Liquid Holdup in an Upflow Cocurrent Packed Bed Reactor Involving

of the phase holdup in upflow cocurrent packed bed reactors, although more work has been done for coun- tercurrent operations. However, the systems in...
0 downloads 0 Views 78KB Size
Download PDF
Ind. Eng. Chem. Res. 2002, 41, 3505-3511

3505

KINETICS, CATALYSIS, AND REACTION ENGINEERING Liquid Holdup in an Upflow Cocurrent Packed Bed Reactor Involving Nitrile Butadiene Rubber and Hydrogen Qinmin Pan, Stuart A. Kehl,† and Garry L. Rempel* Department of Chemical Engineering, University of Waterloo, Ontario, N2L 3G1, Canada

Liquid holdup has been determined by means of a self-designed method in an upflow cocurrent bubble column reactor for the purpose of providing an efficient reactor for continuous homogeneous hydrogenation of nitrile butadiene rubber (NBR). The experimental fluids were gaseous hydrogen and chlorobenzene solution of NBR, analogous to that of NBR hydrogenation in an industrial process, except without using a catalyst. The influence of the gas and liquid superficial velocities and pressure on liquid holdup under NBR hydrogenation conditions has been investigated. The results indicate that three flow regimes exist, depending on the operation conditions employed. A correlation of liquid holdup, which covers those three regimes, has been established with satisfactory agreement by means of a modified dimensionless drift flux against the relative flow velocity of gas to liquid. Introduction Packed bubble columns are important reactors widely used for catalytic operations involving gas-liquid contact, especially for heterogeneously catalyzed reactions because the catalyst can be used as a packing to improve flow and dispersion in gas-liquid systems. Liquid holdup is an important parameter in mass transfer considerations and the design of multiphase flow reactors. The behavior of phase holdup is quite complicated, which is not only affected by material properties but is also sensitive to geometric factors and operation conditions. An efficient reactor configuration, an appropriate measurement method, and a suitable correlation for an extensive operation range are the main concerns. Various measurement techniques for phase fractions have been developed, and they can be found in books or papers.1,2 These techniques include methods of liquid level, change of pressure difference between two points by residence time, measurement of gas content through electrooptic or fiberglass probes, or directly by stopping the flow to measure the phase fraction. The measurement by liquid level is normally only suitable for the measurement in bubble columns or tanks with a batch mode. The way of locally measuring the content of the dispersion phase through electrooptic or fiberglass probes is useful for flow operation, and it can provide the distribution of the liquid holdup, but it needs tedious experiments to obtain the overall phase fractions. The method of measuring pressure difference between two points is easy to use, but as the operation pressure increases, the accuracy decreases quickly. For flow operation, the easiest method to measure liquid holdup * To whom correspondence should be addressed. E-mail: [email protected]. Phone: (519)8884567 ext. 2702. Fax: (519)7464979. † Present address: Imperial Oil, Products and Chemicals Division, Sarnia, ON, Canada.

is by stopping both gas and liquid flow, followed by calculation of the phase holdup. However, such normal methods for flow operation are not convenient for systems operated under a higher pressure. Quite a few papers have reported on the investigation of the phase holdup in upflow cocurrent packed bed reactors, although more work has been done for countercurrent operations. However, the systems involved are mainly with fluids composed of small molecules with low viscosity, such as air/water,3 nitrogen/toluene and hydrogen/toluene,4,5 and nitrogen/water, argon/water, helium/water, carbon dioxide/water, air/water, and nitrogen/ethylene glycol.6-8 Phase holdup is dependent on superficial gas velocity, viscosity, superficial tension, density, density difference, and geometry of the reactor. A number of correlation equations have been proposed in the literature. They mainly can be classified into three types. The first type involves correlating the phase holdup directly with gas velocity or together with liquid velocity.4 The second type correlates the holdup with dimensionless numbers, such as a gas Reynolds number and a liquid Reynolds number.3 The third one correlates drift flux with gas velocity.6-8 All of the correlation equations take gas velocity as the main correlation variable. Because the packing structure and operation conditions may be variable, different adaptable correlation equations which require tedious experiment must be employed. The purpose of the present study is to measure the liquid holdup of hydrogen/NBR solution in a upflow cocurrent packed bed reactor by a self-designed measurement method. This study provided elementary data for the development of an efficient continuous process for the production of hydrogenated NBR, which currently is used widely in the automobile industry.

