776
Ind. Eng. Chem. Process Des. Dev. 1986, 25. 776-7130
Miller, R. J. US Patent 2 523 707, 1950. Mitsui Toatsu Chemicals Inc. Japan Patent 80 82 054, 1980. Maiseev. I. I.; Vargaftlk, M. N.: Syrkin, Y. K. Dokl. Akad. Nauk. SSSR 1960, 130, 801. Moore, W. P. US Patent 3 154589, 1964. Smldt, J.; Hafner, W.; Jira, R.; Sedlmeier, J.; Seiber, R.: Kojer, H. Angew. Chem. 1959, 7 7 , 178.
Stern, E. W. Catal. Rev. 1967, 7 , 73. Williams, W. H.: Ackroid. H.; James, A. E. US Patent 2432551, 1947.
Received for review January 30, 1985 Revised manuscript received July 9, 1985 Accepted January 14, 1986
Axial Mixing and Mass Transfer in Gas-Liquid Karr Columns Nlng S. Yang,+ Blh H. Chen,' and Alan F. McMlllan Department of Chemical Engineering, Technical University of Nova Scotia, Halifax, Nova Scotia, Canada B3J 2x4
The axial mixing and mass-transfer characteristics of a Kan column when used as a cocurrent, gas-liquid contactor were experimentally determined. The liquid-phase backmixing is extremely small, and the plug flow can be safely assumed in this column over the ranges 0.6 cm/s < V , < 4.34 cm/s, 0.7 cm/s < V , < 5 cm/s, and 1.8 cm/s < AF < 7.5 cm/s. Over the same ranges, the liquid-side volumetric mass-transfer coefficient &,a was found to increase significantly with an increasing liquid velocity, gas velocity, or speed of plate reciprocation. The effect of the liquid flow rate is particularly strong because of its simultaneous, favorable influence on the liquid-side coefficient k , and the interfacial area a . Both the speed of plate reciprocation and the gas flow rate were found to have a highly adverse effect on k,. Satisfactory correlations of k,a and of k , based on the liquid velocity at the orifices of the plates are presented.
The effectiveness of the reciprocating plate column developed by Karr (1959) has been well recognized for countercurrent liquid-liquid extraction. Recent reviews by Karr (1980) and by Lo and Prochazka (1983) summarized the operating characteristics as well as design procedures of such columns. Investigations into the possibility of operating the column in cocurrent flow have also been proposed (Karr, 1984; Noh and Baird, 1984). It may be expected that the column of Karr design should also be advantageous if used as a gas-liquid contactor mainly because of the power input through the many performated reciprocating plates. In a recent study, Yang et al. (1985) investigated the hydrodynamics of this column by using an air-water system and reported an extremely large gas holdup, a nearly uniform bubble size in the range of 4-5 mm in diameter, and therefore a very large interfacial area. The result is indeed encouraging. As a part of the continuing research program to assess the feasibility of using this type of column as a gas-liquid contactor, the present study was proposed with the objective of determining the mass-transfer characteristic and axial mixing in the liquid phase.
Experimental Method Apparatus. The experimental apparatus used is shown schematically in Figure 1. The column was constructed from four sections of 5.08 cm i.d. glass tube, with an overall height of 3.96 m. The reciprocating motion was generated by means of a reciprocating shaft connected to a variable-speed electric motor. An assembly of perforated Teflon plates with an even plate spacing of 2.54 cm was attached to the shaft. Mechanisms were provided by which the frequency and the amplitude of the reciprocation could be varied.
