Chemical Engineering and Processing, 32 (1993) 225-231 225

Construction and application of a jet-stirred loop reactor Aufbau und Anwendung eines Kreislaufreaktors mit Gasstrahlpumpe

Stephan Fuchs and Thomas Hahn* Institut fkr Chemische Verfahrenstechnik der Universitiit Karlsruhe (TH), Postfach 6980, W-7500 Karlsruhe I (Germany)

(Received January 25, 1993; in final form March 1, 1993)

Abstract

In this paper, a jet-agitated recycling reactor is presented as a special type of back-mixing system, which enables a reliable investigation of catalytic properties without any contamination of the catalyst. Determination of the operation behaviour indicates the manufactured reactor to be equivalent to a perfectly mixed system with high fluid velocities inside the loop. Investigation of the carbon monoxide oxidation over a platinum foil, as a test reaction, demonstrated the system’s excellent suitability for applications in catalytic research. Limitations of transport processes in the kinetics observed could be revealed unambiguously, leading to correct interpretation of the data obtained. On this occasion, the measurement device for the gas velocity over the catalyst proved to be very useful.

Synopre

Zur Bestimmung reaktionskinetischer Daten heterogen katalysierter Reaktionen werden im Hinblick auf die Miiglichkeit einer einfachen, zuverliissigen Auswertung h&fig Kreislaufreaktoren verwendet. Die Riickvermi- schung derjuiden Phase im Reaktor wird in der Regel mit Hi&e von mechanisch wirkenden Pumpen oder Geblasen realisiert. In speziellen Fallen, so bei Untersuchungen an nicht poriisen Katalysatoren mit sehr kleiner Aktivober- j&he, kann aber a& kaum zu vermeidende Partikel- abrieb von bewegten Teilen der Flirdergeriite zu einer merklichen Kontamination des Katalysators fiihren. Folglich sind Messungen unter station&en Bedingungen nicht miiglich. Diese unerwiinschten Erscheinungen lassen sich jedoch durch die Verwendung eines Reaktors mit Gasstrahlpumpe ohne bewegte Bauteile (Abb. 2) verhin- dern. AuBerdem ist ein sogenannter Treibstrahlreaktor aufgrund seiner apparativ einfachen Bauweise such fur den Betrieb bei sehr hohen Temperaturen bis 1OOOK bestens geeignet.

Das Betriebsverhalten eines Kreislaufreaktors wird durch die beiden Parameter Riickfuhrungsverhiiltnis und Striimungsgeschwindigkeit in der Schlaufe hinreichend beschrieben. Nur unter Beriicksichtigung beider Griipen ist eine oberpriifung hinsichtlich gradientenfreier Ar- beitsweise, die fur reaktionskinetische Messungen gefordert wird, mtiglich. Riickfihrungsverhiiltnis und Striimungsgeschwindigkeit im Kreislauf hiingen bei einem

*Author to whom correspondence should be addressed.

0255.2701/93/$6.00

Treibstrahlreaktor aufgrund des hydrodynamischen Wirkungsprinzips in erster Linie von der kinetischen Ener- gie des Treibstrahls und den geometrischen Abmessungen, sowie von den StofSdaten des Fluids ab (Gl. (4) GI. (5)). Der in dieser Arbeit vorgestellte, aus Quarzglas gefertigte Treibstrahlreaktor mit CuBerem Kreislauf (Abb. 3) wurde weitgehend empirisch ausgelegt. Das Betriebsverhalten, charakterisiert durch Riickfihrungsverhiiltnis und Strii- mungsgeschwindigkeit in der Schlaufe, wurde durch Messung des dynamischen Druckes nach der Netz- meJmethode mit Hilfe von Drucksonden bestimmt. Dabei wurde zum einen der EintuJ des Treibgasvolumen- stroms bei Verwendung von Diisen mit verschiedenen Miindungsdurchmessern (0.32-0.48 mm) und einer Reak- tor temperatur von 300 K untersucht. Wie aus Abb. 4 zu sehen ist, das Riickftihrungsverhdltnis in dem Volumen- strombereich von l-4.51 min-’ niiherungsweise konstant mit Werten von 30, 40 und 55 fur die Diisendurchmesser 0.48, 0.42 und 0.32 mm; die Striimungsgeschwindigkeit im Kreislauf steigt demzufolge jeweils in einem Bereich von etwa 2- 10 m s -’ an (Abb. 5). Zum anderen wurde der Ein$uJ der Reaktortemperatur bei konstantem Treib- gasvolumenstrom, der mit einer Temperatur von 300 K in das System eintritt, untersucht. Dabei wurde durch die Temperaturerhiihung im Reaktor von 300 auf 623 K ein AbfalI des Riickfuhrungsverhiiltnisses um etwa 20% auf den Anfangswert bezogen festgestellt (Abb. 6). Die Strii- mungs-geschwindigkeit in der Schlaufe erhiihte sich dage- gen in gleichem MaBe. Der Einbau eines Katalysators in Form eines auf einem Glasstab fixierten diinnen Pliittchens verursachte keine Verschlechterung des zuvor beobachteten Betriebsverhaltens.