10.1021/ie020098l CCC: $22.00 © 2002 American Chemical Society Published on Web 06/26/2002

3506

Ind. Eng. Chem. Res., Vol. 41, No. 15, 2002

Figure 1. Setup for continuous experiment.

Experimental Section Experimental Fluids. Because of experimental difficulties encountered in carrying out transport measurements in real systems, much laboratory research for transport behavior has primarily been carried out in mimiced fluids, especially in water or water-soluble systems, such as water/air, or water-soluble macromolecular systems, such as carbomethoxycellulose (CMC)/ air, polyacrylamide (PAA)/air, and so forth, to mimic a real process. The advantage of using these mimiced fluids is that they enable the investigation of the transport behavior in a large apparatus without the problems encountered from effluent deposition or reactor cleaning. Successful research of mixing behavior of reaction fluids has been achieved by selecting mimiced fluids with similar flow behaviors to the objective fluids. However, it must be realized that no simple fluid could mimic a real fluid well in all the aspects of the related physical properties, such as flow performance, interface behavior, diffusivity, and conductivity, especially when interface phenomena are involved. Therefore, here, we use the real reactant fluids of the system targeted, monochlorobenzene solution of NBR and hydrogen as the experimental fluids, however, in the absence of the catalyst. NBR (Krynac 38.50), which contained 62 wt % butadiene (80% trans, 15% cis, and 5% vinyl CdC) with a Mn ) 70 000 and a polydispersity of 3.6, was provided by Bayer Inc. The concentration of NBR investigated was 2.2 wt %, with a shear viscosity of about 0.006 Pa‚s at 130 °C. Experimental Apparatus. A packed bed reactor was used for the purpose of the present investigation. Because we use the monochlorobenzene solution of NBR itself as the experimental fluid, a large reactor for laboratory operation is not realistic. A diagram of the self-designed reactor layout is shown in Figure 1. The reactor (I in Figure 1) is a 122-cm long stainless steel pipe with a 1.387 cm internal diameter, tested to 13.75 MPa. It is sealed inside a 5-cm stainless steel outer pipe

Figure 2. Structure of the reactor packing.

which serves as a steam jacket. Ports tapped with 1/8 in. pipe thread are located at five points along the reactor length allowing access to the solution in the reactor. Thermocouples were installed in the first, second, third, and fifth port. The reactor is filled with 10-mm ceramic Intalox saddles (see Figure 2 for the structure), resulting in a measured void fraction of 0.671. The packing has no catalytic purpose but is added to enhance the interfacial renewal between gas and liquid phases, thereby improving the rate of H2 transfer between the gas and liquid. The same packing is also used to fill the transfer line between the preheater and the reactor to reduce the volume of the tubing and to minimize any slugging of the liquid. The NBR solution is transferred into a 12-L polyethylene carboy (A in Figure 1). The solution is purged by bubbling oxygenfree nitrogen through the solution and agitating with a 5-cm magnetic stirring bar. The polymer solution is pumped into a preheater using the high flow side of a dual stream reciprocating piston pump which allows for accurate control of the flow rate. A 300 mL Parr reactor (E) serves as the preheater and heats the solution to approximately 20 °C above the operation temperature in the reactor. Oxygen-free hydrogen is supplied by a high-pressure cylinder, and the flow is controlled by a Brooks mass flow controller (C). A bypass line around the controller with a needle valve can be used for gas flows beyond the range of the controller, generally in

