Hydrodynamics and mass transfer in an airlift reactor

Hydrodynamics and mass transfer in an airlift reactor

Chemical Engineering Science 54 (1999) 2255}2262 Hydrodynamics and mass transfer in an airlift reactor J. Korpijarvi , P. Oinas *, J. Reunanen Tamp...

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Chemical Engineering Science 54 (1999) 2255}2262

Hydrodynamics and mass transfer in an airlift reactor J. Korpijarvi , P. Oinas *, J. Reunanen Tampere University of Technology, Energy and Process Engineering, P.O. Box 589, 30101 Tampere, Finland  Kemira Fine Chemicals Oy, P.O. Box 74, 67101 Kokkola, Finland  Kemira Chemicals Oy, P.O. Box 171, 90101 Oulu, Finland

Abstract Hydrodynamics and mass transfer in internal and external #ow airlift reactors have been studied in this work. Gas hold-ups and liquid velocities have been determined in a concentric tube airlift reactor, while oxygen mass transfer has been measured in an external loop airlift reactor. First, tracer measurements were used to verify a conventional axial dispersion model. Further, a model derived from multi-phase Navier}Stokes equations was veri"ed with experimental data from the oxygen mass transfer measurements. Both models were in a good agreement with the measurements.  1999 Elsevier Science Ltd. All rights reserved. Keywords: Airlift; Reactor; Hydrodynamics; Mass transfer; Axial dispersion; Gas hold-up

1. Introduction

2. Experimental

The use of airlift reactors for multiphase reaction processes has been increased during the recent years. Airlift reactors are especially due to systems with suspended solids. Especially in bioprocessing, such as fermentation and biological treatment of waste water, airlift reactor systems have given good performance. Airlift reactor is a special type of bubble column where the internal structure of the reactor device has been divided into two separate sections: the riser and the downcomer. When gas is fed into the riser a steady circulation of liquid is achieved inside the system. The applications of airlift reactors have so far been restricted mostly to biological three-phase-processes mainly due to the self-induced circulation, improved mixing and heat transfer characteristics compared to ordinary bubble columns. Additional good features of this type of reactors are their simple hermetic structure and total absence of moving parts. In systems with suspended solids, even at low gas feeds particle sedimentation is negligible.

The gas hold-up measurements were carried out in two di!erent concentric tube airlift reactors; airlifts 1 and 2. Airlift 1 had a nominal volume of 15 l and height of 1.25 m. The riser to downcomer crosssectional area ratio could be adjusted by using riser tubes with di!erent diameters. Four riser tubes were used with A /A area ratio ranging from 0.14 to 1.69. P B The downcomer inner diameter was 110 mm. The gas sparger was made of sintered steel tube with a pore diameter of 90 lm. Airlift 2 was otherwise similar to airlift 1, but its nominal volume was 30 l and height 2.5 m. Only one riser tube was used in the measurements with airlift 2. The riser tube had an inner diameter of 90 mm with an A /A ratio of 1.64. Airlift 1 is P B illustrated in Fig. 1 and the riser tube dimensions are given in Table 1. The manometric method was used to measure gas volume fractions in airlifts 1 and 2. Gas volume fractions were measured from three locations in airlift 1 and from 6 locations in airlift 2 both from the riser and downcomer by measuring the pressure di!erence between two consecutive probes during the unaerated and aerated stages. Average gas hold-ups were also obtained by measuring the pressure di!erence between the lowest and highest probes.

*Corresponding author. Tel.: 00 358 10 86 28740; fax: 00 358 10 86 28729; e-mail: [email protected]

0009-2509/99/$ } see front matter  1999 Elsevier Science Ltd. All rights reserved. PII: S 0 0 0 9 - 2 5 0 9 ( 9 8 ) 0 0 4 3 9 - 4

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Fig. 1. Airlift 1 used in the experiments.

Table 1 Riser diameters, cross-sectional area ratio and riser to column diameter ratio Riser diameter D mm P

Fig. 2. The conductivity measurements in the airlift 2.

Riser

Outer

Inner

A /A P B

D /D P 

A B C D

42.4 60.3 76.3 88.9

38.4 56.3 72.3 84.9

0.14 0.37 0.82 1.69

0.35 0.51 0.66 0.77

The liquid velocities were determined (indirectly with the axial dispersion model) by conductivity measurements. The setup for conductivity measurements is illustrated in Fig. 2. Two probes (1, 2) were installed inside the riser and two others (3, 4) in the annulus. The distance between upper and lower probes was 1880 mm. NaOH tracer impulse was fed from the bottom and the change in the tracer concentration was monitored.

