Scale influence on the hydrodynamics of an internal loop airlift reactor

Chemical Engineering and Processing 43 (2004) 1519–1527

Scale influence on the hydrodynamics of an internal loop airlift reactor M. Blažej, M. Kiša, J. Markoš∗ Department of Chemical and Biochemical Engineering, Faculty of Chemical and Food Technology, Slovak University of Technology, Radlinského 9, 81237 Bratislava, Slovak Republic Received 4 August 2003; received in revised form 4 December 2003; accepted 10 February 2004 Available online 24 April 2004

Abstract The overall circulation velocity, the overall riser and downcomer gas hold-ups and the effect of reactor scale on a two-phase circulation regimes were studied in this work in three airlift reactors of different scale. The measurements were carried out in airlift reactor with internal loops (IALRs) with a working volume of 10.5, 32 and 200 l at the range of temperatures 18–21 ◦ C, under atmospheric pressure. Air and water were used as gas and liquid media. The three reactors were of similar geometry, the ratio between riser and downcomer cross-sectional areas, the aspect ratio of the column and the shape of the column bottom were taken as similarity criteria. In order to determine the linear circulation velocities, the magnetic tracer method was used. The riser and the downcomer were studied separately. Based on gas hold-up in both the riser and the downcomer, two regimes (homogeneous bubble (HMG) and heterogeneous churn-turbulent (HTG)) of the two-phase flow were observed. These were defined by Daniels [Chem. Eng. 70 (1995)] and described using the correlation proposed by Chisti [Airlift Bioreactors, Elsevier, London, 1989]. The average of the liquid circulation velocities increased with increasing reactor scale for the same superficial gas velocity. The overall circulation velocity was modelled on the basis of the momentum balance proposed in paper [Chem. Eng. Sci. 52 (1997) 25]. The parameters of both the correlation and the model tend to be constant for larger reactor scales. The value of the driving force (εR − εD ) was found to be important only for lower values of gas flow rate, because at higher values, the circulation velocity seemed to be governed only by friction in the reactor vessel. © 2004 Elsevier B.V. All rights reserved. Keywords: Airlift reactor with internal loop (IALR); Scale-up; Magnetic tracer method; Liquid circulation velocity; Flowfollower; Gas hold-up; Modelling of the hydrodynamics

1. Introduction Liquid circulation velocity and gas hold-up are the major hydrodynamic parameters and their knowledge is essential for a reliable description of an airlift reactor with internal loop (IALR). At the present time, the prediction of these parameters is still limited, particularly for the design of a pilot-plant and an industrial-scale IALR. Recently, many authors have attempted to employ airlift reactors for the commercial production of organic compounds [4,5], waste water treatment [6] and in biotechnology [2,7]. Despite their relatively cheap and simple construction, the application of IALRs is still limited due to several reasons. The most important is a lack of methods which are able to measure primary hydrodynamic parameters (e.g. linear circulation ∗ Corresponding author. Tel.: +421-2-59325259; fax: +421-2-52496743. E-mail address: [email protected] (J. Markoš).

0255-2701/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.cep.2004.02.003

velocity, gas hold-up, gas–liquid mass transfer) and the absence of appropriate hydrodynamic models, that take into account the reactor scale. Thus, our interest was focused on the following points. Measurement of gas hold-up and liquid linear circulation velocity in IALRs of three different scales; study of the influence of both reactor scale and superficial gas velocity on the measured hydrodynamic parameters; definition of the relationships which describe the measured data (gas hold-up and liquid circulation velocity) in an IALR and assessment of the influence of the reactor scale on coefficients in these relationships.

