive. An engineering solution of the problem will be to assume that some distributed macroscopic thermodynamic property of adsorption can be used to describe the unknown microscopic energetic heterogeneity of the adsorbent. The measured overall adsorption equilibria can then be analyzed in terms of the assumed distribution of the macroscopic property. Although this approach is oversimplistic, it is a step in the right direction because it explicitly introduces model parameters to describe the effect of adsorbent heterogeneity. This concept has been extensively used in the past to develop analytical correlations describing single gas adsorption equilibria on heterogeneous solids (Sircar and Myers, 1988). It is found that the choice of the thermodynamic property and the detailed structure of its distribution are not very critical in providing an acceptable correlation (Sircar and Myers, 1984). That is very encouraging. Recently, attempts have been made to incorporate this concept into the framework of ideal adsorbed solution theory in order to calculate multicomponent adsorption equilibria from single gas equilibria on heterogeneous adsorbents (Valenzuela et al., 1988; Moon and Tien, 1988). The result has been promising but these
1034 Ind. Eng. Chem. Res., Vol. 30, No. 5, 1991
methods require time-consuming, numerical and iterative calculations. Thus requirement b is not satisfied. Several empirical correlations such as the Toth model (Valenzuela and Myers, 1989), loading ratio correlation (Yon and Turnock, 1971), and others (Yang, 1987) are also available which provide analytical relationships between ni and P, T, and yi for adsorption on heterogeneous solids. These models, however, do not generally satisfy requirement d. The purpose of this paper is to develop simple, analytical, and thermodynamically consistent correlations between single-component and multicomponent gas adsorption equilibria on heterogeneous solids using the engineering approach outlined above. The work will be limited to analysis of multicomponent adsorption systems where the adsorbates have equal sizes (same saturation adsorption capacities). Adsorption of Pure Gas The patchwise homogeneous model (Sircar and Myers, 1988) for heterogeneous adsorbents is used here. It relates the overall fractional adsorption capacity of a pure gas i [e:(P,T)] on a heterogeneous adsorbent with the local fractional adsorption capacity of that component [@(P,T,E)] on a homogeneous patch of gas-solid interaction energy E by
0p(P,T)= lEMOp(P,T,E)h(E) dE Em
bi = bf exp[qf/RT]
(s)
-bi
at P - 0
(3) (4)
T
bi is the Langmuirian gas-solid interaction parameter for adsorption of pure gas i. It is related to the site isosteric heat of adsorption (9;) for the gas by (3). b; is the limiting value of bi at the limit of T a. bi is also the Henry's law constant (slope of isotherm in q-P domain at P 0) for the homogeneous site as shown by (4). It is further assumed that the adsorbent heterogeneity can be described by a uniform distribution of Langmuirian homogeneous patches with different values of Henry's law constants (bi). Thus the parameter E of (1)is replaced by bi with X(bi) = constant. X(bi) is the normalized probability density of patches with Henry's law constant of bi.
-
~i
-
(6)
= ( b i -~ ba)/2(3)1/2
(7)
A new parameter (J.J called the degree of heterogeneity is defined by $i
= 31/2ui/pi
(8)
Thus, according to this model, #i = 0 represents a homogeneous adsorbent while #i = 1represents the maximum degree of heterogeneity for adsorption of pure gas i. The boundary values of the parameter bi can be expressed in terms of pi and $i as biL
= pi(1 - $i);
biH
+ $i)
=
.
r
[z]
=pi;
P-0
T
d In pi = - - 4P
RP
dT
pip
0%= 1 pip
+
(15)
2zp
Equation 10 describes the equilibrium adsorption of a pure gas i on a heterogeneous adsorbent at P and T. It has three parameters, viz., m,pi, and $c Equation 11shows that pi, the mean of the bi distribution, is also the Henry's law constant for the pure gas heterogeneous isotherm. The temperature dependence of pi is given by (12). @' is the isosteric heat of adsorption of pure gas i on the heterogeneous adsorbent at the limit of P 0. OrH is the fractional adsorption capacity of pure gas i at P and T when J.i 0. In other words, @H represents the pure gas adsorption equilibria of component i on a homogeneous adsorbent having a Langmuirian gas-solid interaction parameter of pi. It can be shown that 0: = when $i
-
-
0
(2:
-
-
0).
