Interfacial areas in agitated gas-liquid contactors

ChemicalEngineeringScience, 1963,Vol. 18, pp. 157-176. Pergamon Press Ltd., Oxford. Printed in Great Britain.

Interfacial areas in agitated gasrliqnid contactors K. R. WmTrz%mt,

L. L. VANDIERENDONCK$ and J. A. DE KRAA

Laboratorium voor Fysische Technologie, Technische Hogeschool, Delft, Holland

(Received 11 July, 1962)

AbslractXhemical reactions with known chemical and physical properties were used for the determination of integral vale of the interfacial areas created with an agitator in a gas-lkjidd contactor. The reactions between oxygen and a sulphite solution and between carbon dioxide and sodium hydroxide solutions were chosen. For the first system the chemical reaction in the liquid boundary layer is proved to be rate determining under our experimental conditions. The existence of two regions is demonstrated: (a) A region without agitation effect. At agitation rates below a minimum agitation rate noD interfacial areas are not a&&d by the stirring; they only depend on the gas load va and the type of gas sparser. (b) A region with agitation effect. At agitation rates above noD the interfacial areas are linearly dependent on the agitation rate and independent of the gas load and type of gas inlet. The value of noD depends on the tank to agitator diameter ratio and probably is independent of the liquid viscosity. Generally valid correlations for the minimum agitation rates and the interfacial area under fully bafiled conditions could be derived for a great number of geometrically similar impellers of different sizes in vessels with diameters ranging from O-14 to 090 m. Although vessels with a daimeter larger than 1 m were not investigated the method of correlation seems to give good results for scaling-up. The influence of the physical properties of the liquid remains uncertain.

INTRODUCTION The

IXEXATURE

interfacial area is the main variable determining the capacity of an agitated gas-liquid reactor, if this reactor type is correctly applied. Many investigations of this interfacial area were published in literature, which, however, often seem to contradict each other. Therefore a new investigation was started and in this article some light will be thrown on the influence of the reactor and agitator geometry and the liquid viscosity on the interfacial area in agitated gas-liquid dispersions. More details on the physical phenomena and the cause of the discrepancy found in literature will be discussed in a following article; also recommendations for the reactor design will be given there. A different method, which has been discussed more extensively elsewhere [I], will be used for the measurement of interfacial areas.

%JRVEY

A summary of the results, published in literature on the specitic absorption rate KS, the specific interfacial area S or the gas hold-up 1 - e in agitated gas-liquid reactors is given in Table 1. All these measurements have been correlated by the various authors in the form of empirical relations between the relevant variables. With respect to the influenceon KS, S or 1 - E of the number of revolutions per unit of time of the agitator n, the linear gas load v, and the power input of the impeller per unit of liquid volume, P/eVR, all correlations are of the type: KS, S or 1- E is proportional

to V$V+ or tp$c(P/~V,)~

In Table 1 therefore the values of the exponents a, /9and y are given together with the most important

t Present address: N.V. Petrochemie AKU-Amoco, Arnhem, Holland. $ Present address: Staatsmijnen in Limburg, Gelecn, Holland.

157

K. R. Wssmmtp,

L. L. VAN DIERENDONCK and J. A. DE KIUA

Table 1. Survey of literature data on agitated gas-liquid contactors Ref. No.

Year

PI

1959 1957

[3]

141 [5] [6] [7] [7] [81 [8] [8] 181 [8] [9] [lo] [lo]

1957 1957 1953 1960 1960 1960 1960 1960 1960 1960 1957 1944 1944

[ll, 121 1959

[13] [14] [15] [16] [17]

1956 1955 1958 1959 1961

[2] [IS] [18]

1959 1958 1944

Type of correlation Variable correlated Exponent Exponent of Exponent of Volume of the the agitator the energy 0.1 speed consumptionof gas load n impeller P/EVR 0.3 KS

KS KS

KS KS KS KS KS KS

KS

KS KS KS KS KS KS r KS KS KS KS

IKS KS S S

s”

Z.68 040 0.67 040-0*84 0.21 0.13 0.14 0.05 0 ? 0.67 0.67 ? ? ? ? ? i.4

3.00 1.67 2.00 3.00

1.29-2.05

0.95 057

-

-1.50

0.50 0.60

-

:::* 41 2.7; 41 0.8 0.8 0.2 1.4 1.4

-

2.04 2.40 2.17 1.79 1.26 2.4 -

0.50

All vessels were equipped with four batBes

-

1.70 2.00

-

1.9 1.9 2.7 1.5

-

20 ; 67 2.7 11; 11,000

0.43-0.95

3.95

i ’ 0.53 &I

26600 6.3; 12.3;104 104

040 0.35

6.3 ; 104 44

0.40 0.47

::;. 104 22;‘8400

A = paddle D = propellor

Vessel D T

0.7 8:;; 0.5 0.5 ? 040 040 8:: 0.47 0.30 0.30 0.30: 0.46

0.4 0.25 0.50 0.33 0.34 0.30 024 0.39 0.20 0.6 0.33 0.33 0.33; 040; 0.47 0.7 0.33 0.32; 0.21

B = turbine E = Hoesch impeller

data of the agitators and vessels investigated. As can be seen from the Table the influence of the gas load on KS varies between v,” and vi” and the influence on KS of the stirring speed between n 1’26 and n3’Ooor of the power input between (P/EVR)“~~ and (P/EV~)“~~. The great variation of the exponents c(, fl and y already indicates that the above mentioned method of correlation is not satisfactory. COOPER et al. [lo] were the first ones who tried to relate KS with the impeller power input (P/&V,) and other investigators followed them. This method of correlation, however, does not seem correct to us because (P/sVJ itself is not an independent variable, but depends in a complicated manner on

Impeller Type Number of impeller blades 0.13 0.13 0.15 0.13 i.15; 0.38 0.15; 0.38 0.10 0.10 0.06 0.12 0.12 0.33 0.15; 044 0.24; 244 0.16

0.16; 0.50

3.05 0.25; 0.51’ 0.20; 0.51 0.21; 0.51 0.38

B B A B D B C B : A A “c A

t 4 6 ? :26 6 6 4 2 4 4 16 2 2 2 8 3

8

6 5

0.13 0.20; 0.51 0.37; 244 C = vaned disk F = Rotadux impeller

the gas load, the stirring speed, the physical properties of the system and the geometry of the vessel and the impeller. Most measurements of KS were done with the system air-sulphite solution. The oxygen from the air dissolves into the sulphite solution and oxidizes the sulphite under influence of copper ions as a catalyst. The conversion rate in this case is independent of the concentration of the sulphite ions. The various authors do not reach a definite conclusion for this particular system on the signikance of the overall mass-transfer coefficient Kin the product KS. Only VERMXULEN et al. [14], CALDERBANK [IS, 161 and PRJ%N[17] determined directly the magnitude

