Adsorption Chromatography Measurements. Parameter Determination

383

Ind. Eng. Chem. Fundam. 1980, 19, 363-367

phase are constant. Then the usual procedure (King, 1971, p p 264-276) of defining flow rates as flow of inerts and defining compositions as weight or mole ratios can be used. Figures 2,3, and 7 will be unchanged except the variables having different meanings. Figure 4 will be valid if the equilibria are linear in the ratio units. The stage efficiency analysis can still be used if the efficiencies are defined in the new composition units. The analysis of continuous contact systems will be considered in part 2. Acknowledgment

Discussions with Drs. Daniel Tondeur and Alden Emery, Jr., were most helpful. The pseudo-equilibrium method was suggested by Professor C. Judson King in a review of the original manuscript. The hospitality of ENSIC in Nancy, France, is gratefully acknowledged. This research was partially supported by NSF Grant Eng. 77-21069.

Downloaded by UNIV OF MANITOBA on September 1, 2015 | http://pubs.acs.org Publication Date: November 1, 1980 | doi: 10.1021/i160076a007

Nomenclature

b, bl, b2 = linear equilibrium parameters in eq 1 and 18 b' = average linear equilibrium parameter, eq 31 and 30 Co, C1 = constants of integration ELy, E L , EL . = Murphree efficiencies in L phase, eq 25 EvmiX, d v X ,Fv2 = Murphree efficiencies in V phase, eq 24 Ewmk,E,, E w = Murphree efficiencies in W phase, eq 26 i = stage number K , K1, K2 = linear equilibrium parameters in eq 1 and 18 K' = average linear equilibrium parameter, eq 31 and 30 L = phase flow rate, mol/h N = total number of stages V = phase flow rate, mol/h W = phase flow rate, mol/h x = composition of solute in phase L , mole fraction x' = average mole fraction in cocurrent phases, eq 28 x * ~= x value in equilibrium with actual yout,mole fraction x*, = x value in equilibrium with actual zout, mole fraction

x * , ~ = x value in equilibrium with weighted mixed average of xout and youtallowed to equilibrate, mole fraction y = composition of solute in phase V , mole fraction y*N+l= y in equilibrium with xh and zh, see eq 6, mole fraction y*, = y value in equilibrium with actual xOut,mole fraction = y value in equilibrium with actual zoUt,mole fraction y*,& = y value in equilibrium with weighted mixed average of .routand Fout,allowed to equilibrate, mole fraction z = composition of solute in phase V , mole fraction z , , ~= composition of solute in entering cross-flow stream in Figure 5 , mole fraction z*, = z value in equilibrium with actual xoUt,mole fraction z * ~= z value in equilibrium with actual yout,mole fraction zmi = z value in equilibrium with weighted mixed average of xout and youtallowed to equilibrate, mole fraction Greek Letters a = V / ( W / K ,+ L/Kd (eq 5) a' = 1/a = (W/VK,) + ( L / V K , ) (see also eq 21) Subscripts and Superscripts i , j , N = stage number in = inlet streams (to column or to stage) out = outlet streams (from column or from stage) * = equilibrium value L i t e r a t u r e Cited Gunn, D. J., Chem. Eng. Sci., 32, 19 (1977). Jacques, M. T., Hovarongkura, A. D., Henry, J. D., AIChE J., 25, I 6 0 (1979). King, C. J., "Separation Processes", McGraw-Hill, New York, 1971. Li, N. N., Ind. Eng. Chem. Process Des. Dev., IO, 125 (1971). Maugh, T. H., Science, 193, 134 (July 9, 1976). Maslan, F., Ind. Eng. Chem. Fundam., 11, 238 (1972). Meltzer, H. L., J. Bo/. Chem., 233, 1327 (1958). Mickley, H. S., Sherwood, T. K., Reed, C. E., "Applied Mathematics in Chemical Engineering", 2nd ed, McGraw-Hili, New York, 1957. Rochelle, G. T., King, C. J., Ind. Eng. Chem. Fundarn., 16, 67 (1977).