Adsorption of Multicomponent Gas The above described procedure for estimating pure gas adsorption on a heterogeneous adsorbent can be extended to obtain the following integral equation for adsorption of a multicomponent gas mixture of composition yi: . I
(5)
bL and biHare, respectively, the lowest and highest values of bi for adsorption of pure gas i on the heterogeneous adsorbent. The mean ( p i ) and the dispersion bution are given by
(ui) of
the bi distri-
(9)
Equations 1 , 2 , and 5-9 can be simultaneously solved to obtain the overall fractional adsorption capacity of the pure gas on the heterogeneous adsorbent as
(1)
h(E) represents the normalized [ S 2 X ( E )dE = 11 probability density of the patches with interaction energy E within the heterogeneous adsorbent. E , and EMare, respectively, the lowest and the highest values of E on the adsorbent. The fractional adsorption capacities are defined by the ratios of actual specific amount adsorbed to the specific saturation capacities (m). It is assumed that the local adsorption equilibria of the gas on a homogeneous patch is given by the Langmuir model:
(biH + biL)/2
pi =
j = 1, 2,
..., i, ... (16)
Bi(P,T,yi) represents the fractional adsorption capacity of component i at P,T,and yi on the heterogeneous adsorbent. 0, is the corresponding fractional adsorption capacity of component i on a Langmuirian homogeneous patch characterized by the pure gm-solid interaction parameters of the components (bj) of the mixture:
0 (i = 1, 2, ...). In other words, eiH represents the component i adsorption equilibria from a gas mixture of composition y i at P and T on a homogeneous adsorbent having Langmuirian gas-solid interaction parameters of pi for pure component i. It can be shown that €Ii = eiH when I+$ (i = 1, 2, ...) 0 (z 0). It should be noted that the function f ( z ) in (24) is identical with the function f(zp) given by (15). The total fractional adsorption capacity of the multicomponent gas mixture 0 (=Cei)on the heterogeneous adsorbent is given by
qi bj = b; exp[qf/RT]
j = 1, 2, ...
(18)
The summation in (17) is over all components of the gas mixture including component i. ,Equation 18 gives the temperature dependence of bj. q j is the isosteric heat of adsorption of pure component j on the homogeneous site described by the matrix b , and b; is the limiting value of bj at T m. Equation 17 can be substituted into (16) and integrated to obtain eiif one knew how the bj values for different pure gases were related on a Langmuirian site. In other words, a relationship between bj (i # j ) and bi is needed for each homogeneous site of the heterogeneous adsorbent. This requirement is called the energetic site matching between the different components of the gas mixture. Since there is no a priori knowledge of the relationship between bi and b, on a site, it calls for the third assumption in the model. The cumulative distribution of the gas-solid interaction parameter bi for component i on the heterogeneous adsorbent is given by
-
Ind. Eng. Chem. Res., Vol. 30, No. 5, 1991 1035
- -
-+
vi)
fi(bi)represents the fraction of patches on the heterogeneous adsorbent having gas-solid interaction parameters between biL and bi for pure gas i. Equation 19 shows that fi(bi)is a linear function of bi. Its values are equal to zero and unity, respectively, for bi values of b L and bN. It is assumed that each component of the gas mixture is adsorbed on every homogeneous patch of the heterogeneous adsorbent and that one common patch exhibits the lowest bj values for each gas and another common patch exhibits the highest bj values for each gas. Thus, f i = f j = 0 represents the patch characterized by blL 0’ = 1, 2, ...) values and f i = f . = 1 represents the patch characterized by blH 0’ = 1,2, values. It is then generally assumed that f i = f j represents a patch characterized by bj 0’ = 1, 2, ...) values. I t follows that
. .I
bi - biL --bj - bjL -biH - biL
bjH - b]L
i, j = 1, 2, ...