2. Theoretical The inner space of an airlift reactor consists of four main parts: a bottom, a riser (internal space of the tube inserted into the vessel), a separator and a downcomer (annular

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section between the internal and the external tube). Each section has its own specific character of the two-phase flow. Therefore, our interest was focused on both the riser and the downcomer which were studied separately as two governing sections of the IALR. 2.1. Characterisation of the co-current two-phase flow Daniels [1] defined four different flow regimes for the co-current two-phase flow in a vertical tube. 1. Homogeneous bubble (HMG) flow is characterised by gas dispersed in a bubble form with a narrow bubble size distribution, bubble rise velocity and a low intensity of turbulence. 2. In heterogeneous churn-turbulent flow, at higher values of the superficial gas velocity, the bubble coalescence is being increased, leading to a wide range of bubble sizes. The intensity of turbulence in the liquid phase is increased, when compared to the homogeneous flow regime. 3. In plug flow the character of the two-phase flow changes rapidly. Taylor bubbles with greater diameter are formed and their diameter is very close to the riser diameter. This is typical for non-Newtonian fluids of high viscosity flowing in narrow tubes. 4. Annular flow is observable only at very high values of the superficial input gas velocity, when a liquid film on the riser wall is created and gas with dragged liquid drops is rising very fast upwards in the riser. 2.2. Circulation regimes of the two-phase flow in an IALR It was not possible to apply only Daniels’s description of the two-phase flow to characterise all hydrodynamic parameters of an airlift reactor. In order to describe the overall circulation velocity, Heijnen et al. [3] determined three circulation regimes of the two-phase flow (Fig. 1) based on both the measured and the visually observed presence of the gas phase in the downcomer. The circulation regimes seem to be influenced and coupled with the two-phase flow regimes in the riser as shown further.

Regime I: gas is not present in the downcomer. This regime occurs only at lowest superficial velocities of the input gas (UG ), when the induced liquid velocity is insufficient to entrain any bubbles into the downcomer. Regime II: stratification and stagnation of bubbles in the downcomer. At higher values of UG , the liquid velocity in the downcomer (VLD ) becomes practically equal to the bubble swarm rise velocity. In addition, axial distribution of the bubble sizes is observed. The transition from this regime to the following regime is mostly gradual. Therefore, it is sometimes difficult to determine the exact point of the transition to regime III, where a complete recirculation of gas (present in the downcomer) exists. Regime III: regime of the bubble recirculation. At high values of the air flow rate, the liquid velocity in the downcomer is sufficiently high for recirculating bubbles (dragged from the separator to the downcomer) through the riser. 2.3. Definition of the superficial, linear and overall velocities Superficial velocity (U) represents the ratio of the phase volume flow to the cross-sectional area through which the volume flow passes. Linear velocity (V) represents the effective phase velocity in a selected place. The dependence between U and V in the riser (or in the downcomer) can be described by Eq. (1): VLR =

ULR 1 − εGR

(1)

The relationship between the liquid circulation velocities in the riser and the downcomer is given by the continuity equation: AD ULD = AR ULR

(2)

Overall circulation velocity (VL-CIRC ) represents an average linear velocity of the liquid phase in the reactor (measured by a flowfollower as it moves with liquid between measuring points). 2.4. Modelling of the overall liquid circulation velocity

Fig. 1. Circulation regimes in an internal loop airlift reactor.

Heijnen et al. [3] published a hydrodynamic model which predicts the circulation velocity in an IALR. This model can be applied for a two- or three-phase flow, in which the liquid is treated as a Newtonian fluid with low viscosity. This model is based on the momentum balance of the reactor, whereby the attention is concentrated on circulation regime III, which occurs mostly in full scale process reactors. The behaviour of regime I can be approximated using the same relationships for IALR as for bubble columns, because the value of gas hold-up in the downcomer is approximately equal to zero. This relationship holds not only for regime I, but also for a part of regime II, and describes a rapid rise of the circulation velocity [3].

M. Blažej et al. / Chemical Engineering and Processing 43 (2004) 1519–1527


VL−CIRC = (0.3 K1 )

0.5

UGC m

0.35 (3)

Regime II is the transition regime between regimes I and III, where the circulation velocity in the downcomer is equal to the bubble swarm velocity. VLD = Vsb

(4)

Regime III is characterised by recirculation of bubbles into the riser. When α is the ratio of gas hold-up in the downcomer and in the riser (constant for regime III) and m is the ratio of the cross-sectional areas of the riser to that of the whole column, then [3]: VL3-CIRC

+ K2 VL2-CIRC

− K1 UGC = 0

4gHe Kf

(6)

2[m + (1 − m)α] Vsb 1−α

(7)