Ind. Eng. Chem. Res., Vol. 41, No. 15, 2002 3507

excess of 2 L/min (STP). A distributing valve located after the gas flow controller enables the hydrogen stream to mix with the NBR solution in the preheater or to bypass the preheater and mix in the transfer line. From the transfer line, the heated gas/liquid mixture passes through a three-way valve (H) into the bottom of the reactor. After passing through the reactor, the gas-liquid mixture is chilled by a water-cooled heat exchanger (J) which reduces the material to ambient temperatures. A three-way valve (H) sequentially distributes the cooled gas and liquid between two 100-mL sight glasses (K) connected in parallel, where the liquid is separated from the hydrogen. The system pressure is measured with a Bourdon gauge (M) located after the check valves. The gas then passes through a back pressure regulator (N) rated for 1500 psi (10.31 MPa) which controls the system pressure. A secondary sight glass (P) after the regulator collects any liquid which may have been carried through as a result of a process upset. Finally, the exhaust gas passes through a rotameter (O) to measure the gas flow rate and is vented to a stack. Measurement Method. Because it is a high-pressure system, a normal shut down method is not practical to view the phase holdup. To overcome this, a gas sampling bomb with a volume of 8.28 cm3 was connected to the top sampling port of the packed column. A digital Omega pressure transducer was also attached to the second highest sampling port to enable accurate measurement of changes in the system pressure during the experiment. When the fluid flow and temperature profile within the reactor had stabilized, the pump settings, rotameter flow, and temperatures were recorded. The valves at the top and bottom of the reactor were then simultaneously closed, and the gas and liquid flow stopped. The liquid in the reactor was allowed to settle for 1 min at which time the reactor pressure was recorded. The valve connecting the reactor to the gas sampling bomb was slowly opened to minimize liquid carryover, and the initial pressure of the combined system was recorded. Pressure readings were again recorded after 1 and 2 min. The valve to the sampling bomb was then closed, and the process valves at the top and bottom of the reactor were slowly reopened. The liquid and gas flow was restarted using the next settings to be investigated. Gas in the sampling bomb was vented to the atmosphere and any liquid carryover allowed to drip out. The system was allowed to equilibrate for roughly three-quarters of an average residence time before the process was repeated for the next measurement. To calculate the liquid holdup, the system reactants were assumed to behave in an ideal fashion. The gas was assumed to follow the ideal gas law and any changes in system pressure were assumed to have no effect on the liquid vapor pressure. The effect of system pressure changes on dissolved hydrogen were taken into the account. On the basis of these assumptions, the gas volume in the reactor can be determined by measuring the change in the system pressure when the reactor volume is increased slightly. A mole balance on the gas phase in the system, before and after the analysis, can be expressed as

(

PAtmVBomb PInitVGas VBomb VGas + ) PFinal + TBomb TReac TBomb TReac

)

(1)

where P represents the pressure. The bomb has a

temperature TBomb, while the reactor is at T{Re}ac. The volume, VBomb, of the bomb is fixed, while the gas volume in the reactor, VGas, can be determined by rearranging eq 1 to obtain

(

)

TReac PFinal - PAtm VGas ) VBomb TBomb PInit - PFinal

(2)

The liquid volume can be determined from this by subtracting the volume of gas from the total void volume in the reactor, VReac. VReac is determined using the same volume change technique at room temperature with no liquid in the reactor. The volume of liquid in the reactor can also be expressed as the liquid void fraction, βL, times the void volume in the reactor.

VLiq ) VReac - VGas ) βLVReac

(3)

To compensate the effects of the released gas, the final pressure was adjusted for the change in the hydrogen concentration in the liquid. The moles of hydrogen released, NH2, can then be estimated from

N H2 )

(

xH2,1

1 - xH2,1

-

)

FMCB β V 1 - xH2,2 MMCB L Reac xH2,2

(4)

where xH2 is the hydrogen mole fraction in the solution, which can be predicted using Henry’s law.9 Subscripts 1 and 2 denote the system before and after the bomb is opened to the reactor, respectively. To determine how much gas is released from the solution, an initial estimate of the liquid fraction must be made on which to base the volume of liquid in the reactor. The increase in pressure which results from this release of hydrogen will be

∆PH2 )

NH2RT (1 - βL)VReac

(5)

The final pressure in the reactor, if the hydrogen had remained in solution, would then be PFinal - ∆PH2. On the basis of this adjusted pressure, a better estimate of βL can be obtained. Experimental Results The liquid holdup in the system with hydrogen and NBR solution is measured under various superficial gas/ liquid velocities and a temperature of 130 °C and pressures of 2.41 and 5.15 MPa. Operation Regimes and Influence of Superficial Gas Velocity. A typical curve for liquid holdup versus superficial gas velocity is shown in Figure 3. The evolution of the liquid holdup, βL, is found with three regimes as superficial gas velocity changes over the investigated range: Regime A, slowly decreasing in liquid holdup; Regime B, fast decreasing in liquid holdup; and Regime C, almost constant in liquid holdup. There are many factors affecting the liquid holdup. These factors include velocities of the gas and the liquid, viscosity of the gas and the liquid, density difference and buoyancy, interfacial tension, interface contamination, packing structure, temperature, and pressure. In the present investigation, the reactor dimension, packing structure, operation fluid, and temperature were given. When pressure and liquid velocity are kept constant, as shown in Figure 3, the factor affecting the