3. Hydrodynamics of airlift reactor The airlift reactor system was modeled by employing a set of ideal blocks for the riser, downcomer and the bottom and top sections of the reactor. The #ow struc-

ture used in the &&network-of-zones''-model is shown in Fig. 3. An ideal continuous stirred tank reactor (CSTR) model was used for bottom and top sections, whereas axial dispersion model was used for the riser and the downcomer of the internal loop airlift reactor. A similar approach was used for the external loop reactor (Fig. 4) with the top gas separator section modeled as two CSTRs, one with and the other without gas. In addition, the downcomer could be modeled as an ideal plug #ow reactor due to the absence of gas after the gas separator. The axial dispersion model was veri"ed with tracer experiments in an internal loop airlift reactor. This model uses super"cial velocities in the riser and downcomer and three dispersion coe$cients as unknown parameters to be determined from the conductivity data. In modeling, the riser was divided into two sections both having a dispersion coe$cient to be estimated in the axial dispersion model. The approach was used also in the paper of Dhaouadi et al. (1996). In the riser and downcomer sections the change of tracer concentration in time can be calculated by axial

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The CSTR equation for the top and bottom sections is written as dC Q 2" * (C !C ). 2  2 dt < *

(2)

4. Mass transfer in airlift reactor Mass transfer was modeled in an external loop airlift reactor illustrated in Fig. 4 by a set of equations, which were derived from the principal multi-phase transport equations used e.g. by Hillmer et al. (1994). The scalar transport equation for phase k in one dimension can be written as



Fig. 3. The modeling scheme used for di!erent sections of internal loop airlift reactor.



* * k *U *(oeU)  e I"! (oeuU) # #SU . (3) I *z p *z *z *t I The following assumptions were made while deriving the equations: The liquid #ow in the di!erent parts of the reactor is uniform, #ow is one-dimensional and #uid densities are constant throughout the reactor. Due to these simpli"cations the momentum equation was not required in deriving the model. The gas-hold-up derivative was derived from the mass conservation equation. Using Eq. (4) and the source terms given in Table 2, the following set of PDEs was derived for the external loop airlift reactor. For the change of oxygen concentration in the riser one can write the following: ¸iquid:



*C *C 1 *e *C *C *"!u *#D * *# * * *z *t *z e *z *z * #k a (C*!C ). * * * Gas:







*y 2 *P 1 *e %# " !u #D % P *z *t e *z % *y 1 *P #D #y !u #D % *z P *z



!k a (C*!C ) * * *

 (4)

*y *z 1 *e % e *z



1!e R¹ % . e P %

(5)

Table 2 Variable U, turbulent Prandtl number p and the source term S for Eq. (3)

Fig. 4. The modeling scheme used for di!erent parts of an external loop airlift reactor.

U

p

Mass

1

R

Momentum

u

1

dispersion equation dC dC dC 2"!u 2#D 2. * dz dt dz

(1)

Concentration

C

1

S

    

* *e k $M I *z  *z I *P e !(o!o ) g $M u # I *z  I I



* *u k e $e e (M !u ) c %  %  U *z  *z I Ro H

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The term k /p was replaced in the concentration  equations by a pseudo-dispersion coe$cient, D, which was used in the model as a free parameter. This parameter is not comparable to the dispersion coe$cient appearing in Eq. (1). The overall mass transfer term M in I Eqs. (4) and (5) was replaced by the conventional k a * presentation derived from the "lm theory. For the gas}liquid separator in the external loop airlift a two-phase CSTR model was used. The following ODEs were written: dC Q I" I (C !C )#c k a (C*!C ), I  I I * * * dt < I where



c "1, I

(6)

for liquid phase,





1!e % for gas phase. e % The unaerated part of the gas}liquid separator and the bottom junction were modeled as a one-phase CSTR c "! I

Fig. 5. Average gas hold-up in the downcomer vs. average gas hold-up in the downcomer in airlifts 1 and 2. The measured values and the "tted correlation are compared to the correlations of Choi et al. (1996) and Bello et al. (1985).

dC Q *" * (C !C ). *  * dt < * Finally, the downcomer, being free from gas, was simply modeled as an ideal plug-#ow reactor *C *C *"!u *. * *t *z

