Ind. Eng. Chem. Process Des. Dev. 1983, 22, 271-280
streams as potential sources of nitric oxide reactant for electrogenerative processing. Acknowledgment
We thank the University of Wisconsin and Eastman Kodak for support of this work. We appreciate helpful discussions with Professor R. L. Burwell, Jr., Robert Pesselman of the Mill Street Foundation, and Jose Colucci. All patent rights are assigned to the Wisconsin Alumni Research Foundation. Registry No. Nitric oxide, 10102-43-9;hydroxylamine, 7803-49-8;nitrous oxide, 10024-97-2; ammonia, 7664-41-7; platinum,7440-06-4,ruthenium, 7440-18-8;carbon monoxide, 630080; perchloric acid, 7601-90-3; sulfuric acid, 7664-93-9; hydrochloric acid, 7647-01-0; nitric acid, 7697-37-2; phosphoric acid, 7664-38-2. Literature Cited Ashmore, P. 0. "Catalysis and Inhlbltion of Chemlcal Reactions”; Butterworths: London, 1963; pp 137-142. Bathla. M. L.; Watkinson, A. P. Can. J . Chem. €ng, 1979, 57, 631. Benson, R. E. U.S. Patent 2268885, Aug 27, 1949. Benson, R. E.; Calms, T. L.; Whltman, 0. M. J . Am. Chem. Soc.1956, 78, 4202. Bond, G. C. “Catalyal8 by Metals”;Academic Press: New York, 1962; p 375. Gadde, R.; Bruckenstein, S. Elecbwanal. Chem. 1974, 50, 163. Gllbert, N.; Daniels, F. I d . €ng. Chem. 1948, 40, 1719. Haldeman, R. 0.;Colman. W. P.; Langer, S. H.; Barber, W. A. A&. Chem. Ser. 1966, No. 47, 106. Haymore, B. L.; Ibers, J. A. J . Am. Chem. Soc. 1974, 96, 3325. Janssen, L. J. J.; &terse, M. M. J.: Barendrecht,E. E k 1 7 m h h .Acta 1977, 22, 27.
27 1
Jockers, K. N/f“ 1987, 50, 27. Kent, J. A. “Rlegel’s Handbook of IndusMal Chemlstry”, 7th ed.; Van Nostrand Relnhdd: New York, 1974. Kolthoff, I. M.; Sandell, E. B. “Quantltatlve Inorganlc Analysis”, Macmllllan: New York, 1948; p 668. Ku, R.: Gbsteln, N. A.; Bonzel, H. P. In “The catalytic Chemlstry of Nhrogen Oxldes”, Plenum: New York, 1975, pp 19-29. Landl, H. P. U.S. Patent 3407096, Oct 22, 1968. Landl. H. P. US. Patent 3527616, Sept 8, 1970. Langer. S. H.; Landl, H. P. J . Am. Chem. Soc. 1964, 86, 4694. Langer. S. H.; Landl, H. P. US. Patent 3248267, Apr 26, 1966. Langer, S. H.; Sakellaropoulos, G. P. J . Ektrochem. Soc. 1975, 122, 1619. Langer, S. H.: Sakellaropoulos, G. P. I d . Eng. Chem. Recess Des. D e v . 1979, 18, 567. Langer, S. H.; Pate, K. T. Netwe ( L o ” ) 1980, 284, 434. Low, M. J. D.; Taylor, H. A. Can. J . Chem. 1954. 37, 544. Meyw, C. D.; Elsenberg, R. J . Am. Chem. Soc. 1976, 98, 1364. Moore, J.; Pearson, R. 0. “Klnetlcs and Mechanism", 3rd ed.;Wlley: New York, 1981, pp 340-342. Otto, K.; Shelef, M.; Kummer, J. J . RIP. Chem. 1971, 75, 875. Paseke, I.; VdkovB, J. Ektrochlm. Acta 1980. 25, 1251. Savodnk, N. N.; Shepelin, V. A,; Zalklnd, T. I. EMtm&Mm!ya 1970, 7 , 424 (English transl). Shelef, M. Cetal. Rev. Scl. €ng. 1975, 1 1 , 1-40. Shepelln, V. A. Zh. MI. KMm. 1974, 47, 713. Snell, F. D.; Snell, C. T. “Colorlmetrlc Methods of Analysis”; Van Nostrand: New York, 1954; Vol. 4, p 55. Snider, B. 0.;Johnson, D. C. Anal. C h h . Acta 1979, 105, 9. Urabe, K.; Aka, K. I.; Ozakl, A. J . Catal. 1974, 32, 108. Voorhles, J. D.; Mayell, J. S.; Landl, H. P. ”Hydrocarbon Fuel Cell Technology”;Academlc: New York, 1965; pp 455-464. VoomOeve, R. J. H.: Trlmble, L. E. J . Catal. 1975, 38, 80.
