The Measurement of Diffusion and Adsorption Using A Jetloop Recycle Reactor

J. Weitkamp, H.G. Karge, H. Pfeifer and W. HBlderich (Eds.) Zeolires and Related Microporous Marerials: &are of rhe A n 1994 Studies in Surface Science and Catalysis, Vol. 84 0 1994 Elsevier Science B.V. All rights reserved.

1201

THE MEASUREMENT OF DIFFUSION AND ADSORPTION USING A JETLOOP RECYCLE REACTOR Klaus P. Moller and Cyril T. O’Connor Catalysis Research Unit, Department of Chemical Engineering, University of Cape Town, Private Bag, Rondebosch, Cape Town, South Africa, 7700.

A bidisperse pore model describing the diffusion of a pulse of tracer gas in a catalyst pellet in a jetloop reactor system has been developed. Model analysis shows that by varying flowrate and crystal size a wide range of diffusion constants can be measured. The diffusion of propane and butane in zeolite SA is measured. The data compares favourably with data in the literature for commercial 5A samples. This system proves to be unique for measuring diffusivities in catalyst pellets.

1. INTRODUCTION The last two decades have seen a significant increase in the study of diffusion in molecular sieves. This is due to the recognition that intracrystalline diffusion provides the key to understanding shape selective catalysis and selective separationladsorption processes. With this information existing processes may not only be further optimised, but also new applications will be proposed and designed. Many methods have been developed for measuring diffusion in zeolite systems, including, gravimetric, volumetric, frequency response, pulse gas chromatography(PGC), pulse field gradient NMR(PFG-NMR), zero length column (ZLC) [ 11 and more recently IR [2]. These methods may be classified into macroscopic and microscopic measurements. Macroscopic methods measure transport diffusivities by inference using a suitable diffusion model while microscopic methods measure the molecular motion which yields self-diffusivities. Much of the early work was in error by not taking precautions regarding additional resistances such as heat and mass transfer. Subsequently, more care has been taken in evaluating diffusion data and many of the large deviations observed, particularly between microscopic and macroscopic data, have been resolved or explained. Most of the diffusion studies have been made on powder systems. Of the macroscopic methods only the PGC and more recently the ZLC method [3] allow easy measurement of diffusivities on pelletised zeolite samples. As indicated by Kiirger and Ruthven [4] it would be advantageous to use recycle reactors to measure diffusivities in catalysts. Ma and Lee [5] measured diffusion using a spinning basket reactor but their results appear to have been controlled by intraparticle diffusion. This paper presents results obtained on the measurement of diffusion in catalysts using a jetloop reactor (JLR) [6]. The jetloop reactor, an internal recirculation reactor with low internal volume, behaves as a CSTR in which heat and mass transfer effects may be neglected. In the present paper the classical bidisperse pore model with a constant crystallite size is

1202

applied to the jetloop system. A theoretical analysis of the applicability of the jetloop reactor for the measurement of diffusion in catalysts is made. The diffusion of propane and butane in 5A zeolite is measured and the results compared to literature data.

2. DIFFUSION MODEL The bidisperse pore model [7] was modified by replacing the packed bed response by that of a CSTR. This eliminates the need to estimate axial dispersion and gas film mass transfer. A constant crystal size was assumed throughout this work. Assuming a linear adsorption equilibrium isotherm (i.e. differential concentration range or Henry’s Law regime) and a pulse input, the equations maybe solved in the LapIace domain. The Laplace solution may be inverted accurately and quickly into the time domain using the FFT algorithm [8]. Applying van der Laan’s theorem [9] to the Laplace domain solution, the first central moment is given by:

[

F1 = T+- ‘cat 0(1+K +(l-O)Kc],

F

and the variance is given by:

3. DATA ANALYSIS To determine model parameters 213data points are collected such that the complete response curve is well represented. Frequency domain and time domain curve fitting are used. For frequency domain curve fitting, the time data are converted into the frequency domain using the FFT algorithm. The parameters of the model are determined by minimising the least squares error between the experimental and model frequency response curves. Time domain parameter estimation is accomplished by inverting the model into the time domain and minimising the least squares error between the logarithm of the model and experimental time data. In both cases a modified Nelder and Mead simplex search algorithm is used. The frequency domain fitting is biased to the initial part of the curve (short time region) while the time domain fitting is biased to the tail of the response curve. Both methods, when applied to simulated data, accurately predict the correct model parameters from simulated response curves. Parameter estimation from the first and second moment are not reliable due to excessive tailing. However, the first moment can be used to generate initial parameter values for the simplex routine. Once the model parameters have been found, the theoretical model is compared to the experimental data. These methods have been found to be robust and accurate.

4. EXPERIMENTAL The experimental apparatus is shown schematically in Figure 1. The jetloop reactor, when used under the conditions of these experiments, has been shown to be well mixed [ 101. The N, carrier flowrate was set at approximately 400 ml/min (STP) with a jet head pressure of 500

1203

kPa giving residence times between 5 and 7s. 0.1 - 0.6g of catalyst was pretreated in situ at 300 "C for 6 h. 150 p1 of propane (99.9%) and butane (99.9%) was injected using a sample valve and simultaneously the data acquisition system was activated. Reproducibility of this technique was excellent. The response was sampled for 10 to 200 residence times using 213 data points depending on the temperature. To test for non-linearities the pulse concentration was diluted 50 fold using nitrogen. Table 1 : Zeolite 5A parameters. PARAMETER

30140 MESH Lot No. 478041

Pp

e

(g/ml)

R, (cm) rp (cm) R, (cm)

1.15

0.32 0.254 3.28-5 I .X-4

The concentration in the reactor was sampled by inserting a 0.32mm ID inert capillary tube into the reactor. A reactor head pressure of 20 FIGURE I : SCHEMATIC OF JETLOOP REACTOR SYSTEM kPa ensured a flow of 27 ml/min to the detector. Having the sampling point flush with the centre tube was shown, from RTD studies, to be the ideal position for measuring the true response of the reactor to a pulse input [lo]. The capillary was inserted into the ionisation detector flame tip. This configuration allowed the extra-system volume to be approximated as dead time. The analog FID signal was amplified and digitised via a 12 bit ADC. This data was logged by a PC using RS232 communications at a maximum rate of 200 Hz with a SBC 8032 110 processor. This data was then processed by the FFT software and the model constants determined. Table 1 shows the parameters of the zeolite 5A which was used as supplied.

5. RESULTS AND DISCUSSION 5.1 Parameter Sensitivity Analysis The results of the parameter sensitivity analysis Table 2 : Simulation model parameters based on the first and second moment are shown in Parameter Value Figures 2 and 3 and the parameters used in the simulations are shown in Table 2. The parameter T~., (s) 0.14 SJp2 represents the fractional contribution of the (s) 9.86 0.05 micro-pore diffusional resistance to p2. The R, (cm) 2.0 R, (w) contribution of micro-pore adsorption to p, is 0.3 independent of flowrate and a function of V,JV,,,. K, 0.0 The contribution of the micro-particle resistances to D, (cm'/s) 0.05 p2 is a function of the flowrate and V,JV,. The Kc 100 D, (cm%) 1.OE-10 maximum contribution that the micro-particle can have on the second moment can be determined from equation (3), which is obtained by differentiating the second moment. Equation (3) depends only on the adsorption properties of the catalyst and therefore allows estimation of the optimum catalyst mass (volume) that should be used in measuring D,. This does however not

1204

indicate whether D, may be estimated accurately, for this the individual contributions must be estimated. Figure 2 shows the dependence of the micro-pore contribution to the second moment on T,,~ and K,. The shape and position of the Sx/p2 curves maximum depends significantly on 5. The position of the curve maxima are given by equation (3). The variation in SJp2 with K, at a fixed t,,, shows that the accuracy of parameter estimation is significantly reduced by not maintaining teat at its optimum value. Clearly, too low teat values should be avoided.

