Ind. Eng. Chem. Res. 1996, 35, 4559-4565
4559
Hydrodynamics and Mass Transfer in a Liquid-Impelled Loop Reactor D. M. R. Mateus,† M. M. R. Fonseca,† and S. S. Alves*,‡ Secc¸ a˜ o de Biotecnologia and Secc¸ a˜ o de Feno´ menos de Transfereˆ ncia, Departamento de Engenharia Quı´mica, Instituto Superior Te´ cnico, 1096-Lisboa-Codex, Portugal
The liquid-impelled loop reactor was studied with respect to hydrodynamics and liquid-liquid mass transfer. The system involved a continuous aqueous phase, a dispersed organic phase (n-dodecane), and sometimes a solid phase (gel beads). Indole was the transferred solute. Drop size, dispersed phase holdup, and continuous phase circulation rate were measured. Experimental overall volumetric mass transfer coefficients of indole were taken from an earlier paper. In the absence of gel phase or up to about 10% gel concentration, circulation and holdup could be reasonably well predicted from standard expressions for pressure balance and single-phase friction pressure loss. This was best achieved by a widely used correlation proposed by Richardson and Zaki. Use of the Zuber and Findlay two-phase drift-flux model was also successful, with an adjusted parameter. Experimental mass transfer coefficients were compared with calculations from existing correlations. The best agreement was obtained with correlations for circulating drops, as expected by the range of drop Reynolds numbers covered in the experiments. 1. Introduction The liquid-impelled loop reactor, or LLR, is a relatively novel type of bioreactor (Tramper et al., 1987), analogous to the airlift in its hydrodynamics; the main difference is that continuous liquid phase circulation, rather than being driven by air dispersed in the riser, is driven by a second immiscible liquid phase with a different density (Figure 1). This kind of reactor may be advantageous if, for some reason, a second liquid phase is necessary or convenient in the bioreactor, e.g., when one of the reagents or products has low solubility in the aqueous phase, where the reaction takes place. Another major advantage over stirred reactors is the avoidance of high-shear regions. Examples of applications include the bioconversion of benzene to cisbenzenoglycol (van den Tweel et al., 1987), the production of antraquinones by plant cell cultures (Buitelaar et al., 1990), the growing of bacteria in tetralin (Vermu¨e and Tramper, 1990), and the biosynthesis of L-tryptophan from indole and L-serine (Mateus, 1994). Hydrodynamics of the LLR has, to the authors’ knowledge, been studied only by van Sonsbeek et al. (1990), who modeled it using the Zuber and Findlay twophase drift-flux model and a friction coefficient derived from one-phase flow theory. The effect of adding a third solid phase, important when an immobilized biocatalyst is at play, was not studied. Large solid phase holdups may be necessary in this case to achieve the required productivity (Mateus et al., 1996). Liquid-liquid mass transfer in the LLR was investigated by van Sonsbeek et al. (1992) and by Mateus et al. (1996). The former determined overall oxygen transfer coefficients between tap water and a dispersed phase consisting of an oxygen-enriched perfluorochemical, FC40. A steady state method was used. Mateus et al. (1996) used a dynamic method to measure overall volumetric mass transfer coefficients of indole between * To whom correspondence should be addressed. Telephone, +351-1-8417188; Fax, +351-1-8499242. † Secc ¸ a˜o de Biotecnologia. ‡ Secc ¸ a˜o de Feno´menos de Transfereˆncia.