Received for reuiew December 14,1981 Accepted September 3, 1982
Adiabatic Adsorption of Bulk Binary Gas Mixtures: Analysis by Constant Pattern Model Shivaji Sircar and Ravi Kumar’ Air Products and Chemlcak, Inc., Allentown, Pennsylvanla 18105
A constant pattern model for adsorption of bulk binary gas mixtures In an adiabatic column is derived. The model is used to estimate the properties of the equilibrium sectlons of the column. Profiles In the transfer zones are then calculated using the linear driving force model for the d i d and the gas-phase mass transfer. Heat transfer between the gas and the solid phases is assumed to be Instantaneous. The effects of the binary equilibrium selectivity, the initlal condition of the column, the heat of adsorption, and the transfer mechanisms on the column profiles are studied. The Langmulr model Is assumed for the adsorption isotherms. Analytical solutions are given for the Isothermal slngle-component bulk and dilute adsorption.
Many mathematical models for gasaolid adsorption in columns have been published during the past three decades. One approach has been to solve simultaneously the partial differential equations (PDE)describing the mass and the heat balance in the column. Various models for adsorption equilibria and the mass transfer mechanism have been used. This approach, although more general and mathematically rigid, requires complicated numerical solutions, and the computation time is often inconveniently long. Analytical solutions have been obtained for the simple case of isothermal adsorption of a dilute singlecomponent solute with linear adsorption equilibrium and different mass transfer mechanisms (Thomas, 1944; Hougen and Marshall,1947;Glueckauf, 1946;Rosen, 1952; Kawajoe and Takeuchi, 1974). The method of characteristics has been used by Amundson et al. (Rhee and Amundson, 1970,1974;Rhee et al., 1970, 1972) to solve the PDEs for (a) adiabatic OI9&4305/83/ 1122-0271$01.50/0
adsorption of dilute multicomponent solute from a carrier gas by assuming Langmuir equilibria for the solutes and local equilibrium for mass and heat transfer and (b) isothermal adsorption of two dilute solutes from a carrier gas where axial dispersion and gas-solid mass transfer resistances are prevalent. Recently, Harwell et al. (1980) have used the method to study adiabatic sorption of two dilute solutes from a carrier gas using Langmuir equilibria and linear driving force models for gas to solid mass and heat transfers. This method is, however, rather complicated. A n alternate approach has been to assume formation of constant pattern mass and heat transfer fronts in the column. This reduces the PDEs to a set of algebraic and ordinary differential equations and the solutions are mathematically simpler. The results can describe the experimental data satisfactorily for most practical design purposes. The major works using this approach, summa@ 1983 American Chemical Soclety
272
Ind. Eng. Chem. Process Des. Dev., Vol. 22, No. 2, 1983
Table I. Summary of Constant Pattern Adsorption Models type of adsorption system thermal conditions dilute single-component isothermal adsorbate in inert binary ion exchange isothermal
mass-transfer adsorp mechanism equilib gas film, solid film two linear sections liquid film Langmuir
Vermeulen (1953)
dilute single-component isothermal adsorbate in inert
gas film, pore diffusion (approx equation)
Leavitt (1962)
bulk sinde-component adsorbate in inert
authors Glueckauf (1947) Mcheaels (1952)
adiabatic, instant heat transfer between gas and solid Vermeulen (1966) dilute single-component isothermal adsorbate in inert Hall et al. (1966) dilute single-component isothermal adsorbate in inert bulk single-component adiabatic, instant Pan and Basmadjian adsorbate in inert (1967) heat transfer between gas and solid Pan and Basmadjian bulk single-component adiabatic, instant heat transfer (1970) adsorbate in inert between gas and solid Thomas and Lombardi dilute two solutes in is0 thermal (1971) inert dilute two solutes in Cooney and Strusi isothermal inert (1972) Fleck et al. (1973) dilute single-component isothermal adsorbate in inert Ruthven et al. (1975) dilute single-component instant heat transfer adsorbate in inert between gas and solid; heat loss to surroundings from column Garg and Ruthven dilute single-component isothermal adsorbate in inert (1979) Miura et al. (1979) dilute two solutes in is0thermal inert Miura and Hashimoto
