Gas-Liquid Mass Transfer and Holdup in Vessels Stirred with Multiple Rushton Turbines: Water and Water-Glycerol SolutionsM. Nocentini, D. Fajner, G. Pasquali, and F. Magelli*Dipartirnento di Ingegneria Chimica e di Processo, Universit) of Bologna, viale Risorgimento 2, 1-40136 Bologna, ItalyGas-liquid mass-transfer coefficient, holdup, and power consumption were measured in vessels stirred with multiple Rushton turbines. Water and glycerol-water solutions were used, with viscosity up to 70 mPas. For measuring kLa, the dynamic oxygen electrode technique was adopted. The following correlation is applicable for the water-glycerol solutions: kLa = C(Pg/ Vr(Usr(AtiA,,,,20)5. For air-water systems the parameter C, while being the same as that for single impellers, is different from that for water-glycerol solutions. At equal PgIV and Us, the mass-transfer coefficient for solutions of low glycerol concentration is higher than that for water, whereas it decreases at an increase in glycerol concentration. This behavior can be attributed to the no coalescing characteristics of these solutions that are superimposed to the influence of viscosity. Cross-checking of kLa and holdup data confirms the interpretation given. The suitability of several equations available in the literature in interpreting the present data is also discussed.1. IntroductionGas-liquid mass transfer in stirred vessels is a process of considerable importance in the chemical and biochemical industries. Excellent review papers were published on the matter, the most relevant aspects covered being the measuring techniques for mass-transfer coefficients and the way to correlate them to the operating parameters and system properties (e.g., van't Riet, 1979; Sobotka et al., 1982; Linek et al., 1987; Zlokarnik, 1978; Judat, 1982; Nienow and 1.11brecht, 1985; Shah, 1991). Attention has mainly been focused on the behavior of vessels stirred with single impellers of several styles. However, even for these, general correlations that prove completely reliable and always useful for design are not available (Tatterson, 1991). The reason for this seems to be the specific role that the various system properties play. In spite of their practical interest (for instance, in the fermentation industry), much fewer efforts have been devoted to the study of multiple-impeller vessels. The few exceptions regard equipment stirred with either standard radial turbines (Taguchi and Kimura, 1970; Roustan et al., 1978; Ramanarayanan and Sharma, 1982; Jurecic et al., 1984; Hickman and Nienow, 1986; Ho et al., 1987; Spanihel et al., 1987; Machon et al., 1988; Cooke et a1.,1988; Oldshue et al., 1988), mixed-flow impellers (Hickman and Nienow, 1986), or proprietary devices (Kipke, 1978; Hickman and Nienow, 1986; Cooke et al., 1988; Oldshue et al., 1988). Gas holdup, which is an index of the gas-liquid mass-transfer ability of the system, has also been the subject of many investigations. In this case, too, relatively few data and correlations are available for multiple-impeller equipment (Lodi et al., 1982; Abrardi et al., 1988; Nocentini et al., 1988a; Smith, 1991).The purpose of this paper is to provide additional information on the behavior of vessels characterized by a high aspect ratio and stirred with multiple Rushton turbines. Both kLa and holdup were measured. Attention was focused on the behavior of water and aqueous glycerol solutions (viscosity up to 70 mPa-s): airwater systems were studied to provide data to be compared with available ones, while the glycerol solutions were used to evaluate the influence of viscous solutions of small molecules on the above-mentioned parameters.2. The Dynamic Oxygen Electrode Technique to Measure kLaVolumetric mass-transfer coefficients can be measured by steady-state and dynamic techniques (e.g., van't Riet,11 1979; Sobotka et al., 1982). In the dynamic techniques," the oxygen concentration of the inlet gas is changed stepwise and the time-varying 02 concentration in the liquid phase CL is measured with an oxygen electrode. Usually, this change is from N2 to air, but several variants have also been adopted (Linek et al., 1987). The dynamic technique in its original formulation (Bandyopadhyay et al., 1967) is very simple. However, several sources of