(20)
Equation 20 provides the desired energetic site matching relationship between the different components of the gas mixture. This method of energetic site matching was previously used in the development of heterogeneous ideal adsorbed solution theory (Valenzuela et al., 1988). Equations 5,9, 16, 17, and 20 can be combined to obtain the mixed gas adsorption equilibria as
Equation 21 describes the fractional adsorption capacity of component i from a multicomponent gas mixture of composition yi on a heterogeneous adsorbent at P and T. eiHis the fractional adsorption capacity of component i from a gas mixture of same composition at P and T when
(26) Equation 25 is identical in form with the pure gas adsorption equilibria on the heterogeneous adsorbent 10. It can be shown from (21) and (22) that ei = piPyi as P 0, which satisfies requirement d. Furthermore, (10) and (21) obey the integral isobaric-isothermal thermodynamic consistency test. Thus the models for pure component and multicomponent gas adsorption equilibria on heterogeneous adsorbents presented in this work satisfy the requirements b-d demanded by practical design engineers. = C0iH
-
Selectivity Distribution The energetic site matching process for the heterogeneous adsorbent also defines the distribution of the site selectivities of adsorption between any two components i and j of the gas mixture on the homogeneous patches. The selectivity of adsorption (Si,) of component i over component j from a gas mixture of composition yi at P and T on a Langmuirian patch is given by the ratio bi/ bj for that patch. Thus, the values of Si, for the sites characterized by blL and blM of the heterogeneous adsorbent are, respectively, Sa[(l- $ i ) / ( l - IC;)] and Sa[(1 + $i)/(l + $,)I. Sg ( = w ~ / F ~is) the selectivity of adsorption for component i over j on a homogeneous Langmuirian patch with pure gas Henry’s law constants of pi (i = 1, 2, ...) for gas i. According to the present model, (20) can be manipulated to provide the relationship between Si, and bi. The normalized probability density function [X(Sij)]for the distribution of Si, on the heterogeneous adsorbent can then be obtained from (5) and (20) as X(S,)
=
SYWi - *jI r
with the mean of the distribution
( p a ) given
(27)
by
Equation 27 shows that the assumption of uniform distribution of the Langmuir interaction parameter for describing adsorbent heterogeneity yields a local site selectivity distribution with an inverse quadratic dependence of Sij when the relationship of (20) is used for energetic site matching. These assumptions generate the simple analytic correlations given by (10) and (21) for pure and mixed gas adsorption equilibria, respectively. Obviously other choices for these properties can be made to generate a family of correlations for describing adsorption equilibria for pure and mixed gases on heterogeneous adsorbents. For the special case, when the adsorbent is homogeneous for component j ($. = 0) but heterogeneous for component i ($i = finite), h ( d j )becomes a constant [X(Sij) = (1/2)-
1036 Ind. Eng. Chem. Res., Vol. 30, No. 5, 1991
Sg+i]. In that case, the local site selectivity is also given by a uniform distribution. Furthermore, when components i and j have the same degree of hetero eneity ($i = $,), h(Sij)becomes equal to zero with & = Sij. If In other words, all sites of the heterogeneous adsorbent have the same selectivity although the parameter bi varies from site to site. The adsorbent is homogeneous when J/i = f+ = 0. X(Sij) in this case is a Dirac 6 function at Sij = Sij.
Adsorption Azeotropy The overall selectivity of adsorption for component i over component j [Sb = (Oi/ej)(.yj/yi)] on the heterogeneous adsorbent at gas composition of yi and P and T may be written from (21)-(24) as
-
The limiting value of S> at P 0 for all values of yi is Sa, which is required by thermodynamics (re:triction c). Equation 29 describes the variation in as a fuflction of yi at constant P and T or the variation in Sij as a function of P at constant T and yi. For a binary system, it can be shown that Si2goes through a value of unity at constant P and T when
z?
p:= pi($i
- 2);
IAST also requires that CPyi/P; = 1 and PTOT, which translate to
(35)
l/e = CPyi/
1E -- *ieiH z?
