Chemical Engineering Sc[ence, Vol. 47, No. 17/l& pp. 43054308, 1992. am-2so9p2 s5m f 0.00 Printed in Great Britain 0 1992 Pcrgamon Press Ltd

DIFFUSION OF OXYGEN AND NITROGEN IN CARBON MOLECULAR SIEVE

DOUGLAS M. RUTHVEN JDepartment of Chemical Engineering, University of New Brunswick, Fredericton, NB,

Canada E3B 5A3

(First received 18 October 1991; accepted in revised form 21 April 1992)

Abstraet4ravimetric measurements of diffusion of oxygen and nitrogen in Bergbau-Forschung carbon molecular sieve at subambient temperatures are reported. The concentration range of the measurements extends well beyond the Henry’s Law region of the isotherm. The sorption-desorption rates are controlled by micropore diffusion and, outside the Henry’s Law region, the diffusivity increases strongly with sorbate concentration in approximate conformity with Darken’s equation. There is no evidence of any significant surface or skin resistance to mass transfer.

INTRODUCTION Carbon molecular sieves are widely used in the pro- duction of nitrogen from air by pressure swing adsorption (PSA). In contrast with most adsorbcnts in which the selectivity arises from differences in sorp- tion equilibrium, the selectivity of carbon molecular sieves depends on differences in sorption kinetics. The results of several experimental kinetic studies have been published (Kawazoe et al., 1974; Chihara and Suzuki, 1979; Ruthven et al., 1986; Dominguez et al., 1988). The adsorbents used in these studies were from different manufacturers and, although all are kin- etically selective to oxygen in preference to nitrogen, their behaviour shows some significant differences. For example, the data of Ruthven et al. (1986) for the Bergbau-Forschung sieve clearly suggest that the sorption rate is controlled by internal diffusion. By contrast, the data of Dominguez et al. (1988) are more consistent with a surface resistance to mass transfer.

Both nitrogen and oxygen are relatively weakly adsorbed and their equilibrium constants are almost identical. At ambient temperatures and pressures be- low atmospheric the isotherms are almost linear and, in this range, the diffusivity is essentially independent of concentration. Pressure swing adsorption systems for nitrogen production, however, operate typically over the pressure range l-7 atm and at higher pressures the equilibrium isotherm shows significant curvature_ A recent theoretical and experimental study of a laboratory scale nitrogen PSA system (Farooq and Ruthven, 1991) showed that the ob- served performance could not be accounted for by a constant diffusivity model. Outside the linear region of the isotherm a strong increase in micropore dif- fusivity with sorbate concentration is commonly ob- served and in many cases this effect can be quantitat- ively accounted for by considering the chemical po- tential gradient, rather than the concentration gradient, as the driving force for transport [see, for’example, Ruthven (1984)]. Such behaviour was observed by Kawazoe et al. (1974) for the Takeda

carbon sieve and a dynamic model based on this assumption has recently been shown to provide a rational interpretation of the experimentally observed behaviour of a bench-scale nitrogen PSA system (Farooq and Ruthven, 1991). However, because of the practical importance of this system and the questions raised by the work of Dominguez et al. (1988) con- cerning the nature of the rate-controlling process, a more detailed investigation of sorption kinetics in the Beigbau carbon sieve was deemed desirable.

EXPERIMENTAL

Sorption and desorption rates for oxygen and ni- trogen in a single pellet of 3ergbau-Forschung carbon molecular sieve were measured gravimetrically in a Cahn vacuum microbalance system. The apparatus was designed to operate only at subatmospheric pressures; so, in order to achieve a sufficiently high loading of the adsorbent, measurements were made at low temperatures (mostly at - 80°C) at which the isotherm is of a highly favourable form. Sorption rate (and equilibrium) measurements were made by in- creasing or decreasing the pressure in steps within the range O-l atm. Prior to the measurements the sample was degassed by evacuation overnight at 10m5 torr, 250°C.

