EXPERIMENTAL TECHNIQUES
An Experimental Method for the Determination of Macropore Diffusivities for Liquids in Molecular Sieve Pellets Lap-Keung Lee and Douglas M. Ruthven’ Department of Chemical Engineering, University of New Bruns wick, Fredericton, New Brunswick, Canada E3B 5A3
A simple method of determining the macropore diffusivity for a liquid in a molecular sieve pellet has been developed. The method depends on measuring the step response of a packed bed using, as a tracer, a species whose molecules are sufficiently large to prohibit adsorption by the zeolite crystals. For such a system the equilibrium ratio of solid phase to adsorbed phase concentrations is simply the macroporosity of the pellet, which may be determined directly by mercury intrusion. Analysis of the effluent concentration curve according to the model of Rosen (1952) yields the macropore diffusional time constant which may be combined with liquid phase diffusivity data to give the tortuosity factor. The tortuosity factors so obtained for liquid phase diffusion in the Davison (525) and Linde 5A sieves agree well with the corresponding values derived from gas phase experiments. This suggests that transport within the liquid filled pores occurs entirely by molecular diffusion with no significant contribution from surface diffusion.
The spread of the breakthrough curve and the corresponding dynamic capacity of an adsorption or ion-exchange column is governed primarily by the mass transfer resistance. Detailed information about mass transfer rates is therefore a prerequisite for the successful theoretical prediction of column performance. With a molecular sieve adsorbent or a macroreticular ion-exchange resin there are three distinct resistances to mass transfer: the external fluid film resistance, the macropore diffusional resistance of the adsorbent pellet, and the micropore diffusional resistance of the actual adsorbent crystals. The relative i,mportance of these three resistances varies greatly depending on the particular system and the conditions and, in many cases, more than one of these resistances may be significant. For such systems it is difficult to extract unambiguous information concerning the individual mass transfer resistances directly from an analysis of experimental breakthrough curves. Chromatographic methods of determining simultaneously both the macropore and micropore diffusional resistances have been developed by MacDonald and Habgood (1972) and by Hashimoto and Smith (1973). These methods depend on the use of either two different carrier gases or two different sizes of adsorbent particles to alter the relative importance of the micropore and macropore resistances. The diffusional time constants for the two processes are obtained from the second moments of the chromatographic peaks. So far these methods appear to have been used only for gas phase adsorbates although, in principle, the technique is equally applicable to liquid systems. The principal disadvantage of the method arises from the difficulty of making reliable and accurate determinations of the second moments. Since the values obtained for the individual diffusional time constants depend on differences in second moments there is always a danger of compensating errors in the values obtained. In order to eliminate the complications arising from the presence of more than one significant diffusional resistance, we have developed a method of measuring macropore diffusivities based on the response of a nonadsorbing tracer (Le., a tracer which can penetrate the macropores of the pellet but 290
Ind. Eng. Chem., Fundam., Vol. 16, No. 2, 1977
which is too large to enter the micropores). This method is particularly suitable for molecular sieves since, for these adsorbents, there is a clear distinction in size between micro and macropores and it is therefore relatively easy to find a tracer system which fulfils the molecular size requirements. The method is in principle applicable to both gaseous and liquid sorbates but it is more suitable for the liquid phase since, for most gas phase systems, the macropore diffusional time constants are inconveniently small.
Theory The method depends on following the response of an adsorbent column to a step change in the inlet concentration of nonadsorbing tracer. An analogous procedure based on a pulse injection of tracer could easily be devised but the step input is somewhat more convenient experimentally. Neglecting axial dispersion, the effect of which is generally small, and assuming negligible external fluid film resistance, the response of the system may be described by the following set of equations
with the appropriate initial and boundary conditions c ( z , O ) = c’(z,r,O) = C’(z,O) = c 1
c(0,t) = c’(z,R, t - z / u ) =.cz
This set of equations is formally identical with the set of equations used by Rosen (1952,1954) to describe the kinetics of sorption in a packed bed for a system in which the equilibrium isotherm is linear and the kinetics of sorption are controlled by diffusion within the adsorbent particles. With
1
0.9
1m --
1
08 07
06
c/c.
u--$ T1
05
x 0025 2 0045 1
04
Figure 2. Schematic diagram of the apparatus (Fl, feed; F2, pure solvent; R, rotameter; D, 3A molecular sieve drying column; S1, S2, sample points; A, adsorption columns (4 in series); P, bypass; T2, storage tank for effluent; T1, storage tank for pure solvent).
