436 Shorter Communications

NOTATION

A molar Helmholtz free energy A(iX,jY) (8”‘AIJX’dY’)

F,, F, functions, Eq. (1) P pressure

’ S ratio of derivatives, Eq. (2) T temperature x mole fraction [ interaction parameter, see ref. [ll.

REFERENCES [ 11 Teja A. S. and Rowlinson J. S., Chem. Engng Sci. 1973 28 529. [2] Rowlinson J. S., Liqaids and Liquid Mixtures, 2nd Edition,

Chapt. 6, Butterworth, 1%9. [3] Kuenen J. P., Theorie der Verdampfung und Ve@ussigung von

Gemischen und der Fraktionierten Destillation. p. 111, Leipzig, 1906.

[4] Gugnoni R. J., Eldridge J. W., Okay V. C. and Lee T. J., A.I.Ch.E.Jl. 1974 20 357.

[5] Teja A. S., Ph.D. Thesis University of London, 1971.

Chemical Engineering Science, 1975. Vol. 30. pp. 436-437. Pergamon Pres Printed in Great Britain

Sorptionof CO2 in Davison 5A molecular sieve

(Receiued 13 June 1974; accepted 6 September 1974)

Several recent papers [l-31 have described experimental studies of the sorption of CO, in molecular sieve adsorption columns. For sorption in Linde 5A sieve Scott [ l] concluded that the kinetics of sorption were controlled by intracrystalline diffusion whereas in 8-12 mesh Davison 4A sieve Carter and Husain[3] found diffusion within the macropores of the pellet to be the rate controlling step. Since the Davison sieve is made from smaller zeolite crystals and has correspondingly smaller macropores than the Linde sieve this differente in behaviour is understandable. We have presented a generalized theoretical analysis of the behaviour of a packed adsorption column under the conditions of macorpore diffusion control and the theory has been shown to provide a satisfactory interpretation of experimental breakthrough curves for propylene and 1-butene in Davison SA sieve (C-521)[4]. We have recently obtained additional experimental data for the sorption of CO, in the same adsorbent and these results can also be interpreted in the same way, thus providing additional evidente in support of the theory and justifying the assumption of macropore control.

3

Fig. 1. Comparison of the experimental breakthrough curves for the sorption of CO, on Davison C-S21-5A (o-adsorption, x- desorption) with the theoretical curves for X’ = 0.25, h = 0.585.

Adsorption and desorption curves were measured under essentially isothermal conditions using the same apparatus and adsorbent bed as in the earlier study[4]. Details of the experimental runs made with smal1 concentrations of CO, in a helium carrier are given in Table 1 and the experimental breakthrough curves are compared with theoretical curves in Figs. 1-3.

Run 1,1.20percent, 50°C.

To calculate the theoretical curves the values of the non- linearity parameter h(= bc,/(l t bc,)) were obtained from the gravimetrie data of Derrah[5]. The other parameters, (the equilibrium constant and diffusional time constant) were obtained by matching the experimental curves to the dimensionless theoretical curves. These values are compared with theoretically predicted values in Table 1.

To calculate the theoretical diffusional time constant the pore diffusivity was estimated from the usual relationship for the transitional regime[6]:

$= T(g-&)

Fig. 2. Comparison of the experimental breakthrough curves for the sorption of CO, on Davison C-521-5A (o-adsorption, x- desorption) with the theoretical curves for X’ = 0.25, A = 0.667.

Run 2,2.34 per cent, 50°C.

Table 1. Summary of experimental conditions and parameters calculated from experimental breakthrough curves

Interstitial Experimental Theoretical Run and Velocity D&Q Calculated D,,ep

figure Co V Temp w(1 - e,)bq,R,* Experimental from w(l- e,)bq,R,‘) Sorbate no. (%Vol.) (cmlsec) “C h X’ (sec-‘) bq, Fukunaga (sec-‘)

CorHe 1 1.20 29.7 50 0.585 0.25 7.36 x lO-’ 6780 CorHe 2 2.34 29.8 50 0.667 0.25 7.85 x IO-’ 6360 6500 6.8 x 10-5 CorHe 3 0.74 30.2 50 0.464 0.25 7.70 x 10-’ 6500

‘The adsorbent was Davison C-521 5A sieve (0.286cmdia. beads). Experiments were carried out isothermally at atmospheric pressure. (Pressure drop across the column was negligible.)

Shorter Communications 437

of-

06-

4 0.4 -

o2-

2 5 10 20 30 50 80

t, min The notation is as defined in Ref. [4]. Fig. 3. Comparison of the experimental breakthrough curves for the sorption of COt on Davison C-521-5A (c+adsorption, x- desorption) with the theoretical curves for x’ = 0.25, A = 0.464.