Vsb is the bubble swarm velocity and α the ratio of gas hold-up in downcomer and riser. The overall friction coefficient Kf is strongly influenced by both the reactor geometry and the existence of circulation regimes which must be estimated empirically. Thus, for the determination of KfI–II in regime I (and the beginning of regime II) experimental data were used, similarly as in the case of KfIII in regime III. 2.5. Gas hold-up The gas hold-up ε is defined as the void fraction of gas in the gas–liquid dispersion. The overall gas hold-up in the IALR consists of the gas hold-ups in both the riser and the downcomer averaged as follows: εGC =

κ1 εGC = 1.488UGC

(9)

κ2 εGC = 0.371UGC

(10)

where the author recommends the following values for κ1 and κ2 : κ1 = 0.892 ± 0.075

(11)

κ2 = 0.430 ± 0.015

(12)

3. Experimental

He is the effective height of column. K2 =

II in the downcomer) and the coalescing churn flow regime (5) in the riser (regime III in the downcomer). The plot of the overall hold-up versus superficial velocity of the input gas can be correlated as follows:

(5)

where K1 and K2 in Eqs. (3) and (4) are as follows: K1 =

1521

εR AR + εD AD AR + A D

(8)

εGC is the overall gas hold-up, εR the riser gas hold-up, εD the downcomer gas hold-up.

The experimental set-up is schematically presented in Fig. 2. The measurements were carried out in three IALRs (Fig. 2) of different scale. The reactors were made of glass, the bottom with the gas sparger was of stainless steel. The gas sparger was located at the bottom in form of a perforated plate made of teflon or stainless steel. The total working volumes of the single columns were 10.5, 32 and 200 l. The three reactors were of similar geometry to avoid the influence of geometry on the hydrodynamic parameters. As similarity criteria were chosen: • column slightness (ratio of column height to column diameter); • ratio of cross-sectional areas of the downcomer and the riser (AD /AR ). These and other geometrical details used in our reactors are listed in Table 1. In all measurements, the internal tube was sparged. The details of the gas spargers used are given in Table 2. In the reactors with a working volume of 10.5 and 32 l, the gas input was controlled by a rotameter. If higher gas input was required (32 and 200 l reactor), the gas input was controlled by a mass flow controller (BROOKS-5853E). All experiments were carried out within the range of temperatures between 18 and 21 ◦ C, under atmospheric pressure. Air and water were used as gas and liquid media.

2.6. Correlation of the overall gas hold-up versus superficial gas velocity

3.1. Measurement of the gas hold-up

Chisti [2] published two correlations which describe separately both the bubble flow regime (4) in the riser (regime

The gas hold-up in the riser and the downcomer was measured using the inverted U-tube manometer method [2].

Table 1 Geometrical details of the reactors used Working volume (l)

DC (m)

HL (m)

HDT (m)

DR (m)

HB (m)

AD /AR (–)

HL /DC (–)

10.5 32 200

0.108 0.157 0.294

1.26 1.815 2.936

1.145 1.710 2.700

0.070 0.106 0.200

0.030 0.046 0.061

1.23 0.95 1.01

11 12 10

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M. Blažej et al. / Chemical Engineering and Processing 43 (2004) 1519–1527

Fig. 2. Scheme of the experimental apparatus.

Pressure differences were also measured by differential pressure sensors and the results were compared to those obtained by the U-tube manometer method. The tubes for the pressure measurement were located about 10 cm above the bottom and 10 cm under the top of the riser to reduce the effect of liquid acceleration [8]. 3.2. Measurement of the liquid circulation velocity The circulation velocity was measured using the magnetic tracer method [9,10]. As a flowfollower waterproof particles of spherical or oval shape were used with a negligible falling velocity (in comparison with the circulation velocity). Each flowfollower contained a magnetic material Table 2 Types of gas spargers used Working volume (l)

Material

Number of holes

Hole diameter (mm)

10.5 32 200

Teflon Teflon Stainless steel

25 25 90

0.5 0.5 1.0

with a high relative magnetic permeability (8000–120000). Each detector was constructed and installed according to the requirements for the given reactor. The signal of the particle, as it passed through two solenoid coils (changing the frequency of the oscillating coil), was registered using an A/D convertor and recorded on a PC. Solenoid coils were located in the distance from 80.2 to 105 cm from each other.