158

Interfacialareas in agitatedgas-liquidcontactors

of the interfacial area; the first ones by measuring the dispersion of light in a gas-liquid mixture, the last one by photographs taken of the dispersion. CALDERBANK[15] also determined local values of the ‘gas hold-up and of the interfacial area and found that both were strongly dependent on the position in the vessel. PREEN [17] took pictures in the upper part of the dispersion above the agitator and by measuring and counting of the bubbles he calculated the spectic interfacial area. He concluded that practically all disintegration takes place in the neighbourhood of the impeller and that in the other parts of the vessel farther away from the agitator coalescence occurs, especially between bubbles with a small diameter ( < O-5 x 10m3m) and with a great diameter (>3 x 10d3m). He concluded from his measurements that not disintegration but coalescence determines the final value of S. In Table 1 also the published investigations of the gas hold-up 1 - E in the dispersion are given. The highest values found for 1 - Ewere about O-30. The gas volumes, which are pumped around by the agitator, make the density of the gas-liquid mixture decrease and consequently also the power input with respect to the power input into a pure liquid at the same rotation speed of the agitator. At overloading of the impeller, when the impeller cannot disperse all the gas supplied, short-circuiting occurs, the gas rises as big bubbles to the surface and the pumping action of the impeller diminishes. According to COOPER et al. [lo] overloading occurs with vaned-disk impellers at values of v, > 25 x 10m3 m/set. The power input into an agitated gas-liquid dispersion is correlated by several investigators [ 15,19,20] with the dimensionless group Q&rD3, mostly in a relation of the type

persion has the same composition. A phase in a heterogeneous system is called perfectly mixed when the chance that a volume element of that phase leaving the continuously fed system is independent of the time that the volume element considered already is present in the system. The residence time distribution of that phase then corresponds with the residence time distribution of an ideal mixer. Only at very low stirring speeds local differences can be found in the liquid concentrations in an agitated gas-liquid reactor. In an agitated gas-liquid reactor the gas always flows continuously through the dispersion,; the degree of mixing in the gas phase is of utmost importance, because the correct average driving force for a gas absorption strongly depends on it. In literature for the calculation of the specific absorption rate in most cases it was assumed that the gas flowing through the dispersion would not exhibit any distribution of residence times at all; as the driving force the logarithmic mean between the driving forces at the inlet and at the outlet were taken. In a recent investigation [22], however, it was demonstrated that the gas also in an agitated dispersion can be considered as perfectly mixed, if the agitation rate is so high that the gas is effectively dispersed. Under these circumstances the average concentration in the gas phase of the absorbed component can be put equal to the concentration of that component in the outlet gas. In our particular case the coalescence rate of the gas bubbles has no influence on the average driving force, because gas absorption essentially is a firstorder process with respect to the component which dissolves from the gas into the liquid [23, 241. OuR INVE~TIOATI~N

APIP, - (Q&D3)o’5 . Here AP = PO - P, where PO is the power input into the pure liquid and P the power input into a gas-liquid dispersion at the same value of iz. Also here the results of the various investigators are not conclusive. The residence time distribution or the degree of mixing in the gas phase and in the liquid phase of the dispersion are very important. The liquid in a well agitated dispersion is perfectly mixed [21]; this means that the liquid in every place in the dis159

Some experiments are described in literature, where the interfacial area in agitated gas-liquid contactors was measured directly by phJuicd methods. These methods have two disadvantages: firstly the natural circulation of the agitated dispersion is disturbed by the measuring devices, which are introduced into the dispersion. Secondly only Zocal measurements can be made; CALDERBANKdemonstrated that the interfacial area differs greatly with the position in the vessel.

K. R. WESTIIRTERP, L. L. VANDIERBND~NCIC and J. A.DEKRAA

Our starting point is that with a chemical method, if a suitable chemical reaction with known kinetics is chosen, in a less direct manner integral values of the interfacial area can be, obtained. From the theory of gas absorption accompanied by chemical reaction in the liquid phase [25-271 it is known that, with a fast first order reaction in the liquid boundary layer the absorption rate is given by5

with the condition that 4 = J(k@/k, > 2. In this equation a, is the absorption rate (kmole/sec), pAJRZHe the concentration at the interface in the liquid of the dissolving component A (kmole/m3), S the specific interfacial area (mz/m3 volume of the dispersion), V, the volume of the dispersion (m3), k the first-order reaction velocity constant (set-‘) for the reaction in the liquid phase between A and a dissolved component B, 9 is the diffusion coefficient of A in the liquid (m’/sec), He a dimensionless distribution coefficient for A (p,/RT = Hec,) and kl is the mass-transfer coefficient in the liquid phase. A similar equation can be given for a second-order reaction in the liquid phase. It can be seen from (3) that in this case the absorption rate is independent of the mass-transfer coefficient k, and only depends on a chemical (k) and a physical (9) property of the system; both properties are independent of the hydrodynamic conditions around the gas bubbles or degree of agitation and therefore measurements of chemical absorption rates under conditions of known cAi, k and 9 can be used for a direct determination of the interfacial area S. As reactions we have chosen the chemical systems oxygen-sulphite solution and C02-NaOH solutions. Sodium sulphite is a cheap raw material and air can be taken as an oxygen source. In an experiment, which is done batchwise with respect to the liquid phase, the absorption rate can be measured directly from the change with time of the sulphite concentration. A choice can be made between Co and Cu as a catalyst. For the catalysis with Co-ions the value of ,/(k@/He is known [l], but the absorption $ Penetration theory and film theory for this case give nearly the same equations. We prefer to use therefore the film theory, which is easier to handle [l].