* Author to whom correspondence should be addressed. Dalian Institute of Technology, People's Republic of China. 0196-4305/86/1125-0776$01.50/0
Air, after passing through a rotameter, was admitted at the bottom of the column through a 9.6 mm stainless steel tube which was extended about 15 cm into the column. The tube was sealed at one end, and six 1.5-mm openings were drilled around the same end to serve as the gas distributor. The air rose in the form of a bubble through a series of 84 reciprocating perforated plates and left the column freely at the top. Tap water was the other fluid used. Its flow rate was measured with a calibrated rotameter. Water temperature was not controlled but remained constant during an experimental run. Specifications of the Karr column used in this study were given in a previous study (Yang et al., 1985). Determination of Axial Dispersion Coefficient. Since a total of 84 perforated plates (a = 0.53) is present in the Karr column, it is anticipated that the axial mixing should be small and the use of the axial dispersion model would be appropriate. For continuous point injection of a tracer, this model gives the following representation of the concentration downstream of the point of injection:
The solution to eq 1 satisfying the boundary conditions a and c = 0 is
z = 0 and c = c, and z =
1 ,
C ln-=---
C,
VL
z
l-eDL
(2)
Thus, a plot of In c / c , vs. z should give a straight line (Figure 2). From its slope, - V L / ( -~ t)(DL), DL can be calculated. Methylene blue solution was continuously injected into the column at a location 170 cm from the bottom. Its flow rate was always less than 8% of the water flow. After steady conditions were achieved, liquid samples were taken at four different levels 10.8, 18.5, 26.2, and 33.9 cm below the point of injection. A Perkin-Elmer Model 983 G in@ 1986 American Chemical Society
Ind. Eng. Chem. Process Des. Dev., Vol. 25, No. 3, 1986 777
4
6
I
t
Figure 1. Flow diagram: (1) variable-speed motor, (2)reciprocating shaft, (3)perforated plates, (4)manometer, (5)water rotameter, and (6)air rotameter.
frared spectrophotometer was used for determining the dye concentrations. Determination of VoIumetric Mass-Transfer Coefficients. Several methods have been frequently used for measuring the volumetric mass-transfer coefficient in gas-liquid bubble columns. These include physical absorption or desorption of a solute and absorption accompanied by a fast chemical reaction. In general, the use of physical methods would require a knowledge of the residence-time distribution of the relevant phase. In the present study, the desorption of oxygen from water using pure nitrogen was used because of its simplicity. For such a system, a differential mass balance of O2gives
Figure 2. Axial concentration profiles: (symbol) V, (cm/s), V 0.621,0.724,and 0; ( 0 )0.621,0.724,and (cm/s), and AJ? (cm/s); (0) 7.5;( X ) 0.621,4.98,and 0.
0
This equation has been solved with the boundary conditions (Danckwerts, 1953) d(c - c*) V V -(cO - c*) = -(c - c*) - DL z=o 1 - E 1 - E dz dc _ -0 z=L dz
Thus, if the values of the dispersion number u1 and inlet and exit concentrations are known, the volumetric masstransfer coefficient kLacan be evaluated from eq 4. As for DL 0, VL co* - co KLa = -In c,* - c, (1 - E)L
-
~
-
which is the solution of plug flow. For DL 03, VL co - e, KLU = -(1 - E)L c, - co*
1
2
3
4
5
6
7
vg
8
9
10
3 cm/s, but this effect becomes negligible when AF < 3 cm/s (Figure 6). The existence of such a critical speed appears to be one of the characteristics of reciprocating plate columns (Tojo, 1974a). Effect of Liquid Flow. In addition to being a factor determining the mass-transfer behavior of a Karr column, the liquid flow rate has also a strong effect on the magnitude of kLa as Figure 7 indicates. In conventional gas-liquid bubble columns, the volumetric mass-transfer coefficient has been found to be rather insensitive to the change of the liquid flow rate, but in gas-liquid bubble columns containing reciprocating plates or packing, the liquid flow rate becomes a factor of considerable importance, particularly at high flow rates. Voyer and Miller (1968) and Chen and Vallabh (1970) studied mass transfer in a screen-packed bubble column over the range 0.5 cm/s 5 V, 5 3 cm/s and found that KLu = VL*where n varies between 0.6 and 0.87 depending upon the type of packing used. Wang and Fan (1978) also reported a similar relation for the packed bed of static mixers, with n falling between 0.46 and 0.63. Tojo et al. (1974b) observed the same behavior in a multistage vibrating-disk column. The reason for this common observation is believed to be that the liquid, while flowing through the column with solid internals, is generating turbulence, the intensity of which would obviously depend on the geometry of the solid internals and the flow velocity. In addition, it is conceivable that the turbulent shear in some cases could be strong enough as to reduce the bubble size, thereby increasing the interfacial area. Therefore, for such cases, the effect of liquid flow rate on