errors have been recognized that include oxygen depletion in the gas phase, the role of electrode dynamics, the influence of the actual fluid dynamic behavior of the gas and the liquid phases, the gas and the holdup dynamics. Some can be accounted for though with increasing complication (Shioya and Dunn, 1979; Ruchti et al., 1981; Sobotka et al., 1982; Linek et al. 1987) or even circumvented (Chapman et al., 1982).One aspect that is important to consider for the multiple-impeller equipment studied in this work is the fluid dynamic behavior of the phases, since perfect mixing (MM model in the following) can hardly be invoked for neither of them (e.g., Nocentini et al, 1988a,b). The extent of the error in kLa determination caused by assuming simple models has been analyzed in particular by Shioya and Dunn (1979) and Nocentini (1990). This last author showed that perfect mixing for the liquid and plug flow for the gas (MP model) often give reasonable estimates for the coefficient provided that the measurement of the oxygen liquid concentration is performed at mid vessel height and aeration is started into a deoxygenated liquid with no gas holdup. When that is not the case, the dispersion model for both phases (DD model) can advantageously be used.As will be discussed in the Experimental Section, the experimental CL curves were treated with all these models: therefore, the relevant dimensionless balance equations (Nocentini, 1990) are given in Table I.3. Experimental SectionThe experiments were carried out in a cylindrical flat-bottomed baffled vessel of 23.2-cm diameter, T/D = 3. Agitation was provided with a multiple-impeller system consisting of a shaft with identical evenly-spaced six-bladed Rushton turbines. The body of the experiments were performed in the vessel with four turbines and aspect ratio HIT = 4; a number of experiments were also done with HIT = 3 and three turbines. The details of the apparatus characterized by HIT = 4 can be found in the papers by Nocentini et al. (1988) and Nocentini (1990). A few additional experiments were also carried out in a bigger vessel (T = 46-cm diameter, three turbines, HIT = 3) geometrically similar to the smaller one.The liquids were distilled water (g = 0.9 mPa-s) and aqueous solutions of glycerol (45, 65, 75, and 83 wt. 70, with viscosity approximately equal to 3.7, 14, 29, and 62 mPas, respectively). Liquid density and viscosity were measured, whereas other physical properties (e.g., diffusivity and surface tension) were taken from the literature or estimated. Water-saturated, filtered air was fed to the vessel through a ring sparger located below the bottom turbine. All the experiments were performed in a semibatch way at room temperature and atmospheric pressure. Air flow rate was in the range 0.1-0.7 vvm, and the rotational Reynolds number was higher than 103. Flooding conditions for the lowest turbine were avoided.In order to determine kLa, the technique suggested by Nocentini (1990) was used. In fact, this technique provides the overall mass-transfer coefficient, KLa; however, since oxygen is sparingly soluble in the liquid, kLa Ko. For the measurements, a liquid stream of reduced flow rate was continuously drawn from mid vessel height (midway between the second and the third turbine in the case of H/T = 4, in front of the second turbine for H/T = 3) and reintroduced into the vessel. The oxygen concentration was measured by means of a fast-response polarographic electrode. This procedure permits the same flow conditions at the probe (and, thus, the same liquid film thickness at the membrane) during either measuring or calibration. This external circuit was of small volume, and the liquid mean residence time was fairly low.The transient concentration curves were digitized and stored in a computer for subsequent treatment. The electrode dynamics was checked by measuring its response to a step disturbance in oxygen concentration of the flowing liquid. A pure delay and a first-order delay (about 2 and 4 s, respectively) adequately represented the electrode dynamics in the experiments with water and increased only slightly as liquid viscosity increased.The influence of the external piping and measuring circuit on kLa measurement was negligible. The results for the airwater