(1979)
dilute two solutes in inert
isothermal
rized in Table I, primarily deal with the isothermal or adiabatic single adsorbate systems. Analysis of dilute adsorbate systems including isothermal sorption of two solutes from an inert carrier gas has received considerable attention. The purpose of the present work is to study the constant pattern adiabatic adsorption from concentrated binary gas mixtures and to demonstrate the effects of the binary selectivity, the initial column conditions, the heats of adsorption, and the transfer mechanisms on the column profiles. In addition, several previously unpublished analytical solutions for sorption of a single adsorbate (concentrated and dilute) are derived. Effects of various design parameters on the column profiles are examined. Binary Adsorption System The isobaric binary gas adsorption process in an adiabatic column consists of flowing a binary feed gas mixture comprising a more selectively adsorbed species (component 1)and a less selectively adsorbed species (component 2) through the adsorbent column which is previously saturated with a gas mixture of the same components at the same temperature (2")and pressure (PO)as the feed gas. The mole fractions of component 1 in the feed and the saturating gases are, respectively, yl0 and yls, (yl0 > yls). The following two types of situations may arise. Type I. Two pairs of mass and heat transfer zones are formed inside the column as shown by the profiles in Figure 1. The column ahead of the front transfer zones
comments analytical solution given analytical solution given
Langmuir
arbitrary
experimental data given
gas film, solid film Langmuir pore diffusion gas film, solid film Langmuir pore diffusion gas film, solid film arbitrary
experimental data given solid film
Langmuir
solid film
Langmuir
pore diffusion
Langmuir, Freundich Langmuir
solid film
experimental data given analytical solution given
gas film, solid film Langmuir
analytical solution given gas film, solid film Langmuir, experimental data Freundich given pore diffusion, surface diffusion gas film, solid film Langmuir analytical solution given
v
jp -
j
+ qIV
II I*I-
I-+-
1-4
k--a
x
-
Figure 1. Type I system: concentration, flow rate, and temperature profiles. (Curve below F: y , n = 0.)
(section I in the column) remains equilibrated with the saturating gas at the starting conditions. The column between the front and the rear zones (section I11 in the column) remains equilibrated with a gas mixture of composition yl* (y: > yl* > yls) at temperature P (P > 7") and pressure PO. The column behind the rear transfer zones (section V in the column) is equilibrated with the feed gas mixture at T' and Po. Type 11. Figure 2 shows the concentration, flow rate, and temperature profiles for type I1 behavior. The key
Ind. Eng. Chem. Process Des. Dev., Vol. 22, No. 2, 1983 273
QS
Q*
I
y.n
5
I
I
I I
I
I
0
Figure 2. Type I1 system: concentration, flow rate, and temperature profiles.
property of this type is the absence of component 1 in sections 1-111 of the column. The column ahead of the front zones (section I) remains equilibrated with pure component 2 at the initial conditions. The column between the front and the rear zones (section 111)also remains equilibrated with pure component 2 but at a temperature T* (T* > P ) and pressure Po. The column behind the rear zones (section V) is equilibrated with the feed gas at P and PO. It should be noted that experimental breakthrough curves may not exhibit well-defined temperature and composition plateaus as shown in Figures 1and 2. This can be due to finite heat transfer resistance between the gas and the solid phases, nonadiabaticity of the column, and other nonidealities. For some type I systems, it may not be possible to measure the difference between yl* and y: because of their closeness. Criteria of the Formation of the Type I and I1 Systems It is generally not possible to predict exactly when type I or type I1 behavior will be exhibited. However, Pan and Basmadjian (1970) have established the following conditions based on their analysis of single-component adsorption with instantaneous mass and heat transfers.