The micro-pore contribution to the second moment may be increased by using high flowrates and large crystallite sizes at constant D,. Figure 3 shows that as either flowrate and/or R, are increased, the upper measurable limit of D, increases from 5.OE-8 to greater than 1.OE-6 cm2/s. The simulations shown in Figure 4 demonstrate that the diffusion model response curves approach those of a CSTR, becoming indistinguishable at small D, values when using high flowrates and large crystal sizes. These simulations correspond to the "10 x Flow, R," curve shown in Figure 3. This is caused by there not being enough time for a measurable amount (E* greater than lo") of adsorbate to be adsorbed on the catalyst. Diffusion control in this case would only become significant at E* values below and most detection systems do not allow accurate analysis of such concentrations. Alternatively, Figure 5 shows that the diffusion model response curves approach those of a CSTR with adsorption control, becoming indistinguishable at large D, values when flowrates are low and crystal sizes small. These simulations correspond to the "Std (Table 2)" curve in Figure 3. This condition corresponds to total adsorption control with the response curve being independent of diffusion. In this case diffusion coefficients cannot be measured.

Figure 2 : Micro-pore contribution as a function of T~.,.

Figure 3 : Micro-pore contribution as a function of D,.

Thus in principle, this apparatus allows the measurement of most diffusion rates by adjustment of flowrate or crystal size. The measurable range is similar to that shown for the ZLC method [l]. Note that semi-log plots of the simulated data produce a linear tail similar to that observed in the ZLC method [4]. Attempts to find an expression for the slope of the response curve have not been successful. The slope, in the case of micro-pore diffusion control would be a function of K, and D,. In principle K, may be estimated from the first

1205

"lr,.l,on

.-. w

,.

*

w

p

B

3

0.I

z

0.1

ti

0

0 w C n

s

I<-# ,r-9

0

B

:

o< oc

It-'

x-,

z

0.0,

-I

?i 8

0

om,

0.WI 0.0

4.0

8.0

12.0

ILD

0.0,

20.1

0.1

NOQtlRLISED TltlE ( T * )

s.O

,2.0

I'.D

ID.0

NORMPaLISEO TIME (1.)

The effect that macro-pore parameters have on the moment analysis are not presented here, but by a similar analysis it may be shown that increasing the flowrate and K, increases the macro-pore contribution to the second moment. The effect of macro-pores on the response curve is easily tested by varying the catalyst particle size. 5.2 Diffusion of propane and butane in 5A

NORMRLISEO TIME (1.)

I

igure 6 : Model prediction of the sorption of propane in SA at 150°C.

Figure 7 : Model prediction of the sorption of butane in 5A at 150°C.

Figures 6 and 7 show that the model prediction of the experimental data in the long time region is good. The apparent noise on the model data is due to the finite resolution of the A/D converter of 1/4000. In the short time region the model prediction is not so good especially for butane. The deviation was shown to increase with decreasing temperature. Simulations indicate that this may be due to the intrusion of macro-pore diffusion resistance. The values of D, that were determined showed erratic behaviour with temperature and were more than an order of magnitude smaller than those estimated from molecular and Knudsen

1206

diffusion mechanisms [9] based on the average macro-pore diameter. Table 3 : Comparison of AHKcwith literature data. Reference

AHKc(kJ/mol)

JLR[this work] PGC[ 171 Chiang et al[l5] Theoreticall91

propane

butane

31 33 35 35

40 49 43

Figure 8 and Table 3 show that the values of K, and AH,, compare very well with those found in the literature. This verifies that the data analysis and experimental methods are Figure 8 : K, as a function o f temperature. A successful. It should be noted that especially comparison with the literature. for strongly adsorbed tracer (e.g. low temperatures) the frequency response method will not yield accurate values of K,. This is a consequence of the above observation that the response curves are not well predicted in the short time region. Time fitting however yields accurate model parameters. Contrary to expectation, K, estimated from the first moment is within 10% of those estimated from curve fitting even for strongly adsorbing tracer. Simulations show that small values of D, are responsible for the extremely long tails. It appears that experimental values of D, were not small enough to influence the moment method significantly. This together with the long sampling times can account for the improved accuracy of the first moment prediction. .