REFERENCES

Run3,0.74percent, 50°C.

Values of the Knudsen diffusivity (DK) and the molecular diffusivity (&) were calculated from the usual formulae[ó] (0.158 cm* sec-’ and 0.666 cm2 sec-’ respectively). The value of the macropore diffusional time constant (e&./w(l - ep) bq.R,2) was then calculated to be 6.8 x IO-‘sec-’ using the value of tortuosity 7 reported by Ruthven and Derrah[7] for this adsorbent with the values of R,, ep and w given in Ref. [4]. This value agrees very wel1 with the experimental values of 7.36-7.85 x

[l] Scott C. D., Nucl. Sci. Engng 1%8 34 214. [2] Fukunaga P., Hwang K. C., Davis S. H. and Winnick J., Ind.

Engng Chem. Proc. Des. Deu. 1968 7 269. [3] CarterJ. W.andHusainH., Trans. Instn. Chem. Ergs. 19725069. [4] GargD. R. andRuthvenD. M., Chem. EngngSci. 197429 1961. [5] Derrah R. I., Ph.D. Thesis, University of New Brunswick,

N.B., 1973. [6] Satterfield C. N., Mass Transfer in Heterogeneous Catalysis,

M.I.T. Press, Cambridge, Mass. (1970). [7] Ruthven D. M. and Derrah R. I., Can. J. Chem. Engng 1972 50

743.

10-’ sec-‘. The agreement between the equilibrium constant (bq,) calculated from the breakthrough curves and the value derived from published equilibrium data[2] is equally satisfactory.

It thus appears that in this system the kinetics of sorption are indeed controlled by macorpore diffusion and the close agreement between the theoretical and experimental curves provides additional evidente in support of the theoretical analysis.

Dept. of Chemical Engineering Uniu. of New Brunswick Fredeticton, N.B. Canada.

D. R. GARG D. M. RUTHVEN

NOTATION

Chemicd Engineering Science, 1975, Vol. 30, pp. 437-439. Pergamon Pres. Printed in Gr.9 Britain

On the PDE-model of a closed end chemical reactor

(Receioed 3 May 1974; accepted 12 September 1974)

The PDE-(plug Aow with axial dispersion and mass exchange between the main flow and stagnant zones) model of chemical reactor has been discussed in recent years[l-31. Usually it is presented in the following form:

+++$+N(C,-Cz)=+%

$++$c,-C,)=O (1)

where

P = ul/D; N = KSl/uV,; <p = V,/(V, t V,).

In this paper an approximate analytical solution of Eqs. (1) for the case of closed end reactor (D = 0 at z < 0 and z > 1) will be presented. When the input signal of the tracer has a Sfunction form the initial and boundary conditions are

t=o c,=c,=o

z=o s(t)+2 (2)

ZE1 gL0.

An analytical solution of this problem was given by Kafarov et al.[3]. However, it is in the form of a slowly convergent series expansion which is not convenient for calculation of the residence-time distribution curves, e.g. the functions C,(l, t). The Laplace transform of the solution CI(l, t) is:

c,(l, s) = C1(l, t) eë” dt 0

4(a/B)eP’* = (1 + a/B)2e”‘28 _ (1 _ a/B)2e-Pa’2s (3)

where

N P N(l-2~) N2 10 ~- '+G+G+ cp(l-cp) cp(l-cp)(stN/(l-cp)) 1 ’ “2.

We shall consider the expansion

slB (1 t s/B)ZeP”‘28-(l - s/B)2eëP”2B

Since this series expansion is absolutely convergent when the real part of s is positive, each term of (4) could be inverted into it’s corresponding original function[4,5]. Using the properties of the Laplace transform shown in Table 1 as (a) and (b) it could be demonstrated that the first term (at n = 0) will give quite accurate results, when the restriction (Pp)“‘> 1 is satisfied. Then, after consequent application of the relations (c), (d) and (e) from Table 1 the following approximate solution of the treated problem may be obtained:

C,(l, t)= h(t, P, (p)e-‘N”“/t”2 + ,+,d[,+,(l _ +,)]

{J, kNJ{-$-$)] h(7, P, (p)e-[N”-2.“‘.“-.‘1 d7 (5) 0

where

h(t, P, <p) = (P/cp~)“‘(Pt t 2~)e-[p(‘-<p)“4*”

-2PePdt[l+$(t+p)].erfc[y. d(s)].