Equilibrium isotherms The experimental isotherms for oxygen and

nitrogen at 193 and 273 K are shown in Fig. 1. At 273 K the deviation from linearity, over the pressure range O-l atm, is minor and the isotherms for oxygen and nitrogen are essentially coincident. At 193 K the curvature of the isotherm in the subatmospheric pressure range is similar to that encountered at am- bient temperatures over the working pressure range of most nitrogen PSA processes. The 193 K isotherm (for oxygen) is of favourable (type I) form and deviates only slightly from the ideal Langmuir model. The heat of adsorption, calculated from the temper- ature dependence of the Henry’s Law constant

4305

4306 DOUGLAS M. RUTHVEN

Fig. 1

77 6-

Adso 0 Des I e

273K

[K = K,exp (- AH/R 7’) (see Table l)], is close to the value obtained previously from measurements at higher temperatures (Ruthven et al., 1986).

Sorption kinetics Representative transient sorption curves are shown

in Fig. 2. For isothermal diffusion in a spherical adsorbent particle (radius r) the sorption curve is

Table 1. Henry constants and limiting heat of sorption for O2 in CMS

-0 100 200 300 LOO 500 600 7ocl 600 P florr)

Equilibrium isotherms for 0, at 193 K and 0, and N, at 273 K.

Fig.

T (“C) K (l3hto~) - AH (kcal/mol)

2.75 x 1O-5 3.7 x10-4 3.40

2 4 6 6 10 12 1L 16 fi (minq

(b)

-.-. 0 200 400 600 600 1000 1200 1400

Time (min)

2. Experimental sorption-dosorption curves for O2 and N, in CMS showing conformity with the diffusion equation: (a) short-time region [eq. (21-J; (b) long-time region [eq. (l)]

CmVe

1 2

:

Sorbate

02 N2

02 02

T (K)

193 273

273 193

Pressure step (torr)

6 - 25 715 4 580

470 250 + - 750 110

Diffusion of oxygen and nitrogen in carbon molecular sieve

to the Darken expression: given by

(1)

This expression assumes that the sorbate pressure remains constant following the initial step change, which is certainly true for the present situation as the quantity taken up by the adsorbent is very small relative to the total system capacity. In the short-time region eq. (1) approaches the limiting parabolic form

m, 6 Df -=_ J-

(2) m* r z .

At longer times the higher-order terms in eq. (1) become negligible so that the expression simplifies to

mt 6 -_=I--_e - aGaP= m, 722 *

In contrast, for a system in which the resistance to mass transfer is concentrated at the surface of the microparticle the uptake curve would be of simple exponential form

m, _ = 1 _ e--PCtlr (4) m,

where k (ems- ‘) is the surface mass transfer coeffi- cient.

In conformity with eqs (l)-(3) the sorption curves are linear in fi in the initial region, while, in the long- time region, the plots of log (1 - m,/m,) vs t are linear with intercept - 6/x2. The observed kinetic behaviour is, therefore, seen to be entirely consistent with diffu- sion control, rather than with surface resistance or external mass transfer control.

The variation of the diffusional time constant (D/r’) with sorbate concentration is shown in Figs 3 and 4, together with the best-fit curve calculated according

o Ads l Des

0 I

0 1 2 3 & 5 6

c (wt %I

Fig. 3. Variation of diffusional time constant with sorbate concentration for 0, at 193 X. Theoretical line is calculated according to eq. (5) with values of d In p/d In q from the experimental equilibrium isotherm and (D,,/r’J = 2

x 10-6 s-1.

D=D,Z with the values of (dlnpldlnc) from the equilibrium isotherm. At 273 K the isotherm is essentially linear (up to 1 atm) and the diffusivity shows no significant concentration dependence. The strong increase in

lo-‘

-I

%

?_ . c3

10-S

F

l

O2 . *

N2 - a-

to-61 I

0 0.5 1.0 1.5 c (wt %J

Fig. 4. Diffusional time constants for O2 and N, at 273 K showing the absence of any significant concentration de- pendence (open symbols: adsorption measurements; filled

symbols: desorption measurements).

lo-= ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ 3.0 4.0 50

103/T (K-‘1

Fig. 5. Temperature dependence of diffusional time con- stants for 0, and N, in Bergbau-Forschung CMS showing comparison with the earlier data: (1) present data; (2)

Ruthven et al. (1986); (3) Farooq and Ruthven (1991).