4. Results and discussion 4.1. Overall liquid circulation velocity In relation to the circulation regimes [3], it is possible to divide the overall liquid circulation velocity curves VL-CIRC versus UGC in Fig. 3 into three parts. At lower values of UGC (regime I and the beginning of regime II) the increase in the circulation velocity was the highest. This can be explained by the fact, that in regime I the gas hold-up in the downcomer was low (Fig. 4). Therefore, the overall liquid circulation velocity rose rapidly and was proportional to an increase of

M. Blažej et al. / Chemical Engineering and Processing 43 (2004) 1519–1527 0.5

0.12 200 L ALR 32 L ALR 10.5 L ALR modelled data

0.4

Churn flow

0.10 0.08 ε GR

0.3

REGIME II

0.1

REGIME III

0.2

REGIME I

VL-CIRC [ m.s-1 ]

1523

0.0 0.00

0.04

0.00 0.01

-1

0.02

0.03

0.00

the gas hold-up in the riser (Fig. 5). As can be seen in Fig. 3, the overall liquid circulation velocity at the same superficial gas velocity in regime I rose with increasing scale of the reactor. In the range of UGC corresponding to regime II, the gas hold-up in the downcomer increased. Thus, the driving force of the liquid circulation decreased. This in turn, influenced the overall circulation velocity, as was observed by changes in the gradient of the velocity curves in Fig. 3. The increase in gas hold-up in the downcomer can be explained also by the fact, that visually observed small bubbles were not separated in the upper section of the column from the liquid media fast enough, due to their lower rising velocity. The reason was that they did not have enough momentum to reach the gas disengager. Therefore, bubbles were entrained into the downcomer. The overall circulation velocity, similarly as in the case of regime I, was the highest in the 200 l IALR. In 10.5 and 32 l IALRs the liquid velocities

0.10

Churn flow

0.08

ε GD

Bubble flow

0.04 0.02

200 L ALR 32 L ALR 10.5 L ALR

0.00 0.01

0.01

0.02

0.03

-1

Fig. 3. Comparison of the measured and calculated data of overall circulation velocities using the Heijnen’s model in all reactor volumes.

0.00

200 L ALR 32 L ALR 10.5 L ALR

0.02

UGC [ m.s ]

0.06

Bubble flow 0.06

0.02

0.03

-1

UGC [m.s ] Fig. 4. Gas hold-up in downcomer in all IALRs with determined regimes of the two-phase flow.

UGC [m.s ] Fig. 5. Riser gas hold-up measured in all IALRs depending on UGC , divided into bubble and churn flows.

were comparable, but significantly lower than in the 200 l IALR. This can be explained by different specific friction against liquid circulation in smaller reactor scales. After the bubble recirculation started (regime III), the gas hold-up increase in the downcomer became only moderate. A further increase in the gas hold-up in the riser caused an increase of the value of the driving force (εR − εD ) and the overall circulation velocity of liquid started to grow moderately again in all scales of IALRs. In regime III, a dependence of the overall circulation velocity upon reactor scale was confirmed. The lowest values were measured in the smallest reactor (10.5 l), higher in the 32 l IALR and the highest values were obtained in the 200 l IALR. The increase of the overall liquid circulation velocity with increasing scale of the reactor is modelled in the next chapter. The circulation regimes estimated from Fig. 3 were in a good agreement with the visual observations based on the presence of the gas phase in the downcomer according to Fig. 1. The best resolution for the visual regime estimation was obtained from measurements in the 10.5 and 32 l IALRs, while in the 200 l IALR the gas phase was always present in the downcomer. In the 200 l IALR the gas phase recirculated even in the case of the lowest values of UGC . However, from the measured values of the circulation velocity (Fig. 3) three different regimes were estimated similarly as for two smaller reactor scales. Therefore, if visual observation of regimes I and II was not possible in 200 l IALR, only Fig. 3 was used for the determination of the circulation regimes. 4.2. Modelling of the overall liquid circulation velocity The overall liquid circulation velocity was modelled applying Heijnen et al. [3] model of momentum balance using Eqs. (3)–(7). The parameter α was determined to be constant for regime III, as shown in Fig. 6. The bubble swarm velocity Vsb in Eqs. (4) and (7) was given by averaging the

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10.0 1.0

9.5 I-II

0.6

10

Kf I-II Kf III

Kf

8

Kf III

α = ε GD / ε GR

0.8

0.4

200 L ALR 32 L ALR 10.5 L ALR

0.2

6 9.0 4

0.0 0.00

0.01

0.02

0

0.03

50

100

150

200 -3

-1

3

Reactor working volume [10 m ]

UGC [ m.s ] Fig. 6. Dependence of the ratio of the gas hold-up in riser and downcomer on the overall superficial gas velocity for all scales of airlift reactors used.