and
in the language of the present model. is the fractional amount adsorbed of pure gas i at PT and T. The overall selectivity of adsorption for component i over component j on the heterogeneous adsorbent by the IAST model [SUIIAST is equal to P;/P:. Thus
qij
(30) This occurs at a y1 value of yt given by z*Kl + PcLz)/PPzJ - $2 y ; = (sn$l - $2) - Z*(S, - 1)
(31)
where z* is given by
This means that the heterogeneous adsorbent will exhibit an adsorption azeotropy at y; given by (31) and (32), provided the value of y 1 falls between zero and unity. The necessary but not sufficient criteria for this to happen is given by (30),which means that the patch on the adsorbent characterized by blz is more selective for component 2 than component 1,even though the mean adsorption selectivity on the adsorbent is in favor of component 1. Comparison with Ideal Adsorbed Solution Theory The surface potential (4:) for adsorption of pure gas i is given by (Sircar, 1985)
Equation 10 can be substituted into (33) to calculate 4: for adsorption of pure component i on the heterogeneous adsorbent as
The ideal adsorbed solution theory (IAST) requires that ~$7 for each component of the gas mixture be equal (Myers and Prausnitz, 1965). Thus, (34) provides one relationship values of each component of the between zp (=$@YH) mixture. zp is related to the pure gas pressure at which the surface potential of that component is 4: by
(e)
For a given P, T , and y i , zp can be obtained for each component by simultaneously solving (34) and (36). The total fractional amount adsorbed (e)and the selectivity [ S i j ] m ~ can then be calculated by using (37) and (38) and the pure gas adsorption parameters. Consequently, the fractional amount adsorbed of each component (ei)on the heterogeneous adsorbent can be calculated. Thus, the IAST can be used to predict multicomponent gas adsorption equilibria on a heterogeneous adsorbent which is characterized by pure gas adsorption equilibria given by (10). I t can be shown that the IAST prediction is identical with those given by the mixed gas equilibria of (21) only Otherwise, IAST overpredicts the fractional when qi = amount adsorbed of more selectively adsorbed component and underpredicts that for the less strongly adsorbed component of the gas mixture. Comparison with Experiment The application of the multicomponent adsorption equilibria model developed in this work is limited to the case where the saturation adsorption capacities of all components are equal (constant m). The data reported by Reich (Reich et al., 1980) for adsorption of pure ethane and ethylene and their mixtures on BPL carbon and that reported by Danner and Wenzel (Danner and Wenzel, 1969) for adsorption of pure carbon monoxide and oxygen and their mixtures on 5A zeolite approximately satisfy that requirement. Equation 10 was used to describe the pure component adsorption equilibria for these systems. Figure 2 shows the best fit of the pure ethane and ethylene adsorption isotherms at 301.4 K on BPL carbon, and Figure 3 shows the best fit of the pure carbon monoxide and oxygen adsorption isotherms at 144.2 K on 5A zeolite by the model (solid lines). The experimental data (circles)for all systems cover three decades of pressure range. It can be seen that the heterogeneous model describes the data fairly well (within k5.070) over the entire pressure range. Table I gives the pure component model parameters. Ethane (component 1) is more strongly adsorbed over ethylene (com onent 2) on the carbon. The homogeneous selectivity (SI2) for ethane over ethylene is only 1.65. Both gases are very weakly adsorbed (low F~ values). The degree of heterogeneity of the carbon for ethane adsorption is very
2
Ind. Eng. Chem. Res., Vol. 30, No. 5, 1991 1037 1.0 (REICH, 1974) -MODEL
a
0.10
+=
“ 3- / /
m = 5.30 mmoleslg p. = 0.85 (atm)” ql = 0.0
0.10
EXPERIMENT (DANNER & WENZEL, 1969) -MODEL 0
-
-
0.1
10.0 P(ATM0SPHERES)
1.0
.m = 5.14 mmoleslg p. = 15.0 (atm).‘ UI = u.u
p. = 600 (atm)”
CL = 1.40 (atm)-’
0.01
I
I
100.0
I 1 1 1 1 1 1
I
I 1 1 1 1 1 1 1
I
I
I I 1111’
Figure 2. Isotherms for adsorption of pure ethane and ethylene on BPL carbon at 301.4 K. Table I. Pure Gas Adsorption Model Parameters m,
gas ethane ethylene carbon monoxide oxygen
adsorbent temp, K BPL carbon 301.4 BPL carbon 301.4 144.2 5A zeolite 5A zeolite
144.2
p,
5.14
1,
.