adsorbed of each gas component present (ni)in the column. In case of an ion-exchange system, it is necessary to account for the parent ion in the exchange resin in addition to the feed ions. Helffrich and Klein (1970) proposed to unify the mathematics of mass balance for ion-exchange and adsorption systems by implementing the concept of a "dummy species" (empty adsorption sites) in the adsorbed phase equivalent to the parent ion in ion exchange. The concept of adsorption sites is, however, ambiguous for microporous adsorbenta. The assumptions made in writing eq 1and 2 are: (i) the gas flow in the column is essentially plug flow; (ii) there is no surface diffusion in the adsorbed phase; (iii) Cp,, e, and p e are independent of yi, ni, and T; (iv) qi's are independent of T and ni; (v) the column is adiabatic and isobaric; (vi) there is instantaneous thermal equilibrium between the gas and the solid phases; (vii) the heat capacity of the adsorbent is much greater than the combined heat capacities of the gas and the adsorbed phases PsCp.
>> +g
+ PeCp*(nl + n2)
In a constant pattern transfer zone, the profiles of the variables y i , ni, T, Q, Cp,, and pBdo not change in shape or size as the zone moves through the column. Every differential element of the zone defined by certain values of the above variables moves with the same constant velocity. This property can be mathematically described by
[awl, =P
(3)
where p is the velocity of the zone. M can be yi, ni, T, Q, C,, or pg. Using the theorem of partial derivatives, one can write
P=
-[ %I,/[ g ]
(4)
t
Equation 4 can be combined with eq 1 and 2 to obtain
n l o / y l o < Cp,/Cpg (for type 1)
Type I behavior is common for adsorption of most bulk adsorbate systems while type I1 behavior is favored for adsorption of very strongly adsorbed (large n:) dilute adsorbate (yl0 1. Equations 46-47 can be used to carry out a parametric analysis of the mass transfer zone for dilute isothermal adsorption. We assume that the zone is bounded by two symmetrical values of cP1 and 9,;i.e., a1+ cP2 = 1. Then for the gas film control, one can show that
-
Table 111. Properties of the Adsorbents and the Langmuir Parameters for the Pure Adsorbates BPL activated carbona A
adsorbates
m
co, CH, NZ HZ
3.65 x 10-3 3.65 x 10-3 3.65 X 3.65 x 10-3
adsorbates
m
b
4
CO,
3.66 X lo-' 3.66 X 3.66 X
1.0 X lo-' 4.7 X lo-' 2.1 X
8870 4950 5000
b
2.8 X 1.5 X 13.5 X 0.5 X lo-, 5A zeolite
4
4900 4700 2500 3300
A
CH, N, E
= 0.763;P , = 0.484;pore diameter = 30 A; Cp, = E = 0.762;P , = 0.731;pore diameter = 5 A;
0.22.
cp, = 0.22. Assuming that the gas phase is ideal, ~1 is proportional to P6and D,is proportional to ! P 5 / P(Reid et al., 1977), eq 30 can be written as A~QO(, - nl)po.kl k,, = dp(l+ ad (50)
Equation 56 can be differentiated with respect to ?o and
Po to obtain
- $&1 aP B ~ ~ , O S O
GEL1
Equations 40, 49, and 50 can be combined to get
apo QWT
Equation 51 shows that L for gas film control is proportional to (dp)(l+al)and (@>ol and inversely proportional to yl0. It can also be shown from eq 51 that
- $,q1 alo
~
0
~
~
- 0.5U1RP
0
,
RP=
(52)
~
(53)
J/B and q1 are positive quantities and $dlis usually larger
than 0.5a1RT. Therefore, the higher the process temperature, the longer is the mass transfer zone and the higher the process preasure, the shorter is the mass transfer zone for the same Qo and yl0. For solid diffusion control, it can be shown that
L= k,, is given by (Hall et al., 1966) k,, = -D, 0e-EIJRT d,2 Equations 40,54, and 55 can be combined to get L=
(55)
Equation 56 shows that L for solid diffusion control is proportional to (d,), and (QO) and inversely proportional to y t or DPo. Therefore, the length of the mass transfer zone is more strongly dependent on Qo for the solid-film controlled system than for the gas-film controlled system since al is typically between 0.3 and 0.5.