S0888-5885(96)00225-4 CCC: $12.00
n-dodecane and water. In neither of these studies was comparison between experimental data and available correlations attempted. In this work mass transfer is linked with hydrodynamics to see how well available correlations perform in predicting measured overall volumetric mass transfer coefficients. 2. Theory and Modelling Drop Size. The mechanism of drop formation at an orifice depends on the regime (Clift et al., 1978). At low flow rates, there is individual drop formation, whereas at high flow rates, a jet is formed and drops break up from this jet. The single-drop regime occurs if (Meister and Scheele, 1969)
[ (
vN e 1.73
)]
DN σ 1FdDN d
1/2
(1)
where vN is the average dispersed phase velocity through the orifice, d is the drop diameter as calculated for the single-drop regime, σ is the interfacial tension, Fd is the density of the dispersed phase, and DN is the orifice diameter. To estimate drop size in the jet regime, Scheele and Meister (1968) proposed
d ) (1.5λm)1/3DN2/3
(2)
where λm is the wavelength of the growing disturbance of the jet surface (Meister and Scheele, 1967). In the single-drop regime, the following correlation has been proposed (Scheele and Meister, 1968)
[
vd ) F
πσDN 20µQDN 4FdQvN + 2 + g∆F 3g∆F d g∆F
(
4.5
)]
Q2DN2Fdσ (g∆F)2
1/3
(3)
vd is the drop volume after break off, F is the Harkins© 1996 American Chemical Society
4560 Ind. Eng. Chem. Res., Vol. 35, No. 12, 1996
Figure 1. Liquid-impelled loop reactor: (a) safety valve, (b) and (c) sampling valves, (d) riser, (e) downcomer, (f) organic phase reservoir, (g) discharge valve, (h) perforated plate (1 mm diameter holes), (i) recirculating pump.
Brown correction factor generally presented as a plot of F vs DN (F/vd)1/3 (Scheele and Meister, 1968), g is the acceleration of gravity, µ is the viscosity of the continuous phase, Q is the volumetric flow rate of the dispersed phase, and ∆F is the density difference between continuous and dispersed phases. For both nozzle and multinozzle distributors, Vedaiyan (1969) proposed an alternative correlation (in cgs units) to obtain the mean drop size, d
( )
vN d )R 1/2 σ 2gDN ∆Fg
( )
β
( )
( )
∑i ∆Pi
(7)
where is the dispersed phase holdup in the riser, ∆F is the difference in densities between the continuous and the dispersed phases, and H is the height of the twophase column (approximately the height of the riser). The various friction losses may be given, as a first approximation for low holdups of the dispersed phase, by Darcy’s equation for single-phase pressure loss
ui2 ∆Pi ) KiF 2
(5)
Holdup and Circulation. Circulation results mainly from a balance between driving force and drag at the walls
∆Pdf )
∆Pdf ) ∆FgH
(4)
with R ) 1.592, β ) -0.0665, and the following restriction for nozzle size
1 σ 1/2 σ 1/2 < DN < π 2 ∆Fg ∆Fg
weight between the riser and downcomer liquid columns
(6)
where ∆Pdf is the driving force and ∆Pi are the friction pressure losses in the various reactor sections and fittings. Driving force is given by the difference in
(8)
where F is the continuous phase density, ui is the continuous phase velocity in section i, and Ki is a factor which in general depends on the Reynolds number and on the type of fitting. It may be given by
Leqi Rhi
Ki ) fi(Rei)
(9)
where fi is the Fanning friction factor for straight pipe, Rei, Rhi, and Leqi are respectively the Reynolds number, hydraulic radius, and equivalent length of section or fitting i. If large holdups and/or a third phase is present, the situation becomes more complicated, as friction is now a function also of the holdup and properties of the dispersed phase(s). Two types of model may then be
Ind. Eng. Chem. Res., Vol. 35, No. 12, 1996 4561 Table 1. Continuous Phase Mass Transfer Coefficients in Liquid-Liquid Systems drop condition
expression
authors
(i) stagnant (ii) stagnant
Shc ) 2.0 + 0.95Rec0.5Scc0.5
(iii) circulating (iv) circulating
Shc ) -126 + 1.8Rec0.5Scc0.42
Shc ) 2 + 0.463Rec0.484Scc0.339
[
0.484
Shc ) 2 + 0.463Rec
( ) ( ) ]
0.339
Scc
Garner and Suckling (1958) Hughmark (1967)
dg1/3 Dc2/3
0.072
dg1/3 Dc2/3
Garner, Foord and Tayeban (1959) Hughmark (1967)
0.072
F
with F ) 0.281 + 1.615K + 3.73K2 - 1.874K3
K ) Rec1/8
()( ) µc µd
1/4
µ c ur σg
1/6