5. Results and discussion The gas hold-up measurements revealed that a linear correlation e "0.84 e , (7) %B %P explains the data with "t 99.8% agreement for airlift 2. This agrees well with measurements made by Bello et al. (1984) and Choi et al. (1996). Bello et al. (1985) used annulus sparged concentric tube reactors with A /A P B ratio from 1.78 to 7.69 and Choi et al. (1996) used rectangular airlifts. This correlation also applies for the measurements with the smaller airlift 1 with riser tube D as can be seen in Fig. 5. The dramatic e!ect of A /A P B ratio on downcomer gas hold-up can be seen from Fig. 6 when comparing draft tubes A and B. Figs. 7 and 8 illustrate the e!ect of super"cial gas velocity on the average gas hold-up in the riser. Fig. 7 shows that the gas hold-ups in the C and D riser are almost equal. The measured values and the values calculated by correlation for riser D are shown in Fig. 8 for comparison. Due to the di!erent geometries of airlifts 2 and 1, the correlation for airlift 2 di!ers somewhat from that of airlift 1 as shown in Fig. 8.

Fig. 6. Average gas hold-up in the riser vs. average gas hold-up in the downcomer in airlift 1. The gas hold-ups are measured using riser tubes A, B, C and D.

Fig. 7. Gas hold-up in the risers A, B, C and D as a function of super"cial gas velocity. Correlations are "tted into measured data for each riser tube.

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Fig. 9. Measured and calculated tracer concentrations in the riser of airlift 2. Gas feed was 220 l/h. Fig. 8. Average gas hold-up in the riser as a function of super"cial gas velocity.

Figs. 9 and 10 show the measured and calculated values of tracer concentrations in the riser and in the downcomer. The axial dispersion model was used to describe the dispersion of the NaOH tracer impulse and the measurements were made by using probes 2 and 4 shown in Fig. 2. The liquid velocities in the riser and downcomer as well as the three dispersion coe$cients, two in the riser (turbulent section above the sparger, D , and top section P of the riser, D ) and one in the downcomer, were estiP mated. We can see that an excellent agreement between the measured data and the calculated values was obtained. The sensitivity analyses between the pairs of estimated parameters show that the parameters chosen are identi"ed surprisingly well. As an example, the pairs D !D , D !D , D !; and D !; are P P P B P * P P * B shown in the appendix for an experiment where gas super"cial velocity was 0.01 m/s. The calculated liquid velocities in the riser increase slightly with increasing gas velocity but the downcomer values increase more with higher gas #ow rates as shown in Fig. 11. Table 3 presents the "tted parameters and velocities for di!erent super"cial gas velocities as well as the relative errors for each "tted parameter. The "rst four points in Fig. 11 follow well the continuity equation (u A "u A ) but the value of liquid velo*P P *B B city corresponding the highest gas velocity appears to be too high. The discrepancy may be due to either erroneous data of gas-hold-up measurements or noisy data from conductivity measurements or both when using high gas #ow rates. The Navier}Stokes model for the external loop airlift reactor (Fig. 4) was coded and veri"ed using the MODEST modeling software (Haario, 1994). Using the data

Fig. 10. Measured and calculated concentrations in the downcomer of airlift 2. Gas feed was 220 l/h.

Fig. 11. Estimated liquid super"cial velocities in the riser and downcomer using the axial dispersion model of an internal loop airlift reactor.

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Table 3 The "tted dispersion coe$cients and super"cial liquid velocities for di!erent gas velocities measured in airlift 2 u %P (m/s)

D P (m/s)

D P (m/s)

D B (m/s)

u *P (m/s) Fitted values

u *B (m/s) Fitted values

Std. error of estimate

R (%)

