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Liquid Holdup in Trickle-Bed Reactors at Very Low Liquid Reynolds Numbers Ru 1 diger Lange,* Markus Schubert, and Tobias Bauer Department of Chemical Engineering, Dresden University of Technology, Mu¨ nchner Platz 3, 01062 Dresden, Germany
The paper presents experimental results concerning hydrodynamic aspects in a trickle-bed reactor, in which both fluid phases (gas and liquid) are fed concurrently downward. The static and dynamic liquid holdup fractions were measured in a trickle-bed reactor (inner reactor diameter 0.034 m) packed with different porous and nonporous particles at very low liquid mass flow rates using the drainage technique. The liquid Reynolds number ReL was in the range of 0.08-1.2 and the gas Reynolds number ReG in the range of 0.13-2.9. The measurements were performed with organic liquids and hydrogen and nitrogen as gas phases. The results are presented graphically. It was shown that the ratio of the reactor diameter to the particle diameter and liquid Reynolds number affect on the liquid holdup. The dynamic liquid holdup increases with an increase in the liquid Reynolds numbers and with a decrease in the particle diameter. The effect of the gas flow rate on the liquid holdup can be neglected. Correlations are derived that are valid for very low liquid Reynolds numbers and are compared to the literature. Introduction Fixed-bed reactors with concurrent downflow of the two-phase flow (trickle-bed reactors) are widely used in the petroleum, petrochemical, chemical, and biochemical industries for hydrotreating, hydrocracking, hydrodesulfurization, and oxidation processes, as well as in the removal of organic compounds from wastewater.1-3 The reactor behavior is very complex and depends on the mass and heat transfer and the hydrodynamics. In general, the hydrodynamics are fundamental criteria for the selection and productivity of multiphase reactors. One of the most important hydrodynamic aspects for the design, scale-up, and modeling of trickle-bed reactors is the liquid holdup, which, simplified, is the ratio of the liquid volume to the reactor volume. The liquid holdup has a significant influence on the liquid residence time distribution, mass- and heat-transfer processes, wetting efficiency, and pressure drop. Furthermore, detailed knowledge is essential for safe processing to prevent hot-spot formations and possible runaways.2,4-7 There is considerable literature dealing with liquid holdup over a wide range of gas and liquid flow rates (collected by Iliuta et al.8 in a trickle-bed flow database), and many correlations have been proposed in the papers. An extensive summary of the holdup correlation has been published in a recent review on multiphase reactors by Dudukovic et al.9 The total liquid holdup (L,t) is defined as the total volume of the liquid phase (VL,t) in the catalyst bed volume (according to the packing length, LP) at any time (eq 1). The total amount of liquid in the reactor bed can be divided into static and dynamic fractions. The dynamic liquid holdup (L,d) is the freely flowing liquid volume relative to the reactor volume, whereas the * To whom correspondence should be addressed. Tel.: +49 351 463 35181. Fax: +49 351 463 37757. E-mail:
[email protected].
Figure 1. Detailed schematic classification of liquid holdup in trickle-bed reactors.
static liquid holdup (L,st) is the fraction of liquid that is trapped in catalyst pores and stagnated liquid
L,i )
4VL,i πdR2LP i ) st (static), d (dynamic), or t (total) (1)
between catalyst particles (eq 2). The latter is also called the external static liquid holdup (L,st,ext), while the liquid fraction inside the catalyst is called the internal static liquid holdup (L,st,int). A detailed classification of the liquid holdup in trickle-bed reactors is given in eqs 2-4 and depicted schematically in Figure 1.