rates are high and only one or two experiments can be done per batch. With Cu as a catalyst the absorption rate is lower, but the value of. J(k@/He is not known from direct measurements. In an indirect manner therefore the value of .J(k@/He for the catalysis with Cu will be determined, and it will be proved that the absorption of oxygen in a sulphite solution with Cu as a catalyst is determined indeed by a fast chemical reaction in the liquid boundary layer. The experiments with the system C02-NaOH solutions will be used in order to get some impression of the influence of the physical properties of the liquid on interfacial areas. In most cases we have investigated how the interfacial area depends on the stirrer type, the stirrer diameter, the agitation speed, the vessel diameter, the type of gas inlet, the liquid height and the gas load. In a following article some power mput measurements will be discussed in order to investigate if there exists a relation between the power input and the interfacial area; also some gas hold-up measurements will be reviewed and general recommendations for the optimum agitator diameter and the design of agitated gas-liquid contractors will be given. THE CHJZMISTRY OF THE REACTION BETWEEN OXYGEN AND A SULPHITJZSOLUTION The chemistry of the oxidation of sodium sulphite dissolved in water and catalysed with Cu ions has not been elucidated, although it has been investigated extensively. From the publications on this subject, however, some properties of this reaction can be considered as established. (a) The reaction is very sensitive to traces of a catalyst. Cu **, Co *., Fe . f ‘, Ce . . * -, Mn * * and O3 increase and ethyl alcohol, glycerol and manmtol decrease the reaction rate. Also impurities, which are present in the sodium sulphite itself or in the water used or which dissolve e.g. from rubber, may inhibit the reaction [28-351. (b) At sulphite concentrations below 0.02 molar the conversion rate is of the first order in sulphite and independent of the oxygen concentration [33]. (c) At sulphite concentrations above O-01 molar the conversion rate is of the first order in

160

Interfacid

areas in agitated gas-liquid contactors

MOTOR

VARIATOR

TOROUEMETER

i TACHOMETEQ

THERMO. METER

/

\ L!AMATOR TOROUMETER

T60 T19

FIG; 1.

Experimental

oxygen and independent of the sulphite concentration [34, 361. (d) At Cu concentrations above O+lOl molar the reaction is independent of the Cu concentration [34]. (e) For the reaction with Cu as a catalyst a chain mechanism is assumed according to 02 Cu.* + SO,N+ complex + Cu.* + SO; Several mechanisms have been proposed for this reaction, although doubt still exists about the true mechanism [33, 37-401 and the rate determining step. (f) Co is a more active catalyst than Cu and is less sensitive to impurities [31, 351. (h) At 30°C ,/(@/He = 7.5 x lo-’ m/sec”.5 for the physical absorption of oxygen in a sulphite solution, which contains 100 kg/m3 Na$O, [l]. (g) The reaction catalysed by Mn * * ions is autocatalytic and only starts when oxygen is present [41].

installations.

(i) At 30°C &&)/He = 144 x 10m4m/set for the chemical absorption of oxygen in a sulphite solution, which contains 100 kg/m3 Na$O, and OXrOlkmol/m3 CoSO, as a catalyst [l]. In view of the above mentioned points the following precautions were taken for the absorption experiments with the oxygen-sulphite system : 800 kg Na,SO, from one batch in the factory of the supplier were bought (constant quality), all solutions were prepared with distilled water, the experiments were all done at 30°C and with a Na$O, concentration of 100 kg/m3 and only selected materials were used for the construction of the vessels and the agitators (Table 2). DJXXIPTION OF THE EXPERIMENTAL APPARATUS The experimental set-up is sketched in Fig. 1. The most important data of the five vessels, which we have used as reactors, are given in Table 2. 161

K. R. WESTERTERP, L. L. VANDIBIENDONCK and J. A. DE KRAA

Table 2. Data on the vessels used in thzkinvestigation Vessel diameter T (m) height (m) height of agitator h (m) n or nmax (set-1) liquid content at H/T = 1 (l.) Materials used : wall baffles flanges shaft agitator spiral gas inlet sample line sample valve

T 14

T 15

T19

T60

T90

0.140 040

0.152 0.35

0.191 040

060 1.10

090 1.10

0.07 24

0.075 12

0.095 60

0.30 25

0.45 1.67

2.2

2-7

5.5

170

570

316 316

316 316

perspex perspex P.V.C. 316 316 P.V.C. glass glass

copper copper copper 316 brass copper copper copper brass

perspex perspex brass 316 brass copper copper copper brass

0

0

00

A

TURBME

IMPELLER

316 316 316 316 316 316 316 P.V.C. 316 316 -

The nomenclature used in the text for the vessels indicates with the figure after T the diameter of the vessel expressed in cm. From Table 2 it can be seen that the height of the impeller, h, has not been varied : KARWAT [l 1, 121 proved h/T = O-5 to be the best position for the agitator if H/T = 1. The vessels were equipped with a spiral for cooling or heating with water and steam respectively, with a thermometer, a sample valve and with four baffles of a width equal to O-1 T. The gas in most cases was supplied through a ring provided with small holes. The air was taken,via a filter and a rotameter from the laboratory air supply system. The hydraulic variators were made by Carter (U.K.), the torque meter by Aspera (Italy) and the revolution-counters by Smith (U.K.). With the torque meter, which had a range of O-70 Nm, small torques could not be measured accurately; the energy consumption of the agitator therefore was measured only in T60 and in T19 for D/T = 0.7. The torque meter and the revolution counters were carefully calibrated. In literature investigations are published on widely varying agitator types; we have restricted ourselves to the more conventional types, which are sketched in Fig. 2. The dimensions are equal to those which have been investigated by ZWIETERING [42]. We distinguish three types: (a) Turbine impellers (Fig. 2a). (b) Paddle impellers (Figs. 2b and 2c) with four or two blades.

a.O.ZSD

FIG. 2.

Impellers used.

(c) Propellor stirrers (Fig. 2d). The impellers were made of brass or stainless steel type 316. The diameters of the agitators investigated are given in Table 3. Table 3. Agitators investigated Turbine impellers T 14: D/T = T 15 : D/T = T 19: D/T = T 60: D/T = T 90: D/T =

in O-52; 0.68 0.47; 0.62 0.2; O-3; 0.4; 0.5; 0.6; 0.7 0.2; O-3; 0.4; O-6; O-7 O-47

Four-bladed paddle impellers in T 15: D/T = O-57 T 19: D/T = O-3; 0.4; 0.5; O-6; 0.7 T 60: D/T = 0.2; O-3; 0.6 Two-bladed paddle impellers in T 19: D/T = 0.5; O-7 Propellor impellers in T 19: D/T = 0.4; O-6; 0.7

162

Interfacialareas in agitatedgas-liquidcontactors EXPERIMENTAL PROCEDURE The absorption experiments with the system oxygen-sulphite were executed in the following way. The vessel was filled partially with distilled water which was heated up to 30°C. ,A weighed amount of Na2S03, under heavy agitation, was dumped into the liquid and afterwards a certain amount of a CuS04 solution was added. Then again distilled water was added until the sulphite concentration was exactly at 100 kg/m3. In most cases a CuS04 concentration of about 10s3 molar was used. The air supply and the agitation rate were adjusted to the desired values and kept constant during the experiment. The temperature was kept constant at 30 + 1°C via the spiral with cooling water. During an absorption experiment at certain intervals of three to ten minutes, in total four samples were taken from the sulphite solution. The sample line was rinsed with the sulphite solution just before every sample taking. The sulphite content in the samples was determined by titration with iodine and thiosulphate and with starch as indicator. The oxygen absorbed reacts with the sulphite according to the reaction equation:

0, + 2so; + 2so; As the gas in the dispersion is perfectly mixed, the conversion rate of the oxygen roz can be calculated with the material balances: Go:

2dt

kmol/sec

In this equation K is an over-all transfer coefficient ; its significance will be determined in a following section. Furthermore &VR= V,. For the oxygen in the gas the following material balance can be written

1

~_L!+

[ “RT

in-

1

@PO, [

“RT

= lolVR kmol/sec

ex

If we neglect the shrinking of the gas due to the absorption of the oxygen, we find for the concentration of the oxygen in the exit gas [%I..

