I n d . Eng. Chem. Res. 1990,29, 988-994
988
Hannay, J. B.; Hcgarth, J. On the Solubility of Solids in Gases. Proc. R. SOC. London 1879,A29, 324. Hannay, J. B.; Hogarth, J. On the Solubility of Solids in Gases. Proc. R. SOC. London 1880,A30,484. Johnston, K. P.; Flarsheim, W.; Hmjez, B.; Mehta, F.; Fox, M.; Bard, A . Solvent Effect on Chemical Reactions at Supercritical Fluid Conditions. Proc. Znt. Symp. Supercritical Fluids 1988, 907. Johnston, K. P.; Kim, S.; Combs, J. Spectroscopic Determination of Solvent Strength and Structure in Supercritical Fluid Mixtures, k Review. In Supercritical Fluid Science and Technology; Johnston, K. P., Penninger, M. L., Eds.; ACS Symposium Series 406; American Chemical Society: Washington, DC, 1989; Chapter 5. Kajimoto, 0.; Futakami, M.; Kobayashi, T.; Yamasaki, K. Chargetransfer-State Formation in Supercritical Fluid: (N,N-Dimethy1amino)benzonitrile in CF,H. J . Phys. Chem. 1988, 92, 1347-1352. Kim, S.; Johnston, K. P. Molecular Interactions in Dilute Supercritical Fluid Solutions. Znd. Eng. Chem. Res. 1987a, 26, 1206-1213. Kim, S.; Johnston, K. P. Clustering in Supercritical Fluid Mixtures. AZChE J. 1987b,33, 1603-1611. Kirkwood, J. G.; Buff, F. P. The Statistical Mechanical Theory of Solutions. I. J. Chem. Phys. 1951,19,774. Labik, S.; Malijevsky, A.; Vonka, P. A Rapidly Convergent Method of Solving the OZ Equation. Mol. Phys. 1985,56,709. Lado, F. Perturbation Correction for the Free Energy and Structure of Simple Fluids. Phys. Reu. A. 1973,87,2548. Lee, L. L. Molecular Thermodynamics for Nonideal Fluids; Butterworths: Boston, 1988. Nicolas, J. J.; Gubbins, K. E.; Streett, W. B.; Tildesley, D. J. Equation of State for the Lennard-Jones Fluid. Mol. Phys. 1979,37, 1429.
Petsche, I. B.; Debenedetti, P. G. Solute-Solvent Interactions in Infinitely Dilute Supercritical Mixtures: A Molecular Dynamics Investigation. J. Chem. Phys. 1989,91,7075. Pfund, D. M.; Lee, L. L.; Cochran, H. D. Application of the Kirkwood-Buff Theory of Solutions to Dilute Supercritical Mixtures, 11. The Excluded Volume and Local Composition Models. Fluid Phase Equilib. 1988,39,161. Rowlinson, J. S.; Swinton, F. L. Liquids and Liquid Mixtures; Butterworths: Boston, 1982; p 254. Schneider, G. M.; Ellert, J.; Haarhaus, U.; Holscher, I. F.; Katzenski-Ohling,G.; Koppner, A.; Kulka, J.; Nickel, D.; Rubesamen, J.; Wilsch, A. Thermodynamic, Spectroscopic and Phase Equilibrium Investigations on Polar Fluid Mixtures at High Pressures. Pure Appl. Chem. 1987,59,1115-1126. Subramanian, B.; McHugh, M. A. Reactions in Supercritical Fluids-A Review. Znd. Eng. Chem. Process Des. Deu. 1986,255, 1.