I OL-07

I OE-07

~

1.OE-08 \

E

I.OE-09

1.OL-09

E

Chiang st 4 1 5 1

I

-

r

c)

1.OE-10

n

2LC(lob)[l 6

"I

I OE-1 I

LOL-124

0 0 0 1 8 0.0022 0.0026

0.0030 0.0034 00038 1 /T(K)

00016

,

.

0.0020

,

,

00024

1

ZLC(Linde)[16]

,

.

*.

0.0028

.

I

0.0032

I /T(K) I

rigure 9 : The diffision of propane in 5 A as a function of temperature compared to the literature.

Figure 10 : The diffision o f butane in 5 A as a function of temperature compared to the literature.

Figures 9 and 10 show that D, compares well with other measurements made on commercial 5A samples for propane and butane respectively, but not with those made on laboratory synthesised crystals. Propane diffusion data correlates well with that measured by the PGC methods, except in the case of Chiang et a1 [15] who used powder as opposed to pellets. It is generally accepted [4] that the propane data of Chiang et a1 [ 151 was not micropore diffusion controlled. In the case of butane the data correlates well with ZLC and PGC measurements. In all cases the measurements made using laboratory synthesised crystals are

1207

between 1 and 2 orders of magnitude greater than measurements made using commercial samples. Diffusional activation energies are compared in Table 4. Other than the data of Chiang et a1 [ 151 for propane diffusion in SA, all the values are in reasonable agreement although, if it is assumed that the experimental uncertainty in ED,is 2 kJ/mol [4], then the data obtained by the PGC and JLR measurements are slightly too large. The expected trend of increasing ED, with carbon number is reflected by the JLR measurements. A number of precautions were taken to ensure that the JLR data is as representative as possible Table 4 : Comparison of ,E with literature data. of micro-pore diffusion control. The deviation in Method E,(kJ/mol) [Reference] K, and D, with a 50 fold variation in pulse C,H* CJ,, concentration was less than 10 % and 30% JLR[this work] 20 25 respectively for most of the data presented. Only PGC[17] 21 in cases where the detector response limitations NMRWl 15 17 15 17 zLc[14,161 clearly caused tailing errors were these limits 45 23 PGC[IS] exceeded. The variation of catalyst mass produced no significant variation as shown by the repeatability of the data at 125 and 100 "C shown in Figures 8,9 and 10. The contribution to the second moment of the experimentally obtained data was in all cases greater than 10%. Simulations have shown that such data is adequate for determining accurate values of the model parameters. The estimation of macro-pore diffusion in the usual way [9] based on the macro-pore diameter estimated from mercury porosity measurements contributed between 2 and 20% to the overall diffusion contribution. There is a rapid increase of the macro-pore difhsion contribution at the lower temperatures corresponding to an rapid increase in K,. This is a property of the zeolite sample and no macroscopic method will be able to make better measurements. The problems encountered with fitting the response data at the low temperatures may be related to macro-pore diffusion resistances. However, as mentioned before, unexpectedly low values of D, were obtained. Nevertheless this did result in larger values of D, at the lower temperatures, and would thus reduce the magnitude of ED,. During catalyst manufacture, the hydrothermal treatment may result in the reduction of diffusivity due to the blocking of the interior windows or the formation of a surface barrier due to the obstruction of the pore entrances [4]. It is possible that both these phenomena might well occur. The effect of a surface barrier on the response curve are still to be investigated. It is expected that the surface barrier will have the largest influence in the short time region and that this will have a similar effect as the fitting of D,,, thus reducing the magnitude of ED,. The JLR measures the true dynamic response of a sorbate-sorbent system to a pulse response. These data would in principle be used in the determination of adsorbent performance. The NMR measurements on the other hand provide more fundamental understanding of the behaviour of adsorbed molecules. The limitations of the JLR system is that the system response must be linear for parameter estimation and the adsorbent must be in pellet form. Currently investigations are underway to construct a JLR system which can measure diffusion in powdered samples. 6. CONCLUSIONS