(A) 0.9
I C 4
( 8 ) 0.9 (C) 0.9 (D) 0.1
m
0.8
:
0
1
1
0.2
0.4
0.6
I
1
0.8
1.0
Y1-
Figure 4. Role of adsorbent heterogeneity on binary amounta adsorbed at constant pressure (P= 20 atm, p1 = 1.0, p2 = 0.2 atm-’).
amounts adsorbed of both components are within f10.0% even though the two systems significantly differ in their adsorption characteristics. This quality of prediction is as good as, if not better than, that from other predictive models described earlier (Valenzuela and Myers, 1986). Obviously, more rigorous testing of the model is necessary in the future. The present lack of published data satisfying the condition of constant m prevents that. Parametric Study The flexibility of the proposed heterogeneous multicomponent adsorption equilibria model (21) can be dem-
+ Ethylene (2) on BPL Carbon at 301.4 K e2
01
press., atm component 1 gas composn 1.422 0.682 0.682 3.415 6.836 0.682 13.497 0.682 2.149 0.472 5.421 0.472 11.180 0.472 1.360 0.240 3.040 0.240 7.272 0.240 0.240 13.231 19.550 0.240
exptl 0.4696 0.5750 0.6850 0.7690 0.3790 0.4780 0.5400 0.1580 0.2110 0.2550 0.2790 0.3050
calcd 0.4570 0.5793 0.6430 0.6810 0.3893 0.4710 0.5076 0.1870 0.2426 0.3292 0.2980 0.3048
Table 111. Adsorption of Carbon Monoxide (1)
% error
exptl 0.1467 0.1930 0.2330 0.2880 0.2990 0.3870 0.4740 0.4050 0.5150 0.6350 0.7350 0.8150
-2.6 +0.7 -6.1 -11.4 +2.6 -1.5 -6.0 +18.4 +15.0 +29.1 +6.8 0.0 av i8.6
exDtl 0.7606 0.8810 0.9105 0.9242 0.9461
calcd 0.1508 0.2019 0.2317 0.2500 0.3000 0.3748 0.4106 0.3800 0.5010 0.5880 0.6284 0.6440
% error
+2.8 +4.6 -0.6 -13.2 0.0 -3.1 -13.3 -6.1 -2.5 -7.3 14.5 -20.0 av h7.3
+ Oxygen (2) on 5A Zeolite at 144.2 K (Pressure = 1 atm)
81
comoonent 1 eas comDosn 0.126 0.363 0.535 0.671 0.891
$2
0.1 0.5 0.9 0.9
15.00 0.000
high while the adsorption of ethylene on the carbon is essentially homogeneous. Carbon monoxide (component l ) , on the other hand, is very strongly and selectively adsorbed over oxygen (component 2) on the 5A zeolite. The homogeneous selectivity for CO adsorption over O2 is 40.0. The degree of heterogeneity of the zeolite for CO adsorption is also very high while the zeolite acts like a homogeneous adsorbent for O2 adsorption. The pure component heterogeneous adsorption parameters of Table I for these systems were used in conjuction with (21) to calculate the binary adsorption equilibria for Cz&-C2H4 and C&OZ mixtures under various conditions of total gas pressure and composition at constant temperature. Tables II and III compare these calculations with binary experimental data. It may be seen from these tables that the proposed multicomponent heterogeneous model predicts mixed gas adsorption data from the pure gas adsorption data very well. The average error in calculating Table 11. Adsorption of Ethane (1)
tcc
atm-’ J. 1.40 0.900 0.85 0.OOO 600.00 0.975
mmol/g 5.30 5.30 5.14
calcd 0.7775 0.9175 0.9528 0.9703 0.9906
e2
% error
+2.2 +4.2 +4.6 +5.0 +4.7 av *4.2
exDtl 0.1727 0.0683 0.0439 0.0285 0.0067
calcd 0.2065 0.0746 0.0416 0.0246 0.0065
% error +19.6 +9.2 -5.2 -13.7 -3.0
av i l O . l
1038 Ind. Eng. Chem. Res., Vol. 30, No. 5, 1991 k , = 1.0, p 2 = 0 . 1
*2
0.9
0.1
0.9
0.9
0.5 0.9
0.1
0.9
x
t
?! cn 0.7-
0.6
I
0
0.2
I
0.4 y1-
I
1
I
0.6
0.8
1.0
Figure 5. Effect of adsorbent heterogeneity on binary selectivity at constant gas pressure (same values of P, p l , and pCzas in Figure 4).