Received for review November 26, 1979 Accepted June 18, 1980

Adsorption Chromatography Measurements. Parameter Determination N. Wakao, S. Kaguei, and J. M. Smith" School of Engineering, Yokohama National University, Yokohama, Japan 240

Pulse-response data were obtained at 293 K and atmospheric pressure for the physical adsorption of nitrogen in beds of activated carbon particles. Error analysis of the response curves in the real-time domain confirmed that an accurate value of the adsorption equilibrium constant could be obtained from a single measurement. Data as a function of gas velocity were required in order to establish reliable values of the axial dispersion coefficient and intraparticle effective diffusivity (De). Steady-state measurements of De were also made. For particles of uniform porosity the effective diffusivity obtained by the dynamic and steady-state measurements were in good agreement. For particles with a central core of lower porosity, the dynamic method gave higher De values. There is a particular advantage of error maps obtained by analysis of response data in the real-time domain. Such maps establish the range of operating conditions in which to make measurements for most accurate evaluation of parameters. I f data are analyzed only by the moment method, such optimum operating conditions are not known.

Chromatography has been applied by many investigators (Kubin, 1965; Kucera, 1965; Schneider and Smith, 1968; Clements, 1969; 0stergaard and Michelsen, 1969; Anderssen and White, 1970; Gangwal et al., 1971; Boxkes and Hofmann, 1972; Suzuki and Smith, 1972; Wakao, 1976a)

* Department of Chemical Engineering, University of California-Davis, Davis, Calif., 95616.

to the determination of kinetic and transport rate parameters. In the conventional model for reversible adsorption of a tracer in a packed bed of adsorbent particles, five parameters are involved: the axial fluid dispersion coefficient D,, particle-to-fluid mass transfer coefficient kf, intraparticle effective diffusivity De, adsorption rate constant k,, and adsorption equilibrium constant KA. In a recent article (Wakao e t al., 1979) the authors showed that K A and a relation between D, and De were

0196-4313/80/1019-0363$01.00/00 1980 American Chemical Society

364

Ind. Eng. Chem. Fundam., Vol. 19, No. 4, 1980 H2

I '-c

r Input Signal

Output Signai

I i

1

N2 injection

Glass Beads Tungsten Filament I Activated Carbon Particles

Tungsten Filament II

I

+

Activated Carbon Particles

Time ( s e c l

Figure 2. Measured (solid curves) and calculated (dotted curves) input and response curves for run 1-4.


Figure 1. Packed column for chromatographic measurements. Table I. Experimental Conditions for Adsorption Measurements a

shape particle diameter, cm particle porosity bed void fraction

Type 1 particles

Type I1 particles

spherical 0.20 0.59 0.38

spherical 0.28 0.66 0.39 ~~

run 1-1

2 3 4 5 6

Re

run

0.051 0.11 0.21 0.30

11-1 2 3 4 5

0.39

~

Re 0.10 0.23 0.33 0.46 0.59

0.47

effective 0.0035 diffusivity, cm2/ cmz/s (steadystate result)

0.013

a Carrier gas, hydrogen; tracer gas, nitrogen; temperature, 20 "C;pressure, atmospheric.

the only accurate results obtainable from a single measurement. The objective of the present paper is to identify the parameters that may be reliably determined from data obtained a t a series of flow rates in the laminar regime. To verify the conclusions, experimental data were obtained for the adsorption of nitrogen in a bed of activated carbon particles a t 293 K and 1 atm.