It has been shown that the JLR is able to measure diffusion in catalyst pellets under gradientless conditions. The system could be used to study any commercial catalyst system

1208

over a wide range of diffusion coefficients by varying the flowrate and crystal size, provided the concentration of the tracer gas is low enough to ensure constant K, and D,. The equilibrium adsorption coefficients and diffusivities of propane and butane in molecular sieve 5A have been measured. The values obtained compare favourably with those found in the literature for commercial zeolite samples. The formation of surface barriers needs to be investigated to see whether this can improve the prediction of the response curves in the short time region. This system offers a good alternative for determining diffusivities in commercial catalyst pellets. 7. SYMBOLS Micro-pore diffision coefficient, [cm2/s] Macro-pore. diffusion coefficient, [cm2/s] Dimensionless response, E/T Diffusional activation energy, [kJ/mol] Carrier gas volume flow, [ml/s] Micro-pore adsorption constant Macro-pore adsorption constant Average macro-pore radius [cm] Average micro-particle radius, [cm] Average pellet radius, [cm] Dimensionless time, th Volume of catalyst, [ml]

Volume of reactor excluding catalyst, [ml]

Pellet voidage, [ml/ml] First moment, [s] Second moment, [s] Pellet density, [g/ml] Reactor residence time based on V,,,, [s] Catalyst residence time based on V,,I, [s] Optimum catalyst residence time from eq. 3, [SI

REFERENCES 1.

2. 3. 4.

5. 6. 7. 8.

9. 10.

11. 12. 13. 14.

15.

16. 17.

Post, M.F.M., Introduction to Zeolite Science and Practice, H. van Bekkum, E.M. Flannigen and J.C. Jansen (Eds), Studies in Surface Science and Catalysis 58, Elsevier, 391 (1991). Karge, H.G. and Niessen, W., Catalysis Today,9,45 1 (1991). Ruthven, D.M. and Xu, Z., Chem. Eng. Sci.,48(18),3307 (1993) Kiirger, J. and Ruthven, D.M., "Diffusion in Zeolites and other microporous materials",Wiley,New York (1992),p272;p422. Ma, Y.H. and Lee, T.Y., AIChE.J.,22,147 (1976). Shermuly, G . and Luft, O., Chem.Eng.Tech.,49,907 (1977). Hsu L.-K.P. and Haynes, H.W., AIChE.J.,27,1,81 (1981) Brigham, E.R.,The Fast Fourier Transform and its Application,Prentice Hal1,New Jersey, (1988). Ruthven, D.M., Principles of Adsorption and Adsorption Processes,Wiley,New York,242 (1984). Maller, K.P., Becker, R.J., Fletcher, J.C.Q. and O'Connor, C.T., AIChE Annual Meeting, 2-6 Nov, (1992). Ruthven, D.M. and Stapleton, P., Chem.Eng.Sci,48( 1),89 (1993). Shah, D.B. and Ruthven, D.M., AIChE.J.,23(6),804 (1977). Heink, W., Khger, J., Pfeifer, H., Salverda, P., Datema, K.P. and Nowak, A., J.Chem.Soc.Faraday Trans.,88(3),515 (1992). Kiirger, J. and Ruthven, D.M., Zeolites,9,267 (1989). Chiang, A.S., Dixon, A.G. and Ma, Y.H., Chem.Eng.Sci.,39(10),1461(1984). Eic, M. and Ruthven, D.M., Zeolites,8,472 (1988). M6ller, K.P., PhD thesis, University of Cape Town, 1989.