= [s]

in +s%

With the measured values of V,, cPOand dc/dt and with the known value Of [po,/RT]i, (taken as 8.46 x 10e3 kmol/m3) the concentration of the oxygen in the exit gas can be calculated and then the product KS/&He follows from KS z

- (dcso,Pdt) set- 1 =

(P~,/RT),,

KS/&He is the product of an over-all transfer coefficient, based on the liquid side, and the interfacial area per unit of liquid volume. The term KS/&He gives us the absorption rate of oxygen in a sulphite solution per unit of liquid volume and per unit of driving force; therefore we call it the “specific absorption rate.” Tm SPECIFICABSORPTION RATEATDISPERSION WITH TURBINE IIWELL~S(OXYGEN-SULPHITE SYSTEM)

The turbine impellers proved to be efficient gas dispersers and therefore have been investigated extensively. We will discuss the influence of the various relevant variables separately. The influence of the liquid height H

In the smaller vessels the liquid volume diminished gradually due to the sample taking and so did the effective height H, which the liquid would have if no gas were supplied. The influence of H/T on the specific absorption rate was investigated in order to correct the results to the standard condition H/T = 1. In every series of experiments v,, D, T and agitator type were constant. The measured values of KS/&He for every series were plotted against H/T on double-logarithmic paper; the best str&ht line was drawn through the points and the value of KS/EHe at H/T = 1 was determined. In the relation KS/&He = const x (H/T)e the individual values of a varied between -0.7 and - 1 2. On the average u was about - 1 for the turbine impellers and for the other agitator types as well. A dependency of u upon D, v,, T or agitator type could not be observed within our accuracy limits. For the correction we have applied therefore the relation =-

kmol/m3 K/T= 1

B

163

KSH EHeT

K. R. WIZSTERTERP, L. L.

VAN DERENDONCK

and J. A.

0 0,62 + 0,41 x 0.50

A 0870

DE KRAA

T19 T15 T15 T19 T60 T15 T19 Ti9 T19

TURBINE TURBINE TURBlNE TURHNE TURBINE‘ PADDLE (L) RADDLE .I41 F#DDLE (21 PRDPELLOR

FIG. 3~ Influence of the liquid height.

In Fig. 3 we have plotted the results of all the experiments. We see that inthe region investigated (0.6 < H/T < 1.6) the speczc absorption rate diminishes with increasing liquid height, if other conditions remain constant. In all other experiments H/T varied between the limits 0.85 and 1.10. The infuence of the impeller speed n

The influence of the impeller speed n at constant geometry, gas load and liquid height is demonstrated in Fig. 4. We see that at very low impeller speeds the specific absorption rate does not improve due to the stirring. A’ slightly noticeable improvement takes place in the neighbourhood of a certain speed no. If this impeller speed no has been passed, KS/eHe increases quickly and linearly with increasing n. If the transition region in the neighbourhood of no is neglected, two regions can be distinguished. (a) The region without agitation effect (n < no). %nthis region the specific absorption depends on the $as load and not on the impeller speed. There is no sense to agitate with impeller speeds below no. Although in the neighbourhood of no the value of KS/&He slightly increases, the improvement obtained is still not great enough to warrant the

installation of an expensive agitator; therefore we have not investigated the region without agitation effect. (b) The region with agitation effect (n > no). Here the absorption rate is influenced by the impeller speed. In all vessels and with all agitator types the same picture as in Fig. 4 was found. In this region KS/&He is improved so much that the installation of an agitator can become warranted economically. Therefore for this region only we will further examine how K,S/sHe is influenced by the various process and design variables. We see that a good description must be possible with the relation KSH. KTw(n-no),

ifn>n,

The proportionality constant and n, must be examined as a function of the other variables. Visually, it can be observed [I] that at low impeller speeds the gas is not dispersed at all. Once in the neighbourhood of the minimum impeller speed no some effect can be seen, the amount of gas bubbles below the stirrer is still very low, fine bubbles are only found in the region above the stirrer. If rr,, once has been passed, the dispersion gets finer and

164

*

I&rfacial areas in agitated gas-liquid

contactors

so-

m-

I 20-

T19 ~.ll,7XlO

FIG. 4.

-3,

/s

I&hence of the impeller speed.

more homogeneous, although the gas bubbles in the neighbourhood of the impeller always remain much smaller than elsewhere in the dispersion.

ratio of the slopes is about proportional to the ratio! of the agitator diameters, thus: KSH sHe(n - n,)T -D

The influence of the agitator diameter D In Fig. 5 the results of several series in T19 with similar turbine agitators of different diameter at constant gas load are given. We see that at increasing agitator diameter the slope of the straight lines in the region with agitation effect increases and that at the same time the value of no becomes lower. The

_I.

and no =f(D> KS/sHe depends linearly on nD, :which is a measure of the linear tip velocity of the agitator. We will call nD the “agitation rate” and n,D the “minimum agitation rate”. 165

K. R. WESTERTERP, L. L. VAN DIERENWNCKand J. A. DE KRAA LO

r

0,0

20

10 FIG. 5.

30

-

LO

50

60

Influence of the agitator diameter.

The influence of the gas load v,

The inflirence of the vessel diameter T

In Fig. 6 experimental values of the specific absorption rate determined in T15 are given for two agitators at varying gas load v, and constant agitation rate (> n&). No significant influence of v, is found. This means that in a graph as Fig. 4 the slope of the straight line in the region with agitation effect is not influenced by the gas load. For widely varying conditions (10e3 < v, < 35 x 10- 3 m/s) this phenomena has been investigated [I] : no influence of the gas load was found in this region. On first sight it seems strange that the gas load has no influence on the specific absorption rate in the region with agitation effect, but it has to be realized that the gas volumes in the dispersion circulate much more rapidly than fresh gas is supplied. With data taken from literature on pumping rates of impellers the amount of gas circulated can be estimated; the circulation rates result to be an order of magnitude higher than the supply rates. The gas supply rate has no influence because the agitation effect predominates. In literature nevertheless an influence of v, at constant agitation rate is found; there are two reasons for this fact, firstly experiments were also done in the region without agitation effect and secondly the use of the logarithmic mean of the driving forces at the gas inlet and gas outlet instead of the driving force at the gas outlet as the average driving force for the absorption introduces a dependence on v,.