Watts, R. 0. Percus-Yevick Equation Applied to a Lennard-Jones Fluid. J. Chem. Phys. 1968,48, 50. Yonker, C. R.; Smith, R. D. Solvatochromic Behavior of Binary Supercritical Fluids: The Carbon Dioxide/2-Propanol System. J. Phys. Chem., 1988,92,2374-2378. Yonker, C. R.; Frye, S. L.; Kalkwarf, D. R.; Smith, R. D. Characterization of Supercritical Fluid Solvents Using Solvatochromic Shifts. J. Phys. Chem. 1986,90,3022-3026. Zerah, G.; Hansen, J.-P. Self-consistent integral equations for fluid pair distribution functions: another attempt. J. Chem. Phys. 1986,84,2336. Received for review September 12, 1989 Revised manuscript receiued December 5, 1989 Accepted January 5, 1990
Reynolds Shear Stress for Modeling of Bubble Column Reactors Thomas Menze1,t Thomas in der Weide, Oliver Staudacher, Ondra Wein,$and Ulfert Onken* Fachbereich Chemietechnik, Lehrstuhl Technische Chemie B, University of Dortmund, Postfach 500500, 0-4600Dortmund 50, FRG
A general model for the design and scale-up of bubble columns and airlift loop reactors requires the exact prediction of their flow structure. The deterministic and stochastic components of the liquid flow in these gas-liquid contactors have therefore been measured. With the aid of a newly developed measuring technique, the hot-film anemometry with triple split probes, the local mean velocities, the turbulence intensities and, for the first time in bubble-column reactors, Reynolds shear stresses were determined. On the basis of a large amount of experimental data, a hydrodynamic model for the radial profile of the mean axial liquid velocity and an empirical correlation for the prediction of the turbulence intensities have been developed. The hydrodynamic model and the correlation are valid for various reactor geometries, gas and liquid flow rates, and various properties of the liquid. 1. Introduction
Because of their simple construction and ease of maintenance, bubble columns and airlift loop reactors are widely used as gas-liquid contactors. Their application covers typical chemical processes such as hydrogenation and oxidation of hydrocarbons, as well as aerobic fermentations of various types in the field of biotechnology (Deckwer, 1985). The widespread application leads to various constructions and to reactor sizes that extend from a few liters, as in the growth of plant or animal cells (Katinger et al., 1979), to thousands of cubic meters, as in wastewater treatment (Zlokarnik, 1982). 'Present address: Bayer AG, ZF-TVT 4, Bayerwerk, D-5090 Leverkusen, FRG. *Presentaddreas: Institute of Chemical Process Fundamentals of the CSAV, Suchdol, CS-16OOO Prague, Czechoslovakia. 0888-5885/90/2629-0988$02.50/0
Although bubble columns and airlift loop reactors have been the topic of a large number of publications in the last decade, no reliable general model for their design and scale-up has been developed until now. The main reason for this lies in the lack of data about their complicated flow structure. The description of the flow in these reactors has often been based on visual observations or on measurements with techniques that do not meet the special requirements of two-phase flow. Therefore, older models disregard the flow structure or use very simplified assumptions (Joshi and Shah, 1981). In the past years, progress in the field of computer design and data processing induced the development of a number of advanced measuring techniques for the investigation of two-phase flow (Schiigerl et al., 1985;Buchholz, 1987). While a visual observer of bubble columns must draw the conclusion that the flow is of a totally stochastic nature, a closer examination using one of the novel 0 1990 American Chemical Society
Ind. Eng. Chem. Res., Vol. 29, No. 6, 1990 989 measuring techniques reveals regular structures. It was found that liquid flow in bubble columns is characterized by parabolic radial profiles of the mean axial velocity, the deterministic component of the flow, with superimposed strong stochastic fluctuations described by turbulence intensities in the range of the maximum mean axial liquid velocity (Franz et al., 1984, 1985). (The turbulence intensity is the standard deviation of the liquid velocity.) The flow in airlift loop reactors is similar, with the only difference being that the velocity profiles are shifted due to the superficial liquid velocity (Menzel et al., 1985). This knowledge about the flow structure resulted in considerably improved mixing models for bubble-column reactors. For example, Rustemeyer et al. (1989) correlated local tracer concentrations with known radial profiles of axial liquid velocities and turbulence intensities. A similar approach has been used by Kantorek (1988). Their computations were supported by local tracer experiments. Local concentrations of reactants and local reaction rates are thus made available, and the yields and selectivities of the chemical reactions can be calculated accurately. Unfortunately, the application of these new mixing models is problematic, because the local flow structure must be known. Since measurements with the novel measuring techniques are very expensive and require much experience of the experimentaton, the best way of solving the problem is to develop general models for the radial profiles of the mean axial liquid velocity and turbulence intensities. Whereas no model for the stochastic flow component is given in the literature, the deterministic flow component is often modeled by the Reynolds equation, a local momentum balance. Most often the simplified version for steady and axisymmetric flow has been used:
where 7
=
7,
+ it= -PLY,
dlf,/dr
+ p L ( l - cG)u,u,,d
(2)
The term taking into account molecular viscosity, v, can be neglected. Equation 1is solved with the aid of empirical correlations for the radial profile of local gas holdup and Reynolds shear stress. The latter quantity is evaluated by using measured profiles of mean axial liquid velocity and expressing as a function of turbulent kinematic viscosity, vt (Boussinesq type of equation, eq 3) (Boussinesq, 1896; Riquarts, 1982; Linneweber, 1981; Miyauchi and Shyu, 1970; Ueyama and Miyauchi, 1979; Miyauchi et al., 1981; Kojima et al., 1980; Kawase and Moo-Young, 1986; Sekizawa et al., 1983; Hills, 1974),or Prandtl mixing length, 1 (eq 4) (Prandtl, 1925; Clark et al., 1987), and the radial gradient of mean axial liquid velocity: r = -vmpL dUa,/dr - vtpL dD-/dr = -(vm + v S P L d o m / d r (3) (4) By use of measured radial profiles of mean axial liquid velocity and local gas holdup, a number of empirical correlations for the model parameters v, or 1 were developed by various authors with the aid of eq 1. On the basis of only a few available experimental data, various assumptions for the radial profiles of local Reynolds shear stress and local gas holdup were made, and different boundary conditions for the solution of eq 1 were used with the consequence that greatly differing results were obtained. Figure 1 shows the model parameter v, as a function of an
R i q u a r t s 8Linneweber KOjimO e t a I - - Kawase8Moo-Young Ueyama 8 Miyauchi Miyouchi et 0 1 Miyauchi8Shyu - - - _ - _Sekizawa e t a l
-_
I 0.1
I
1
1
0.5
I
I
!
O
1.0
D [ml
Figure 1. Turbulent kinematic viscosity, vt, as a function of column diameter, D. Correlations of different authors.
essential parameter, the column diameter, D. Apparently the values of vt obtained by different authors show deviations up to a factor of 6. Thus, it can be concluded that ut is only an empirical fitting parameter without real physical meaning. These models are therefore restricted to applications within the range of conditions from which data are used for the calculation of the correlations of ut. For more general applications, a physical model is needed to describe the relationship between the profiles of local mean axial liquid velocity, local Reynolds shear stress, and local gas holdup by physical means. For this purpose, measurements of these data must be performed in a wide range of operating conditions. 2. Measuring Techniques A novel measuring technique has been employed for the measurement of the local Reynolds shear stress. By use of hot-film anemometry with triple split probes, the sign and value of two components of the instantaneous velocity vector can be determined simultaneously (Jargeneen, 1982; Menzel, 1989). With this information, it is possible to determine the correlation between axial and radial velocity fluctuations, uarurad,and the Reynolds shear stress can be calculated with known local gas holdup and eq 2. Furthermore, the measuring technique provides the time-averaged values and the turbulence intensities of two directional components of the liquid velocity. A schematic diagram of the triple split probe is shown in Figure 2. The sensitive part of the probe consists of a 2-mm quartz fiber with a diameter of 400 pm. The fiber is coated with three nickel films applied by vapor deposition. To protect these from electrolysis in electric conducting media, the nickel films are coated by a 2-pm quartz layer. The special geometry of the films is responsible for the directional characteristics of the probe. Before a measurement, the velocity and directional characteristics of the probe must be calibrated in defined flow conditions. The calibration procedures and a more detailed description of the measuring technique are given elsewhere (Menzel et al., 1989; Menzel, 1990). In addition, the local gas holdup was measured by the well-known one-point electroconductivity microprobe technique (Serizawa et al.,
990 Ind. Eng. Chem. Res., Vol. 29, No. 6, 1990
S p l i t -Width
LOOpm
Quartz - F i b r e
N I kei ~ 12en
Triple S p i i t ,enso-
I-L,
1
j--=F18
Figure 2. Schematic diagram of a triple split hotfilm probe.