onstrated by a parametric study of the effects of the model variables on adsorption from a binary gas mixture. Figure 4 shows the effect of degree of adsorbent heterogeneity on binary amounts adsorbed. It plots the ratio (ei/eiH)of the amounts adsorbed of each component of the mixture on the heterogeneous adsorbent to the corresponding amounts adsorbed on a homogeneous adsorbent with same values of p i , as a function of gas phase composition at constant P and T. Component 1 is more strongly adsorbed over component 2 with a homogeneous adsorption selectivity of 10 (= S'F2 = p1/p2). The total gas pressure is 20.0 atm and the values of pl and p2 are, respectively, 1.0 and 0.1 atm-'. The curves A-D in Figure 4 correspond to different values of q1and tc/2. Curves A-C exhibit the adsorption characteristics of binary gas mixtures where the adsorbent is fairly heterogeneous for component 1 (tl= 0.9) while the degree of heterogeneity for component 2 is (A) low (1Ci2 = O.l), (B) medium (q2= 0.5), or (C) high ($, = 0.9). The amount of component 1 adsorbed is not much affected by such drastic change in $2 over the entire gas composition range. 8' is always less than elHand O1/€llH vary between 0.92 and 0.975 only. An interesting feature, however, is that 8' increases when rCiz decreases in the low concentration range of component 1 while €$ decreases with decreasing #, in the medium to high concentration range of that component. The crossover occurs when y1 N 0.1. The effect of varying & on coadsorption of component 2, on the other hand, is drastic. 82/& increases significantly when q2is decreased, particularly in the high concentration range of component 1. In fact, 8, > 8 2 H when , ) I is sufficiently lower than $1 (curves A and B). 8, becomes less than eZH only when $z is also high (curve C). This result suggests that when the adsorbent is heterogeneous for adsorption of component 1 and $' > $, it is preferable to have the degree of heterogeneity for component 2 close to that of component 1, in order to minimize the coadsorption of component 2 which is always detrimental for separation application. Curve (D) represents the case where $, > #', even though pl > p2. in this case, is larger than e 1 H at low concentrations of component 1, and it is approximately equal to e 1 H at higher concentrations. e2is always lower than This represents the ideal adsorbent because of higher capacity of adsorption of component 1 and lower coadsorption of component 2. Figure 5 shows the variation of binary selectivity (S;,) of adsorption with gas-phase composition for the cases A-D of Fi ure 4. The ordinate of Figure 5 plots the ratio 5 It may be seen that S;, decreases with increasing S;2/S12. y1 for cases A, B, and D, where I)' # +2. The selectivity is constant and equal to Sy2 for $' = $, which represents the situation where all patches of the heterogeneous adsorbent have same local selectivities of adsorption. The decrease of SE with increasing y1 is more pronounced when +2 is much lower than I )' (curve A). S;, I Syz at all con-
*,
0.0 I
I
10
0
Ib2= 0.2
= 0.8, I 20
I
I
30
40
50
P-
Figure 6. Effect of adsorbent heterogeneity on binary selectivity at constant gas-phase composition (Pin atmospheres). 1 .o 0.9-
SH = 1.5
0.7-
$2
AZEOTROPE
= 0.0
- - HOMOGENEOUS - HETEROGENEOUS 0
0.2
0.6
0.4
0.8
1.0
y1-
Figure 7. Adsorption azeotropy on heterogeneous adsorbent.
centrations when Jil > 1,5~. S;, L Sy2when $l < Pl
while
> P2.