In Fig. 7 specific absorption rates are compared in two vessels for the same agitators (D = 0.12 m in T19 and D = 0.12 m in T60). In the bigger vessel the minimum agitation speed is higher and the slope of the straight line is lower than in the small vessel. The slopes of the straight lines are approximately inversely proportional to the square root of the vessel diameter T. From all experiments it follows, that the influence of T can be described by:

166

KSH 1 &He(n - n,JDT rv 3 75

0

0

0 ---_o_

0 -----

0

4

_

TlS.n.12

lo-t fB

--5-

0

0

___+o,Ei2 0

8 ~------_@--Q-_f=,

D 047

tB

5

FIG. 6.

1 10

15

Influence of the gas load.

Interfacial areas in agitated gas-liquid contactors

M-

t

20 -

10 .-

FIG. 7.

Influence of the vessel diameter.

The influence of the type of the gas inlet All vessels were equipped with a ring with small holes below the impeller as gas sparkers (Fig. 8a). Some series of experiments in T19 were done with distinct types of gas inlets: (a) A big ring with a diameter of 14 cm around the agitator. In the ring are small holes, through which the gas blows against the impeller blades (Fig. 8b). (b) A porous glass plate below the agitator (Fig. 8~). The experimental results are given in Fig. 9. In this Fig. also the lines are drawn for the normal gasinlet ring below the agitator and for the two agitators investigated. The type of gas inlet has no further influence when the minimum agitation speed has been passed. This is in accordance with the fact that the gas in the region with agitation effect is perfectly mixed [22], because at perfect mixing it does not matter where and how the gas is introduced.

boundary layer governs the absorption rate. Firstly, however, we have to prove that the mass-transfer resistance for the oxygen transport through the gas boundary layer is negligible. This is the case when k, % &&)/He holds. For gas bubbles the internal Sherwood number k&,/Q varies between 10 for small rigid bubbles and 25 for bubbles with completely developed internal circulation [43]. The bubble diameter in the region with agitation effect varies approximately between 1 and 5 mm and the diffusion coefficient of oxygen in air is about 2 x 10e5 m2/sec. The most unfavourable estimation of k, is about 4 x 10W2m/set and this value is about 500 x higher than the value of ,/(k.@/He in our experiments, as will be proved in the following. The mass-transfer resistance in the gas phase therefore can be neglected.

THE TRANSFER COEFFICIENTK FOR THE SULPHITE OXIDATION In thissectionwe will determine the value of K

and show that a chemical reaction in the liquid 167

Fro. 8. Gas inlet devices investigated (a) Normal ring with holes below the agitator. (b) Ring around the agitator. (c) Porous glass plate below the agitator.

K. R. WFISTERTEIIP, L. L. UN DIERENDONCK and J. A. DE KRAA

o RING AROUND AGITATOR .WROUSPLATE LINE: NORMALRING

FIG. 9. Experiments with various types of gas inlets.

Comparisonof cobalt and copper as catalysts The value of J(kB)/He for the reaction between oxygen and a sulphite solution under influence of cobalt ions as catalyst has been measured under our experimental conditions (3O”C, 100 kg/m’ Na,SO, in distilled water) in laminar liquid jets [ 1] : and

,/(k$@/He = 144 x 10s4 m/set

k = 37,000 set- ’ for the catalysis with 1.00 x 10d3 kmol/m3 CoS04. The value of ,/(kG@)/He for the catalysis with copper ions could not be obtained in liquid jets : a strongly varying and non-constant absorption rate was observed, which was equal to or higher than the physical absorption rate of oxygen in a sulphite solution. This leads us to the assumption that the reaction under influence of copper ions would be autocatalytic, but this is not the case with cobalt ions as catalyst. PRITCHFXT[41] found that the reaction under influence. of Mn.. ions as a catalyst also is autocatalytic ,;and that high reaction rates were obtained after say 0.2 sec. Contact, times in a laminar liquid jet are about an order of magnitude lower, thus a value of d(kg)/He cannot be determined with this technique. In an agitated gasliquid contactor, however, where samples are taken

with intervals of three to ten minutes, we will not notice that the reaction needs a few seconds before it starts after contacting with oxygen. The value of J(k@/He for copper then can also be obtained in a series of comparative experiments in a gas-liquid contactor. If we assume that the interfacial area is not affected by the substitution of lo- 3 molar cobalt ions by about lo- 3 molar copper ions, the ratio of the specific absorption rates with both catalysts will be proportional to the square root of the ratio of their respective reaction velocity constants. A number of experiments were done with both catalysts under equal conditions: cobalt concentration was 1.00 x 10d3 kmol/m3 and the copper concentration varied between 0.5 and 4-O x 10m3 kmol/m3. The results are given in Fig. 10: the copper concentration has no significant influence on the speciGc absorption rate. ‘From the ratio of the slopes of both straight lines, which were calculated with the method of the least squares, we find for the ratio of the reaction velocity constants at 30°C and in a solution with 100 kg/m3 Na,SO, : : J(kg)/He = &k@/He

(Co = 10d3 molar) (Cu N lo-’ molar)

Interfacial areas in agitated gas-iiqtid

contactox~

60-

@ 0

/

J

CObLTCATALY5T

Ilk)

1.

__)

“ii----FIG.

.,

3

5

v

10

10. Comparison

15

al

-

of copper and cobalt catalysts.