used to estimate pressure drops (Holland and Bragg, 1995): homogeneous flow models and models for separated flow such as the Lockhart and Martinelli model (Lockhart and Martinelli, 1949). In the present case, where most of the pressure drop occurs in vertical pipes with no apparent stratification of phases, simpler homogeneous flow models are likely to be applicable. Equations 6-9 relate the continuous phase velocity to physical properties, geometric and operational variables, and the holdup of the dispersed phase. This may be independently related with the slip velocity, us, and the superficial velocities of the two phases in the riser, uc for the continuous and ud for the dispersed, through the theoretically derivable formula
uc ud us ) 1-
(11)
where n is an empirical quantity, found to be around 2 for Re > 500. An alternative is the two-phase drift-flux theory of Zuber and Findlay (1965), who proposed the following expression
ub ) c0(uc + ud) + ut
(12)
where c0 may be taken as an empirically adjustable parameter and ub is the drop rise velocity. An approximate relationship between ub and the slip velocity has been proposed by Ayazi Shamlou et al. (1994)
ub ) us(1 - )
(13)
Equations 6-10 may be solved together with either eq 11 or eqs 12 and 13 to give both the velocity of the continuous phase, uc, and the holdup, , for any given value of the dispersed phase flow rate, as long as the drop terminal velocity is known. This may be calculated using, for example, the graphical correlation given by Hu and Kintner (1955). Mass Transfer Coefficient. The overall mass transfer coefficient is given in terms of the partial mass transfer coefficients of the two phases by
1 m 1 ) + K d kd kc
kd ) -
d 6t
[
(14)
where m is the equilibrium coefficient and Kd is the
∞
ln 6
(10)
For many two-phase systems, it has been found that the slip velocity is related to the terminal velocity, ut, by (Richardson and Zaki, 1954)
us ) ut(1 - )n-1
overall mass transfer coefficient, while kd and kc are the film coefficients for the dispersed and continuous phases, respectively. In the general case where both phases control mass transfer, the dispersed phase coefficient kd depends on the magnitude of the continuous phase coefficient, kc, which may be estimated using the empirical correlations in Table 1. To calculate the dispersed phase coefficient, kd, for the general case where both phases control mass transfer, Jakob (1949) derived the following expression for stagnant drops
(
Cn exp -ψn2 ∑ n)1
)]
4Ddt d2
(15)
where Dd is the solute diffusivity in the dispersed phase and t is the contact time. For circulating drops, Elzinga and Banchero (1959) suggested that the correlation proposed by Kronig and Brink (1950) for the case in which mass transfer is controlled in the dispersed phase alone be adapted to the general situation where both phases control. The Kronig and Brink equation is as follows
kd ) -
d 6t
[
ln
3
∞
(
∑ Bn2 exp -64λnDd 8n)1
t
d2
)]
(16)
Coefficients Bn, Cn, ψn, and λn in eqs 15 and 16 are given, for the general situation where both phases control, in Elzinga and Banchero (1959) as a function of kc. The referred equations for film coefficients have been deduced for clean systems. Impurities, and particularly tensioactive substances, may significantly increase or decrease the overall mass transfer kinetics. The phenomena involved are complex, and to date, there is no general treatment of the problem. 3. Experimental Section Reactor. The liquid-impelled loop reactor (LLR) is shown in Figure 1. It consists basically of two glass pipes (riser and downcomer) connected at the top and bottom. It is operated in a way similar to an airlift reactor, except that the dispersed phase is a liquid instead of a gas. In the present case, an organic solvent (n-dodecane), with density lower than water, is continuously dispersed into the aqueous phase through the perforated plate at the bottom of the riser. The dispersed organic phase coalesces at the top of the reactor and is recirculated. A sheet of polyurethane foam at the disengagement section of the LLR helps coalescence and avoids the formation of emulsions (Fonseca et al.,
4562 Ind. Eng. Chem. Res., Vol. 35, No. 12, 1996 Table 2. Physical Properties of the Two Liquid Phases Mutually Saturated with Indole at 37 °C density viscosity (kg m- 3) (kg m- 1 s- 1) n-dodecane phosphate buffer (0.1 M, pH 8.0) a
735 1006
0.00163 0.00075
interfacial tension (mN m- 1) 44a
38b
Between 0 and 4 s. b For t f ∞.