0 1993 - Elsevier Sequoia. All rights reserved

226

Zur ijberprtifung des Reaktors hinsichtlich der Eig- nung fur reaktionskinetische Messungen wurde als Testreaktion die Oxidation von Kohlenmonoxid an polykristalliner Platinfolie in einer gegen die Atmosphiire offenen Kreislaufapparatur durchgefuhrt (Abb. 7). Durch die Verwendung des Treibstrahlreaktors kann eine sys- tembedingte Kontamination des Katalysators aus- geschlossen werden, wie Standzeitversuche iiber mehrere Tage bewiesen haben. Durch die experimentelle Bestim- mung der Striimungsgeschwindigkeit unmittelbar am Katalysator ist es miiglich, TransporteinJiisse quantitativ zu ermitteln (Abb. 9) und somit eine zuverhissige Inter- pretation der erhaltenen Daten zu gewiihrleisten.

Continuously operated recirculation reactors are widely used for kinetic studies of heterogeneously catalysed reactions [ 11. Recycling provides a simple but effective means to realize the continuous, stirred tank reactor (CSTR) mode of operation. In this limiting case, by definition, no gradients occur in the reactor. Therefore, the composition and the temperature of the fluid surrounding the catalyst can be measured directly at the outlet of the system and the catalytic activity is easily available from a simple mass balance of the CSTR. The activity, obtained under such carefully con- trolled conditions, is independent of the experimental configurations and can be associated unambiguously with exactly one set of control variables, concentrations and temperature [2].

In addition, the precise measurement of great differ- ences between feed and effluent reactant concentrations makes it more suitable to use a recycling reactor than a single-pass differential reactor limited to slight differ- ences in composition between the inlet and outlet.

In most types of recycle reactor, recycling is provided either by an external pump or by means of an internal impeller. However, serious difficulties may accompany the use of these devices, including the following:

the catalyst may be poisoned by abraded particles removed from the pump or from rotating impeller elements;

the operation at high temperatures often requires expensive set-ups, because, in the case of an external recirculation, the recycled stream must be cooled before and reheated after the pump and, in the case of an internal recirculation, adequate sealing materials have to be found;

the hydrodynamics in the vicinity of the catalyst, necessary for a reasonable evaluation of mass transfer phenomena, is not always known exactly.

A jet-agitated loop reactor can be employed as an alternative device to overcome the drawbacks outlined

above. It was the aim of the present work to imagine and to realize such a reactor, choosing the suitable geometry and determining the operating characteristics. The capa- bility of the device was subsequently verified by the investigation of a test reaction, i.e. the kinetics of carbon monoxide oxidation on polycrystalline platinum.

Theoretical considerations

General aspects of recycling reactors A very simple recirculation system set-up is presented

schematically in Fig. 1. The device consists of a differ- entially operated reactor (broken lines) containing the catalyst and a pump in order to recycle part of the fluid from the exit to the entrance of the reactor. The degree of mixing in the recirculation system (dotted lines) is controlled by the recirculation ratio R, defined as the ratio of the amount flow rates of the recycled (&) to the feed stream (&), i.e.

R=z (1)

The variation of R from zero to infinity describes the transition from a simple flow reactor to the ideal CSTR mode [3]. As the system is gradientless in the CSTR case, the catalytic activity as a function of reactant concentrations and temperature is simply obtained by mass balancing the open system in the steady state.

If we use the reaction rate related to the surface area F of the catalyst

1 d5 rf=Fz to quantify the catalytic activity (5 denotes the extent of reaction), this mass balance leads to

where P denotes the constant volume flow through the recirculation system, and c~,~ and cE, i are the molar concentrations of a reactant species i at the entrance and the exit of the control volume (dotted lines).