3 0.080 4
5
03
T2
0.200 0.250
02 1-0 01
09
M
05
00
15
10
25
20
30
T/ X
08
Figure 1. Theoretical tracer response curves calculated from eq 7 . 07
appropriate changes of variable Rosen's solution therefore gives directly the theoretical response curve for the nonadsorbing tracer c =- c - C ] co
+
c/c. 0 5 e
c2-c1
1 =2
06
2 - Jm a
1
[
x
0.4
+
l11
X(sinh 2X sin 2X) exp -X cash 2X - COS X X(sinh 2X - sin 2X) dX X sin TX2- X - (7) X cash 2X - COS 2h
1
A
03
RunNo Xmatch 37 0.030 42 0380 44 0.203 Theoretical Curve
I
02
where the dimensionless column length parameter ai XE3L12E.tpDpZ
uR2
t~
a.~ c 00
and the dimensionless time
05
?-O
1.5
2.0
2.5
3.0
T iX
D
T G ~ ~ ( ~ - z / u )
R
Figure 3. Comparison on theoretical and experimental tracer response curves.
A family of theoretical response curves was calculated from eq 7 for an appropriate range of X values. Representative curves showing C / C O plotted against
(4-
T/x~ 2 - . x . -1- . 3 1- €B
1)
€p
with X as parameter, are shown in Figure 1. For an experimental run the parameters t ~tp,, u , and z are known so the experimental response curve may be plotted on the same time scale. The appropriate value of X may then be found by superimposing the experimental curve on the family of theoretical curves.
Experimental Section A schematic diagram of the apparatus is shown in Figure 2. The adsorption column (i.d. 3.5 cm) was made in four sections with a total packed length of 140 cm. In each section of the column a layer of glass beads was placed on top of the molecular sieve packing to serve as a flow distributor. Connections were of fine bore copper tubing to minimize the dead time for the system. Before the start of a run pure solvent (or a mixture of known
composition) was pumped through the system in order to establish a uniform initial concentration through the macropores of the adsorbent. With the column isolated, the rest of the system was then purged with liquid of a different known composition. At time zero the flow of this second liquid was switched to the column to give essentially a step change in concentration at the column inlet. During the course of a run the effluent flowed continuously through the sample point 6 2 ) a t a flow rate of 35-40 cm3/min; %-mL samples were taken a t short intervals and the composition was monitored by measuring the refractive index using an immersion refractometer (Carl Zeiss). All experiments were conducted at room temperature (23-25 OC). A small rise in bed temperature (1-3 "C) was observed during the course of a run but this was probably due to the heat generated by the pump since, in this type of process, a heat of assorption is not involved. In calculating the response curves a small correction was applied for the dead time between column outlet and sample Ind. Eng. Chem., Fundam., Vol. 16, No. 2, 1977
291
Table I. Details of Bed and Absorbent Adsorbent Run no.
Type
tP
Z
'B
Fluid velocity, u , cm s-l
34 36 37 40
Davison 5A 525 (7 mesh)
0.34
2
Linde 5A % in.
123.7 130.7 129.7 129.7 128.4 128.4 128.4 129.4 129.4
0.386 0.387 0.379 0.379 0.372 0.372 0.372 0.389 0.389
0.719 1.001 0.601 0.891 0.804 0.996 0.709 0.953 0.718
43 44 45
Bed
0.33 10.33 0.33
Linde 5A H s in.
Table 11. Details of Tracers and Diffusivities" Run no.
Bed sat. with tracer
Feed
D , x 105 cm2 s-1
rspz)x 105
34
D , x 105 cm2 s-l
T
s:i)
Tlit.