The standard deviation is O-16. With kc0 = 37,000 set-’ this gives kc. = 9800 set-‘. With a standard deviation of 0.13 x low4 m/set in &@/He for the cobalt catalysis the total standard deviation in ,/(k!@/He for the copper catalysis now becomes 0.9 x IO-‘m/set. Underourexperimentalconditions: ,/(k@/He[,

,“00

= (7.3 + 0.9) x low5 m/set

The temperature dependence of the specific absorption rate

The activation energy for a chemical reaction is in general higher than 10,000 kcal/mol and for a masstransfer coefficient lower than 3000 kcal/kmol. From the influence of the temperature on the specific absorption rate therefore it can be deduced if a chemical reaction or a mass-transfer process is rate determining. A series of experiments at different temperatures was done in order to determine the activation energy of the absorption rate. This cannot be done in an agitated gas-liquid contactor because in this apparatus the combined effect of the influence of the liquid properties and a

possible reaction rate on both K and S would be measured. A different method was followed, as outlined below. In a glass tube with a length of 60 cm and a diameter of 1. cm and ,provided with a double wall, through which hot water was circulating, 30 cm3 of a coppercatalysed sulphite solution was brought. From a cylinder via a rotameter pure oxygen was introduced into the lower end of the tube. Before and after an experiment, which lasted from 05 to 1.5 hr, the sulphite content was determined and the specific absorption rate was calculated after correction for the water-vapour pressure. The individual oxygen bubbles which leave the gas inlet join quickly together and form big bullet shaped gas bubbles with a length of 2 to 8 cm and a diameter equal to the tube diameter. The liquid flows downwards in a thin layer between the bullet shaped bubble and the glass wall. The rising velocity of these bubbles [44] is constant and independent of temperature:

169

K. R. WEWEXTXRP, L. L. VANDDZRENDONCK and J. A.

DE

KruA

can be calculated, so that the activation energy of

0

the reaction velocity constant k must be 12,300 kcal/kmol. From these data can be concluded that at 3O”C,with 100 kg/m3 Na,SO, in water and for the catalysis with more than 0.5 x low3 kmol/m’ CuS04, the reaction velocity constant is approximately k N 7.7 x 1012 exp (- 12,3OO/RT) set- ’

SULPHITE SOLUTION WITH COPPER CATALYST

Estimation of the chemical acceleration factor The reaction takes place in the liquid boundary layer if I$ = J(k@/k, > 2. As He = 69 under our experimental conditions, we find ,/(k9) = 5 x 10m3 m/set. The value of kl for the physical mass transfer in the liquid boundary layer around the gas bubbles is not exactly known in agitated gas-liquid contactors. CALDWBANK [ 161 found that k, in agitated gas-liquid contactors is only related to the diffusion coefficient of the dissolving component in the liquid and to the bubble size. Under our conditions 9 = 2.7 x lo-’ m’/sec [l]: we find that kl = 8 x 10m4m/set for bubbles with a diameter ~2 mm, according to CALDERBANK. HEERTJESet al. [45] found that

\

nl 2,s ‘0

I

I

290

3,W

3,lO

3.20

3.30

340

3.50

3.60

FIQ. 11. Absorption of oxygen in sulphite solutions in a narrow tube at different temperatures.

At a constant gas-supply rate therefore the interfacial area will be constant and independent of temperature. According to the crude penetration theory for physical absorption the liquid mass-transfer coefficient is kl = ~(~/xz)~‘“, where t - d& is the contact time between a volume element of the liquid and the gas bubble. With pure physical absorption only the activation energy of ,/g would be found, because vb and d, both are independent of temperature. The experimental values of KS/&He were multiplied with twice the distribution coefficient of oxygen in water at the corresponding temperature, and KS/s was plotted in Fig. 11 against T-l (“K-l). The distribution coefficient He = p/RTc for oxygen in a sulphite solution of 100 kg/m3 Na$O, is 2-Ox higher than for oxygen in pure. water. From Fig. 11 an apparent activation energy for K,of 8250 kcal/kmol can be calculated. This activation energy is so high that the absorption rate must be:governed by chemical reaction in the liquid boundary layer, thus r = cJJ(k9). The .activation energyfor kg now is 16,500 kcal/kmol, for 9 an activation energy of 4200 kcal/kmol

k, = 1.13@vb/d& In our experiments 06 = v,/(l - &) varies in the region with agitation effect between O-1and 0.01 m/set and d,, between 1 and 5 mm. This leads us to 1.9 x lo-‘< kl < 2.8 x lo-’ m/set. If we take the highest value of kl, then we find as the minimum value for the chemical acceleration factor : Because 4 > 2 under our experimental conditions the absorption rate of oxygen is determined by chemical reaction in the liquid boundary layer and consequently the increase of the absorption rate at increasing agitation speeds is exclusively due to the increase of the interfacial area. THE INTERFACIALAREA AT DISPERSIONWITH TURBINEIMPELLERS(C02-NaOH SYSTEM) For the reaction between CO, and a NaOH solution the required data can be taken from

170

Interracialareas in agitated gas-liquid contactors literature [46-511. The reaction in the liquid phase is.second order and the absorption rate is determined by chemical reaction in the liquid boundary layer at sufficiently high hydroxide concentrations

J000,

so that the interfacial area can be calculated from specific absorption rates, as was done previously. Furthermore the reaction is insensitive to impurities : physical properties of the liquid can be altered by addition of other liquids without affecting too much the chemical kinetics. A great disadvantage is the high solubility of CO,: resistance to mass transfer in the gas phase will interfere if CO2 is mixed with an inert gas and also absorption rates are so high that the heat withdrawal is a great problem. Another disadvantage is that the reaction can become “infinitely fast” (cour/2~~~~ < #Q), in which case the transfer coefficient K = kl (1 + corn/ is influenced (k,) by the hydrodynamic 2cc02i) conditions around the gas bubbles and the bubble diameter. In order to remove these difficulties as much as possible an installation was built wherein a strongly cooled NaOH solution was fed continuously to an autothermal agitated gas-liquid reactor and contacted with pure COz. The reaction heat is absorbed by the cold feed and there is no mass-transfer resistance in the gas phase. The installation and the experiments are described elsewhere [I] ; we will only mention a few results. In Fig. 12 the results are given for NaOH solutions to which various amounts of glycerol were added: the minimum agitation speed probably is not affected by the liquid viscosity. Visually it can be observed that bubble diameters decrease strongly with increasing liquid viscosity; in the region with agitation effect the bubble diameter was about 0.5 mm in a solution with 37.5 weight per cent glycerol of q = 11.9 cP. The slope of the straight lines in the region with agitation effect increase with increasing liquid viscosity. In Fig. 13 these slopes are plotted against the viscosity; the slopes are approximately proportional to q and the point measured with the system oxygen-sulphite corresponds to the points measured with the system C02-NaOH. This phenomena probably must be explained by the fact that coalescence of gas bubbles is diminished if the

FQo. 12. Interfacial areas, measured with the system COa and NaOH in water-glycerine mixtures. liquid viscosity increases. Additions of a few per cents ethyl alcohol (2-5 per cent) increased the interfacial area two- to threefold [l]. This is not attributed to an influence of surface tension but to the Maragnoni-effect [52, 531: if ethyl alcohol is added in small amounts a non-coalescing system is created and consequently much higher interfacial areas can be expected.

SULPHITE

1 -

10 \ 1

FIG.

171

13.