Fig. 7. Dependence of KfI–II and KfIII coefficients from Heijnen’s model on the reactor working volume.

circulation velocities, as regime II was examined for each reactor volume. The overall friction coefficients KfI–II (regime I and the beginning of regime II) and KfIII (regime III) include all partial resistances against the gas–liquid dispersion circulation, especially the wall friction as well as the resistance at the top and the bottom of the reactor. KfI–II , KfIII were determined by fitting the measured overall circulation velocity values VL-CIRC . Both the measured and the calculated data are presented in Fig. 3. As shown in Table 3 and in Fig. 7, the KfI–II values were reduced only moderately with increasing reactor scale. This means, that the resistance against liquid circulation at this stage was not significantly dependent on reactor scale. A different situation occurred in regime III: KfIII decreased considerably with increasing working volume of the reactor. Based on Fig. 7, both the KfI–II and KfIII values tend to be constant for larger reactor scales with a working volume in order of m3 . However, confirmation of this assumption, by further experiments in larger reactor scale is needed. A decrease in the overall friction seems to be the governing phenomenon with a major influence on the liquid circulation velocity in the range of higher values of UGC . On the other hand, we may suppose that the difference between the gas hold-up in the riser and the downcomer plays an important role only for lower values of UGC , because it causes a rapid increase in the overall circulation velocity (Fig. 3). A further increase in UGC seemed to reduce the influence of (εGR −εGD ), because even if this difference is the lowest in the 200 l IALR, the measured circulation velocity is then higher in the other reactors

and vice versa. The decrease of the friction coefficient with reactor scale increase cannot be described in detail without knowledge of further local hydrodynamic parameters, e.g. wall shear stress or velocity profiles of both the gas and the liquid phases [11]. However, this trend was found to be inversely proportional to the ratio of the gas–liquid dispersion volume to the wall surface in direct contact with the circulating media (the value of VDISP /AWALL is approximately 12, 17 and 33 for the 10.5, 32 and 200 l IALRs, respectively). Otherwise, in the first approximation the decrease of the friction coefficient can be explained by an increase of the ratio of the circulation driving force (momentum of the gas–liquid dispersion due to gas phase expansion) to the resistance against dispersion movement (represented by both the effect of the wall surface and the effect of the top and bottom sections of the reactor).

Table 3 Average values of friction coefficients in Heijnen’s model Working volume (l)

KfI–II

KfIII

10.5 32 200

9.57 9.12 9.10

11.27 6.83 3.66

4.3. Riser and downcomer gas hold-ups Figs. 4 and 5 are plots of the gas hold-up both in the riser and the downcomer versus superficial velocity of the input gas for each reactor scale. From four known two-phase flow regimes in a vertical tube, only two regimes could be measured in this work. A number of descriptions of gas and liquid flow-patterns can be found in the literature [1,12,13]. However, many of them arose from the subjective way in which flow-patterns are characterised. In the most cases, the researches used gas hold-up as a parameter, from which the transition between regimes could be estimated. Gas hold-up is an important parameter, because it determines the amount of the gas phase retained in the system at any time. The slope of the increase of εGR or εGD with UGC depends on the existing two-phase flow regime. Therefore, the change of the slope in the dependence of the gas hold-up versus UGC in the riser and the downcomer was used for the estimation of transition of the flow-patterns from the bubble flow regime to the churn flow regime. For the homogeneous

