Hydrodynamics of the gas phase in stirred gas—liquid contactors

The Chemical Engineering Journal, 36 (1987) 161 - 167

161

Hydrodynamics of the Gas Phase in Stirred Gas-Liquid Contactors* G. ROVERO,

S. SICARDI, G. BALDI, M. OSELLA and R. CONTI

Dipartimento

di Scienza dei Materiali e Zngegneria Chimica, Politecnico di Torino, Torino (Italy)

(Received December 3, 1986; in final form March 25, 1987)

ABSTRACT

The residence time distribution function (RTDF) of a gas was measured in a gas-liquid stirred contactor with coalescing and noncoalescing systems using a gaseous tracer. It was found that the influence of the tracer solubility, even for a compound of very low solubility, was an important parameter which caused very long tails to the response curves. A methodology for the accurate evaluation of this effect was developed. The experimental results show that part of the gas moves in a plug-flow manner, this part depending on the gas-liquid hydrodynamic regime; the data can be satisfactorily interpreted by using a model which considers the partial recycling of the gas phase in the stirrer zone. 1. INTRODUCTION

The residence time distribution function (RTDF) of the gas in a multiphase reactor can affect the performance of the system when the conversion of the gaseous reactant is high, as occurs in some chlorinations of organic compounds, in the Fisher-Tropsch synthesis etc. Chang and Smith [l] calculated that variations of up to 18% could occur in conversion because of the axial mixing of the gas phase, Several investigations were carried out on the gas RTDF in stirred vessels [2 - 51 but they provided rather conflicting results; indeed, Hanhart et al. [2] found that the gas could be considered, for practical purposes, as perfectly mixed; according to Gal-or and Resnick [3 ] the gas distribution could be interpreted as two perfectly mixed stages in *Part of this paper was presented at the 3rd World Congress of Chemical Engineering, Tokyo, September 21 - 25,1986. 0300-9467/87/$3.50

series followed by a piston stage; the results of Chapman et al. [4] indicated that at high gas flow rates the gas phase showed plug flow behaviour whereas at low flow rates the behaviour was intermediate between a perfectly mixed reactor and a plug flow system; lastly Hubbard and Hoag [5] modelled the gas phase as a single stirred cell with a dead space. The experimental apparatus and the fluid systems used by all these authors were very similar; hence the disagreement in the results can probably be ascribed to the methodology used to calculate the RTDF of the gas. In fact the response curves of the system can be significantly affected by the “end effects” (i.e. the part of the RTD curve connected with the gas sampling devices and lines) and by the interphase transfer of the gaseous tracer. The latter effect was neglected by the above-mentioned authors, whereas it was shown very recently for bubble columns [ 61 that the tracer transfer might affect the results to a significant extent. In examining the RTD of the gas in a stirred vessel with coalescing and non-coalescing systems, we have also taken the transfer of the tracer into account. A quantitative estimation of this effect is presented in order to define a methodology which allows the calculation of the gas RTD with an accuracy sufficient to model the hydrodynamics. Furthermore, we have interpreted the data with a simple model, which also takes the recirculation of the gas into account.

2. INFLUENCE OF TRACER SOLUBILITY

2.1. Moment analysis A theoretical evaluation of the influence of the tracer transfer on the moments of the RTD curves is carried out; two limiting models for the gas phase are examined: 0 Elsevier Sequoia/Printed in The Netherlands

162

(a) gas phase perfectly mixed; (b) gas phase in perfect plug flow. The liquid phase is always considered as perfectly mixed. The initial tracer disturbance is represented by a Dirac function. 2.1.1. Case (a) The unsteady-state mass balances of the tracer are

d&l -

(1)

+(CGI-CGO)=-AB(HCGI-CL)

d8

A(HCG1 -

CL) = -

d8

where

4

8=

TG =

TG

VG -

QG

A = kLaTG

By introducing the Laplace transform of Co 1 and CL eqns. (1) and (2) can be solved to give the following moments of the system transfer function /.+yrn=l+BH I-h9m =

/.Q~~=~+BH P2JYP= 2

(7) (1 + BH)2

1+2BH

(8)

ABH 11 - exp(-ABH) As can be seen from eqns. (3) and (7), the expression for the dimensionless first moment of the response curve is the same for the two models examined and does not depend on the transfer rate but only on the equilibrium term BH; for our system experimental values of BH up to 7 were obtained showing the importance of this phenomenon. As far as the second moment is concerned, Fig. 1 shows the influence of the transfer parameters A and BH on ~~8; the data are calculated from eqns. (4) and (8). Even at relatively low BH values (low solubility of the tracer) very high variations of p20 occurred (up to two orders of magnitude). The ratio /J,s~/E.L~~~~ as a function of BH at various A values is shown in Fig. 2; the shaded zone refers to the parameter values 1000

rtooo

I

(3)

(1+BH)2+-;i-

BH

In eqns. (1) and (2) the product BH denotes the amount of tracer which can be dissolved in the liquid, and A the product of the mean gas residence time and the gasliquid volumetric mass transfer coefficient. 0

2.1.2. Case (b)

acG

-

av

1 ED J

+ BA(HCG -

VG

AB(HCG -

acG

CL) + -

as dCL

CL) dV = B -

d6

= 0

I

Cl

2

3 BH

In this case the mass balances are vG

1

Fig. 1. Influence of the transfer parameters A and BH on dimensionless ~28.