100%CsH12 100%Cf& 1.76 2.83 0.29 1OO%C6H 1 0 0 % ~ ~ ~1.76 ~ 3.02 0.31 4.9-6.Bb 43.7%CsH12 100%C6H6 1.69 3.10 0.32 5.3 100%C6H6 28.5%CC14 1.86 2.98 0.31 6.1 41 28.5%CC14 100%C6Ht3 1.86 6.14 0.85 2.2 Linde 1 0 0 % ~ ~ 38.1%CsH12 ~ ~ 1.67 7.69 1.06 1.67 7.14 0.99 5A 38.1%C&12 100%C6H6 1.66 2.10 0.73 100%C6Hfj 36.996C6H12 2.05 0.71 2.3 2.3f 1 0 0 % ~ ~ 1.66 ~ ~ 36.9%c6Hl2 Concentrations in mole %. * Ruthven and Derrah (1972). Sargent and Whitford (1971). Vandeginste (1971). e Hashimoto and Smith (1973). f Roberts and York (1967). Davison 525
point. Typical curves showing the dimensionless effluent concentration plotted against the modified time variable are shown in Figure 3 and relevant details of the adsorbents and flow conditions are summarized in Table I. Experiments were performed with two different molecular sieve adsorbents (Davison 525,5A sieve and Linde 5A sieve) and two different tracer solutions (benzene-cyclohexane, benzene-carbon tetrachloride). The choice of tracer solution is dictated by the following considerations. (1)The dimensions of the molecules of both components should be large enough to prevent adsorption in the 5A zeolite crystals. (2) There must be a measurable difference in refractive index between the two components. (3) The molecular diffusivity of the liquid mixture must be known and should be reasonably constant over the relevant range of composition. (4) The liquids should be nonvolatile and of similar density to avoid errors due to evaporation or large convective effects. These conditions are well satisfied for the benzene-cyclohexane system, but for the benzene-carbon tetrachloride system the difference in densities is large and to obtain consistent results it was necessary to restrict the range of concentration (e.g., pure benzene-3Wo carbon tetrachloride). Results and Discussion A comparison between representative experimental and theoretical response curves is shown in Figure 3 from which it may be seen that the theoretical model provides a very satisfactory fit of the experimental data. The values of X and the corresponding values of DPlRp2for each of the experimental runs are summarized in Table 11. If transport through the macropores occurs only by molecular diffusion, with no significant contribution from surface diffusion, the pore diffusivity (D,) is related to the molecular diffusivity of the liquid mixture (D,) by D, = D m / r ,where the tortuosity factor ( T ) is in principle a structural parameter which is independent of the nature of the diffusing species. Liquid phase diffusivity data for cyclohexane-benzene and for benzene-carbon tetrachloride have been given by Sanni 292
Ind. Eng. Chem., Fundam., Vol. 16, No. 2, 1977
and Hutchison (1973) and Staker and Dunlop (1973), respectively. For these systems the diffusivity is somewhat dependent on concentration and in the analysis of the tracer data we have therefore used integrated average values over the relevant concentration ranges
D,=-.
c2
- c1
LflD(c)dc
(8)
For both the Davison and Linde sieves consistent values of r were obtained with both tracer liquids. Experiments with two different particle sizes of the Linde sieve also gave consistent values for D , and 7 although the time constants ( R 2 / D p differed ) by a factor of 4. The numerical values of r for both the Davison and Linde sieves are consistent with previously reported values. For the Davison sieve values of 7 within the range 4.9 -6.8 were obtained by Ruthven and Derrah (1972) from an analysis of gravimetric uptake curves for CsH8, Cs&, and 1-C4Hs and the present values are close to the mean of this range. Published tortuosity data for the Linde 5A sieve are less consistent. From an analysis of tracer exchange curves for COz, Sargent and Whitford (1971) obtained values of 7 within the range 1.71-1.84 while, for the same system, Vandeginste (1971) gives a value of 3.3: The chromatographic measurements of Hashimoto and Smith (1973) which were made using tracers of N2 and n-C4Hlo in a helium carrier yielded values of 7 in the range 2.7-4.1 while the liquid phase adsorption study of Roberts and York (1967) with n-hexane gave a value of 7 = 2.3. For the Davison sieve the agreement between the values of 7 obtained for different sorbates in both liquid phase and gas phase systems provides strong evidence that surface diffusion makes no significant contribution to the transport mechanism. The same conclusion may be extended to the Linde sieve although, in view of the greater range in the tortuosity values reported in the literature the argument, for this system alone, would be less cogent. The significant difference in tortuosity factors between the
Table 111. Comparison of Film Coefficients and Diffusional Time Constantsa
34 36 37 40 41 42 43 44 45
4.86 5.42 4.51 5.47 4.17 4.16 3.72 12.61 11.49
4.25 4.53 4.65 4.47 9.21 11.54 10.71 3.15 3.08
013
3
114.4
119.6
97.0 122.4 45.2 36.1 34.7 40.0 37.4 a Values of k f were calculated from the expression k f = 3/R. k, = 3/R. 1.09 L'. (Re.Sc)-2/3and values of k , from k , = 15 D,/R2. PORE DIAMETER,