1994). The density difference between the riser and downcomer induces the desired circulation of the continuous phase, which may include a solid third phase. More details of the LLR and its operation can be found in Mateus et al. (1994). Physical Properties. Measured physical properties of the two liquids relevant to this work are presented in Table 2. The liquids were mutually saturated by mixing and settling, prior to measurement. Viscosities were determined with a Schott-Gera¨te micro-Ostwald viscometer, densities were obtained using a pycnometer, and interfacial tension was measured by the HarkinsBrown drop volume technique. Drop Size. Drop diameters were measured using the photographic method. To avoid lens effect, photos were taken through a water-filled transparent cubic chamber with an engraved scale, which enveloped a section of the riser. Sauter mean diameters were calculated from 3-4 photos for each experimental condition, each photo containing 100-200 drop images, depending on operating conditions. The dispersed phase was dyed with red oil to improve contrast. This dye is appropriate, since it has a minimal effect on interfacial tension (Hu and Kintner, 1955), as was experimentally confirmed. Holdup and Circulation. To determine the continuous phase velocity, a flow-follower technique was used. The time a colored gel bead takes to cover a fixed distance in the downcomer was measured. This measurement was repeated at least 15 times to take into account any deviation from a flat velocity profile. The continuous phase velocity was taken as the difference between the average bead velocity and the experimental bead terminal velocity. Holdup was determined by an unconventional tracer injection technique, as follows. At some point in time, the dispersed phase is suddenly dyed. From the time the dyed front takes to reach the top of the riser, the known dispersed phase flow rate, and the riser volume, the holdup can be easily calculated, as long as plug flow is assumed. A similar pulse experiment was enough to show that the effect of axial dispersion was indeed negligible for this determination.
Figure 2. Drop diameter as a function of flow rate of the dispersed phase: 9 experimental values; s predicted drop diameter using Scheele and Meister eq 3 for the single-drop regime; ‚ - ‚ predicted drop diameter using Scheele and Meister eq 2 for the jet regime; 0 predicted drop diameter using Vedayian eq 4 without adjusted parameters; - - - predicted drop diameter using Vedayian eq 4 with adjusted parameters.
Figure 3. Terminal rise velocity of n-dodecane drops in phosphate buffer (mutually saturated in indole), given by the Hu and Kintner correlation (1955).
mutually saturated in indole, as a function of drop diameter using the correlation of Hu and Kintner (1955). Friction Pressure Loss Calculation. In order that holdup and circulation rate may be calculated, the various friction losses must be accounted for (eqs 6, 8, and 9). Two situations were considered: with and without a third, solid phase, consisting of gel beads. Without solid phase, all pressure losses except those in the riser are single phase. Even for the riser, since the organic phase holdup never exceeded 6%, pressure losses could be calculated assuming single phase; twophase homogeneous flow calculation gives very similar results. Six terms are considered in eq 6: two sections of straight pipe (riser and downcomer), two 90° elbows, and two cross-sectional changes. Values of Ki for various fittings may be found, e.g., in Perry and Chilton (1973), while straight pipe friction factors for smooth pipe were obtained using the Blasius equation
4. Results and Discussion Drop Size and Terminal Velocity. Both visual observation and the threshold estimated by eq 1 indicated that the prevailing regime was single drop. Figure 2 compares the prediction of drop size using eqs 3 and 4 with experimental measurements. The result is reasonable without parameter adjustment. Adjustment of parameters in Vedaiyan’s equation, (eq 4), gives R ) 1.753 and β ) -0.0787 and very good agreement with experiment. Thus, for the remainder of the work, where experimental measurement of drop size was not carried out, Vedaiyan’s equation with adjusted parameters was used instead. Figure 3 presents the terminal rise velocity of ndodecane drops in 0.1 M phosphate buffer, pH 8.0,
f)
0.0781 Re1/4
(17)
With the gel phase present, on the other hand, the situation becomes more complicated. Three phases are now at play, the continuous aqueous phase and two dispersed phases, the organic and gel phases. The organic phase, while being the driving phase due to its density, has little effect on friction losses owing to its small holdup. The gel phase, on the other hand, while not contributing to the circulation driving force, because its density is that of water, does affect friction losses due to its large holdup. The contribution of gel holdup to friction losses is difficult to calculate, because of the complex reactor geometry; hence, experimental values
Ind. Eng. Chem. Res., Vol. 35, No. 12, 1996 4563
Figure 4. Overall friction coefficient as a function of gel holdup (volume of gel/volume of aqueous phase).