kLa should be particularly strong (see eq 8). Correlation of kLa. As the liquid flow is such an important parameter, its characterization for the purpose of data correlation becomes crucial. Consistent with the idea that a gas-liquid Karr column may be considered as a packed column, the true velocity of the liquid phase V,, which is equal to VL/(l - €)(a) for the present case, becomes the most appropriate one to use. Furthermore, the use of V, would take into consideration some of the influence that both the gas flow rate and the speed of reciprocation of plates have on kLa and therefore would reduce the importance of these two factors in correlating kLa data. Using the linear regression techniques, the present 52 data points were found to be well represented by the empirical equation IzLa = 0.00359V,0.164V~~738(AF)0.143 (7) over the ranges 0.724 cm/s IV, I4.98 cm/s, 0.931 cm/s 5 VL I4.34 cm/s, and 1.8 cm/s 5 (AF) I7.5 cm/s. The s-l. stand deviation is 3.94 x It is noted that when the superficial liquid velocity V, was used, no satisfactory correlation of all data points was obtained, but for data obtained when the liquid flow rate
VL was greater than 2 cm/s, the following correlation was possible kLa = 0.00401 Vg0,42VLo.918(AF)0,'8
(8)
with standard deviation of 0.000475 s-l. Equation 8 is comparable to those reported in earlier studies using similar equipment (Tojo et al., 1974a,b) except that the exponent on VL is much greater. As pointed out previously, the enhanced effect of VL may be a result from the breakup of bubbles occurring when these bubbles are rushed through the orifices of the plates by the flowing liquid at moderately high speeds. Correlation of the Liquid-Side Mass-Transfer Coefficient, kL. In a previous study, Yang et al. (1985) reported that the interfacial area in a gas-liquid Karr column can be represented to within *20% by a = 0 333v 0 . 9 1 ~0 . 1 3 3 ( ~ ~ ) 0 . 5 9 3 '
,
L
(9)
However, this representation can be considerably improved if VL is replaced by the true velocity V,. The refined correlation is of the form (Figure 8) a = 0.301V,0.897Veo,125(AF)0,592
(10)
having a standard derivation of 0.0568 cm-'. Dividing eq 7 by eq 10 yields
kL = 0.0119
V2605(AF)-0.45
(11)
The strong, positive effect of the liquid flow rate is of course expected, and it has also been frequently observed in earlier studies of gas-liquid contact in packed or plate bubble columns with or without reciprocation. The reason as pointed out before is attributed to the turbulence-generating capability of the liquid when it is accelerated or decelerated at or around the orifices of the plates. However, the strong, negative effect indicated by both the gas flow rate and the speed of reciprocation is indeed surprising. Although the decrease of the liquid-side coefficient kL with increasing gas flow or speed of reciprocation is obvious in studies with low liquid flows through staged bubble columns (Miyanami et al., 1978) the reason is unclear. For the present study, it might be rasonably speculated that the large adverse effect due to V, and (AF) should be closely related to their large, favorable influence on gas holdup. The rapid increase in gas holdup combined with the use of baffle plates has considerably depressed the bubble rise velocity (approximately from 30 cm/s in bubble columns to 14 cm/s in the present column), but in the meantime, it has promoted the liquid flow velocity; for example, the velocity has increased from initially 4.35 to 7.25 cm/s for 0 cm/s -< V,.I 4.98 cm/s and AF = 6 cm/s, because of the increase in gas holdup. Therefore, a significant reduction of the slip velocity between the two phases has occurred, and this should lead to the lowering of kL as observed. Attempts have been initiated to look carefully into the interaction between the moving plates, system hydrodynamics, and gas flow, in particular the turbulence of the system which is believed to be the basic factor affecting the performance of this column.
Summary and Conclusion This study has shown the following main mass-transfer characteristics of a cocurrent flow Karr column when used as a gas-liquid contactor:
780
Ind. Eng. Chem. process
1. The liquid-phase axial mixing is very low, and the plug flow can be safely assumed for all cases studied. 2. The volumetric mass-transfer coefficient is of the same order of magnitude as in a conventional stirred vessel for corresponding bubble sizes. 3. The volumetric mass-transfer coefficient kLa is favorably affected by the three velocities studied: Vg,VL, and (AF). 4. The liquid-phase flow significantly enhances the mass transfer by simultaneously increasing the mass-transfer coefficient, kL,and the interfacial area, a. This may imply that a gas-liquid Karr column is best suited for continuous operations with high throughputs. 5. Both the energy input and the gas flow rate greatly increase the interfacial area but have an adverse effect on the mass-transfer coefficient, k L , presumably due to the decreased activity a t the gas-liquid interface as a result of the reduced slip velocity.