system were the same as with the probe inserted directly inside the vessel (at the same height of the withdrawal). For the airwater system, an evaluation of the overall measuring technique was also made by comparing the results obtained by means of the steady-state sulfite method with those obtained through the dynamic technique summarized above.The value of kLa was evaluated from the experimental curves in terms of both the MM and the MP models. That based on the latter was usually adopted. Only when its value was significantly different from that obtained with the MM model, the DD model was also used for further check (the dispersion coefficient De- being determined as described by Nocentini et al. (1988b)) and the corresponding kLa value was retained. As can be noted from Figure 1, the MP model proves quite satisfactory in nearly all the cases, thus supporting previous findings of Nishikawa et al. (1981a), Chapman et al. (1982), Stenberg and Andersson (1988), and Smith (1991).Gas holdup and power consumption due to agitation were also determined with the simple techniques used by Nocentini et al. (1988a).4. Results4.1. kLa Values, Air-Water System. The results obtained with water were evaluated first in order to check for their consistency with published data. kLa values were correlated with the usual relationship:kLa = C1(Pg/V)a(Us)3(6)For the smaller vessel with four Rushton turbines (HI T = 4), the following set of parameters (SI units) was calculated with data regression:C1 = 1.5 X 10-2= 0.590 = 0.55By imposing 0 = 0.4, the following values were obtained though with a slight decrease of the correlation coefficient (see Table II):C1 = 5.5 X 10-3a= 0.620 = 0.4which are in reasonably good agreement with the values given by Linek et at. (1987) for single Rushton turbines (namely, C1 = 4.95 X 10-3, a = 0.59, 0 = 0.4).Equation 6 with the same set of constants fits the data obtained with three Rushton turbines in the smaller and the bigger vessels as well as the previous data of Roustan et al. (1978) and Machon et al. (1988) obtained with two and three Rushton turbines, respectively.4.2. Holdup, Air-Water System. Holdup data were correlated satisfactorily with the following equation:eG = 8.35 x 10-2(pgi vr.375(ux.62(7)which is in very good agreement with the correlation proposed by van't Riet (1975) for single Rushton turbines.The data can also be fitted with other existing correlations including that proposed by Abrardi et al. (1988) for single and dual turbines:(G = C2[(P5i V)(1 EG)?Usc'(8)This correlation fits our data with the following set of constants (all parameters in SI units):C2 = 0.0761,1/ = 0.364) = 0.55The correlation proposed by Smith (1991) as a means to correlate data for various geometries (including double and triple impellers)EG = C3(Re Fr F1)135(D/T)L25(9)applies to oar data with the same best fit value, C3 = 1.25.It can be noticed at this point that-in spite of lack of symmetry in the fluid dynamic behavior of the lowest turbine and the other one(s) as noted by Smith et al. (1987), Nocentini et al. (1988), and Hudcova et al. (1989)-the use of the actual value of PS V proves quite satisfactory to represent overall equipment behavior in terms of both cc and /kn. It is also confirmed that correlations in the form of eqs 6-9 provide a good fit of the data regardless of the specific geometric configuration (van't Riet, 1979).4.3. t for Aerated Aqeuous Glycerol Solutions.Each set of data for the various glycerol concentrations (determined only in the smaller vessel, H IT = 4) was fitted with eq 8-see Table II. Since the average 0 value was about 0.4 (except for the most concentrated solution, for which, however, lesser and more scattered data were available), this last value was retained for the whole data. The overall results are plotted in Figure 2: for the lowest concentration solution (45 wt %, 3.7 mPas) the mass-transfer coefficient is higher than that for pure water, whereas further increase in glycerol concentration (and, therefore, in viscosity) results in markedly lower coefficients. This behavior is consistent with reported knowledge. At low to medium concentration (5-50 wt %) the main glycerol effect is to turn liquid behavior from coalescing to noncoalescing, thus increasing interfacial