M. Blažej et al. / Chemical Engineering and Processing 43 (2004) 1519–1527 0.12 0.10

200 L ALR 32 L ALR 10.5 L ALR linear fit data

0.08 0.06 GD

flow, the evolutions of εGR were in fact identical for all reactor scales. The bubbles were distributed equally across all riser volumes. In this flow regime, bubble coalescence was not expected. In the downcomer, the gas hold-up was coupled with the riser gas hold-up and the evolution was only slightly different. At the lowest values of UGC (Fig. 4), gas was not present in the downcomer. Thus, εGD = 0, what corresponds to regime I. This was not observed only in the 200 l IALR, where bubbles were visually observed in the downcomer already at the lowest UGC , but also the behaviour of the system was found to correspond to that in regime I. At higher values of UGC , the rise in the gas hold-up in the downcomer followed appropriate trends of the gas hold-up in the riser. A further increase in the superficial velocity of the input gas phase (UGC > 0.015 m s−1 ) caused changes in the flow characterisation, as can be seen in Figs. 4 and 5. Transition between the homogeneous and churn flow in the riser occurred at about UGC ∼ = 0.015 m s−1 , what approximately corresponded to the published data given in flow-pattern maps available in the literature [1,12]. As the gas flow rate increased, the bubbles became closely packed and coalesced to form larger bubbles, which steadily increased in size with the gas flow rate, what caused a slower increase in the gas hold-up. The most significant change in the slope of the riser gas hold-up dependence was observed in the 10.5 l IALR, while in the 32 l IALR the change was not so significant. In the 200 l IALR was the lowest change in comparison with other reactor scales. The possible explanation of these differences could be as follows: The lower the riser tube diameter, the higher is the wall friction coefficient described in more details in the above given chapter “Modelling of the overall liquid circulation velocity”. As can be seen in Table 3, the friction coefficient in the 200 l IALR is almost four times lower than that in the 10.5 IALR. We supposed, that as a consequence of the smaller riser tube diameter, the bubbles were dragged from the layer of the stagnant “slow” liquid at the riser wall to the axial axis space with lower pressure and higher values of the overall circulation velocity [11]. Afterwards, the bubbles were grouped together and coalesced much more intensively, than in the case of larger riser tube diameters, where the ratio of the “slow” liquid width to the riser tube diameter is expected to be significantly lower. The differences between reactor scales in the gas hold-up in the churn flow are more significant in the downcomer. Similarly as in the riser, the most significant change in the slope of the gas hold-up dependence was observed in the 10.5 l IALR. Again, the 200 l IALR showed the lowest change. The reasons were assumed to be the same as in the riser. Due to bubble coalescence, higher bubble diameters are expected. The larger bubbles with a higher rise velocity were better separated in the gas separator at the upper section of each reactor, while smaller bubbles were dragged back into the downcomer volume. Therefore, where higher bubble coalescence was expected (10.5 l IALR), the decrease in the downcomer gas hold-up was more significant, as in the case of the larger reactor scales (32 and 200 l IALR).

1525

0.04 0.02 0.00 0.00

0.02

0.04

0.06

0.08

0.10

0.12

GR

Fig. 8. Linear but regime dependent relationship between εD and εR .

4.4. Relationship between εR and εD It is important to know the relationship between εD and εR for design purposes and scale-up. A few studies dealing with identification of the two-phase flow regimes are available in the literature [1,14–16], e.g. the reported changes in the logarithmic dependence VLD on UGC . In Fig. 8, regime changes can be observed where the dependence of εD versus εR for each regime is linear (εD = αεR − β). The values of the coefficients α and β for each regime and reactor scale are summarised in Table 4. Fig. 8 reveals that for smaller reactors the relationship εD versus εR is linear, but regime dependent. The influence of the existing two-phase flow regime decreased with increasing reactor scale, as for the largest reactor the plot εD versus εR was linear in the whole range of the investigated superficial gas velocities UGC (Fig. 8). Based on this observation, there is a great promise, that for larger reactor scales this dependence remains linear. This is a similar result than that obtained in paper [2] dealing with larger airlift reactors. 4.5. Correlation of the overall gas hold-up In Fig. 9, a comparison between the measured and calculated data is presented. As it is possible to see, the data computed from the relationships (9) and (10), correlated the measured values accurately. Coefficients κ1 and κ2 (Table 5) Table 4 Coefficients α and β for regimes II, III and reactor scale Working volume (l)

10.5 32 200

Regime II

Regime III

α

β

α

β

0.857 0.885 –

0.0095 −0.0065 –

0.432 0.670 0.967

0.0139 0.0037 −0.0068

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etry, additional measurements are required to obtain more empirical data for different geometries.