L,t ) L,ext + L,int ) L,d + L,st
(2)
L,ext ) L,d + L,st,ext
(3)
L,st ) L,st,ext + L,st,int
(4)
A similar description of liquid holdup fractions has also been published by Al-Dahhan and Highfill10 and Lange.11 The reported correlations for dynamic and total liquid holdup, as summarized, e.g., by Al-Dahhan et al.,3,12 Saroha and Nigam,13 and Dudukovic et al.,9 are mainly
10.1021/ie048906r CCC: $30.25 © 2005 American Chemical Society Published on Web 04/20/2005
Ind. Eng. Chem. Res., Vol. 44, No. 16, 2005 6505 Table 1. Physical Properties of the Liquid-Gas System at 293 K and 1 atm system cumene ethyl alcohol nitrogen hydrogen
viscosity (kg‚m-1‚s-1)
density (kg‚m-3) 861 789
Liquid Phase 0.000795 0.00122
1.25 0.09
surface tension (N‚m-1) 0.028 0.022
Gas Phase 1.75 × 10-5 0. 87 × 10-5
empirical approaches based on modified single-phase flow equations. Different measurement methods were discussed by Al-Dahhan and Highfill,10 who divided the liquid holdup measurements into integral, semi-integral, and local measurement methods. Investigations carried out by Urrutia et al.14 focused especially on the drainage method for the determination of the dynamic liquid holdup. To summarize, it can be observed that the reported correlations fit reasonably to the particular setup and conditions used. However, if compared with each other, the correlations agree poorly because of complex interaction between the system and the fluid flow. The strong deviations in the results show that the correlations are restricted to their specific narrow range of process conditions and the system studied. This is very impressively demonstrated by Dudukovic et al.,9 who show a parity plot of 8000 external liquid holdup data against the prediction calculated with an empirical correlation of Ellman et al.15 It is important to predict the liquid holdup as a function of the operating conditions and physical properties of the system. To our knowledge, there exists no detailed paper proposing correlations valid only for very low liquid Reynolds numbers (ReL < 1.2), which is the operation range in a typical laboratory-scale trickle-bed reactor. Experimental Section Reaction System. The experiments to determine the liquid holdup were performed in a reaction unit, consisting of a stainless steel reactor with an inner diameter of 0.034 m with a double jacket as a cooling loop to ensure isotherm conditions and other facilities such as valves and flowmeters for controlling the gas and liquid flow rates. The liquid phase was fed into the reactor at the top by a pump from a tank, while gas was provided by high-pressure cylinders. The length of the packed bed within the reactor was 0.7 m. The gas and liquid flow conditions for the collected liquid holdup data were selected in the low trickle flow regime, characterized by low interaction between the gas and liquid phases. The liquid holdup was investigated experimentally using different fluid Reynolds numbers, varying in the range of 0.08-1.2 for the liquid phase and 0.13-2.9 for the gas phase. The physical properties of the gases and liquids used are listed in Table 1. The packing materials were a porous palladium-supported catalyst with γ-Al2O3 as the carrier material (the porosity was 0.39) and nonporous SiO2 beads with a particle diameter of 0.72 mm. The catalyst was divided into five narrow particle size ranges from 0.57 to 3.0 mm. The bed voidage B was nearly constant
Figure 2. Total liquid holdup versus liquid Reynolds number for different packing materials and different gas Reynolds numbers (dP ) 0.72 mm): 2, ReG ) 0.46; 9, ReG ) 0.68; 0, ReG ) 0.17; ×, ReG ) 0.35; 4, ReG ) 0.52; O, ReG ) 0.69; +, ReG ) 0.86.