3508

Ind. Eng. Chem. Res., Vol. 41, No. 15, 2002

Figure 3. Liquid holdup versus superficial gas velocity. The data on the figure are pressure at liquid velocity of 0.83 mm/s.

liquid holdup is mainly the gas velocity. The gas velocity will influence the speed of bubble formation, the resistance of the packing structure to the bubbles, fluid turbulence, and the fluid behavior around the interface of bubbles and, thus, control bubble size and bubble residence time. When gas velocity is very low, the bubble number is also low, so the bubbles travel like in an infinite liquid, and the interaction between bubbles and between the bubbles and packing is negligible. As gas velocity is increased, the fluid turbulence and the bubble number will increase, and the interference between bubbles and the coalescence/resplit will occur, which reduces bubble size and increases the residence time of bubbles in the reactor and then reduces the liquid holdup quickly. Also, with increasing gas velocity, the resistance of the packing structure to the bubbles increases, which could smash the bubbles and increase the residence time of the bubbles in the reactor, which consequently reduces the liquid holdup. The increase in gas velocity will also increase the shear rate in the boundary layer around the bubbles and then change the rheological behavior of the fluid in loci because the rheological behavior of NBR solution varies with the shear rate,10 affecting the bubble residence in the reactor. In addition, because increasing the gas velocity results in a decrease in the liquid holdup, the liquid phase will gradually lose the capacity to be a continuous phase with the increase in gas velocity, and a phase inversion between gas and liquid phases may possibly happen. During the phase inversion, the phase fraction will possibly be constant. After completion of the phase inversion, a further increase of gas velocity will be expected to decrease the liquid holdup quickly. All of the factors involved could be coupled at the same time or some of them could become more predominant over others, depending on the operation conditions employed. In Regime A, VG is very low, and the volume occupied by bubbles in the reactor is much less than the liquid volume in the reactor. The behavior of each bubble is similar to a single bubble rising in an infinite liquid. The bubble velocities mainly depend on the buoyancy and viscous stress exerted on the bubbles, and there

appears to be no significant resistant effect of the packing on the bubble movement and almost no interference between bubbles. The rheological behavior of the polymer solution around the bubbles can be considered constant. So, the gas volume in the reactor increases linearly with the increase of VG, which results in liquid holdup decreasing nearly linearly with the gas velocity. Therefore, the characteristic of Regime A is that of a stress equilibrium and this regime can be considered as a bubble freely rising regime. In Regime B, with the further increase in VG, both the rheological stress on the interface of the bubbles and the resistance from the geometry of the packing increase, and the coalescence and resplit of bubbles become significant, which retard the movement of the bubbles and result in an increase in gas content in the reactor more quickly than in Regime A. So, the liquid holdup reduces sharply. Hence, the characteristic of Regime B is that of reaching a dynamic equilibrium of bubble coalescence/resplit, and this regime can be termed as a bubble coalescence/ resplit regime. In Regime C, because of the increase in gas holdup, both gas and liquid content seems to reach a point where they could exist in either a continuous or a discontinuous phase, so the mutual transmission between the continuous and discontinuous phase possibly happens. On one hand, in this regime, increasing gas velocity helps reduce liquid holdup as in other regimes. On the other hand, the increase in gas velocity results in the phase inversion and, during the gas phase, changes from the discontinuous phase into continuous phase, more gas leaves the reactor, which helps increase the liquid holdup. Consequently, in this situation, increases in gas velocity have little effect on the liquid holdup. Furthermore, high gas velocity probably promotes the slip of the bubbles from the drag of the polymer solutions. Thus, the increase in gas velocity would not help in increasing gas content significantly in the reactor. The characteristic of this regime is the phase inversion equilibrium, and this regime can be called a phase inversion regime. The results obtained in this investigation seem somewhat different from the literature regarding the flow regimes. Most of the research reported in the literature were, however, carried out with simpler systems, such as air/water, nitrogen/water, carbon dioxide/water, and nitrogen/ethylene glycol, and so forth, rather than polymer solutions of the type used in the present work. In all of the previously reported studies, as was the case with this work, the predominate factor found to affect the liquid fraction in the column was the gas velocity.6,11 A few studies reported high liquid holdups with little dependence on the gas velocity.4 However, to our knowledge, no previous reports have indicated three regimes. The phenomenon observed in the present work probably arises from the special interaction between bubbles and polymer solution as well as the different response of this interaction to the change of gas velocity. In water or other small molecule fluids, the rheological behavior is normally invariable when the gas velocity changes. However, in polymer solutions, the rheological characteristics would change with the shear stress between the bubbles and the liquid phase, which would strongly affect the coalescence and respilt of the bubbles. The packing structure could also be an important factor for the liquid holdup behavior. If the void size in the packing were too large (or even without packing) or too small, the resistance of the packing exerted on the