4308 DOUGLAS M. RUTHVEN

Table 2. Summary of limiting difRrsivity data for Bergbau CMS (D,@), s-1

T 6)

193 273

300

333 Activation energies (kcal/mol)

0,

2 X 10-e 2.4 x lo-+

3.5 x 10-S 2.3 x lo-’

6.2 6.0

6.6

N,

3.5 x 1o-6 4 x 1o-5

1.1 X 10-L 6 x 1O-s

3.5 x 10-b -

$3, 7:4’

References

This work This work Ruthven (1986) Ruthven (1986) Farooq (1991) Ruthven (1986) This work Ruthven (1986) Kawazoe (1974) Chihara (1979).

?Takeda CMS. *Treated Takeda CMS.

diffusivity with sorbate concentration at 193 K is in conformity with eq. (5), suggesting that the concentra- tion dependence arises simply as a consequence of the non-linearity of the isotherm rather than from any variation of the mobility.

The temperature dependence of the corrected time constant (BO/rz) is shown in Fig. 5 and Table 2 together with the previously reported values. The values of Do/r2 for both oxygen and nitrogen are substantially smaller than the earlier data and the selectivity ratio (D,,/D,,) is larger. Despite this differ- ence, the diffusional activation energy is similar to earlier reported values.

(1)

(2)

(3)

CONCLUSIONS Sorption rates of nitrogen and oxygen in Bergbau-Forschung carbon molecular sieve are definitely controlled by internal diffusion rather than by a surface resistance to mass transfer. At low temperatures where the measurements extend well outside the linear region of the isotherm the diffusivity increases strongly with concentration. However, this effect can be quantitatively accounted for by the non-linear- ity of the equilibrium relationship. Corrected diffusivities calculated according to the Darken equation (i.e. based on chemical potential gradient as the driving force) are effectively constant. This provides experimental support for the use of the concentration-dependent dif- fusivity model to simulate the performance of PSA processes using this absorbent (Farooq and Ruthven, 1991). A similar conclusion was reached by Kawazoe et al. (1974) for the Takeda carbon sieve although the diffusional time con- stants are quite different. Since the molecular sieve sample used in the present study was from the same batch as that used by Farooq and Ruthven (1991), the differ- ence in the time constants must reflect differences between individual particles rather than between different batches of CMS. Despite the difference in the diffusional time constants, the diffusional activation energy for O2 (- 6.2 kcal/mol) is similar to the values ob- tained previously for both O2 and N,

(4)

(6.5-7.4 kcal/mol). This may suggest that the diff’erences between samples lie mainly in the dimensions of the microparticles rather than in the width of the (slit-shaped) micropores. Since this study was carried out only with Bergbau carbon sieve the results are not necessarily in conflict with the results obtained by Dominguez et al. (1988). It is entirely pos- sible that differently activated and pre-treated carbon sieves may show different rate limiting kinetics.

Acknowledgement-The capable assistance of Ms. Elizabeth Richard, who carried out the laboratory work, is gratefully acknowledged.

c D

D,

P r t T

NOTATION

adsorbed phase concentration microparticle diffusivity “corrected” diffusivlty or limiting value of D as c-0 surface resistance mass transfer coefficient fractional approach to equilibrium in a gravimetric uptake experiment partial pressure of sorbate microparticle radius time temperature

REFERENCES

Chihara, K. and Suzuki, M., 1979, Control of micropore diffusivities in molecular sieve carbon bv denosition of hydrocarbons. Carbon 17, 339.

Dominauea J. A._ Psaris. D. and La Cava. A. I.. 1988. La&n& kinetics as an?accurate simulation of the’rate oi adsorption of nitrogen and oxygen on carbon molecular sieves. A.Z.Ch.E. Symp. Ser. 84(264), 73.

Farooq, S. and Ruthven, D. M., 1991, Numerical simulation of a kinetically controlled pressure swing adsorption bulk separation process based on a diffusion model. C/tern. Engng Sci. 46.2213-2224.

Kawaxoe, K., Suzuki, M. and Chihara, K., 1974, Chromato- graphic study of diffusion in molecular sieve carbon. J. them. Engrrg Japan 7, 151-157.

Ruthven, D. M., 1984, Principles of Adsorption and Adsorp- tion Processes, Chap. 5. Wiley, New York.

Ruthven, D. M., Raghavan, N. S. and Hassan, M. M., 1986, Adsorption and diffusion of nitrogen and oxygen in car- bon molecular sieve. Chem. Engng Sci. 41. 1325-1332.