1975; etc.). The probes were improved and had a tip of 60-80 pm. 3. Measuring Results and Modeling 3.1. Deterministic Component of the Flow. Measurements were performed in reactors of different geometries (bubble columns, D = 150 mm, H = 2575 mm, D = 600 mm, H = 3455 and 5440 mm; airlift loop reactor, D = 600 mm, H = 5440 mm) varying the gas (air) and liquid flow rates, molecular viscosity (water and glycerol/water: u, = (0.9-280) X lo4 m2/s), and coalescence behavior (water, coalescing; 0.22 wt %; propanol (2)/water, noncoalescing) of the liquid phase. As an excerpt of the measurement program with the triple split film probes, radial profiles of the mean axial liquid velocity and the correlation between axial and radial velocity fluctuations, r&Urad, are presented in Figure 3. The radial profiles of the mean axial liquid velocity exhibit the above-mentioned parabolical shape with an upflow region near the column center and a downflow
region close to the wall. This type of profile has been found for all conditions with the exception that, with rising molecular viscosity, the profiles become bell shaped and more asymmetric. On the other hand, the radial and tangential mean velocities are negligibly small. The radial profiles of u&& also show a typical shape. Close to the wall and in the column center, the values are nearly zero, while at negative radial positions negative values with a local minimum are found and at positive radial positions positive values and a local maximum are found. A comparison of the profiles of the mean axial liquid velocity and the correlation U & r d reveals that there is a direct connection. The minima and maxima of u & , d are located at the radial positions with the maximum slope of the velocity profile, and in the column center, where the mean axial velocity is at a maximum, u,urad is zero. The gradient of the radial profile of liquid velocity is therefore directly proportional to u-urad, and the Boussinesq type of equation (eq 3) appears to hold. To confirm thi? assumption, (1 - €G)U&rad is plotted as a function of dU,/dr in Figure 4 (example: 80 wt % glycerol/water). The result is a straight line for -0.7 < r / R C 0.7. The data close to the wall diverge and were omitted for more clarity. Since the slope of the straight line corresponds to the turbulent kinematic viscosity, ut (eq 3), ut is constant for the upflow region of the column. This is in close agreement to Miyauchi and Shyu (1970) and Miyauchi et al. (1981),who assumed a constant turbulent kinematic viscosity over the column diameter. The function for the entire profile of the turbulent kinematic viscosity can be obtained by dividing (1 t&,Ur,d by dU,/dr for each radial position: (5?
This is problematic, because dUJdr is the gradient of a 1000
100
t
8 00
600
1
i
LOO
200
0
-
-
'ax*
"rad
'ax"red
-100
-coo
I
"56
I
.
,.-I
-80
4-
-
r
[ m m l
-
Figure 3. Radial profiles of the mean axial liquid velocity, i7=,and the correlation
u,u,,d (bubble column, D
= 600 mm, water/air).
Ind. Eng. Chem. Res., Vol. 29, No. 6, 1990 991
-loo$ I
1
1 -2
0
2 ;+Is-?
Figure 4. Reynolds ehear stress divided by liquid density, (1 c o ) ~ versua , the gradient of mean axial liquid velocity, dU=/dr. Bubble column, D = 600 mm. Liquid phase: 80 w t 7% glycerol/ water.
-0.4
0 rlR
-
0,4
0.8
Figure 6. Radial profiles of the local gas holdup in a bubble column, % propanol (2)/water.
D = 600 mm, for (a)water and (b)0.22 w t
and 0.22 wt 7% propanol (2)/water as the liquid phase. The profiles can be distinguished into two types: flat profiles in the homogeneous flow regime (solid lines) and parabolic profiles for the heterogeneous flow regime (dashed lines). The profile with water as the liquid phase and superficial gas velocity of 4.8 cm/s lies in the transition between the flow regimes. In the noncoalescing medium (Figure 6b) homogeneous flow prevails at all superficial gas velocities and flat profiles can be observed. The best fit for these profiles is given by functions that are normalized by the cross-sectional average ( t G ) of the gas holdup and with finite values for the gas holdup at the column wall:
10 2.L
V,
-0.8
homogeneous flow regime tG(X)
= 1.2(tG)(1 - 0 . 5 ~ ~ )
(8)
1.0
0.5
heterogeneous flow regime
"R
Figure 5. Radial profiles of turbulent kinematic viscosity, ut. Bubble column, D = 600 mm, water/air, compared with curves calculated by eq 6 for optimum u,(r=O).