Ind. Eng. Chem. Res., Vol. 41, No. 15, 2002 3509

Figure 4. Effect of liquid velocity on liquid holdup. The data on the figure are superficial liquid velocity with unit of mm/s at 2.41 MPa pressure.

bubbles would not change significantly and Regime B would be suppressed and Regimes A and B would possibly merge into one if other factors were not dominant. Influence of Superficial Liquid Velocity. Figure 4 shows the effect of liquid velocity on the liquid holdup. A similar trend with three regimes as shown in Figure 3 can be found in Figure 4 for the investigated range of liquid velocities. On comparison with the gas velocity, the effect of the superficial liquid velocityVL, on the liquid holdup is quite small, although it appears to increase slightly in βL for a given VG in Regimes A and B and decrease a little in Regime C as VL increases. However, the liquid velocity may influence the point at which the regime changes. The role of liquid velocity is difficult to assess at these conditions, because only a narrow range of the liquid velocity was examined. At a VL of 0.39 mm/s, a lower slope is observed than for the other two velocities. However, the results at VL of 0.55 and 0.83 mm/s are quite close, leading to the conclusion that the liquid velocity has a small influence, if at all. There appears to be much less consensus about the influence of the liquid flow rate on the liquid holdup. Thanos et al.4 found that the liquid velocity had no influence on the holdup, while Lamine et al. recorded that this was the case only when large particles were used.11 For small particles, Lamine et al. observed that the liquid holdup increased slightly as the velocity increased. Larachi et al.,6 Fukushima and Kusaka,12 Ohshima et al.,13 van Gelder et al.,14 and Steigel and Shah3 also observed this small, positive influence on the liquid holdup. Achwal and Stepanek’s study was the only one to record a slight decrease in the liquid holdup as the liquid velocity was increased.15 This discrepancy in results and the inconsistent effect of VL were caused by competing forces.3 As the liquid velocity increases, it raises the rate at which the gas rises and therefore decreases gas holdup. However, the increased liquid flow also increases the turbulence which tends to reduce the bubble coalescence. This results in smaller bubbles which have a lower rise in velocity, resulting in an increase in the gas holdup. Depending on whether a

study was carried out where the two forces were counterbalancing each other or not, different results would be obtained. Influence of Operation Pressure. The behavior of the liquid holdup with respect to the gas velocity is similar for both pressures of 2.41 and 5.15 MPa (see Figure 3). However, at the higher pressure of 5.15 MPa, the curve is shifted slightly to the left so that the liquid holdup is lower than that at lower pressure under a given VG. Larachi et al. also found that the system pressure had a negative effect on the liquid holdup.6 As the pressure was increased from 0.3 to 5.1 MPa, the liquid holdup decreased for a given superficial gas velocity. This effect was more significant over the range of 0.3-1.1 MPa with little change from 1.1 to 5.1 MPa. Higher gas velocities also seemed to accentuate this trend. A similar pressure effect was also observed in our system; however, it was not very significant. This may be due to the fact that the pressure was only varied from 2.5 to 5.3 MPa, which would place it in the range of pressure where the influence is greatly reduced, according to Larachi et al.6 Correlation and Discussion Liquid holdup is a complex function of inertia of the gas and the liquid, viscosity of the gas and the liquid, density difference and buoyancy, surface tension and surface contamination, packing structure, temperature, and pressure. This has led to the pursuit in this field of a model or a correlation equation that is valid over a wide operation range but with as few model (or correlation) parameters as possible. This may be achieved when the effects of all of the factors are well-understood in bubble columns. However, it is not that easy to understand all of the factors at present. Nevertheless, a simple model, which takes into account the appropriate characteristic parameters without the details of the flow, can be quite useful for organizing experimental results and for predicting design parameters. It appears from the literature and from the present study that the superficial gas velocity has the most significant effect on the liquid holdup. However, it is obvious that we could not take all of the diverse data from Figures 3 to 5 into one correlation equation if we directly correlate βL with VG . A drift flux was first proposed by Wallis16 with the definition of a volumetric flux of gas relative to a surface moving at the average velocity. It had been used by Larachi et al.6 and Molga and Westerterp8 and found to correlate holdup data well, obtained in high-pressure cocurrent packed bubble column reactors. Although they did not explore the reason for such, they found that the drift flux defined as