- El RP'
= - -A
PO
(57) (58)
Since q1 and El are positive quantities but $, can be both positive or negative, depending on the values of bl and y,: the temperature coefficient of L depends on the sign of $, and the relative magnitudes of the terms $,ql and El. The pressure coefficient of L depends on the sign of $,. Thus, the effects of the system pressure and temperature on L can be markedly different for the solid diffusioncontrolled mass transfer than those for the gas-film control transfer. Numerical Solutions The adiabatic constant pattern adsorption model developed in this paper can be used for analyzing any binary system with nonlinear adsorption equilibra and linear maw transfer mechanisms. Adsorption of several binary systems with Langmuir equilibria and the LDF models for the mass transfer have been studied. An Amdahl470 computer was used for the numerical solutions. Typical execution time for analyzing a system was less than 5 s. The objectives were to examine the effects of (i) the binary selectivity, (ii) the initial column conditions, (iii) the heat of adsorption, and (iv) the mass transfer mechanisms, on the properties of the equilibrium sections and the transfer zones in the column. The effects of these parameters are interrelated in a real system; however, these effects have been separated by appropriately choosing the systems and operating conditions. Laboratory tests showed that the pure component adsorption isotherms for CO,, CHI, N,, and H2 on BPL activated carbon and 519 zeolite can be fitted satisfactorily by the Langmuir equation over a temperature range of 0-70 "C and a pressure range of 0-2 atm. Table I11 summarizes the Langmuir parameters. It is assumed that the mixture adsorption equilibria for these components can be calculated by the mixed Langmuir model (Young and Crowell, 1962) n, =
mbLY, 1 + Cby,
(59)
Thus, eq 59 and the parameters of Table 111were used to
Ind. Eng. Chem. Process Des. Dev., Vol. 22, No. 2, 1983 277 I
. ..
w-
>
o.20
00
I
I
I
0 99
1 00
101
t
F tm
t 1.oo
0.80
1.20 F t/tm
*
Figure 4. Effect of selectivity on the spread of breakthrough curves. Film model for mass transfer. COz- Nz(') and COP- CH,@)on BPL carbon (Table IV). (Abscissa: t/tmF.)
Figure Effect of selectivity on the spread of breakthough c w e s . Solid diffusion model for mass transfer. COz- Nil) and COz- CHiz) on BPL carbon (Table IV). (Abscissa: t/tmF.)
l5tf
1.24
..
50.0
d
t 1.o
10.0
. 0.40
0 80
I
1.w
0.99 ti&
1 40
titm
Figure 7. Variation in temperature and flow rate for COP- Nil) and COP- NHi2) on BPL carbon. Solid diffusion for mass transfer (Table IV). (Abscissa: t/tmF.) 1 00
analytically describe eq 13-15 and 22-23. The gas phase was assumed to be ideal and ita pressure was 1 atm (= PO) for all the test runs. The gas-phase heat capacity was calculated by C = CCp2i.k, values for various adsorbates were calcuyated using the correlation of Petrovic and Thodos (1968). k, values for the adsorbates were estimated by calculating the pore diffusivity using the correlation of Satterfield (1970) and assuming k, = [60DP]/d,2. Variation of k, with Q and T and variation of k, with T were taken into consideration. The adsorbent column for each run was assumed to be 6 f t long. The properties of the adsorbents are given in Table 111. Effects of Binary Selectivity. The selectivities for adsorption of COzfrom binary mixtures with N2and CHI on BPL activated carbon are, respectively, 12 and 2.6 at 30 OC. ~ u i l i b r i u msection properties and transfer profiles for adsorption of these two binaries, using a pure C02feed into a column initially saturated with 25.0% C02at 30 OC were evaluated. Qofor the runs were kept identical. Table IV shows the properties of the equilibrium sections of the columns for these systems. Both systems exhibit type I behavior. y t and yl* are equal and the rear zones consist of a thermal shock only. Figure 4 shows the y-t curves for the front zones for the gas film control model. Figure 5 shows the corresponding variations in k, and Tin the front zones. In these plots dimensionless time variable is used for comparison. The COZ-CH4binary which has lesser selectivity for C02shows longer transfer zones ( L = 4.72 cm) and small T* than those for the C02-N2 binary mixture ( L = 2.88 cm) despite the larger k, values for the COz-CH, system (Figure 5).
40.0
F
1.01
Figure 5. Variation in temperature and k, for COz - Nz(') and COS - CHt2)on BPL carbon (Table IV). (Abscissa: t/tmF.)