OXIDATION

d, (kg/f=4 xl

1000

Influence of the liquid viscosity on the interfacial area. . ’

K. R. Wrsrrnrxap, L. L. VAN CORRELATION FOR THE INTERFACIAL AREA

DEFCENDONCK and J. A. DE

KRAA

CREATED

WITH TURBINEIMPELLERS With the known value of ,/(kg)/He for the sulphite oxidation with CuSO, as catalyst the experimental results of the specific absorption rate can be converted in data for the interfacial area per unit of liquid volume S/E. When deriving generally valid correlations it is most important to pay attention to the physical interpretation of the influence of the independent variables. Visually it can be observed that very near to the impeller many very small bubbles and thus a high interfacial area is created, but that, when the dispersion is pumped away from the direct neighbourhood of the agitator, the growth of the gas bubbles (due to coalescence) diminishes the local specific interfacial area. The coalescence rate is higher’ the more the gas bubbles are withdrawn from the action of the impeller and get farther away from the impeller: a measure for the range of action is the agitation speed nD. The minimum agitation rate

From the experiments described it follows that the agitator must have a minimum agitation rate n,D in order to disperse the gas effectively. n,D was independent of the gas load v, and becomes smaller the nearer the impeller blades approach the baffles and the vessel wall (T/D smaller). As a physical interpretation of the occurrence of a minimum agitation rate, it can be assumed that the impeller tip velocity must exceed the gas rising velocity a certain number of times, in order that all big gas bubbles supplied can be broken up into small bubbles. The rising velocity of big gas bubbles in a stagnant liquid [54] is of the order of magnitude (as/p)“‘“5 and so the group noD(ag/p)-0’25 can be formed. This group however will not be constant, because n,D is not an absolute measure of the real relative velocity difference between the agitator blades and the liquid; a certain amount of slip occurs and therefore also a certain influence of T/D will be found (less slip when T/D gets smaller). All experiments in the various vessels and with twelve geometrically similar turbine impellers of different sixes could be correlated well by n,,D

T

(ag,p)o.z5 = A + B _d

y_i::I

, 3

4

5

FIG. 14. Correlation for the minimum agitation rate for

turbine impellers.

where A = 1.22; B = 1.25, as is shown in Fig. 14. This equation .says that the linear tip velocity of the impeller 7mop must be at least 8 to 30 times higher than the rising velocity of the gas bubbles for a good dispersion, depending on the ratio D/T. This interpretation has not been proved because a and p were not varied in our experiments; we only have some indications that the liquid viscosity should not have much influence on the value of n,D (Fig. 12). The, spk~% interfacial a$itation effect

area

in the region

with

From the measurements of the specific absorption rates, it can be concluded that the investigated region of variables holds:

2 E

N

D(n- now)f(v, a , p 9

g)

H

The physical properties q, a, p and g have not been varied in the experiments with the system oxygensulphite, and with the system CO,-NaOH only q. The remarks at the beginning of this section may lead to the assumption that the magnitude of the interfacial area averaged over the whole vessel is the result of a dynamic equilibrium between the inertia forces (which make the bubble diameters decrease) and the surface tension forces (which make the coalescence rate and also the bubble growth increase). In this case p and a have a strong influence 0nS.. t

Interfacial areas in agitated gas-liquidcontactors

VERMEULEN et al. [ 141found experimentally that S is proportional to cr-l. On theoretical considerations HINZE [55] concluded that in a turbulent field the maximum bubble size, to which S is inversely proportiqnal, becomes greater if a/p increases. From our experiments with the system CO,-NaOH it follows that S is approximately proportional to q. After introducing these liquid properties accordingly, we have correlated our experiments with a dimensionless combination, which resembles a Weber number : SH = C(n - no)D E

-

with C = (O-79 f 0.16)~ deviation is 0.16 cP-‘. ,/(kg)/He = 7.3 x 10e5 specific absorption rate sulphite :

(q in cPj. The standard With q = I.30 CP and m/set we find for the for the system oxygen-

HS,/(k@/eHe = (7.5 * 1.2) x lo+@

+

.Tl9 +?&I

2._

l-

-4

“7

2

3

4

The same varitibles as for the turbine impellers were investigated and the same phenomena were found, The minimum agitation speed could be correlated by n0D/(a&)o’z5

- n,)DJ(pT/a)

This relation is tested in Eig. 15 for the sixteen geometrically similar turbine impellers of different sizes (3.8 < D < 42 cm), which have been investigated in five different vessels. OTHER AGITATORTYPE A number of measurements were done with four-bladed paddle agitators in T14, T19 and T60.

5

FIG. 16. correlation for the minimum agitation rate for four-bladed paddle agitators.

= A + B+/D

with A = 2.25 and B = 0.68. This relation is tested in Fig. 16. In comparison with the turbine impeller the minimum agitation speed for the four-bladed paddle agitator is less sensitive to T/D. The relation between the specific interfacial area and the other variables is of the same type as for turbine impellers, only the influence of D and T is somewhat different: F

= C’(n - no)D(D/T)“3,/(pT/o)

with C’ = (O-80 f 0.14)~ (q in cP) The standard deviation is 0.14 cP- ‘. According to this equation the correlation for the specific absorption rate for the system air-sulphite has been tested in Fig. 17. The propellor agitators are discussed elsewhere [l]. For the two-blkded paddle agitators the minimum agitation four-bladed

rates are about the same as for the

ones,

but

Jhe

agitator creates only about

FIG. 15. Correlation for.?$eqecilic absorption ratq, with torbme lmpelbrs.

two-bladed

paddle

50 per cent of the interfacial area as the four-bladed one does at the same nD and D/T. The experimental results for the twobladed paddle agitator are compared with those of COOPER et al. [lo], who also published eliperimental data with the system oxygen-sulphite.