Experimental Section A 21.4-mm (i.d.) column, shown in Figure 1, was used for the adsorption measurements. The hydrogen carrier gas flowed first through a calming section packed with 1.8-mm glass beads, then through the test bed of carbon particles (packed to a length of 20.4 cm), and finally through an after bed of the same carbon particles. Tungsten filaments were placed before and after the test bed in the middle of open sections of the column, each section of 0.82 cm length. Other experimental conditions are given in Table I. A thermocouple inserted in the test bed indicated that the temperature rise following the introduction of a pulse of nitrogen was less than 0.5 "C. For parameter estimation the bed was supposed to be isothermal. The solid curves in Figure 2 show typical input and response curves for type I particles. Two types (I and 11) of spherical particles were studied. Type I is a commercial grade activated carbon (from

Nippon Carbon Co.) and was used without further treatment. These particles have a heterogeneous pore structure. Microscopic examination reveals a hard central core of low porosity surrounded by more porous material. Due to the two-step method of manufacture, there is a sharp boundary between the dense core and more porous outer shell. This boundary is clearly observed in the microscope. Type I1 particles, from the Dai-ichi Carbon Co. were conventional activated carbon particles of approximately uniform porosity. Before use they were treated with steam a t 950 "C for 1 h in order to obtain a more uniform porosity throughout the particles. In addition to the dynamic experiments, effective diffusivities for particles I and I1 were determined from steady-state, countercurrent diffusion measurements. A conventional Wicke-Kallenbach type apparatus (Satterfield, 1970) was used, inserting several particles in a plastic holder in order to provide measurable diffusion rates. The ends of the spheres were shaved off to give a near-cylindrical shape. By removing spherical sections so that the length of the near-cylindrical particle is about 0.4 of the original diameter of the sphere, the variation in area for diffusion is reduced to about 10%. Hence, the use of an average area and an average diffusion length for the nearly cylindrical shape leads to diffusivities within the expected experimental error. Evidence for this is the agreement (see Discussion) between De values obtained from dynamic and steady-state experiments for type I1 particles. Results of the steady-state measurements for hydrogen-nitrogen a t 20 "C gave (De)N2 = 0.0035 and 0.013 cmz/s for particles I and 11, respectively. Estimation of Parameters in the Time Domain. Equations for calculating the response curve, Cdc vs. t , in terms of assumed values of the parameters are readily available (for example, Schneider and Smith, 1968). The method of correcting Cdc for the dead volumes (associated with the detecting tungsten filaments) is described elsewhere (Kaguei et al., 1980). These corrected, calculated curves are then compared with the experimental curves Cexp to evaluate the parameters. In other words, we evaluate the root-mean-square-error, e, between the two curves Cexpand Ccdcand search for a least-error point on an error map plotted in terms of the parameters to be determined. The error is given by

Ind. Eng. Chem. Fundam., Vol. 19, No. 4, 1980 365 8

6

4 4 a 2

I

I

I

1

0.2

I

0.4

I 0.6

1

FbDax'Dv

Figure 3. Error map in plot of

p F A

D,,

cm2 sec

Figure 5. Error map in plot of c&,/D, vs. c&,/Dv

vs. De for run 1-4.

for run 1-4.


0.4

0

6

0.01

0.005

0.015

D, , cm2 I sec

Figure 6. Error map in plot of c&,/D, for various flow rates. Figure 4. Error map in plot of

pp KA

vs. De for type I particles

vs. De for run 1-4.

Results Of the five parameters in the model, kf and k, do not affect significantly the response curve. This is because, first, the Sherwood number for gases in packed beds is greater than 2. A recent empirical correlation (Wakao and Funazkri, 1978) gives Sh = 2 + l . l ( S ~ ) l / ~ ( R e ) O . ~ (2) Second, for physical adsorption, such as for nitrogen on activated carbon, the adsorption rate constant k, is very large (Schneider and Smith, 1968; Gangwal e t al., 1971; Wakao et al., 197613) and, hence, has a negligible effect on Ccalc. These conclusions are explained in the Appendix. It is shown there that changing kf in the range of 2 < Sh < a and k, in the range 80 cm3/(g s) C k, < a has a negligible effect on Ccdc. The data obtained for type I particles are used to illustrate the errors associated with evaluating the three remaining parameters D,, De, and K A . Curves A, B, C in Figure 2 are calculated response curves and will be discussed later. First we consider the effect of D,, on the evaluation of K A . Since De is not yet known, calculations are made for two extremes De = 0.004 and 0.01 cmz/s. The error map in Figure 3 shows that for either value of De, and for any value of the axial dispersion parameter, D,, the least-error contour is for p F A = 5.23. Figure 4 is a similar error map displaying the effect of De for extreme values of q,Dax/Dv. Again the least-error contour corresponds to p#A = 5.23. We conclude that a single run determines an accurate value for K A . Using this result for p A, the error map for various values of q,Dax/Dvand Lf! are shown in Figure 5. For example, the values of these two parameters within the shaded part of the figure show that Ccdcdiffers from Cexp