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

s-$lm$-p . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Fig. 1. Schematic diagram of a recirculation system with different control volumes: - ~ -, reactor; , recirculation system.

221

Theoretically, the ideal CSTR mode requires an infi- nitely large value of the recirculation ratio R. Neverthe- less, it has been shown that the absence of concentration and temperature gradients is practically achieved, even at finite recirculation ratios of about 20-25 [4, 51. However, in addition to the proper choice of the recircu- lation ratio R, knowing the fluid velocity across the catalyst is of equal importance. While the values of R characterize the degree of mixing in the bulk phase, the possible gradients between the bulk fluid phase and the outer catalyst surface are governed by the velocity pattern in the fluid. Therefore, it must be kept in mind that the control of a fixed value of the recirculation ratio, indicating a perfectly stirred reaction vessel, is not a sufficient condition to obtain absolutely unambiguous data by kinetic measurements.

Jet loop reactor The use of small-scale jet-stirred loop reactors in

heterogeneous catalysis has been proposed frequently in the literature [6, 71. However, only a few cases are known where reactors of this type, either with internal or with external recirculation, have b&i developed [8-lo] to be used under extreme conditions of tempera- ture and pressure. Both configurations are shown sche- matically in Fig. 2. The operation can be illustrated by use of the internal recirculation device (Fig. 2(a)), where simplified velocity profiles (arrows) are also rep- resented. The feed is accelerated through nozzle ‘a’ and issues as a jet with a high velocity into the concentri- cally arranged inner tube ‘b’, where momentum transfer occurs to the recirculating stream. During this transfer, the surrounding fluid elements penetrate into the jet and merge with its elements. Simultaneously, the jet width increases with increasing distance from the nozzle orifice. The mixing of the two streams is completed at the upper end of the tube, resulting in a uniform

Fig. 2. Types of jet-agitated loop reactors: (a) internal and (b) external recirculation. a, nozzle; b, mixing tube; c, catalyst.

velocity profile. Subsequently, the fluid passes down- stream across catalyst bed ‘c’ and is partially returned to the inlet of the mixing tube.

The recycled mass flow essentially depends on the momentum of the injected mass flow and on the pres- sure losses along the flow path inside the reactor. In the simplified case of an incompressible fluid, an isothermal flow system at steady state and neglecting the shear stress at the reactor walls, the momentum balance in the inner tube of the reactor yields

ti,w, + ti,w, - (fir + riz,)w, - (PL -PR, r)A = 0 (4)

where tir and tiR are the mass flow rates of the incoming and the recycled streams, respectively, wr, wR and wL are the flow velocities at the locus stated, and pR. F and pL denote the static pressures at the inlet and the outlet of the mixing tube respectively. A is the cross-sectional area of the mixing tube (cf. Fig. 2(a)).

The pressure increase (pL -pR, F) inside the mixing pipe has to compensate the pressure loss caused by the flow resistances outside this pipe. Usually it is written in the following way:

where & denotes the different pressure drop coefficients which are functions of the local Reynolds number and pertinent dimensionless geometrical quantities.

Equations (4) and (5) may be used in a qualitative analysis of the flow pattern. However, proper correla- tions of the pressure drop coefficients & are missing and neither the optimal geometrical proportions of the reac- tor nor the hydrodynamics in such a device can be calculated accurately. Therefore, an experimental inves- tigation is generally necessary for the development of a small-scale jet-stirred reactor and the determination of its flow characteristics. Although, in some work [7, 10, 111, several design criteria for the achievement of favourable hydrodynamic operation have been devel- oped, the validity of these criteria is restricted to the scale of pilot plants. The application to small labora- tory-scale reactors is normally not allowed and this fact has led to the following experimental study.

Experimental investigation of a jet-stirred reactor

Description of set-up Both configurations represented in Fig. 2 have been

built using the design criteria reported in the literature. However, preliminary measurements rapidly proved the superiority of the mixing behaviour obtained in the external recirculation device. Consequently, the configuration in Fig. 2(b) was chosen. The reactor is represented true to scale in Fig. 3 and consists mainly

d\

I=

Fig. 3. Sectional view of the reactor: a, nozzle; b, fittings; c, catalyst with sample holder; d, reactor outlet.

of two U-shaped tubes of quartz glass. Both parts can be assembled by means of flange mounting. The reactor loop is provided with several fittings to insert pressure probes, thermocouples or the catalyst holder. The noz- zle, also made of quartz glass, is mounted on a special fitting which includes the reactor outlet. The whole reactor can be enclosed by an electrical heating jacket. The temperatures obtained are determined along the axis of the straight part of the tubes, using thermo- couples.