area and consequently the volumetric coefficient (Linek et al., 1987). The average values IX = 0.62 and {J = 0.4 were calculated for the whole data, which are in reasonable agreement with the theoretical predict ion made by Kawase and MooYoung (1988) and Ogut and Hatch (1991) on the basis of Higbie's penetration theory and Kolmogoroffs theory of isotropic turbulence (i.e., IX = 0.65 and fJ = 0.5). The influence of viscosity (which is the parameter exhibiting the most significant variation with glycerol concentration) can be better seen in Figure & Owing to the no coalescing behavior of the low concentration glycerol solution, the values of for aqueous solutions of electrolytes were also calculated with the correlation proposed by Linek et al. (1987) and are plotted in the same figure for comparison (dashed area at A = 0.9 mPa-s). The consistency of the whole trend can be observed and supports the explanation given above about the behavior of the low concentration glycerol solutions. The same general trend was recently reported by Dawson (1992) for CMC solutions.A simple correlation of the date (glycerol solutions only) can be attempted by implementing eq 6 with a viscosity term:kLa = C4(Pg/17)"(Usr(A/Aw.206(10)With a = 0.62 and 13 = 0.4 and by arbitrarily assuming constant a, linear regression of the whole data yields (5 = -1.17. A plot of the correlation is given in Figure 4.No agreement can be found in the literature about the viscosity influence on kLa, the experimental value of (5 ranging from 0 to -1.3 (e.g., Hattori et al., 1972; Nishikawa et al., 1981b; Jurecic et al., 1984; Kawase and Moo-Young, 1988; Baker et al., 1988; Ogut and Hatch, 1988, 1991; Cooke et al., 1988). In fact, these values have been obtained with a variety of air-liquid systems and in different viscosity ranges. It is worth noting that 8 was also evaluated on a theoretical basis by Kawase and Moo-Young (1988) who took also into account the influence of DL and a and obtained b = -1.25. A further discussion on the merits of this approach and the theoretical values of (5 is developed in the Appendix.4.4. Holdup for Aerated Glycerol Solutions Gas holdup depends on aeration, power absorption, and glycerol concentration. At low concentration (45 wt %) holdup is higher than for water (at equal U. and P5/ V), whereas at higher concentration it becomes lower: at 83 wt % small bubbles are present, but a number of big ones are visually noticed even at high power inputs.When correlated with a power-law equation similar to eq 7, data exhibit dependence to (U3)1 /3with negligible differences in the exponent at the various glycerol concentrations. Instead, holdup dependence on Pg/ V decreases at increasing glycerol concentration, as shown in Figure 5a. If liquid viscosity is arbitrarily assumed as the only additional parameter affecting EG, then the term (/q 20)-1/3 is enough reduce the data to a single curveat least for Pgl V greater than 500 W/m3 (Figure 5b). The structure of this correlation is similar to that set forth by Cooke et al. (1988) for paper fiber suspensions.4.5. Relation between kLa and Holdup. Since the holdup is correlated to the specific surface area through the relationshipa = 6EG/dB(11)Where dB is the mean volume-to-surface bubble size, the interrelation between experimental values of kLa and holdup seems to be of some significance.This relation between kLa and EG (Figure 6) is quite different for pure water and glycerol solutions, thus confirming the difference in behavior discussed above. For water these parameters are nearly proportional:kLa = 2.31(EG)I.22(12)while for glycerol solutions the data are more scattered and a correlation like eq 12 is less meaningful.The plot of kLa/EG (which is proportional to kL/dB) against Pg/ V reveals an influence of this last parameter raised to about 0.3 (Figure 7). Since for a given system dB (PG/ V)4).4 (Kawase and Moo-Young, 1990), kL is affected very slightly by PG/ Vas usually reported. There is a significant, monotonic reduction of the ratio kL/dB when passing from water to lean glycerol solutions and, further, when increasing glycerol concentration. This behavior can be explained primarily with kL reduction as the consequence of liquid viscosity increase; for the 45 wt To solution, this last