1 20
1 00
10.0
5-
1.40
>
080
L = 3 02 cmr Y s = 0 25
0 99
100
101
t tm
Figure 8. Effect of yInon the spread of breakthrough curves. Film model. COz - Nz on BPL carbon (Table V). (Abscissa: t/tmF.)
Figures 6 and 7 show, respectively, the y-t curves and the variations in Q and T in the front transfer zones for the solid film transfer resistance model. The average values of (k,)co2,(k,)CH,, and are, respectively, 0.25, 0.32, and 0.30, and they do not vary significantly across the zone. Figure 6 shows that the front transfer zone is more dispersed for the C02-CH4 mixture ( L = 123.3 cm) than the COZ-Nz mixture (L = 69.4 cm). The front zone velocity for the COZ4H4binary is slower than that for the COZ-N2system. The rear zones for both systems move with equal velocities. The loading of COz in section I11 is more for the C02-CH4 mixture because of lower T* for that system.
278
Ind. Eng. Chem. Process Des. Dev., Vol. 22, No. 2, 1983
ua
t-
l i 9
m m
0
u3
c?
0 0
Y
0 W
c9
N
8
Y
S
m
f
* c
'9 W
rl
m
2
* ?
cu
c? r3
? N
rl
> 0
=I
2 *e
P
i
9
m 0 m
9
rl
9 rl m
c?
rl
E: 0
h
F.l
zg zn
+3 3"
A : %&
c
Ind. Eng. Chem. Process Des. Dev., Vol. 22, No. 2, 1983 270
?
3
99
00
9 0
99 9 ? im m m 3
00
0
?
99
z
co*0 a
rl
n
3
x ?
3
mm 00
v-! 00
m
0.1
c?
0
Effect of Initial Column Condition. Figure 8 shows the breakthrough curves for the adsorption of pure C02 feed on columns initially saturated with three different mixtures of C02-N2 (0,25, and 50% CO& 80 and P are kept constant for these runs. Only the gas film control model is considered. The systems exhibit type I behavior with y: = yl*. Table V shows the properties of the equilibrium sections. It can be seen that higher y i gives (i) longer transfer zone, (ii) lower T* and hence higher loading for C02 in section III, and (iii) higher velocity for the front transfer zone. The rear zone velocities are practically independent of yl*. Effect of the Heat of Adsorption. Table VI shows the properties of the equilibrium sections for the adsorption of 80.0% C02 from binary mixtures with H2 and N2 on BPL carbon and 5A zeolite. The selectivity for C02 adsorption is very large for both systems and C02 is adsorbed almost exclusively. @, P (= 30.0 "C), and yls (= 0) are identical for both systems. These systems exhibit type I behavior with y: yl*. The isosteric heat of adsorption for C02 on the carbon and the zeolite are, respectively, 4900 and 8870 cal/mol. Consequently, T* for the zeolite is much larger (105.6 "C) than that for the carbon (54.5 "C). As a result, the capacity for C02 in section I11 is much more reduced for the zeolite (nl*/n: = 0.53) than for the carbon (nl*/n: = 0.67) as compared to the C02capacities at the feed conditions. The zeolite still shows higher capacity for C02 than the carbon in section III. However, it is possible that an adsorbent which has less capacity for an adsorbate at the feed temperature actually offers more capacity in an adiabatic column than an adsorbent which has more capacity for the adsorbate at the feed temperature. Thus the effect of q in an adiabatic adsorption process is very important in adsorbent selection. Table VI shows the properties of the equilibrium sections of the columns for isothermal adsorption of the two binaries. It may seem that nonisothermal operation substantially increases the velocity of the front zone resulting in much earlier breakthrough of C02. The effect is more pronounced for the zeolite due to higher heat of adsorption. Acknowledgment The authors are grateful to Air Products and Chemicals, Inc., for kind permission to publish this paper. Nomenclature al, a2 = constants in eq 30 A = constant in eq 30 Al = constant in eq 50 A2 = constant in eq 55 4 = 6PeqlRT= constant in Langmuir equation, dimensionless b = Langmuir constant at infinite T, atmosphere-' C = gas-phase heat capacity, cal/(mol K) $ f = adsorbent heat capacity, cal/(g K) Cp, = adsorbed phase heat capacity, cal/(mol K) d = adsorbent particle diameter, cm dp O , = pore diffusivity at infinite T, cm2/s D, = pore diffusivity at T, cm2/s D, = gas-phase diffusivity, cm2/s El = activation energy for diffusion, cal/mol k = constants in eq 7,8, and 32 k , = gas film mass transfer coefficient, mol/(g s) k , = solid film mass transfer coefficient, s-l L = length of the transfer zone, cm m = Langmuir constant, mol/g M = variable representing, y, n, T, Q,pg, Cpg n = amount adsorbed, mol/g ii = equilibrium amount adsorbed at P, T, and y, mol/g P = pressure, atm q = isosteric heat of adsorption, cal/mol Q = gas flow rate, mol/(cm2 s)
-
b
ow
rl
rlrl
m
r9
900
9
9
E-
cv
m
co ?=? -?