at about 0.55. The values for the bed voidage of the crushed catalyst just differ in the second decimal place. The temperature was controlled at 293 K, and all experiments were performed under atmospheric pressure. Holdup Measurements. The liquid holdup was measured using the drainage technique in the absence of reaction. This integral measurement method provides direct information on the liquid volume inside the reactor. The method is preferred because of the simplicity in cost of the apparatus and a sufficient accuracy compared to other methods, such as the tracer or gravimetric methods.10 With the drainage method, the gas and liquid supply to the steady-state operating trickle-bed reactor is interrupted simultaneously by closing corresponding valves and switching off the liquid pump. The dynamic liquid holdup was calculated on the basis of the freely leaving liquid relative to the effective reactor volume. The remaining liquid in the reactor, which was also divided by the reactor volume, is the static liquid holdup that is measured by running dry the bed through generation of heat and condensation of the formed vapor phase. To achieve steady-state conditions and reproducible liquid holdup data, the fluids were fed into the reactor at constant flow rates for at least 2 h before starting a holdup measurement. Results and Discussion To show the important influence of the packing material on the total liquid holdup, measurements with porous crushed pellets of γ-Al2O3 and nonporous particles of SiO2 of the same diameter were performed at the same liquid and gas mass flow rates, presented as gas and liquid Reynolds numbers (based on the bed voidage). The results are depicted in Figure 2. In general, the total liquid holdup increases with an increase in the liquid flow rate. The total liquid holdup of the porous pellets is more than twice that of the nonporous particles, which can clearly show the impact of particle porosity. The measured total liquid holdups agree in quality with the reported results comparing porous and nonporous materials from Schwartz et al.16 and Kohler and Richarz.17
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Figure 3. Static and dynamic liquid holdup versus liquid Reynolds number for the γ-Al2O3 catalyst for different gas Reynolds numbers (dP ) 0.72 mm): 0, ReG ) 0.17; ×, ReG ) 0.35; 4, ReG ) 0.52; O, ReG ) 0.69; +, ReG ) 0.86.
Figure 4. Static liquid holdup versus gas Reynolds number for the γ-Al2O3 catalyst for different reactor diameter to particle diameter ratios (ReL ≈ 0.11): 0, dRdP-1 ) 60.2; ×, dRdP-1 ) 47.6; O, dRdP-1 ) 30.2.
This effect appears to be due to the capillary forces of the porous catalyst, which result in an increase in the static liquid holdup. The findings are in accordance with previous investigations by Mao et al.18 and Ortiz-Arroyo et al.,19 which suggested increasing static liquid holdup with increasing porosity. The following observations apply only to the porous catalyst material as used in catalytic reaction applications. In Figure 3, the dynamic and static liquid holdups for different gas flow rates versus liquid Reynolds numbers at constant particle diameter are illustrated. In general, the dynamic liquid holdup increases with an increase in the liquid Reynolds numbers. The effect of the gas and liquid flow rates on the static liquid holdup can be neglected. As illustrated in Figure 3, the static liquid holdup for porous material (here L,st ≈ 0.28) is much higher than the dynamic liquid holdup with L,d ≈ 0.10-0.17 for the operating conditions used. There is no significant dependency of the gas flow rate on the dynamic or static liquid holdup at these very low liquid Reynolds numbers, as represented in Figures 3 and 4. The latter shows the static liquid holdup versus
Figure 5. Logarithmic representation of the dynamic liquid holdup versus liquid Reynolds number for the γ-Al2O3 catalyst for particle diameter: 0, dP ) 0.57 mm; ×, dP ) 0.72 mm; 4, dP ) 1.13 mm; O, dP ) 1.80 mm; +, dP ) 3.00 mm.
gas Reynolds number for different reactor diameter to particle diameter ratios, where the result is an approximate horizontal linear graph. The general trend of linear increase in the total liquid holdup with an increase in the liquid Reynolds numbers in a double-logarithmic plot depending on the particle diameter has been reported by Satterfield and Way,20 Tsamatsoulis and Papayannakos,21 and Fu and Tan.22 Because the static liquid holdup is not a function of the gas and liquid Reynolds numbers in the investigated range of operating conditions, the same behavior was found for the dynamic liquid holdup, measured as shown in Figure 5. Figure 5 illustrates the strong impact of the particle size on the dynamic liquid holdup, where an increase in the particle size results in an increase in the dynamic liquid holdup. The different particle sizes result in parallel curves. The dynamic and total liquid holdups are mainly a function of the liquid Reynolds number, which includes liquid properties and superficial velocity, as well as the reactor diameter to particle diameter ratio. The estimated dynamic and total liquid holdups were correlated according to these findings, and eqs 6 and 7 are proposed.