0.10

0.08

5. Conclusions

ε

GC

0.06

0.04 200 L ALR 32 L ALR 10.5 L ALR correlated data

0.02

0.00 0.00

0.01

0.02

0.03

0.04

0.05

-1

UGC [m.s ] Fig. 9. Comparison of measured and calculated overall gas hold-ups depending on the overall superficial velocity of the input gas.

Table 5 Values of coefficients κ1 and κ2 for all reactor scales Working volume (l)

κ1

κ2

10.5 32 200

0.829 0.815 0.792

0.505 0.449 0.427

obtained from the data correlation are shown in Fig. 10 as a function of the working volume of the reactor. Both coefficients have lower values with increasing reactor volume. From Fig. 10 it is possible to predict these coefficients for different reactor volumes. Since these coefficients are also dependent on ratios concerning reactor geometry (i.e. AD /AR ) the curves are limited to the specific ratios used. Therefore, if we want to take into account the reactor geom-

In the present work, new data are reported for two-phase air–water flow in internal loop airlift reactors of three different scales (10.5, 32 and 200 l). According to papers [1,2], two different regimes of two-phase flow were identified on the basis of gas hold-up: homogeneous bubble and heterogeneous churn-turbulent (HTG) flow regimes. The gas hold-up was described using an appropriate correlation. The parameters of this correlation tend to be constant for higher volumes of the reactor. However, in order to confirm this assumption, at least one measurement in pilot-plant scale is required. The average liquid circulation velocities increased with increasing reactor scale for the same superficial gas velocity. The value of the driving force (εR − εD ) was found to be important only for lower values of UGC . In the range of higher values of the input gas flow rate, the circulation velocity seemed to be governed only by friction in the reactor vessel. Using a different approach, given in paper [3], the overall circulation velocity was modelled. Similarly as in the previous correlation, the values of friction coefficients showed the same trend of approaching a constant value with increasing working volume. Using the results of this work, it can be generally assumed that reactor scale can significantly influence the two-phase gas–liquid flow, especially in the heterogeneous regime. To provide higher circulation velocities (shorter mixing times) and a better distribution of the gas phase (higher gas hold-up), it is suitable to use larger reactor volumes to avoid unfavourable influences of the gas hold-up reduction due to wall effects. Acknowledgements This work was supported by the Slovak Scientific Grant Agency, grant number VEGA 1/0066/03.

0.54 0.83 0.52 κ1

0.82

κ2

0.81

0.48

0.80

0.46

0.79

0.44

a, b A D g H He κ1 , κ2 KfI–II , KfIII m

κ1

Appendix A. Nomenclature κ2

0.50

0.42

0.78 0

50

100

150

200 -3

3

Reactor working volume [ 10 m ] Fig. 10. Dependence of κ1 and κ2 coefficients on the reactor working volume.

coefficients of linear fit cross-sectional area (m2 ) diameter (m) gravitational constant (m s−2 ) height (m) column effective height (m) loss coefficients for pressure drop overall friction coefficients, obtained from measured data ratio of cross-sectional areas of the riser and the whole column

M. Blažej et al. / Chemical Engineering and Processing 43 (2004) 1519–1527

U V

superficial velocity (m s−1 ) linear velocity (m s−1 )

Greek symbols α ratio of gas hold-ups in the downcomer and the riser ε gas hold-up κ1 , κ2 Chisti’s correlation coefficients of the overall gas hold-up Subscripts B bottom section from sparger to the beginning of the riser tube C column D downcomer DT internal tube G gas GC index of the column superficial velocity of the input gas L liquid L-CIRC overall circulation R riser sb bubble swarm

References [1] L. Daniels, Dealing with two phase flow, Chem. Eng., June 1995, 70–78. [2] Y. Chisti, Airlift Bioreactors, Elsevier, London, 1989. [3] J.J. Heijnen, J. Hols, R.J.G.M. van der Lans, H.L.J.M. van Leeuwen, A. Mulder, R. Weltevrede, A simple hydrodynamic model for the liquid circulation velocity in a full-scale two- and three-phase internal

[4]

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