moo O b mm m
m 0 m
2 22 3 0
OQ,
0
0.
> c E 0 d
ZL I
" "" "
E
m
mm
rl
rlrl
m
H
280
Ind. Eng. Chem. Process Des. Dev. 1883, 22, 280-287
R = gas constant Re = d p Q / p , = Reynolds number, dimensionless S = nly2/nyl = binary selectivity Sc = . p , / p P , = Schmidt number, dimensionless t = time, s tmF= time for midpoint of the front zone to reach the exit end of the column, s T = temperature, K x = distance variable X = length of the column, cm y = gas-phase mole fraction 7 = gas-phase mole fraction in equilibrium with n,P, and T Greek Letters
B = velocity of transfer zones, cm/s
/3” = velocity of rear zone, cm/s @*= velocity of front zone, cm/s
@ = velocity of zone for isothermal system, cm/s t
= adsorbent column void fraction, dimensionless
pg = gas-phase density, mol/cm3 ps = adsorbent density, g/cm3
e = ( T - T ~ )K, wLB= gas-phase viscosity, mol/(cm s) CP = (y/l - y)/(yo/l -lo), dimensionless $, = [ b , / ( l + b l ) ] - [A / ( 2 - AO)], dimensionless $, = [((A0 - 2)2 - 2)/(2 - AO)] + [l/(l + b J ] , dimensionless X = n/m, dimensionless Superscripts and Subscripts 0 = feed or section V conditions * = section I11 conditions s = saturating gas or section I conditions i = component i ( i = 1, 2) = pure component
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Received for review May 19,1980 Revised manuscript received August 11, 1982 Accepted September 8,1982
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This paper was presented at the 88th National Meeting of AIChE in Philadelphia, June 8-12, 1980.
Adsorption of a Dilute Adsorbate: Effects of Small Changes in the Column Temperature Shivall Slrcar’ and Ravl Kumar Alr Products and Chemicals. Inc., Allentown, Pennsylvanla 18105
A constant pattern adiabatic adsorption model is used to analyze both types I and I1 adsorption of a singiecomponent &lute adsorbate. Analytical solutions are obtained by use of constant gas and solid film mass transfer coefficients in conjunction with partially linearized Langmuir equilibria with respect to temperature dependence. The front mass transfer zone of a type I system is sharpened by the column temperature rise, and an isothermal analysis yields a lower mass transfer coefficient than its true value. The rear mass transfer zone of a type 11 system is elongated by the column temperature rise and an isothermal analysis gives a larger mass transfer coefficient than its true value. The isothermal analysis gives a lower equilibrium capacity for the adsorbate for type I systems while correct estimation of adsorbate equilibrium capacity may be obtained for type I1 systems by the bothwmai analysis. Several criteria for the formation of type I cf “combined wave” and type 11, sometimes referred to as “pure thermal wave” adsorption systems, are developed.
It is commonly assumed in modeling the adsorption of a dilute adsorbate from an inert carrier gas that the adsorbent column remains isothermal during the process. The assumption is justified by the fact that the temperature changes inside the column are small. Table I summarizes the major works on this subject. The purpose of this study is to show that even a small change in the adsorbent temperature may cause a serious error in the 0196-4305f83f 1122-0280$01.50l0
analysis of the column data by isothermal models. The present work consists of solving the mass and the heat balance equations for the isobaric adsorption of a single-component dilute adsorbate in an adiabatic column by assuming that constant pattern mass and heat transfer zones (Sircar and Kumar, 1983) are formed inside the column. Effects of temperature changes in the column on the shapes and the sizes of the transfer zones, their ve0 1983 American Chemlcal Society