The fluid dynamics measurements are made with pure nitrogen, stored in cylinders. The mass flow of the gas fed through the nozzle is adjusted by means of a pressure controller, followed by a needle valve. The gas flow is measured at the reactor outlet using a soap bubble flowmeter. The volumetric flow rate inside the loop is determined using the point velocity measure- ment technique. For this purpose, the local fluid veloc- ities at several points of the same cross-section are evaluated using dynamic pressure heads in conjunction with an inclined tube manometer. The relationship be- tween this local fluid velocity u and the measured dynamic pressure pan is given by a Bernoulli equation, which is valid for steady flow at a constant fluid density p in the absence of losses:

r/2 u=

( > 4 P&n (6)

Averaging the local flow velocities over the whole cross- section yields an average fluid velocity and the volumet- ric flow rate. A detailed description of the experimental technique may be found in the literature [ 121.

The measurements are mainly carried out in that part of the straight tubes where the catalyst is to be placed. The gas flow rates in the loop and the recirculation ratio are determined by varying either the feed flow rate at different constant reactor temperatures or the reactor temperature at different constant feed fluxes. The tem- perature of the feed gas at the system inlet is always adjusted to 300 K. The effect of varying the diameter of the nozzle orifice is studied in the range between 0.2 and 0.5 mm.

Results and discussion Figure 4 represents the variation of the recycling

ratio R as a function of the volumetric gas flow rate vr through the nozzle at ambient temperature. R is nearly constant in the case of the two larger nozzles within the flow range 0.5 < pr -C 4.5 1 min-‘. The experimental values are around 30 and 45 respectively. The smallest nozzle (0 = 0.32 mm) seems to indicate a slight maxi- mum around 55. In that case, the gas flow had to be limited at values below 2.3 1 mm-’ to avoid static pres- sures inside the nozzle exceeding 3.5 atm.

These results are in agreement with observations reported by Dreyer [8] and Seyfert and Luft [ 131. They observed a similar increase in the recirculation ratio R with diminishing nozzle diameters and a distinct opti- mum value of R for nozzles with an orifice diameter smaller than 0.3 mm.

If the recirculation ratio remains constant, the mean flow velocity wL in the reactor loop must increase with increasing gas flow rate. This is illustrated in Fig. 5. The experimental values show an approximately linear rela- tionship between wr and VF.

The effect of the temperature in the reactor was studied at a fixed value of the gas temperature at the entrance of the nozzle. The results obtained at a feed

30-

20- diameter of

nozzle orifice

lO- A 0.32 mm

0 0.41 mm

0 0.48 mm 0 ,,,,,,,,,

0 0.5 1 ls 2 2.5 3 3.5 4 4.5 5

VW/I mid

Fig. 4. Recycle ratio R as a function of feed gas volumetric Bow rate (NTP) at a reactor temperature of 300 K for different nozzles.

0 I , , , , , , lq”.“P”y 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

VW/I mid

Fig. 5. Mean velocity in the loop us. feed gas volumetric flow rate (NTP) for the use of different nozzles at a reactor temperature of 300 K.

60 I I 10

VW = 2000 ml min-’

0, I 1 I 1 / I I IO 250 300 350 400 450 500 550 600 650

T&

Fig. 6. Effect of temperature in the loop on the recycling ratio and mean velocity.

temperature of 300 K, in the case of a nozzle size of 0.38 mm, are plotted in Fig. 6 against the reactor temperature. Both the recirculation ratio and the flow velocity are slightly affected in the range 300 < T,/ K < 600: R decreases and wr increases with increasing temperature in the reactor. Both quantities attain some- what constant values at temperatures above 600 K. It is unknown how the expected decrease in the recycling ratio due to the density change in the entering feed gas is compensated.

It has been verified experimentally that the gas flow is nearly undisturbed by the presence of the catalyst if the catalyst is inserted in the form of a flat plate &ted on a glass rod, as was shown schematically in Fig. 3. No additional friction loss could be observed and the flow across the catalyst plate seems to be well defined. In conclusion, the experimental investigation of the jet- stirred loop reactor in the present configuration has

229

shown clearly its applicability in kinetic studies. Recir-

culation ratios greater than 30 guarantee sufficient back-mixing. Its constancy at varied flow rates gives the additional possibility of varying the gas velocity by changing the volume flow rate vr and thus of examin- ing the effect of outer transport phenomena under well-defined conditions.