(5)

(6)

In eqn. (5) the gas concentration Co is considered as a function of space and time, whereas CL is a function of the time only (liquid perfectly mixed). By applying the Laplace transforms, eqns. (5) and (6) can be solved to give the transfer function of the system; the first and second moments are

0

I

3

2 BH

Fig. 2. p2,+’ to ~20~’ ratio as a function of BH for various A values,

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covered by our experimental conditions. The difference between the second moments calculated with the two models is considerable when the tracer is not soluble; when H = 0 the ratio p28P/p26mis equal to 0.5. The solubility of the tracer, even at low levels (BH = 0.2 - 0.3), causes an increase in ~2~p/c(28m especially when the gas-liquid mass transfer coefficient is low; hence with A values of 0.01 - 0.1 from the second moments of the response curve, it is very difficult to define whether the gas is in a plug flow state or perfectly mixed. 2.2. Time analysis In order to evaluate the influence of the transfer of the tracer on the response curves of the system a cascade of N mixed stages (exchanging mass with a perfectly mixed liquid) was considered. The mass balance equations to be solved are

d&n d9

+(CGn-

CGn-

1)= --AB@cGn W Eqs.)

- cd (9)

C

lo'-

li'-

A=0

\

BH=O

2

6

3

Fig, 3. Dimensionless concentration at the outlet as a function of 6 for 40 stages in series with A and BH asparameters.

the gas hydrodynamics related to the gas flowing in plug flow (recycle model).

dG = AH(‘G~

-is-

+CGZ+CG~+...+CGN)

N-CCL

3. EXPERIMENTAL

(10) where Con is the gas concentration of the tracer in the nth reactor. Equations (9) and (10) were solved numerically for various values of N with a step decrease input. As an example the dimensionless concentration of the outlet gas when N = 40, at various A values, is shown in Fig. 3. Within the range of our A and BH values, the influence of the transfer of the tracer was negligible for values of 9 up to 1 but became very important for values of 19higher than 2 where very long tails appeared. This result was practically independent of the number N of the stages in series chosen to model the system. Similar conclusions were presented in the paper by Joseph and Shah [ 6 1. This result, according to which the first part of the RTD curve is independent of the transfer of the tracer may be considered an important and general indication which complements the suggestion by Chapman et al. [4] who also made use of the initial response data for modelling purposes. The initial part of the response curve was used in this work to model

3.1. Apparatus The scheme of the apparatus is shown in Fig. 4. A cylindrical vessel of 0.39 m inside

Fig. 4. Scheme of the apparatus: 1, sparger; 2, bottom orifice; 3, gas sampler; 4, rotameter; 5, gas to the FID; 6, gas to vent; 7, electrical level sensors; 8, multiswitch; 9, time integrator; 10, water manometer.

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diameter, equipped with four baffles, was employed; the impeller was a six-flat-blade Rushton turbine 0.13 m in diameter, placed 0.13 m from the bottom. Air was introduced through a sparger or from an orifice; water and an NazS03 aqueous solution were used as the liquid phase. The gas holdup was determined by measuring the local variation in level of the dispersion with an electrical device, in several radial and angular positions. The average level variation was calculated by integrating these values. More details concerning the procedure adopted can be found elsewhere [ 71. The gas residence time distribution was determined by analysing the composition of the gas leaving the system after an input disturbance of CH4 in air. Two different inputs were used: a pulse and a step decrease. The gas was sampled at the liquid free surface by a funnel-shaped device; it was withdrawn at a rigorously constant rate and sent to a flame ionisation detector for analysis. The electrical signal from the detector was recorded as a function of time on a personal computer. Specific tests proved that the radial position of the hood on the liquid surface had no influence on the experimental results and hence that the gas sample was representative of the whole phase. In order to take the end effects into account, tests were carried out with the same sampling device placed directly on the gas sparger, using a minimum amount of liquid. Figure 5 shows typical response curves of the whole system together with the curves for the end effects for a pulse input and for a step decrease respectively. It appears quite clear from the figure that the end effects curves have a considerable effect on those of the system. The figure shows also that very long tails exist; they are more evident in the step-decrease test. 3.2. Results In order to estimate the moments of the curves, the experimental results were extrapolated to t + ~0 by an exponential line and were corrected with the moments of the end effects as shown elsewhere [ 81. The first and second moments of the RTD of the gas obtained from a pulse and a step decrease were compared; the agreement is