Linde and Davison sieves appears to be related to the difference in crystal size and macropore diameter since the Davison sieve is made from much smaller crystals and has correspondingly smaller diameter macropores. The difference in the pore size distributions is illustrated in Figure 4 which summarizes the results obtained by mercury intrusion porosimetry. It is assumed in the analysis that external fluid film mass transfer resistance is negligible in comparison with the diffusional resistance of the macropores. That this is a valid approximation under the conditions of the present experiments my be confirmed by a comparison of the fluid film mass transfer coefficients, as estimated from the correlation of Wilson and Geankoplis (1966), with the equivalent coefficients obtained from the linearized driving force representation of the diffusion process (hp = 15D,/R2) (Glueckauf, 1955). This comparison is shown in Table I11 from which it is evident that the contribution of fluid film resistance is in all cases small (1-3%). The other important approximation in the analysis is the neglect of axial dispersion. The relative importance of axial dispersion and mass transfer resistance is determined by the dimensionaless parameter a defined by
where h (s-l) is the overall mass transfer coefficient. I t has been shown that if a is less than about 0.1 the effect of axial dispersion in broadening the breakthrough curve will be negligible in comparison with the effect of mass transfer resistance (Garg and Ruthven, 1975). Measurements of axial dispersion in the flow of liquids through packed columns generally yield reciprocal axial Peclet numbers (Ddud) within the range 1-3 and essentially independent of Reynolds number (Carberry and Bretton, 1958; Liles and Geankoplis, 1960). That these values are somewhat greater than the comparable values for gaseous systems probably reflects the greater importance of deviations from the ideal velocity profile in liquid systems. Assuming DL/ud = 3.0, the values of a for the present systems range from 2 X (run 44) to 1.6 X 10-3 (run 43) thus justifying the original assumption that the effect of axial dispersion can be neglected. Conclusion The use of a nonadsorbing tracer provides a simple and convenient method of measuring macropore diffusivities for liquid phase adsorption systems. For both Davison and Linde 5A sieves the tortuosity factors, calculated from the experimental diffusivities, are found to be consistent with the values obtained previously from experiments with gaseous adsorbates. This agreement provides a very satisfactory confir-
Figure 4. Comparison of macropore size distribution for Davison 525 and Linde 5A sieves. mation of the validity of both the experimental method and the theoretical anslysis and implies that, for the liquid phase systems, transport within the macropores occurs entirely by molecular diffusion with a negligible contribution from surface diffusion. Acknowledgment We are grateful to Dr. Hanju Lee of W. R. Grace and Co. for providing us with the pore size distribution measurements which are shown in Figure 4. Nomenclature c = fluid phase concentration in bulk liquid c' = fluid phase concentration a t a point within a macropore E' = macropore fluid phase concentration averaged over a pellet c = initial steady-state fluid concentration cp = final steady-state fluid concentration d = pellet diameter D = molecular diffusivity in fluid phase DL = axial dispersion coefficient D, = integrated average molecular diffusivity in fluid phase D, = macropore diffusivity k = overall effective mass transfer coefficient (s-l) h f = fluid phase mass transfer coefficient (s-l) k , = equivalent solid phase mass transfer coefficient (=15 D,/R2) r = radial coordinate R = pellet radius t = time from step input T = dimensionless time (=2(D,/R2)(t - z / u ) ) u = interstitial fluid velocity X = dimensionless column length parameter
z = distance measured from column inlet Re = particle Reynolds number
Sc = Schmidtnumber
Greek Letters a = definedbyeq9 tg
= voidageofbed
tp
= porosity of adsorbent pellet
X = dummy variable T = tortuosity factor
Literature Cited Carberry, J. J., Bretton, R. H., A./.Ch.€.J., 4,367 (1958). Garg, D. R., Ruthven. D. M., Chem. €ng. Sci., 30, 1192 (1975).
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Glueckauf, E., Trans. Faraday Soc., 51, 1540 (1955). Hashimoto, N., Smith, J. M., Ind. Eng. Chem., Fundam., 12,353 (1973). Liles, A. W., Geankoplis,C . J., A.I.Ch.E.J., 6, 591 (1960). MacDonald, W . R., Habgood, H . W., Can. J. Chem. Eng., 50,462(1972). Roberts, P. V., York, R., Ind. Eng. Chem. Process Des. Dev., 6, 516 (1967). Rosen, J. E.,J. Chem. Phys., 20, 388 (1952). Rosen, J. E.,Ind. Eng. Chem., 46, 1590(1954), Ruthven, D. M., Derrah, R. I . , Can. J. Chem. Eng., 50, 743 (1972). Sanni, S.A,, Hutchison, H. P., J. Chem. Eng. Data, 16,62 (1973). Sargent. R. W. H.,Whitford,C. J., Adv. Chem. Ser., No. 102, 161,(1971).