effect more than counterbalances the decrease in dB.4.6. Other kLa Correlations. A number of selected correlations taken from the literature that include system properties were also tested with the present kLa data.The dimensional correlation of Kawase and Moo-Young (1988)kLa = 67.5(Pg/ V)a(Uds(il/Aw,20)5/32-50's (13)did interpret the air-water data fairly well (R2 = 0.98) with the set of parameters given by these authors (a = 0.65, = 0.5, r5 = -1.25). In contrast, eq 13 underestimates kLa for glycerol solutions by an order of magnitude. Overall there appears to be no single correlation which will represent the whole data (water and water/glycerol solutions). This seems to be due to the noncoalescing behavior of the glycerol solutions that can hardly be described by means of surface tension only.Similarly, the use of the empirical parameter (Linek et al., 1987) defined as= po.268pLo.51,1/60.-3/5(14)to implement eq 6 for correlating glycerol data proved rather poor in this case. Better results were obtained with W2 (Figure 8).Yagi and Yoshida's correlation (1975)kLaD2/DL = 0.06Re1-5Fe-19Scas(ii U,/ a)-6(ND/ U5).32

proved quite satisfactory in interpreting the data for water and low concentration glycerol solutions (45 and 65 wt %), but it failed to interpret the data obtained with the highest concentration solutions.The general correlation proposed by Zlokarnik (1978):K* = C6(Pg/QG)*z(16)

where Kt = ko(V I QG) and (Pg/QG)* = Pg/ [QoP(gv)2/9, produced fair correlation of the air-water data but gave just an order-of-magnitude estimate for the other data; the best fit parameters where C6 = 0.9 x 10-3 and z = 0.81, to be compared with the values C6 = 1.5 X 10-3, z = 0.66, and C6 = 1.5 x 10-2, z = 0.5, reported by Nienow and Ulbrecht (1985) and Zlokarnik (1978), respectively. For glycerol solutions (but not for pure water), a better correlation is possible by implementing eq 16 with the Schmidt number as suggested by Hacker et al. (1981):Kt = C7(Pg/QG)*PScq(17)The best fit values of the parameters are p = 0.56 and q = -0.35, which are in good agreement with those found by Hacker for (carboxymethyl)cellulose solutions (p = 0.59, q = -0.3). Figure 9 shows this correlation, which exhibits approximately the same scattering of Figures 4 and 8.5. ConclusionsVolumetric mass-transfer coefficients and holdup were measured in vessels stirred with multiple Rushton turbines.For-air-water systems the results can be correlated with* equations that are independent of the geometrical configuration of the vessel. Specifically, correlations based on power consumption per unit volume and superficial gas velocity, eqs 6 and 7, that hold for a single Rushton turbine apply also to multiple turbines:. It is also confirmed that eq 9 with C3 = 1.25 (set forth for multiple impellers) is independent of turbine number and spacing. For air-glycerol solutions, mass-transfer coefficients were found that are higher than those for water at low to medium glycerol concentration and lower at higher glycerol concentration. Similar results were obtained for holdup as well. This behavior is postulated to depend on two concurrent factors, namely, coalescence depression of glycerol (that increases interfacial area per unit volume) and mass-transfer reduction (typical of viscous solutions). The former playa a major role at low glycerol concentration, while the latter gets increasing importance at high,:- glycerol concentration.Mass-transfer data for glycerol solutions were correlated first to liquid viscosity through the term 12, whose exponent 6 is in the range of values proposed in the literature for single impellers and in agreement with theoretical estimates. The use of additional terms for diffusion and surface tension (either as dimensional terms or in the form of dimensionless groups) while proving satisfactory to correlate the specific data for glycerol solutions does not permit correlation of the data of water as well. In view of the results obtained with water, this is hardly attributable to the multiple-impeller configuration. Instead, the noncoalescing behavior of the glycerol solutions that superimposes on their viscous characteristics seems responsible. This fact stresses the importance of taking into account this factor.AcknowledgmentThis work was