0.4

.d

0-

0.2

c1

0 0

0.01

0.005

0.015

0, , m2Isoc

Figure 7. Map of mean error in plot of c&,/D, vs. De for type I particles (least error corresponds to point labeled +).

by t I0.025. The region with the least error may be visualized as a valley in a three-dimensional error map. Figure 6 shows the effect of flow rate (designated by the different runs I-l,I-2,etc. as described in Table I). The regions for t I 0.025 are steep with respect to t&,/D, a t high flow rates and nearly flat a t low flow rates (runs 1-1 and 1-2). Thus, De has a larger effect on the response curve a t high flow rates but is not important a t low flow rates; the situation is reversed at low flow rates. The best values of D, and De correspond to the basin where all six valleys overlap. This is shown more clearly in Figure 7. This graph is a map of the mean error (arithmetic mean of the six error maps) for all six runs. The least-error point (+ in Figure 7) corresponds to t&,/D, = 0.25 and De = 0.0063 cmz/s. The relatively low value of the first quantity is due to the fact that all six runs were a t very low flow rates (maximum Re = 0.47, Table I).

Ind. Eng. Chem. Fundam., Vol. 19, No. 4, 1980

366

Table 11. Parameter Values for Calculated Response Curves A, B, and C in Figure 2 parameter values for calcd curves curve

ppKA

A B C

5.23 5.32 5.05

ebDax/Dv De, cmz/s 0.25 0.25 0.25

0.0063 0.0063 0.0063

error,

E

0.02 0.05 0.1

0.4

0.11 10

,

,

. , I . . . ,J 100

1000

k,, cc g sec

. >

n

Figure 9. Error map in plot of Sh vs. k , for run 1-4.

x

0


w=

0.2

10

1

0 D, , cm2/sec

Figure 8. Error map in plot of c$,/D,

vs. De for type I1 particles.

With these results for the three parameters, the predicted response curve Cdc vs. t is that labeled A in Figure 2. It agrees well with the experimental curve; the rootmean-square error is 6 = 0.02. Curves B and C illustrate the large effect of p6(* on the response. A 5% drop in the value of this parameter, from 5.23 to 5.05, increases the error from e = 0.02 to 6 = 0.10. The parameter values employed for calculated curves A, B, C are summarized in Table 11. A similar analysis in the real time domain for type I1 particles gives the values: p&A = 5.06, q,Dax/Dv= 0.29, and De = 0.014 cmz/s. The effect of flow rate on the values of D, and De for these particles is shown in Figure 8. The two curves for each flow rate (i.e., for each run, 11-1,II-2, etc.) define the region where 6 I 0.025. The effect of flow rate is similar to that for particles I, shown in Figure 6.