measured quantity and measuring errors bring about high deviations. Nevertheless, the results are satisfactory (Figure 5). The data for U&,,d and 0- were made symmetrical with the column center as the symmetry axis. As expected, ut is nearly constant in the region -0.7 C r/R C 0.7. Closer to the wall, ut decreases and becomes zero in the laminar boundary layer at the wall. This type of curves can be described very well by a function derived by Reichardt (1951) for single-phase pipe flow:
(7) The Reichatdt equation consists of two parts, i.e., turbulent kinematic viscosity in the column center ut(r=O) or more precisely at the distance R from the wall, and a function that depends only on the dimensionless radial position, r / R . The turbulent kinematic viscosity at the column center is defined as a constant, kN/6, multiplied by the square root of the wall shear stress divided by the liquid density. Having obtained the radial function of the turbulent kinematic viscosity, a function for the local gas holdup must be found as the next step of the solution of eq 1. Figure 6 shows the measured radial profiles of local gas holdup in the bubble column, for D = 600 mm and water
EG(x) =
1.33(~G)(l - 0.5~')
(9)
Contrary to the findings of Kat0 et al. (1975), who first used this type of equation, in this work a constant ratio of gas holdup in the column center to gas holdup at the column wall, as well as a constant exponent in the radial dependence, can be assumed for all operating conditions examined. Having established the functions for the radial profiles of the turbulent kinematic viscosity and Reynolds shear stress as well as the functions for the local gas holdup, eq 1 can now be solved to obtain the radial profiles of the mean axial liquid velocity. The model chosen uses as parameters the coefficient kN of the Reichardt viscosity profile and the slip velocity, S, i.e., the relative velocity between gas bubbles and liquid. The slip velocity is used in a mass balance and has the advantage that the gas holdup can be also calculated by the model. A more detailed description of the model is given by Menzel(1990). Some results of the model calculations are presented in Figure 7 . The calculations (curves) correspond well to the measured local mean liquid velocities (points). The liquid velocity profiles were made symmetrical. For these calculations, an optimum constant value of 1.13 for the bubble column and of 3.35 for the airlift loop reactor was taken for kN. It can be seen that these values hold for different superficial gas velocities, for different superficial liquid velocities (airlift loop reactor), and for coalescing and for noncoalescing media. Furthermore, for a smaller bubble column (D = 150 mm), the same optimum of 1.13 leads to good results. For higher viscous glycerol-water mix-
992 Ind. Eng. Chem. Res., Vol. 29, No. 6, 1990
O
v
I
V
301'
10
05
10
0
-r/Rl-i
-rlR
05
Figure 7. Symmetrical profiles of the mean axial liquid velocity, experimental data (points), and calculated values (curves). Filled symbols (left), 0.22 wt % propanol (2)/water; open symbols (right), water. (a) Bubble column, D = 600 mm, k~ = 1.13. (b) Airlift loop reactor, D = 600 mm,kN = 3.35.
4 T
[Pal
v
-
7 2
0
rtR
-
O L
08
rlR
Figure 8. Comparison between calculated (curves) and measured (points) Reynolds shear stresses. (a) Bubble column, D = 150 mm; (b) airlift loop reactor, D = 600 mm;liquid phase, water.
tures, a kN value of 1.8 is obtained. For all data, the cross-sectionalaverage of the gas holdup was fitted with an optimum slip velocity. The optimum slip velocity is identical with the slip velocity calculated by the balance:
(om) = WSL + WSG - ( C G ) S
1
1. I
10
1-1
0
-2L
-16
-6
0
8
16
2L
r [cml Figure 9. Radial profiles of axial and radial turbulence intensity. Bubble column, D = 600 mm; liquid phase, 80 wt % glycerol/water.