L,t ) 0.16(dR/dP)0.33ReL0.14
(6)
L,d ) 0.002(dR/dP)1.28ReL0.38
(7)
Figures 5 and 6 point out the mathematical explanation for the derivation of the proposed holdup correlations. Both equations have the same structure but differ in exponents for liquid Reynolds number and reactor diameter to particle diameter ratio. Figure 7 compares the proposed correlation for the prediction of the total liquid holdup (eq 6) with correlations suggested by Fu and Tan22 and Larachi et al.24 and the total liquid holdup calculated with the neural network from Iliuta et al.6 The latter is based on the phenomenological holdup model proposed by Holub et al.23 and extended by Al-Dahhan et al.25 The correlations used in Figure 7 are listed in Table 2. The correlations propose minor values for the total liquid holdup. No published correlations can be used, particularly in the range of very low liquid Reynolds numbers.
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the liquid holdup, while decreasing the particle diameter results in an increase in the liquid holdup. Two empirical equations (eqs 6 and 7) are proposed for the prediction of the dynamic and total liquid holdups at liquid Reynolds numbers ranging from 0.08 to 1.2. In comparison with previously published holdup correlations, the experimental data were fitted well. Acknowledgment We take great pleasure in writing a paper for this issue, which is dedicated to Milorad P. Dudukovic. In addition, we thank him for his benefit, support, and encouragement in investigations into multiphase reactors, especially in the field of trickle-bed reactors. Nomenclature Figure 6. Graphical representation of the estimated correlations for dynamic and total liquid holdups for the γ-Al2O3 catalyst: +, total liquid holdup, PL,t; ×, dynamic liquid holdup, PL,d.
a ) dimensionless parameter dh ) hydraulic diameter, m dP ) particle diameter, m dR ) inner reactor diameter, m g ) acceleration due to gravity, m‚s-2 G ) gas mass flow rate, uGFG, kg‚m-2‚s-1 Ga ) Galileo number, F2dP3gµ-2 L ) liquid mass flow rate, uLFL, kg‚m-2‚s-1 LP ) packing length P ) pressure, bar Re ) Reynolds number based on the bed voidage, uFdPµ-1B-1 Re′ ) Reynolds number based on the superficial velocity, uFdPµ-1 u ) superficial velocity (m‚s-1) We ) Weber number, u2FdPσ-1 XG ) modified Lockhart-Martinelli parameter ) uGFG0.5uL-1FL-0.5 V ) volume Greek Letters
Figure 7. Total liquid holdup versus liquid Reynolds number for the γ-Al2O3 catalyst (dP ) 0.72 mm, ReG ) 0.17, and B ) 0.55): 4, measured total liquid holdup; 1, proposed correlation (eq 6); 2, Larachi et al.;24 3, Fu and Tan;22 4, Iliuta et al.6 Table 2. Correlations for the Total Liquid Holdup in Trickle-bed Reactors author correlations Fu et al.22 L,t ) 1.505Re′L0.29GaL-0.32dh-0.22B (8) dh ) {16B3[9π(1 - B)2]-1}1/3dP Larachi et al.24 L,t ) B(1 - 10-Γ) (9) Γ ) 1.22WeL0.15XG-15Re′L-0.20 Iliuta et al.a,6 (5) present work L,t ) 0.16(dR/dP)0.33ReL0.14 (6) a
conditions; approach
empirical; ReL < 2.3 empirical; ReL < 28 neural network empirical; 0.05 < ReL < 1.5
http://www.gch.ulaval.ca/bgrandjean/pbrsimul/pbrsimul.html.