Discussion and Conclusion The agreement between the De values (0.013 and 0.014 cmz/s) from steady-state and chromatographic data for type I1 carbon demonstrates that either method is suitable for particles of uniform porosity. For type I particles the two methods give different results (0.0035 vs. 0.0063 cm2/s). This is understandable since the type I particles have low-porosity central cores. In the steady-state measurements this central region acts as a barrier to diffusion and, in effect, reduces the area available to transport. In the chromatographic method, the transient, radial diffusion from the outer surface takes full advantage of the larger porosity in the outer region. With respect to parameter estimation by adsorption chromatography, analysis of the data in the real-time domain shows that the adsorption equilibrium constant has the largest effect on the response curve. An accurate value of K A can be determined from one such curve. In order to establish accurate values of the axial dispersion coefficient and the effective diffusivity in the particles, response curves need to be measured over a range of gas velocities. These conclusions apply when the gas-to-particle mass transfer process and the adsorption step itself have little effect on the response curve. Such conditions are usually met for physical adsorption of gases in beds of adsorbent particles. When these two steps are not intrinsically fast with respect to the other rate processes,

* L: 0.1

. . . 1

O2 0 001

0 01

01

1

D, , cm2 rec

Figure 10. Error map in plot of Sh vs. De for run 1-4.

measurements with different particle sizes can be helpful to obtain De. It should also be noted that the intraparticle diffusivity cannot be accurately determined solely from response curves measured at low rates. This is evident from Figure 6, where the least-error valleys extend horizontally for runs 11-1and 11-2, which are for the lowest flow rates (lowest Re in Table I). Error maps such as Figures 6-8 are particularly useful for determining the range of operating conditions best suited for evaluation of accurate parameter values. For example, if De were to be obtained by analyzing response data by the moment method (Schneider and Smith, 1968), the proper flow-rate range over which to obtain moment data would not be known without such maps. Once the error maps are evaluated good results can be expected from the moment procedure. We have calculated second moments for all the runs shown in Table I and plotted kz vs. 1/V. Relatively well-established straight lines were obtained for both particles. The intercepts of these lines give (by the method of Schneider and Smith) De = 0.0053 and 0.012 cm2/s for particles I and 11. These results are close to the values established by the analysis in the real-time domain. However, if only the two data points for the lowest flow rates are used, De for particle I is 0.0030 cm3/s, which deviates considerably from the preferred result of 0.0063 cm2/s obtained by timedomain analysis.

Appendix The measured response curve for type I particles (run 1-4) was used to evaluate the influence of the gas-to-particle mass transfer coefficient and the adsorption rate constant. Calculated response curves were obtained for t@,/D, = 0.25 and De = 0.0063 cmz/s and for various values of Sh and k,. Figure 9 is the resulting error map. The curves show that for Sh L 2 any value for k , greater than about

367


Ind. Eng. Chem. Fundam. 1980, 79, 367-373

80 cm3/(g s) will have a very small ( t 0.025) effect on the response. Figure 10 shows the influence of gas-to-particle transport (Sh) for various effective diffusivities. The computed curves for this figure were based upon k , = m and q,DaX/Dv = 0.25. If Sh > 2, there is little effect of external mass transfer on the response curve, if the correct value of De is used. Note, however, that if the effective diffusivity is chosen to be larger than its correct value, minimizing the error 6 would give too low a value for S h and kf. This would explain the low Sherwood numbers reported by Wakao e t al. (1976b). Acknowledgment The financial assistance of a grant from the Japan Society for the Promotion of Science and National Science Foundation Grants ENG76-01153 and INT-12107 are gratefully acknowledged. Nomenclature Ccdc = calculated response concentration Cexp= measured response concentration D , = axial fluid dispersion coefficient in the bed of adsorbent particles, cm2/s De = intraparticle effective diffusivity, cm2/s D , = particle diameter, cm D, = molecular diffusivity, cmz/s 12, = first-order adsorption rate constant, cm3/(s g) k f = particle-to-fluid mass transfer coefficient, cm/s

= adsorption equilibrium constant, cm3/g Re = D Uq,f Y , Reynolds number Sc = v/Dv, Schmidt number Sh = kfD,/Dv, Sherwood number t = time, s U = interstitial fluid velocity, cm/s Greek Letters t = error representing the difference between the experimental and calculated output curves, as defined by eq 1 tb = bed void fraction v = kinematic fluid viscosit , cm2/s p, = particle density, g/cm H