financially supported by the Italian Ministry of University and Research (funds "MURST 40%"). The valuable collaboration of Messrs. G. Alberti, S. Amidei, and D. Bonanno in carrying out the experimental program is gratefully acknowledged. Thanks are also due to Idronaut srl (Brugherio, Italy) for their assistance in selecting the d09 probes and the related hardware equipment.Nomenclaturea = surface area per unit volume of dispersion (m-1)C; = constantsCG = dimensionless oxygen concentration in the gas phase CGe = dimensionless oxygen concentration in the gas phase at the inletCL = dimensionless oxygen concentration in the liquid phase dB = mean bubble size (m)D = turbine diameter (m)DeG = dispersion coefficient for the gas phase (m2 s-1) DeL = dispersion coefficient for the liquid phase (m2 s-1) DL = oxygen diffusivity in the liquid (m2 s-1)Fl = gas flow number = QGIND3Fr = Froude number = N2DI gg = gravitational acceleration (m s-2)H = dispersion height (m)K = dimensionless mass-transfer coefficient = kLatF, Kt = dimensionless mass-transfer coefficient, eq 16kL = mass-transfer coefficient (liquid side) (s-1 m)m = partition coefficientn = exponent in eq 18Pg = gassed power consumption (W) PeG = gas Peclet number = UsH / 6.13,6PeGL gas-liquid Peel& number = V,1-1/(GDei, p, q = parametersQG = volumetric gas flow rate (m3 s-') R2 = correlation coefficientRe = Reynolds number = ND2p/aSc = Schmidt number = v/DLt = time (s)T = vessel diameter (in)tB = mean gas residence time = EG.HI U5 (t) Us= superficial gas velocity (m a-1)V = volume of the liquid in the vessel (m3)W = system properties parameter, eq 14 x, y, z = exponentsZ = dimensionless axial coordinateGreek Lettersa, 0, 6 = constantsEG = fractional gas holdup0 = dimensionless time = tItR= dynamic viscosity of the liquid (Pas)pw.20 = reference viscosity (water at 20 C) (Pa-s) P = kinematic viscosity (m2 s-1)p = liq .lid density (kg m-3)a = surface tension (Ncb, = constantsSt; = constantsAbbreviationsDD = dispersion model for the liquid and the gas MM = perfect mixing for liquid and gas phasesMP = perfect mixing for the liquid and plug flow for the gas win = volume of air/volume of liquid/minute = QG/ V (miri-')

AppendixIn section 4.3 the average value l = -1.17 was obtained for water-glycerol solutions. In fact, the change in viscosity due to the change in composition is usually paralleled by a change in other properties (primarily DL and Cr). Therefore, eq 10 does implicitly provide the change of these properties as well.In order to compare the above result with theory, the change of DL can be expressed in terms of viscosity influence with the following relationship (Ho et al., 1986):DLyn = constant(18)and implemented in the theoretical equation set forth by Ogut and Hatch (1991): kLa = C5(Pg/ V)"(UX(11/Aw,20)21DL22 (7(19)where SI, = -0.25, f12 = 0.5, 03 = -0.6 apply for low-viscosity liquids and S-11 = -0.375, Ste = 1, C13 = -0.25 apply for high-viscosity liquids. Ogut and Hatch assumed constant DL and a and obtained 6 = -0.25 in the former case (large, nonrigid bubbles) and S = -0.375 in the latter (small, rigid bubbles).The influence of surface tension is neglected here since its variation in the experimental range investigated was fairly weak. In eq 18 n = 1 (Stokes-Einstein equation) holds for diffusion in dilute solutions of small molecules and n = 2/3 (Eyring's rate theory) holds for the diffusion in a viscous solution of large molecules (or associated, small molecules). It is worth noting in passing that for the wide spectrum of substances encountered in practice the change of DL with composition is system-specific and complex (Ju and Ho 1986) and is still far from being completely understood. By using eqs 18 and 19, the influence of viscosity on kLa in terms of eq 10 can be evaluatedat least for selected limiting cases. The values of 6 calculated are given in Table III. As is apparent, the experimental value 6 = 1 (20%) for our solutions (consisting of a mixture of small and big bubbles) is in reasonable agreement with the pertaining theoretical values. However, the lack of precise information about bubble characteristics and their distribution in the stirred system at different operating conditions prevents us from drawing reliable, quantitative conclusions.