In summary, it can be concluded that the model has been proved to describe the connection between the radial profiles of the mean axial liquid velocity, the Reynolds shear stress, and the gas holdup by physical means. This model therefore allows the determination of the deterministic flow component over a wide range of operating conditions. 3.2. Stochastic Component of the Flow. Figure 9 shows an example for experimentally determined radial profiles of axial and radial turbulence intensity. For all operating conditions, both parameters exhibit flat profiles with nearly constant values over the cross section of the column. Only a small error is therefore incurred by reducing the model to the calculation of the cross-sectional averages of the turbulence intensities ( uL)and (u',d). Furthermore, the ratio ( u ; * ~ ) / ( uisLconstant ) at about 0.6 for all operating conditions. The same holds for ( u ' ~ /)( u ' ~ ) (Franz et al., 1984). These results have been used to develop an empirical correlation for the turbulence intensities. First the total kinetic energy of the liquid phase per unit of reactor volume was determined: Kge, = Kmit + K,,
(11)
with
(10)
The deviation between calculated and measured gas holdup was smaller than 5%. The difference between the optimum value of S calculated by the model and by eq 10 was also smaller than 5 % . On the other hand, the model can be used to calculate Reynolds shear stress. This quantity is not a fitting parameter but rather a result of the model. The difference between measured and computed Reynolds shear stresses is quite small (Figure 8). Only a t higher gas velocities does the error in the maximum of the shear stress increase to about 30%. It must be mentioned here that the measured Reynolds shear stresses are the data with the highest measuring errors. For example, small deviations in the determination of the flow direction lead to higher errors in the correlation, u,u,,+ Keeping in mind that the turbulent kinematic viscosity (see Figure 1) could only been predicted to within a factor of 6 by older models, the agreement of measured and calculated data of this paper is quite satisfactorily.
The total kinetic energy consists of two parts, the deterministic kinetic energy (eq 12) and the stochastic kinetic energy (eq 13). Because radial and tangential mean liquid velocities are zero, only the axial component must be considered in eq 12. If the total kinetic energy is plotted versus the mean power input per unit of reactor volume (eq 14), a straight line is obtained (see Figure 10):
The slope of the straight line is a time constant, th, that can be used to determine the turbulence intensities. With the information on the ratio of the tangential and radial
Ind. Eng. Chem. Res., Vol. 29, No. 6,1990 993
K = kinetic energy per unit volume, J/m3 LOO 350
-
300
-
250
-
200
-
150
-
0
X
8S.m W n / L ALSR W n I L
Slope 0 . 5 2 s
BSI
Slope C.17 s
Wa/L
kN = Reichardt constant I = Prandtl mixing length, m P = power input per unit volume, W/m3 p = pressure, Pa p o = external pressure, Pa r = radial position, m R = column radius, m S = slip velocity, m/s tb = slope of plot KgB.versus P, s U = time-averaged mean liquid velocity, m/s u' = turbulence intensity, m/s WSG = superficial gas velocity, m/s WSL = superficial liquid velocity, m/s x = dimensionless radial position r / R z = axial position, m
Slope 0 . 6 1 s
mo 50
0
100
SO
300
LOO
500
600
700 P[W/m3l
Figure 10. Total kinetic energy per unit of reactor volume as a function of power input per unit of reactor volume. Liquid phase: water. ( 0 )Bubble column, D = 600 mm, tb = 0.61 s. ( 0 )Airlift loop reactor, D = 600 mm, tldn= 0.52 s. (X) Bubble column, D = 150 mm, tb = 0.17 s.
components and with known deterministic kinetic energy (e.g., velocities calculated by the above-mentioned model for the deterministic flow component), the turbulence intensity can be determined from
Since a comparison of tkinfrom two bubble columns with D = 600 mm and D = 150 mm yields a ratio of 4, a direct proportionality between tldnand the column diameter can be assumed as a first approximation for the calculation of the turbulence intensities for different column diameters. 4. Conclusions With the models for the deterministic and stochastic velocity components of the liquid flow in bubble columns derived in this paper, methods are at hand to determine the radial profiles of mean axial liquid velocity, turbulence intensities, and gas holdup in bubble columns and airlift loop reactors. The models are valid over a wide range of operating conditions so that one of the new mixing models (Rustemeyer et al., 1989; Kantorek, 1988) can be applied. With local concentrations of the reactants, local yields and selectivities can be calculated directly with known parameters like the column diameter, superficial gas and liquid velocities, and properties of the liquid phase. Thus, more reliable design and scale-up of bubble-column reactors is possible.
Acknowledgment We thank Priv. Doz. Dr. R. Buchholz for his interest and discussions. Furthermore, the support of this work by Deutsche Forschungsgemeinschaft, Fonds der Chemischen Industrie, and Studienstiftung des Deutschen Volkes (grant for T.M.)is gratefully acknowledged.