KA

Literature Cited Anderssen, A. S., White, E. T., Chem. fng. Sci., 25, 1015 (1970). Boxkes, W., Hofman, H., Chem. Ing. Tech., 44, 882 (1972). Clements, W. C., Chem. Eng. Sci., 24, 957 (1969). Ganawal. S. K.. Hudains. R. R.. Brvson. A. W.. Silveston, P. L.. Can. J. Chem. &g., 49, 113 (1571). Kaguei, S., Matsumoto, K., Wakao, N., Chem. f n g . Sci., in press, 1980. Kubin, M., Collect. Czech. Chem. Commun., 30, 1104 (1965). Kucera, E., J. Chromatogr., 19, 237 (1985). Dstergaard, K., Michelsen, M. L., Can. J. Chem. fng., 47, 107 (1969). Satterfield, G. N., "Mass Transfer in Heterogeneous Catalysis", p 30, M.I.T. Press, Cambridge, Mass., 1970. Schneider, P., Smith, J. M., AIChf J., 14, 762 (1968). Suzuki, M., Smith, J. M., Chem. Eng. J., 3, 256 (1972). Wakao, N., Chem. Eng. Sci., 31, 1115(1976a). Wakao, N.,Tanaka, K., Nagai, H., Chem. Eng. Sci., 31, 1109 (1976b). Wakao, N., Funazkri, T., Chem. Eng. Sci., 33, 1375 (1978). Wakao, N., Kaguei, S., Smith, J. M., J. Chem. Eng. Jpn., 12, 481 (1979).

Received for review December 3, 1979 Accepted July 28, 1980

Response of Catalyst Surface Concentrations to Forced Concentration Oscillations in the Gas Phase. The NO, CO, O2 System over Pt-Alumina L. Louis Hegedus, Charles C. Chang, Davld J. McEwen, and Elaine M. Sloan General Motors Research Laboratories, Warren, Michigan 48090

Experiments were carried out over a Pt-alumina catalyst exposed to mixtures of NO, CO, and O2at 505 'C. The stoichiometry of the feedstream was periodically switched between net reducing and net oxidizing. An infrared beam was passed through the catalyst disk to monitor the concentration of species on its surface. The surface concentration of isocyanate and CO responded sensitively to the frequency of feedstream concentration oscillations. At the high-frequency limit, the surface was covered by an intermediate amount of CO and it was free of isocyanate. Experiments with an integral reactor, operated under conditions similar to the infrared experiments, showed that both CO and NO conversions increased wfth increasing cycling frequency. These results show proof that the transient response characteristics of this system are determined by catalyst surface events. The rate of growth of the isocyanate band was found to be second order in terms of the unoccupied sites, suggesting that two surface species may be involved in its formation.

Introduction A promising method to simultaneously control the emissions of hydrocarbons, carbon monoxide, and nitrogen oxides in automobile exhaust involves catalytic converters which operate near the stoichiometric air-fuel ratio (A/F). The system employs a closed-loop A / F control scheme (Canale et al., 1978) which causes the stoichiometry of the feedstream to oscillate between net reducing and net oxidizing, a t a variable amplitude and frequency. Complex, multicomponent catalysts are required to provide adequate performance and durability (Hegedus e t al., 1979). Despite the intensive work in this area, relatively little is known about the details of some im0196-4313/80/1019-0367$01.00/0

portant aspects of catalyst operation, such as the strong dependence of catalyst performance on the frequency and amplitude of A / F oscillations (Hegedus et al., 1979; Schlatter et al., 1979; Adavi et al., 1977). Most of the work on forced-cycled catalytic reactions was conducted in such a way that only gas-phase concentrations were monitored. On the other hand, there are strong indications that the nature of the catalytic surface (i-e.,the rate of relaxation of surface composition) determines the characteristic time scale of the transient processes, since transport lags are a t least one order of magnitude shorter than the typical response time of the catalyst. Therefore, it seems to be of some importance to understand how the

0 1980 American Chemical Society

Adsorption Chromatography Measurements. Parameter Determination

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