I

1

[l-i; E(t) .2

0

0

16

24

32 t

40

[$I

Fig. 5. Pulse and step decrease response curves for the end effects and the whole system.

satisfactory as far as the first moment is concerned (see Fig. 6), but less good for the second moments because of the increased importance of the tails (Fig. 7). The results obtained with the step decrease are more reliable because in this case the extrapolation of the tails of the curves is safer. In order to compare the first moment of the experimental curves with the theoretical value of 1-1 1* = 1 + BH, the value of B = VL/Vi was obtained from the gas holdup data. Figure 8 shows the comparison between the values of ~~8 calculated from the step decrease response curves and the values obtained from the measurements of the gas holdup through eqn. (3). The systematic 10 p,, PuI:e 5

Fig. 6. Comparison between pulse and step decrease first moments.

165

OY 0

I

1

2

3

4

5

6

1

I za

Csl Fig. 9. Delay time compared with gas mean residence time for coalescing and non-coalescing systems. Symbols as in Fig. 8; the shaded zone includes td’ values calculated from eqn. (13).

Fig. 7. Comparison between pulse and step decrease second moments. See Fig. 8 for definition of symbols.

1Y

1

2

4

6

I

I

10

l+BH

Fig. 8. Comparison between experimental and calculated first moment values. Coalescing system: QG = 2.95 X 10m4 m3 s-l: V; QG = 5.67 X 10e4 m3 s-l: 0; QG = 7.80 X 10e4 m3 s-l: 0; QG = 13.30 X low4 m3 s-i: A; QG = 20.00 X 10e4 m3 s-r: 0. Non-coalescing system: QG = 7.80 X lob4 m3 s-i: *.

caused by a part of the gas flowing in a plug flow manner in the vessel, the remaining part being mixed to a certain extent. Figure 9 shows the behaviour of td as a function of ro for coalescing and noncoalescing systems. The ta values were obtained from the response curve to the pulse; on the basis of the results shown in Fig. 3 their experimental evaluation should not be influenced by the tracer transfer because this value is lower than 9 = 1. Coalescing and non-coalescing systems behave similarly. At low To values, that generally occur with a poor gas distribution in the vessel (low stirrer speed, high gas flow rate) the time delay is very similar to To. As the dispersing capacity of the stirrer is increased, To increases much faster than the time delay. This may suggest that the part of the gas moving in plug flow tends to reach an asymptote, whereas the part of the gas which is mixed increases as ro increases.

4. HYDRODYNAMIC

discrepancy may probably be ascribed to the experimental difficulty in calculating the parameters ple and B;in any event the figure shows that the role of the tracer transfer cannot be neglected. As far as the second moments of the RTD curves are concerned, the experimental data confirmed the theoretical results previously presented in Fig. 2, i.e. the impossibility of using these moments to identify the hydrodynamics of the system. It was observed that the response curves of the gas present a considerable time delay (see for example Fig. 5). This time delay td is

REGIMES

AND THE RE-

CYCLE MODEL

In a previous paper Sicardi et al. [9] proposed a simplified model which considered the gas recirculation in the vessel in connection with the hydrodynamic regimes. Three main hydrodynamic regimes are defined in a gas-liquid stirred vessel [lo] : the bypass regime (a), the loading regime (b) and the total aeration regime (c). In the recycling model it is assumed that at the transition between (b) and (c) the bubbles are distributed throughout the whole section of the impeller plane and move in the liquid at

166

their terminal velocity ut (in plug flow). Under this condition the gas holdup is equal to Ho* and corresponds to *=

HG

vG

(11)

-

Ut

where uo is the superficial gas velocity. By increasing the rotation velocity and keeping the gas flow rate Qo constant, part of the bubbles recirculates and the recirculation rate QR can be correlated with the gas holdup according to the equation