Kinetic studies

Experimental details Kinetic measurements were made in a recirculation

system including the jet-agitated loop reactor, as shown in Fig. 7. The different gases CO (99.997 mol%), O2 (99.995 mol%) and the balance N, (99.999 mol%) were fed into the system from cylinders via mass flow controllers. The gas stream was conducted either di- rectly or after passage through the reactor to the gas analysers. The concentrations of CO and CO* were measured by non-dispersive IR spectrometers (Ultra- mat, Siemens; Uras, Hartmann & Braun). In the case of 02, a magnetic device (Magnos, Hartmann & Braun) was employed. During the experiments, a recycling ratio of at least 30 was maintained to realize almost complete back-mixing of the gas phase. The catalyst consisted of a foil of polycrystalline platinum (99.99 wt.%, Heraeus) of dimensions 10 mm x 10 mm and was activated in air at 1200 “C for 1 h before being placed in the reactor, as described in the preceding paragraph.

The reaction rate r’ was obtained by mass balancing the open system in a steady state. The reaction rate is related to the geometric area F of the catalyst by I’ = l/F. dc/dt (i.e. eqn. (2)), where c represents the extent of the reaction

co + $o,- co2

N2 CO 02

bypass

Fig. 7. Simpliied flow sheet of the experimental set-up for kinetic studies.

230

Results and discussion 510-7

Before the kinetic study itself, the absence of poison- ing of the catalyst had been verified by.exposing it to a gas flow of 1 1 min-’ at different compositions. The CO partial pressure was kept constant at 5 mbar and the 0, content varied between 1 and 30 mbar. Within periods up to 50 h, in each gas mixture no loss of catalytic activity could be observed, thus clearly indicating the cleanness of the system and the absence of poisoning.

4*X)-’

r’

mol/(cm2 f)

3*x)-7

n’COJW

mol/(cm2 s)

The results of a typical rate measurement are shown in Fig. 8, where the surface related rate r’ is plotted as a function of the CO partial pressure at a constant 0, partial pressure and constant temperature, the gas velocity across the catalyst being fixed at 10.5 m s-‘. The well-known pattern can be observed showing two kinetic domains separated by a sharp variation in the rate values. This discontinuity occurs at a CO pressure of 2 mbar. At lower pressures, the rate increases linearly with pco; in the high partial pressure region, the reac- tion is of negative order with respect to CO.

z*lo-7 - li’c0.m. ca I I I 1 5 7 9 11 13

Fig. 9. Effect of the approach velocity on the measured reaction rate and calculated virtual maximum rate of mass transfer at fixed temperature and constant composition.

In this high pressure domain, the measured rates are independent of the gas velocity across the catalyst, thus clearly indicating the absence of outer transport resis- tances. In contrast, the values in the range of the first-order reaction are affected by this gas velocity. This is illustrated in Fig. 9, in the velocity range be- tween 6 and 14 m s-‘, which shows the effect of outer mass transport limitations. If the measured rate were entirely mass transfer controlled, it should equal the maximum molar flow to the surface, i.e.

The virtual maximum rates, calculated by means of the corresponding mass transfer coefficients (/?) and varying from 0.14 to 0.23 m s-l, are included in Fig. 9. The negligible difference between the experimental and calculated values gives irrefutable proof that the rate is entirely mass transfer controlled in the first-order re- gion. A similar course of the kinetics with a mass-trans- port-controlled rate was determined by Garske and Harold [ 141, who investigated the CO oxidation on electrically heated platinum wire placed in a flow reac- tor. However, transport phenomena were studied more qualitatively.

., 12 co, max - - b,O, b (7)

where cco, b is the CO concentration in the bulk of the gas phase and B is an appropriate mass transfer co- efficient. The value of B can be obtained via the Sher- wood number, according to eqns. (Al) -(A6) in Appendix A, which lead to Sherwood number values between 27 and 45 for the adjusted flow conditions.

Conclusions

The jet-agitated loop reactor presented in this work is an external recycling reactor employing an injector to realize gas circulation inside the loop. The approxima- tion to the behaviour of an ideal CSTR requires the insertion only of catalysts with a streamlined shape (e.g. flat plates) into the apparatus, owing to its increased sensitivity to flow resistances. However, beside this apparent weakness, the reactor offers several significant advantages in comparison with a conventional recircu- lation system.