JDF ) VGβL - VL(1 - βL)

(6)

is a unique function of the gas velocity

JDF ) aVGb

(7)

where the exponent b was close to 1 and the factor a was thought to be a characteristic parameter of the distribution quality of both gas and liquid and was in the range of 0.5-0.9. Larachi et al.6 reported a ) 0.400.54 and b ) 0.91-1.07. Molga and Westerterp8 reported a ) 0.39 ( 0.05 and b ) 0.85 ( 0.04.

3510

Ind. Eng. Chem. Res., Vol. 41, No. 15, 2002

Figure 5. Liquid holdup at 5.15 MPa pressure. The data on the figure are superficial liquid velocity with unit of mm/s.

Here, the drift flux is also applied to our data, and it is found that the correlation is variable with the change of the regimes. The correlation results are, for Regime A, a ) 0.839 and b ) 0.972; for Regime B, a ) 0.60 and b ) 0; and for Regime C, a ) 0.471 and b ) 1.07. Obviously, the correlations for Regime C are very close to the correlation equations of Larachi et al. 6 in which a ) 0.40-0.54 and b ) 0.91-1.07, and the results in Regime A are close to the correlation equation of Nacef et al. (which was provided in ref 6) in which a ) 0.8 and b ) 1.0. The index is probably related with the flow behavior of the fluids. It is obvious that the drift flux defined by eq 6 cannot hold for all three regimes into one equation. Furthermore, also there is a dimension inadequacy in eq 7. The dimension in the left of eq 7 is “length/time”. However, the value of the parameter b is variable with the operation conditions. It implies that the coefficient a in eq 7 is with a dimension, which is variable, depending on the parameter b. Therefore, it is not convenient for application. Here, we tried to define a modified drift flux as

JDF* )

JDF VL

(8)

and to correlate it with a relative velocity between gas and liquid phases, VG* ) VG/VL. The results are shown in Figure 6. It is now found that all of the three regimes lie along one curve, and the type of the correlation equation can be as follows:

JDF* ) c(VG*)d

(9)

We believe that c and d are functions of the properties of fluids and packing structures. For the present system investigated where VG < 3.1 cm/s and 0.28 e VL e 1.7 mm/s, c ) 1.09 and d ) 0.806. This correlation equation possesses several advantages as compared to previously reported normal correlation equations. As mentioned previously, compared to eq 7, it can cover all three regimes and overcome the dimension inadequacy. In

Figure 6. Modified drift flux versus relative velocity. The data on the figure are superficial liquid velocity with unit of mm/s and pressure with unit of MPa.

addition, it represents no problem, whether a superficial flow velocity or a real flow velocity is used in the equation because both gas and liquid velocity will be enlarged or reduced by the same proportion in eq 9. Conclusions Liquid holdup has been determined experimentally for the purpose of the development of an efficient continuous NBR hydrogenation process. The existence of three regimes (i.e., bubble freely rising regime, bubble coalescence/resplit equilibrium regime, and phase inversion regime) can justify the dependence of liquid holdup on operating pressure and gas and liquid velocity. Some mechanism was postulated to explain the experimental phenomena in different regimes, but further direct observation experiment is desired for the validation. A correlation equation of a modified dimensionless drift flux JDF* against a relative superficial velocity of gas to liquid flow has been established, which covers all three regimes. The results indicate that JDF* is able to embody the effects of many operational parameters in all three regimes; therefore, it can now be used for an acceptable estimation for scaling-up or down of the reactor under consideration. Further investigation over a wider range of conditions with variable fluid properties and packing structures is suggested to characterize c and d in eq 9. Acknowledgment Support from the Natural Science and Engineering Research Council of Canada (NSERC) is gratefully acknowledged. Nomenclature a ) coefficient in eq 7 (m/s)1-b b ) exponent in eq 7 JDF ) drift flux, defined as JDF ) VGβL - VL(1 - βL), m/s JDF* ) modified drift flux, defined as JDF* ) JDF/VL M ) molecular weight