Figure 5. Continuous phase velocity (9 experimental, s model) and dispersed phase holdup in the riser (0 experimental, s model) as a function of dispersed phase flow rate. Model predictions were made using eqs 6-10 plus the Richardson and Zaki eq 11.
Figure 6. Continuous phase velocity (9 experimental) and dispersed phase holdup in the riser (0 experimental) as a function of dispersed phase flow rate. Model predictions were made using eqs 6-10 plus the Zuber and Findlay model eqs 12 and 13: s model predictions using c0 ) 0.5; - - - model predictions using c0 ) 1.
were obtained for an overall K h , on the basis of continuous phase velocity in the riser, defined as (from eqs 6-8)
K h )
2∆FgH Fucriser2
(18)
Figure 4 shows the effect of gel phase holdup on K h. As expected, the presence of gel beads increases friction, thus decreasing circulation. Each individual point was obtained by linear regression of experimental values of vs Fucriser2/(2∆FgH), assuming K h to be approximately constant for the range of organic flow rates used. The curve in Figure 4 results from fitting the experimental points. Holdup and Circulation. Figures 5 and 6 compare calculated continuous phase velocities and dispersed
Figure 7. Experimental vs calculated volumetric mass transfer coefficients as a function of dispersed phase flow rate. 9 experimental; ‚ - ‚ kd from eq 15, kc from eq i in Table 1; s kd from eq 15, kc from eq ii in Table 1; ‚‚‚ kd from eq 16, kc from eq iii in Table 1; - - - kd from eq 16, kc from eq iv in Table 1.
phase holdups with experimental values, for low gel loads. The use of the two-phase drift-flux model of Zuber and Findlay (1965), eqs 12 and 13, together with eqs 6-10 only gives acceptable results for low values of the adjusted parameter, i.e., c0 ) 0.5 (Figure 5). This parameter has to do with the continuous phase velocity profile: it is shown to be equal to 1 for a flat velocity profile and increases as the velocity profile approaches a parabola, in which case c0 ) 1.6. However, in the literature, c0 has taken values as high as 5.0 or as low as 0.7, being considered more an empirically adjustable parameter than a theoretical one (Ayazi Shamlou et al., 1994). Good agreement, on the other hand, without any adjusted parameter is found when the slip velocity required for the solution of eqs 6-10 is calculated using Richardson and Zaki eq 11, as an alternative to the Zuber and Findlay model (Figure 6). Mass Transfer. Figure 7 compares experimental and calculated overall volumetric liquid-liquid mass transfer coefficients, Kda, referred to the dispersed phase, a being the interfacial specific area. Experimental values are from Mateus et al. (1996), obtained in the absence of gel phase. Calculated values were obtained using eq 4 with adjusted parameters for drop size calculation and eqs 6-11 for hydrodynamics calculations ( and uc). Specific area a was calculated assuming spherical drops, hence
a)6 d
(19)
The slope of the equilibrium curve, m, required in eq 14 for the calculation of the overall mass transfer coefficient, kd, was taken as an average from experimental equilibrium data in Mateus et al. (1996). The dispersed phase film coefficient, kd, was calculated for two different situations, rigid drops and circulating drops, using eqs 15 and 16, respectively. The continuous phase film coefficient, kc, was also calculated for rigid and circulating drops, using two expressions for each regime (equations in Table 2). Comparison between calculated and experimental overall mass transfer coefficients (Figure 7) shows that rigid drop correlations give values somewhat lower than experimental, as would be expected, since drop Reynolds numbers were in the range 120-200, for which circulation usually occurs inside drops. The best agreement between calculation and experiment was obtained assuming circulating drops, using eq 16 for the determi-
4564 Ind. Eng. Chem. Res., Vol. 35, No. 12, 1996