Nomenclature D = column diameter, m g = acceleration due to gravity, m2/s H = column height, m
Greek Symbols t~ = local gas holdup, % CG~ = integral gas holdup, % v, = molecular kinematic viscosity, mz/s v, = turbulent kinematic viscosity, mz/s pL = liquid density, kg/m3 T = Reynolds shear stress, Pa TW = wall shear stress, Pa Subscripts
ax, rad, tan = column coordinates ges = total mit = due to the mean liquid velocity tur = due to the turbulent fluctuations
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Received f o r review September 6, 1989 Accepted January 5, 1990
Percolation and Blocking in Supported Liquid-Phase Catalysts: Styrene Catalyst as a Particular Case Ewald Wicke and Achim Bartsch* Znstitut fur Physikalische Chemie der Uniuersitdt Miinster, SchloDplatz 4,0-4400 Munster, FRG
Supported liquid-phase catalysts (SLPCs) provide promising possibilities for heterogenization of homogeneous catalysis. On the other hand, there are catalysts with liquid components at reaction conditions that have a well-established and technically important tradition, e.g., the catalysts for SO2 oxidation and for styrene production. The consistent results of a reaction rate maximum with increasing liquid loading of the porous support led t o the development of different theories; those that prevailed were based on the blocking concept. Recent developments of percolation theory set this concept on the more general basis of mathematical models. The styrene catalyst, containing a melt of KOH/K2C03 as promoter in a bulky framework of magnetite crystal needles, represents a special kind of a SLPC. At the reaction temperature of 600 " C , the transport behavior of gases in the porous structure and the distribution of the melt (blocking effects) were investigated by stationary diffusion measurements. A number of problems, e.g., instability of the melt a t 600 "C, were solved successfully. Measurements with different potassium contents in the support provided the basis for process modeling in a single-pellet and in a fixed-bed reactor. 1. Supported Liquid-Phase Catalysts 1.1. General Information. SLP (supported liquid phase) catalysts are catalysts whose active components are dispersed on an usually porous support material and are either totally or at least partially liquid under reaction conditions. In view of the sites of reaction, there are three groups of SLP catalysts to be distinguished: Group I: homogeneous reaction in the volume of the liquid phase; examples, transition-metal complexes as catalytic centers in a solvent with low vapor pressure under reaction conditions (heterogenized homogeneous catalysis), Vz05/ KzS2O7melt for SOp oxidation (Villadsen and Livbjerg 1978). Group 11: reaction at the surface of the liquid phase; examples, liquid metals (alkali metals, tin, zinc) (Kenney, 1975). Group 111: reactions at the phase boundaries liquid phase/solid framework; this occurs when the liquid as well as the solid contains active components and/or promoters; example, styrene catalysts on the basis Fe304/KOH. Special advantages of the fine dispersion of the catalyst on a porous support are the large gaslliquid exchange area,
*Presentaddreas: Technische UniversiGt Hamburg-Harburg, Verfahrenstechnik IV, Eipendorfer Str. 40, D-2100Hamburg 90, FRG. 0888-5885/90/2629-0994$02.50/0
short diffusion paths in the liquid phase, and the performance of the reaction in a fixed bed reactor that can easily be operated in chemical engineering. A further advantage is the ease of separation of the gaseous reaction products from the liquid catalyst phase. As recent investigations have shown (Ohlrogge 1988), it seems to be possible to apply SLP catalysts in a fluidized-bed reactor, too. There also occur some specific problems of the SLPC, such as, e.g., loss of liquid phase by conveyance of vapor with the reaction gas flow due to the small, but still perceptible, vapor pressure of the liquid. Some important examples for application of SLP catalysts are listed in Table I. For future developments, the SLP technique offers promising applications of coordinatively unsaturated transition-metal complexes as heterogenized catalysts. Above all, the usually low working temperatures and the high selectivities, especially for reactions as complicated as oxo synthesis and a large number of hydrocarbon transformations (Parshall, 1980; Henrici-Oliv6 and Oliv6, 1977; Collmann and Hegedus, 1980), are outstanding features of these catalysts used in a solvent with low vapor pressure-one of the best known is the Wilkinson catalyst (Osborn et al., 1966). Hydroformylation (Rony, 1969; Gerritsen et al., 1980), isomerization (Acres et al., 1966; Rony, 1975),and hydrogenation of hydrocarbons are some 0 1990 American Chemical Society