Ed i-

po, = 30.5 mbar I I I

0.1 0.5 1 5 l0

pdmbar

Fig. 8. Reaction rate as a function of CO partial pressure at constant temperature and constant 0, partial pressure.

poJI = 30.5 mbai L,,.“,, = 12.5 mm

u/m s4

The entire device could be made of quartz glass, which provides for negligible catalytic activity of the device itself and also permits operation over a wide temperature range up to 1000 K.

Poisoning of the catalyst by abraded particles, which possibly occurs in a system equipped with mechanicafiy driven mixed elements, is of course excluded by the use of the jet-agitated reactor.

Moreover, accurate velocity measurements in the vicinity of the catalyst can be carried out under the operating conditions of the system. As demonstrated, the information obtained on this occasion enables quantitative determination of the mass transfer rates,

231

which are absolutely necessary for a reliable interpreta- tion of the observed kinetic data.

Accordingly, it can be stated that the jet-agitated loop reactor is well suited to perform reasonable studies of catalytic properties.

Nomenclature

A c D F L rh ri .I n

P r’ t

U

v

W

P

P

5

V

cross-sectional area (m’) concentration (mol mV3) diffusion coefficient (m2 s-‘) outer surface area of the catalyst (m2) length (m) mass flow rate (kg SC’) amount flow rate (mol s-‘) amount flux (mol cm-’ s-‘) pressure (Pa) reaction rate (mol crnm2 s-‘) time (s) local flow velocity (m s- ‘) volumetric flow rate (m’ s-‘) mean flow velocity (m s-‘)

mass transfer coefficient (m s-‘) density (kg me3) extent of reaction (mol) kinematic viscosity (m2 s-‘)

Dimensionless numbers R recycling ratio Re Reynolds number SC Schmidt number Sh Sherwood number

r, pressure drop coefficient

Subscripts

A species A b bulk E exit F feed i arbitrary species i L loop N NTP R recycling

dyn dynamic lam laminar turb turbulent

References and

1 J. R. Anderson and M. Boudart, Catalysis and Technology, Vol. 8, Springer, New York, 1987, p. 207.

2 L. Riekert, Appl. Catal., 15 (1985) 89-104. 3 0. Levenspiel, Chemical Reaction Engineering, Wiley, New

York, 1972, 2nd edn. 4 J. M. Berty, Cafal. Rev., 20 ( 1979) 75. 5 J. J. Carberry, S. C. Paspec and A. Varma, Chem. Eng. Educ.,

14 (1980) 78. 6 G. Luft, R. Riimer and H. Rader, Chem. Zng. Tech., 45 (1973)

596-602. 7 E. Just and J. Wermann, Chem. Technol., 20 (1968) 449-

459. 8 H. D. Dreyer, Dissertation, TH Darmstadt, 1980. 9 W. Weisweiler and W. Schlfer, Chem. Zng. Tech., 60 (1988)

146-147. 10 H. Sommers, Chern. Zng. Tech., 43 (1971) 10-17. 11 H. Blenke, K. Bohner and S. Schuster, Chem. Zng. Tech., 37

(1965) 289. 12 J. Hengstenberg, B. Sturm and 0. Winkler, Messen, Steuern

und Regeln in der Chemischen Technik, Vol. I, Springer, Berlin, 1980, 3rd edn.

13 VDI-Berichte 567, Vol. I, VDI, Dfisseldorf, 1985, pp. 139% 156.

14 M. E. Garske and M. P. Harold, Chem. Eng. Sci., 47 (1992) 623-644.

15 V. Gnielinski, VDI- W&neat/as, VDI, Diisseldorf, 1984, 4th edn.

Appendix A

Mass transfer is characterized by the Sherwood num- ber [ 151, which is defined by

Sh=L D

where L is the characteristic length and D the diffusion coefficient.

Taking the present case to be equivalent to a flow parallel to a flat plate, the mass transfer can be pre- dicted by means of the following correlations of the Sherwood number:

Sh = ( ShIam2 + Shturb2) “2

with

Sh,, = 0.664Re’/2Sc’/3

and

(A2)

(A3)

Sh,,,b = 0 037Re0.‘Sc

* 1 + 2.443Re-0.‘(Sc2/3 - 1) (A41

se; C-W

Re=$ (‘46)