Ind. Eng. Chem. Res., Vol. 41, No. 15, 2002 3511 P ) pressure, MPa T ) temperature, K V ) reactor volume, m3 VG ) superficial gas velocity, m/s VG* ) dimensionless velocity, defined as VG/VL VL ) superficial liquid velocity, m/s x ) mole fraction F ) density, kg/m3 βL ) liquid holdup Subscripts G, gas ) gas phase H2 ) hydrogen L ) liquid phase MCB ) monochlorobenzene

Literature Cited (1) Fan, L.-S. Gas-Liquid-Solid Fluidization Engineering; Butterworth Publisher: Kent, U.K., 1989; Chapter 2. (2) Deckwer, W.-D. Bubble Column Reactors; Field, R. W., Ed.; John Wiley and Sons: New York, 1992; Chapter 7; translated by V. Cottrell. (3) Stiegel, G. J.; Shah, Y. T. Backmixing and Liquid Holdup in a Gas-Liquid Cocurrent Upflow Packed Column. Ind. Eng. Chem. Process Des. Dev. 1977, 16, 37. (4) Thanos, A. M.; Galtier, P. A.; Papyannakos, N. G. Liquid Flow Non-Idealities and Hold-up in a Pilot Scale Packed Bed Reactor with Cocurrent Gas-Liquid Upflow. Chem. Eng. Sci. 1996, 51, 2709. (5) Thanos, A.; Menagias, Ph.; Galtier, P.; Papyannakos, N. Operating Pressure and Gas-Phase Proerties Effects on the Liquid Flow Nonidealities in Small-Scale Upflow Reactors. Ind. Eng. Chem. Process Des. Dev. 1999, 38, 3817. (6) Larachi, F.; Laurent, A.; Wild, G.; Midoux, N. Some Experimental Liquid Saturation Results in Fixed-Bed Reactors Operated under Elevated Pressure in Cocurrent Upflow and

Downflow of the Gas and the Liquid. Ind. Eng. Chem. Res. 1991, 30, 2404. (7) Larachi, F.; Wild, G.; Laurent, A.; Midoux, N. Influence of Gas Density on the Hydrogdynamics of Cocurrent Gas-Liquid Upflow Fixed Bed Reactors. Ind. Eng. Chem. Res. 1994, 33, 519. (8) Molga, E. J.; Westerterp. K. R. Gas-Liquid Interfacial Area and Holdup in a Cocurrent Upflow Packed Bed Bubble Column Reactor at Elevated Pressures. Ind. Eng. Chem. Res. 1997, 36, 662. (9) Parent, J. S.; Rempel, G. L. Solubility of Hydrogen in Chlorobenzene. J. Chem. Eng. Data 1996, 41 (2), 192. (10) Pan, Q.; Rempel, G. L. Investigation of Rheological Behavior of Diene Based Polymer Solutions. Presented at 50th Canadian Chemical Engineering Conference, Montreal, Quebec, Canada, Oct 15-18, 2000. (11) Lamine, A. S.; Colli Serrano, M. T.; Wild, G. Hydrodynamics and Heat Transfer in Packed Beds with Cocurrent Upflow. Chem. Eng. Sci. 1992, 47, 3493. (12) Fukushima, S.; Kusaka, K. Gas-Liquid Mass Transfer and Hydrodynamic Flow Region in Packed Column with Cocurrent Upward Flow. J. Chem. Eng. Jpn. 1979, 12, 296. (13) Ohshima, S.; Takematsu; T.; Kuriki, Y.; Shimada, K.; Suzuki M.; Kato, J. Liquid-Phase Mass Transfer Coefficient and Gas Holdup in a Packed-Bed Cocurrent Upflow Column. J. Chem. Eng. Jpn. 1976, 9, 29. (14) van Gelder, K. B.; Westerterp, K. R. Residence Time Distribution and Hold-up in a Cocurrent Upflow Packed Bed Reactor at Elevated Pressure. Chem. Eng. Technol. 1990, 13, 27. (15) Achewal, S. K.; Stepanek, J. B. Holdup Profiles in Packed Beds. Chem. Eng. J. 1976, 12, 69. (16) Wallis, G. B. One-Dimensional Two-Phase Flow; McGrawHill: New York, 1969; Chapter 1.

Received for review February 4, 2002 Revised manuscript received May 1, 2002 Accepted May 7, 2002 IE020098L