K. R. WESTERTERP, L. L. VANDIERENLKINCK and J. A.

d-

DE KRAA

0

oT60 .T 19

”

mo-4

10

,

I

100

x)00

FIG. 17. Correlation for the specific absorption with four-bladed paddle agitators.

rates

They measured the absorption rate in a vessel with 11,000 1. liquid hold-up, that is 2000 x bigger than our vessel Tl9. There are many uncertainties in their experiments: they do not mention the temperature at which they did their experiments and only speak of room temperature ; the sulphite content and the quality of the Na,SO, and tap water they used are unknown. Assuming they did their experiments at 20°C we corrected their results to 30°C with the data given in Fig. 11 and plotted their and our results in Fig. 18 as KSX/sHe against taking values for n,D from the experimental results. We see that there is not much difference between the specific absorption rates, although there is a great difference in vessel size. This is an indication that our method of correlation for extrapolation to greater vessels also can give good results.

t

@

0

KSHP/S) EHe

. .* ./

wish to acknowledge Prof. Ir H. for his constant help and advice. All the chemical analyses were done by Mrs. L. A. ABSPOEL-CHOUFOER and Miss M. T. BEUVENS. The Delftse Hogeschool Fonds has granted stipendia to the authors L. L van DIER~NWNCKand J. A. de KRAA. Acknowledgement-We KRAMERS

\ NOTATION C

D 9

h

H He k krI kg kc K 1 n nD f:

0 ::I [lo]

PO rA

R s ; T 08

FIG. 18. Experimental

Concentration

in liquid phase

db Diameter of a gas bubble di”bEZ Tube diameter D Diameter of the impeller

(D/T)O’33(n - n,)Dj(pT/o)

-2 10 -

With the chemical method we used, integral values of interfacial areas can be derived directly. The strong influence of the vessel diameter and the agitator diameter is demonstrated in the region with agitation effect and the existence of two distinct regions in a S-n plot is shown. More generally valid expressions for the specisc interfacial area in the region with agitation effect were derived, although not sufficient experimental evidence has been attributed for the influence of the physical properties of the liquid. Our method of correlation also seems to give good results for scaling up to vessels with diameters larger than 1 m, although some safety margin has to be taker?

results for two-bladed agitators.

paddle

Vl VR 8

174

kmol/ms m m m mr/sec m/se@ m m -

Diffusion coefficient in the liquid phase Acceleration due to gravity Height of agitator above tank bottom Height of liquid above tank bottom = p~/RTcs, distribution coefficient First-order reaction velocity constant WC-' Second-order reaction velocity constant m3/kmol set Partial mass-transfer coefficient, gas side m/set Partial mass-transfer coefficient, liquid side mlsec Over-all transfer coefficient m/set Boundary-layer thickness set: Number of revolutions of agitator per second Agitation rate m/set Partial pressure N/ma Energy consumption of agitator in gas-liquid dispersion W Energy consumption of agitator in liquid W Conversion rate of component A kmol/m3sec J/kmol”K Gas constant Specific interfacial area m2/m3 Time SeC Tank diameter Temperature “C, 0; Linear gas velocity, based on empty cross-section of tank m/set m3 Liquid volume in the dispersion ma Volume of the dispersion Volume fraction of liquid in the dispersion

Interfacial areas in agitated gas-liquid contactors , Q,$ 5 p 0 7

Dynamic viscosity of the liquid Chemical acceleration factor Molar mass flow Volumetric flow Density Surface tension Contact time

kg/m set kmol/sec mQec kg/ms kg/se@ SeC

Subscripts A Component A B Component B i Location in liquid phase at the boundary between gas and liquid 1 Location iu the buIk of the liquid 1 Liquid phase

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175

K. R. WESTWTW~, L. L. VANDIERENDONCKand J. A.

DE KRAA

ZUIDBRWEG F. J. and HARMENSA., Chem. Eagng. Sci. 1958 9 89. PEEBLESF. N. and GARBERH. J., Chem. Engng. Progr. 1953 49 88. HINZE J. O., Amer. Inst. Chem. Engrs. 1955 1289.

R&m&-Gn a choisi des reactions chimiques dont on conndt les proprietes chimiques et physiques pour determiner les valeurs int&rales de l’aire interfaciale cr&e par un agitateur dam un contracteur gaz-liquide. Ces systemes sont: la reaction entre l’oxygene et une solution de sultite et celle entre l’anhydride carbonique et la soude caustique. Dans le premier cas c’est la reaction chimique dans la couche limite qui controle la vitesse du ph&romene, dam nos conditions experiment&s tout au moins. La resultats r&&lent l’existence de deux regions: a) une region dam laquelle l’agitation n’a aucun effet : en dessous dune certaine vitesse d’agitation, noD, l’aire interfaciale n’est pas affect& par l’agitation et ne depend que du debit gazeux et du .. dispositif de barbotage. b) une region dans laquelle l’agitation est effective: aux vitesses d’agitation d&passant noD l’aire interfaciale est independente du debit gazeux et du dispositif de barbotage. La valeur de noD depend du rapport des diametres du reservoir et de l’agitateur mais ne depend probablement pas de la viscosite du liquide. On a derive des correlations generalea pour la vitesse minimum d’agitation et pour l’interface pour un grand nombre d’helices g&om&riquemknt similaires et des cuves ayant des diametres de 0,14 a 0,90 m et munies de chicanes. La methode de correlation semble permettre une extrapolation au dela de ces diametres. L’irdluence des prop&es physiques du liquide demeure incertaine. Zusanuneufassung-Die mit einem Riihrer in einem Gas-Fliissigkeits-Reaktor erzeugte totale Phasengrenz&che wurde mittels chemischer Reaktionen bestimmt, deren Reaktionsgeschwindigkeiten genau bekannt war. Es handelte sich dabei um die Oxydation von Sulphit-losungen mit Sauerstoff und urn die Reaktion zwischen Natrium-hydroxidlosungen mit Kohlendioxid. Ftir die erste Reaktion wurde bewiesen, dass die chemische Reaktion in der Fliissigkeitsgrenzschicht unter den angewandten experimentellen Bedingungen geschwindigkeitsbestimmend ist. Es wurde gezeigt, dass zwei Eintlussgebiete unterschieden werden konnen : a) Eine Region ohne Einfluss der Rtihrung. Rei Riihrgeschwindigkeiten unterhalb eines Grenzwertes noD wird die Grosse der Grenztlbhe unabhangig von der Riihrwirkung. b) Eine Region mit Riihreinfluss. Oberhalb der kritischen Rtihrgeschwindigkeit noD ist die PhasengrenztIache unabhangig vom Gasdurchsatz oder von der Art der Gaseinleitung. Die kritische Riihrgeschwindigkeit noD ist abhtigig vom Verh&hnis Tankdurchmesser zu Riihrerdurchmesser und vermutlich unabhangig von der Viskositit der Fltissigkeit. Es konnten allgemein gtiltige Gesetzmassigkeiten ftir die Mindestrtihrgeschwindigkeit und die erzeugte PhasengrenzfCiche fur Riihrkessel von 0,14-0,90 m Durchmesser mit geometrisch ahnlichen Riihrem verschiedener G&se abeleitet werden. Wenn such Kesseldurchmesser von mehr als 1 m nicht untersucht wurden, so muss doch angenommen werden, dasse die Reziehung such in diesem Rereich zur Dimensionienmg noch verwendet werden darf. Der Einfluss der physikalischen Eigenschaften der Fhissigkeit ist noch nicht abgekkirt.

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