0.010 0.049 0.078 0.094 0.132

0.0140 0.0099 0.0100 0.0139 0.0413

0.0052 0.0074 0.0138 0.0076 0.0003

0.0110 0.0200 0.0234 0.0543 0.0321

0.135 0.169 0.206 0.211 0.228

0.206 0.263 0.281 0.310 0.481

0.031 0.029 0.025 0.038 0.027

95.13 93.70 94.37 86.85 89.50

measured elsewhere (Dhaouadi et al., 1996) the parameters (D, k a and k a ) were "tted to model. *  *  The measurements of Dhaouadi et al. (1996) were made in six di!erent locations in the riser. Air was fed into the airlift reactor to saturate water with oxygen. After the system had attained steady state, air was rapidly switched to nitrogen. The oxygen concentration was monitored using a clark-type probe for dissolved oxygen. Finally, when the dissolved oxygen concentration had reached zero, air was again turned on to replace nitrogen. Figs. 12 and 13 show the measured and modeled change of oxygen concentration in the riser of external loop airlift reactor at locations 20 and 75 cm from the gas sparger. Oxygen solubility was assumed to obey Henry's law with pressure correction along the height of the column, but the measurements showed that increasing hydrostatic pressure does not increase oxygen solubility. The homogenizing e!ect of the liquid circulation in the reactor was assumed to be the reason for this phenomenon. The model at its present state could not predict this.

Fig. 13. Measured and calculated values of the oxygen concentration in liquid. Values measured from the riser of an external loop airlift.

Table 4 The dispersion coe$cient and k a values "tted in the Navier}Stokes * model. R is 98.1% for the estimate Parameter

Location

Value

Est. relative std error (%)

D, m/s k a , 1/s *  k a , 1/s * 

Riser Bottom-sparger Riser/gas-liquid separator

0.0941 0.2510 0.0471

14.1 20.4 28.8

It can be seen from Table 4 that the "tted k a values * for the riser section are approximately ten times larger than those obtained by Dhaouadi et al. (1996). This is due to the formulation of the mass-transfer model presented in this paper, where the k a values in Eq. (6) are multi* plied by ((1!e )/e )(R¹/P) (+0.1), which was omitted % % by Dhaouadi et al. (1996).

6. Conclusions Fig. 12. Measured values compared to the values given by the model. The calculated values correlate up to 98.1% with the measured ones.

The study showed that the #ow phenomena of airlift reactors can be described reliably enough with

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a conventional, simple axial dispersion model if the riser section is treated as presented with two separate dispersion coe$cients. Namely, the gas dispersion indeed changes along the riser, and a system of two averaged dispersion coe$cients in the lower and upper part of the column can be taken as parameters for estimation. The axial position along the riser where the switch from one to another dispersion coe$cient can also be estimated from experimental data. The mass transfer phenomena could be determined easily by a model derived from the original Navier} Stokes model. This approach is most interesting, since it gives one the opportunity to reduce the original equation system to a simpler one and also to investigate the system with experimental data by estimating only a few unknown parameters. Parameter estimation procedures using experimental data with CFD-codes with full Navier}Stokes models are not available for the moment. The natural continuation of this work is to compare the results obtained from the reduced model to CFD results. To our knowledge, there is no published information about investigating airlift reactor performance with CFD-programs.

Notation a C C* * C 2 D D k * M I P Q R R SU t ¹ u < < * y z

interfacial area, 1/m concentration of species A, mol/m "lm concentration, mol/m tracer concentration, mol/m dispersion coe$cient, m/s modi"ed pseudo-dispersion coe$cient, m/s liquid-phase mass transfer coe$cient, m/s overall mass transfer term total pressure, Pa volumetric #owrate, m/s reaction (Table 2), dimensionless universal gas constant, J/(mol K) source term, dimensionless time, s temperature, K super"cial velocity, m/s volume, m liquid volume, < "< (1!e ), m * 0 % mole fraction of species A in gas, dimensionless axial/coordinate, m

Greek letters e k o p U

holdup, dimensionless dynamic viscosity, Pa s density, kg/m turbulent Prandtl number, dimensionless general variable (Table 2), dimensionless

Subscripts B d e! G in j k ¸ R r ¹ sus

bubble downcomer e!ective gas inlet reaction index phase liquid phase reactor riser tracer suspension

Appendix The result in this appendix is a sensitivity analysis of the experiment shown in Table 3 where u is 0.01 m/s. %P Parameters in "gures are as follows: Parameter Parameter Parameter Parameter Parameter

1 2 3 4 5

D P D P D B u * u *B

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References Bello, R.A., Robinson, C.W., & Moo-Young, M. (1984). Liquid circulation and mixing characteristics in airlift contactors. Can. J. Chem. Engng, 62, 573}577. Bello, R.A., Robinson, C.W., & Moo-Young, M. (1985). Gas holdup and overall volumetric oxygen transfer coe$cient in airlift contactors, Biotechnol. Bioengng, XX