nation of kd and Hughmark’s correlation (eq iv in Table 2) for kc. The correlation of Garner et al. (1959) for kc in the circulating regime (eq iii in Table 2), on the other hand, gives much too high estimates, reflecting the difference in predicted values for the same situation from available correlations in the literature and the difficulty of a priori choice of appropriate liquid-liquid mass transfer correlations. 5. Conclusions Hydrodynamics and liquid-liquid mass transfer in a liquid-impelled loop reactor can be described by a model which integrates expressions and correlations available in the literature. For low holdups of the dispersed phase, and in the absence of a third phase, holdup and circulation can be calculated from standard expressions for pressure balance and single-phase friction pressure losses, together with some way of calculating the slip velocity between the two phases. This is best done by a widely used correlation proposed by Richardson and Zaki (1954). The Zuber and Findlay two-phase driftflux model can also be used, with an adjusted parameter. The presence of a third, solid phase may be accounted for using an empirical correction to the friction factor. Mass transfer is well described using eq 16 for the determination of kd and Hughmark’s correlation (eq iv in Table 2) for kc. In brief, this integrated model predicts the mass transfer behavior in the LLR solely from knowledge of the geometry, physicochemical properties of the system, and operating conditions (dispersed phase flow rate and gel load). It thus opens possibilities for optimization of reactor design and operation. Acknowledgment The authors thank Teresa Reis for help with interfacial tension measurements. The fellowship awarded to D.M.R.M. by the CIENCIA/PRAXIS XXI programme (B.D. 2827) is also gratefully acknowledged. Nomenclature a ) interfacial specific area, m-1 Bn ) coefficients in eq 16 c0 ) parameter in eq 12 Cn ) coefficients in eq 15 d ) drop diameter, m Dd ) solute diffusivity in the dispersed phase, m2 s-1 DN ) orifice diameter, m f ) Fanning friction factor for straight pipe g ) acceleration of gravity, m s-2 H ) height of the two-phase column, m K h ) total number of velocity heads lost by friction based on continuous phase velocity in the riser kc ) mass transfer film coefficient for the continuous phase, m s-1 kd ) mass transfer film coefficient for the dispersed phase, m s-1 Kd ) overall mass transfer coefficient for the dispersed phase, m s-1 Ki ) number of velocity heads lost by friction in section or fitting i Kda ) overall volumetric oxygen transfer coefficient, s-1 Leqi ) equivalent length of section or fitting i, m m ) equilibrium coefficient ∆Pdf ) pressure driving force for circulation ∆Pi ) friction pressure losses in section or fitting i, N m-2 Q ) volumetric flow rate of the dispersed phase, cm s-1 Re ) Reynolds number
Rei ) Reynolds number in section i Rhi ) hydraulic radius, m t ) contact time, s ub ) drop rise velocity, m s-1 uc ) superficial velocity of the continuous phase in the riser, m s-1 ud ) superficial velocity of the dispersed phase in riser, m s-1 ui ) superficial velocity of the continuous phase in section i, m s-1 us ) slip velocity, m s-1 ut ) drop terminal velocity, m s-1 Va ) volume of aqueous phase vd ) drop volume after break off, m3 vN ) average dispersed phase velocity through the orifice, m s-1 Vs ) volume of gel phase R ) parameter in eq 4 β ) parameter in eq 4 ) dispersed phase holdup in the riser λm ) wavelength of the growing disturbance of the jet surface, m λn ) coefficients in eq 16 µ ) viscosity of the continuous phase, kg m-1 s-1 F ) density of the continuous phase, kg m-3 ∆F ) difference in densities between the continuous and the dispersed phases, kg m-3 Fd ) density of the dispersed phase, kg m-3 σ ) interfacial tension, N m-1 ψn ) coefficients in eq 15
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Biotransformations; Moody, G., Baker, P. B., Eds.; Elsevier: London, 1987; p 231. Vedaiyan, S. Hydrodynamics of two phase flow in spray columns. Ph.D. Thesis, University of Madras, 1969. Vermu¨e, M. H., Tramper, J. Extractive biocatalysis in a liquidimpelled loop reactor. Proceedings of the 5th European Congress on Biotechnology; Munksgaard Int. Pub.: Copenhagen, 1990; Vol. I, p 243. Walis, G. B. One-dimensional two-phase flow; McGraw-Hill: New York, 1969. Zuber, N.; Findlay, J. A. The effect of non-uniform flow and concentration distributions and the effects of local relative velocity on the average volumetric concentration in two phase flow. Trans. ASME, Ser. C: J. Heat Transfer 1965, 87, 453.
Received for review April 16, 1996 Revised manuscript received September 29, 1996 Accepted September 26, 1996X IE960225B
X Abstract published in Advance ACS Abstracts, November 1, 1996.