Concluding Remarks The total and dynamic liquid holdups in a trickle-bed reactor at very low gas and liquid Reynolds numbers were measured using the drainage method. Experimental results indicated that the ratio of the reactor diameter to the particle diameter and liquid Reynolds number effect on the liquid holdup. Mainly, increasing the liquid Reynolds number results in an increase in
B ) bed voidage L ) liquid holdup F ) density, kg‚m-3 µ ) viscosity, kg‚m-1‚s-1 Γ ) dimensionless parameter σ ) surface tension, N‚m-1 Subscripts L ) liquid phase d ) dynamic st ) static t ) total ext ) external int ) internal
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(7) Silveston, P. L.; Hanika, J. Challenges for the periodic operation of trickle-bed catalytic reactors. Chem. Eng. Sci. 2002, 57, 3373. (8) Iliuta, I.; Ortiz-Arroyo, A.; Larachi, F.; Grandjean, P. B. A.; Wild, G. Hydrodynamics and Mass Transfer in Trickle-Bed Reactors: An Overview. Chem. Eng. Sci. 1999, 54, 5329. (9) Dudukovic, M. P.; Larachi, F.; Mills, P. L. Multiphase Catalytic Reactors: A Perspective on Current Knowledge and Future Trends. Catal. Rev. Sci. Eng. 2002, 44, 123. (10) Al-Dahhan, M. H.; Highfill, W. Liquid Holdup measurement techniques in laboratory high-pressure trickle bed reactors. Can. J. Chem. Eng. 1999, 77, 759. (11) Lange, R. Zur stationaeren und periodischen Betriebsweise von Trickle-Bed Reaktoren. Habilitation Thesis, Technical University of HamburgsHarburg, Harburg, Germany, 2001. (12) Al-Dahhan, M. H.; Dudukovic, M. P. Pressure Drop and Liquid Holdup in High-Pressure Trickle-Bed Reactors. Chem. Eng. Sci. 1994, 49, 5681. (13) Saroha, A. K.; Nigam, K. D. P. Trickle Bed Reactors. Rev. Chem. Eng. 1996, 12, 207. (14) Urrutia, G.; Bonelli, P.; Cassanello, M. C.; Cukierman, A. L. On Dynamic Liquid Holdup Determination by the Drainage Method. Chem. Eng. Sci. 1996, 51, 3721. (15) Ellman, M. J.; Midoux, N.; Laurent, A.; Charpentier, J. C. A New, Improved Pressure Drop Correlation for Trickle-Bed Reactors. Chem. Eng. Sci. 1988, 43, 2201. (16) Schwartz, J. G.; Weger, E.; Dudukovic, M. P. A New Tracer Method for Determination of Liquid-Solid Contacting Efficiency in Trickle-Bed Reactors. AIChE J. 1976, 22, 894. (17) Kohler, M.; Richarz, W. Study of Liquid Holdup in Trickling Bed Reactors. Chem. Ing. Tech. 1984, 56, 784.
(18) Mao, Z. S.; Xiong, T. Y.; Chen, J. Theoretical Prediction of Static Liquid Holdup in Trickle Bed Reactors and Comparison with Experimental Results. Chem. Eng. Sci. 1993, 48, 2697. (19) Ortiz-Arroyo, A.; Larachi, F.; Iliuta, I. Method for Inferring Contact Angle and for Correlating Static Liquid Holdup in Packed Beds. Chem. Eng. Sci. 2003, 58, 2835. (20) Satterfield, C. N.; Way, P. F. Role of the Liquid Phase in the Performance of a Trickle Bed Reactor. AIChE J. 1972, 18, 305. (21) Tsamatsoulis, D.; Papayannakos, N. Axial Dispersion and Holdup in a Bench-Scale Trickle-Bed Reactor at Operating Conditions. Chem. Eng. Sci. 1994, 49, 523. (22) Fu, M.-S.; Tan, C.-S. Liquid Holdup and Axial Dispersion in Trickle-Bed Reactors. Chem. Eng. Sci. 1996, 51, 5357. (23) Holub, R. A.; Dudukovic, M. P.; Ramachandran, P. A. A Phenomenological Model for Pressure Drop, Liquid Holdup, and Flow Regime Transition in Gas-Liquid Trickle Flow. Chem. Eng. Sci. 1992, 47, 2343. (24) Larachi, F.; Laurent, A.; Midoux, N.; Wild, G. Experimental Study of a Trickle-Bed Reactor Operating at High Pressure: Two Phase Pressure Drop and Liquid Saturation. Chem. Eng. Sci. 1991, 46, 1233. (25) Al-Dahhan, M. H.; Khadilkar, M. R.; Wu, Y.; Dudukovic, M. P. Prediction of Pressure Drop and Liquid Holdup in HighPressure Trickle-Bed Reactors. Ind. Eng. Chem. Res. 1998, 37, 793.
Received for review November 12, 2004 Revised manuscript received March 22, 2005 Accepted March 28, 2005 IE048906R