QR -=

HG -HG* (12) HG

QG

The recirculation rate Qa includes both internal recirculation (i.e. the flow rate of gas that recirculates inside the impeller and can mix with the inlet stream) and the external recirculation, i.e. loops of bubbles which do not pass through the impeller. According to this model, the gas bubbles, which enter the tank with a gas flow rate Qo, join the gas bubbles of the recycling gas and travel along the vessel in piston flow with a mean gas flow rate Qo + &a, as is schematically shown in Fig. 10. The time delay td of the gas is the time necessary for the bubbles to travel along the reactor and depends only on the bubble terminal velocity ut, which, according to the model, should not be strongly affected either by the agitator speed or by the gas flow rate. The hypothesis of a constant Ut and hence time delay of the gas bubbles is verified experimentally with satisfactory agreement in regime (c) as shown in Fig. 9. Here, for comparison, a shaded area is depicted, which includes the calculated values of the time delay which is due to the bubble rising from the sparger to the liquid free

surface. This value of td (designated was calculated from

2 T - (13) 3 vt where (2/3)T is the distance travelled by the bubble from the sparger to the liquid free surface and ut is the value of the single bubble terminal velocity estimated from eqn. (11) for a bubble diameter ranging from 1 to 3 mm. In Fig. 9 the data points for td are, in general, within the shaded zone of the t,’ values with the unique exception of the points (asterixes) referring to a coalescing system at high turbine rotation speed (high values of the gas residence time), which are probably characterized by much smaller bubbles (diameters smaller than 1 mm). According to the above model we can write +

td

HG*

76

HG

-=_

(14)

The experimental values of td/TG are compared with those of HG*/HG in Fig. 11. The points on the plot give a satisfactory confirmation of the assumption contained in the proposed model. Obviously the values of HG*/Hc > 1 refer to the regime conditions of loading (regime (b)) i.e. a hydrodynamic situation in which all the gas bubbles are in plug flow. In this case the time delay coincides, within the range of experimental errors, with the mean residence time ro.

-I

tQG

Fig. 11. td to TG ratio values compared with HG* to HG ratio values: symbols as in Fig. 8; -, from eqn. (14).

1

’

",-"G

-

tt

QR

by td ‘)

H;

l

tt d 5. CONCLUSIONS

vtttttt t

Q6

Fig. 10. Scheme of the recycle model.

Contrary to the findings of other researchers, the first conclusion is that, in a coalescing system, the transfer of the tracer

167

affects the trends of the response curves significantly; the first moment of the curve can reach values of up to 8 compared with the value of 1 which corresponds to an absolute absence of transfer. Moreover we have reached the conclusion that the moment method is not suitable for modelling the gas hydrodynamics, because of the importance of the curve tails on the higher moments; for this reason the RTD in the time domain should be employed. One useful result in this direction is the negligible influence of the tracer transfer on the part of the curve in the range of 6 values up to 1: this is in agreement with other authors’ findings [4,6] who made use of the initial part of the RTD curve for modelling purposes. In this paper the initial part of the curve was examined in order to model the gas hydrodynamics connected with the volume of the gas which flows in piston flow; in particular the time delay of the RTD curve td was calculated. A model based on gas recirculation is proposed here for the interpretation of the gas hydrodynamics; according to the results, the model is able to correlate the gas holdup with the time delay td and can be applied to the system in the regime of total aeration (regime (c)).

5 D. W. Hubbard and B. C. Hoag, 10th Eng. Fundam. Conf. on Mixing, Henniker, 1965. 6 S. Joseph and Y. T. Shah, Can. J. Chem. Eng., 64 (1986) 380. 7 M. Osella, Laurea Thesis, Pohtecnico di Torino, 1985. 8 A. J. Colombo, G. Baldi and S. Sicardi, Chem. Eng. Sci., 31 (1976) 1101. 9 S. Sicardi, R. Conti and G. Baldi, Zng. Chim. Ital., 20 (1984) 70. 10 R. Conti, S. Sicardi and G. Baldi, 3rd Jug. Ital. Austrian Chem. Eng. Conf., Graz, September 14 - 16, 1982.

APPENDIX

A: NOMENCLATURE

a A

B CGO, CGl, CGn CL

H HG, HG*

kr., QG

QR ACKNOWLEDGMENT

t

The work was carried out with the financial support of a grant from the Ministero della Pubblica Istruzione, Fondi 40%.

td

REFERENCES H. Chang and J. M. Smith, AZChE J., 29 (1983) 699. J. Hanhart, H. Kramers and K. R. Westerterp, Chem. Eng. Sci., 18 (1963) 503. B. Gal-or and W. Resnick, Znd. Eng. Chem., Process Des. Dev., 5 (1966) 16. C. M. Chapman, L. G. Gibilaro and A. W. Nienow, Chem. Eng. Sci., 37 (1982) 891.

T V VG. VL

Greek symbols 8 cl18 P2s TG

specific area (m-l) &cro vLlvG

gas concentrations (kmol me3) liquid concentration (kmol me3) Henry constant gas holdup gas-liquid mass transfer coefficient (m s-l) gas flow rate (m3 s-l) recirculation flow rate (m3 s-i) time (s) time delay (s) vessel diameter (m) gas volume (m3) volume occupied by the gas (m3) volume occupied by the liquid ( m3)

t /TG

first moment second moment VG/QG, gas mean residence time (s)