Acknowledgment We thank the Natural Sciences and Engineering Research Council of Canada for financial support. Nomenclature AF = reciprocating speed, cm/s a = interfacial area, cm
Des. mv. iga8, 25. 780-786 kL
= liquid-side mass-transfer coefficient, cm/s
kLa = volumetric mass-transfer coefficient, L/s
L = liquid height in column, cm V , = effective liquid velocity, cm/s V, = superficial gas velocity, cm/s t = distance, cm Greek Symbols c =
gas holdup
u = fractional open area of plate
Subscript e = exit stream value 0 = reference value Literature Cited Chen, B. H.; Vailabh, R. Ind. f n g . Chem. Process D e s . Dev. 1970, 9 , 121. Danchwerts, P. V. Chem. fng. Sci. 1953, 2 , 1. Karr, A. E. AIChE J . 1919, 5 . 446. Karr, A. E. Sep. Sci. Techno/. 1980. 15, 877. Karr, A. E. AIChE J . 1984, 30,697. Kim, S.D.; Baird, M. H. 1. Can. J . Chem. Eng. 1978, 5 4 , 81. Lo, T. C.; Prochazka. J. "Handbook of Solvent Extraction"; Lo, T. C., Baird, M. H. I . , Hanson, C., Eds.; Wiley-Interscience: New York, 1983. Noh, S.H.; Baird, M. H. I.AIChf J . 1984, 30,120. Miyanami, K.: To@, K.; Yano, T. J . Chem. f n g . Jpn. 1973, 6 , 518. Miyanami. K.; Tojo, K.; Yano, T. Chem. fng. Sci. 1978, 33,601. Tojo, K.; Miyanami, K.; Yano, T. J . Chem. f n g . Jpn. 1974a, 7 , 123; 1974b, 7, 127. Voyer, R. D.; Miller, A. I. Can. J . Chem. f n g . 1988, 46, 339. Wang, K. B.; Fan, L. T. Chem. Eng. Scl. 1978, 33,945. Yang, N. S.;Chen, 8. H.; McMilian. A. F.; Shen. 2. Q. Ind. Eng. Chem. Process D e s . Dev., in press.
c = concentration, mol/L c* = concentration at the interface, mol/L DL = axial dispersion coefficient, cm2/s
Received for review April 29, 1985 Revised manuscript received November 11, 1985 Accepted January 21, 1986
Pyrolysis of Hydrocarbons in a Large Pilot-Scale Reactor. 1. Experimental Design Lester S. Kershenbaum" and Patrick W. Leaneyt Depafiment of Chemical Engineerhg and Chemical Technolw, Imperlel College, London S W7, England
An experimental technique is presented which eliminates many of the uncertainties associated with the determination of the kinetics of fast, complex reactions (such as the pyrolysis of light hydrocarbons) by minimizing the effects in the experknental system. Constructionof a welunstrumented of heat transfer, mass transfer, and large-scale reactor enabled measurements to be made within the reactor by the use of probes which could travel continuously through the reactor space, both radially and axially, measuring point compositions and temperatures. A detailed design and analysis of the probes ensured small but quantifiable errors for the measurements and for the disturbance to the flow pattern. The experimental measurements yielded a complete set of data (conversion and product distribution vs. residence time) from a single run in an experimentally verified isothermal zone and for a well-characterized set of operating conditions.
The pyrolysis of light hydrocarbons has been studied extensively over the past 50 years with varying objectives. Early work sought to determine product distributions over a range of operating conditions (Frey and Smith, 1928; Schneider and Frolich, 1931; Schutt, 1947) or overall kinetic expressions which could predict the gross behavior of these complex reaction systems (Laidler et al., 1962; Martin et al., 1964; Kershenbaum and Martin, 1964). Despite a significant amount of experimental work, discrepancies between the various workers was widespread, t Current address: Chevron
Research Co., Richmond, CA. 0 7 96-4305f86f 1 125-078080 1.5010
both in terms of product distribution and apparent activation energies for the overall reactions. Recent work has attempted to correlate the conflicting experimental data through complex kinetic models which more closely reflect the chemical steps involved in these reactions (Powers and Corcoran, 1974; Allara and Edelson, 1975; Sundaram and Froment, 1978 Edelson and Allara, 1980, Purnell, 1980). In taking this approach, workers have either assumed a steady-state concentration for the radical species or, alternatively, solved the stiff set of differential equations for the concentrations of all species, a much more difficult computational chore. Some workers have chosen to use in their models, the rates of the various 0 1986 American Chemical Society