Such decrease in adsorbent selectivity with increasing y1 at constant P and T is commonly exhibited by most
heterogeneous adsorbents. Thus the present model is very consistent with the observed behavior. Figure 6 shows the variation of binary selectivity of adsorption as a function of total gas pressure at constant y and T. The ordinate again shows the ratio of Si2to S;. The parameters used for this study are given in the figure. It may be seen that Si2decreases with increasing P and the effect is more pronounced when y1 is high. This behavior is again consistent with experimental observations. Figure 7 demonstrates a special feature of the proposed model-its ability to predict adsorption azeotropy. The figure plots adsorbed-phase mole fraction (xl) of component 1against the gas-phase composition (&). The model parameters are given in the figure. The adsorption of component 1 is highly heterogeneous while that for component 2 is homogeneous. The homogeneous selectivity is relatively low (SE= 1.5). Under these conditions, the model predicts an azeotrope (xl = yl) at y1 = 0.82. The conditions required for formation of azeotrope by this model are discussed earlier. The parametric study proves that the role of adsorbent heterogeneity on mixed gas adsorption can be very complex. However, the proposed model of adsorption on heterogeneous adsorbents, although simple and analytical, is very flexible, and it is capable of describing many facets of observed behavior of mixed gas adsorption on such adsorbents. Many previously proposed correlations for mixed gas adsorption fail to exhibit this flexibility. Conclusions Adsorbent heterogeneity plays a very significant and complex role on adsorption of pure and multicomponent gas mixtures. Although it may not be possible to quantitatively identify and estimate magnitudes of energetic heterogeneity in practical microporous adsorbents, simple mathematical description of heterogeneity can be intro-
Ind. Eng. Chem. Res., Vol. 30,No. 5, 1991 1039 duced into adsorption equilibria models depicting the effect of adsorbent heterogeneity. There may be many ways to achieve this goal. The model proposed in this paper provides an analytical, simple, thermodynamically consistent, yet very flexible description of adsorption of pure and mixed gases on heterogeneous adsorbents. The model uses only three parameters including an explicit heterogeneity parameter to describe the pure gas adsorption isotherms, and it can predict mutlicomponent adsorption isotherm from pure gas data. One key limitation of the proposed model is the requirement of equal specific saturation capacities for the components of the gas mixture. Future extension of this model to describe mixed gas adsorption of nonequal adsorbate sizes and extensive testing of the model using multicomponent adsorption data are needed. Energetic site matching for different components of a gas mixture constitutes one of the most crucial assumptions in the model. A sensitivity analysis of this assumption using different site-matching correlations is also needed. Nomenclature b = pure gas Langmuir gas-solid interaction parameter bL =I smallest value of b on the heterogeneous surface bH = highest value of b on the heterogeneous surface E = adsorption energy for a homogeneous patch E, = lowest value of E on the heterogeneous surface EM = maximum value of E on the heterogeneous surface f = cumulative distribution of parameter b f ( z ) = function defined by (15) and (24) K = Henry's law constant for adsorption of a pure gas m = specific saturation adsorption capacity of a pure gas n = specific amount adsorbed P = gas-phase pressure P'= pure gas pressure at surface potential 4 q = isosteric heat of adsorption R = gas constant S, = selectivity of adsorption of component i over component
i
Sf = selectivity of adsorption on the heterogeneous adsorbent S i . = selectivity of adsorption on a homogeneous adsorbent (S(~)IAST = selectivity of adsorption calculated by ideal ad-
sorbed solution theory T = temperature x = adsorbed-phase mole fraction y = gas-phase mole fraction y* = gas-phase mole fraction at azeotrope z = function defined by (14)and (23) z* = parameter defined by (32) Greek L e t t e r s u = dispersion of b distribution p = mean of b distribution: Henry's law constant p$ = mean of Si, distribution e = fractional amount adsorbed on a homogeneous surface 8 = fractional amount adsorbed on a heterogeneous surface = degree of heterogeneity defined by (8) $I = surface potential A = probability density of parameter describing heterogeneity
+
S u p e r s c r i p t s and Subscripts
o = pure gas adsorption on heterogeneous surface * = pure gas adsorption on homogeneous surface i = component i j = component j H = homogeneous surface
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Received for review December 10,1990 Accepted February 11, 1991