Staker. G. R., Dunlop, P. J.. J. Chem. Eng. Data, 18,62 (1973). Vandeginste,J. P., M.A.Sc.Thesis, University of Toronto, 1971. Wilson, E. J., Geankoplis,C. J., Ind. Eng. Chem., Fundam., 5 , 9 (1966).
Received f o r reuiew December 29,1975 Accepted October 1,1976 T h i s paper was presented at t h e 68th Annual Meeting Los Angeles, Calif., Nov 16-20, 1975.
of A.I.Ch.E.,
Continuous Mass Spectrometric Analysis of High-Temperature Kinetics in Static Vessels Normand M. Laurendeau’ The Combustion Laboratov, School of Mechanical Engineering, Purdue University, West Lafayette, Indiana 47907
Robert F. Sawyer Department of Mechanical Engineering, University of California,Berkeley, California 94 720
Evaluation of kinetic mechanisms requires continuous analysis of all stable species concentrations. We have achieved this goal for the static vessel method at high temperatures by using remote mass spectrometric analysis. G a s samples are continuously exhausted through a 10-pm isentropic leak integrated into a wall of the reactor. By allowing the reaction to proceed to chemical equilibrium, we do not require “initial time” approximations; moreover, reaction mechanisms controlling the approach to equilibrium may be investigated.The experimental technique has been substantiated by considering the decomposition reaction, 2N02 2 N 0 4-02.Results are in agreement with previous work.
Introduction Basic knowledge concerning the elementary kinetics of both NO and NO2 decomposition is essential to our understanding of several air pollution problems. These reactions are quite slow, and hence can be studied at high temperatures using classical static vessel techniques (Laurendeau, 1972). Unfortunately, such methods present several disadvantages. (1)Continuous, in situ chemical analysis is usually impossible. (2) Proposed mechanisms must be consistent with all stable species in the system, but in general, only one or two species are measured. (3) Data analysis may require initial time approximations due to mixture equilibration effects. In this paper, we describe experimental and analytical methods which overcome these difficulties. Experimental procedures have been evaluated by considering the bimolecular nitrogen dioxide decomposition reaction
N O ~ + N O&~N O + N O + O ~
(1)
kb
This reaction probably affects the measured proportions of NO and NOz found in gas turbine exhausts (AiResearch, 1971).
Experimental Methods Goldfinger et al. (1963) have applied continuous mass spectrometric analysis to static systems, but only for photochemical reactions near room temperature. This research effort extends their method to the study of thermal reactions a t higher temperatures. Hence, for our case, we must separate the mass spectrometer from the reaction vessel. Nevertheless, 294
Ind. Eng. Chem., Fundam., Vol. 16, No. 2 , 1977
the results presented here demonstrate that a combination of (1)slow reaction time and (2) rapid transport of gases from the reactor to the spectrometer produces reliable concentration-time profiles. For comparative purposes, we have obtained rate constant data by both continuous mass spectrometric and manometric measurements. The sample is withdrawn through a 10-km leak introduced into a wall of the reaction vessel. In this way, excellent chemical data can be obtained for all stable species without stopping or disturbing the chemical reaction (Goldfinger et al., 1963). Moreover, the inherent simplicity of the static method is preserved since the leak is small, and thus any pressure loss (0.04%/s) correction has little effect on the pressure rise induced by the NO2 decomposition process. Equipment. Chemical reaction takes place inside a quartz vessel, suitably placed in an Astro Model 1000.4-3060 graphite resistance furnace, manufactured by Astro Industries, Santa Barbara, Calif. An essentially constant temperature environment exists throughout the reaction volume (f3K at 1700 K). The temperature is regulated by a feedback circuit composed of a calibrated Astro BGT-2 boron-graphite thermocouple and a Leeds and Northrup Electromax 6261 C.A.T. controller. The set point temperature is reproducible to f 2
K. The reaction vessel is depicted in Figure 1, and its integration into the furnace assembly is shown in Figure 2. The isentropic sampling orifice (pressure ratio E lo3) is formed in a manner similar to the work of Goldfinger et al. (1963).A thin cone-shaped section is molded at one end of the reactor. After pulling a vacuum inside the vessel, a Tesla discharge is applied along a fine copper wire through the 5/16-in. diameter tube, to
