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Ind. Eng. Chem. Process Des. Dev., Vol. 17, No. 4, 1978
Greek Letters
though the bed is much larger (31 tons vs. 7 tons). This all comes from the severe bypassing of reactant in the large bubbles. Reducing the size of bubbles will greatly improve the performance of the fluidized reactor.
a = wake volume/bubble volume yi = volume of solids in region i/volume of bubbles 6 = volume of bubbles/volume of bed emf = void fraction of bed at minimum fluidizing conditions K = effective reaction rate constant in the fluidized bed,m3/kgs ps = density of solids, kg/m3 7 = W/uo = weight-time, the capacity measure for catalytic
Nomenclature A, R, S, T, U = reaction components C = concentration, moi/m3 d b = effective or mean bubble diameter, m D = diffusion coefficient for reacting gases, m2/s e = efficiency of contacting in the fluidized bed for a particular reaction k = rate constant for a catalytic reaction, m3/kg.s Kbc = gas interchange coefficient between bubble and cloud,
flow reactors, kgs/m3
Superscript A, R = refers to components A, R
b = bubble phase c = cloud phase e = emulsion phase mf = at minimum fluidizing conditions Literature Cited
S-1
K , = gas interchange coefficient between cloud and emulsion,
Carberry, J. J., "Catalytic and Chemical Reaction Engineering", McGraw-Hill, New York, N.Y., 1976. Denbigh, K. G., Chem. Eng. Sci., 8, 125 (1958). Kunii, D., "Notes on Fluidized Reactor Design." A short course given at Monash University, Clayton, Victoria, Australia, 1975. Kunii, D., Levenspiel, O., Ind. Eng. Chem. Fundarn., 7, 446 (1968). Kunii, D., Levenspiel, O., Ind. Eng. Chem. Process Des. Dev., 7, 481 (1968). Kunii, D., Levenspiel, O., "Fluidization Engineering", Wiley, New York, N.Y., 1969.
S-1
-rA = rate of catalytic reaction, mol/kg.s ub = rise velocity of bubbles in a fluidized bed, m/s Ubr = rise velocity of a single bubble in a bed which is otherwise
bubble-free, m/s umf = minimum fluidizing velocity, m/s uo = superficial entering gas velocity, m/s uo = volumetric flow rate of entering gas, m3/s W = weight of catalyst in the bed, kg
Received for reuiew October 14, 1977 Accepted April 11, 1978
Multiple Hydrodynamic States in Cocurrent Two-Phase Downflow through Packed Beds Kin-Mun Kan and Paul F. Greenfield* Department of Chemical Engineering, University of Queensland, St. Lucia, Australia, 4067
Evidence for the existence of multiple hydrodynamic states in trickle bed reactors with small particles is produced. These states are characterized by significantly different pressure gradients and different liquid holdups for identical gas and liquid flowrates. The determining factor is the maximum gas flowrate to which the packed bed has been subjected.
often used in model trickle bed reactor systems. The small packings, together with the very high gas flowrates generally used, cause an early onset of flooding unless the fluids flow cocurrently. In this work, evidence is provided for the existence of a multiplicity of hydrodynamic states, the attainment of each being dependent on the past history of operating conditions of the packed bed. These states were characterized by different pressure drops which were measured. The existence of various hydrodynamic states has important implications in the design and operation of trickle bed reactors. Current design procedures are invariably based on liquid holdup in the reactor which determines the residence time of the reactants in the liquid phase. Since the holdup varies as a function of the particular hydrodynamic state, so must the performance of the reactor. Additionally, since the pressure drop in one hydrodynamic state can differ from that of another by as much as 5073, the operating costs must also be affected. Finally, the existence of these states implies that scale-up from small reactors presents problems and may help
Introduction There is presently considerable interest in trickle bed reactors particularly with regard to their application to the hydrodesulfurization of crude oil. They are also being considered for biochemical systems where enzymes, immobilized on the pores and surfaces of packings, are employed to catalyze reactions between the gas and liquid phases. Satterfield (1975) has provided an excellent review of the current state of the art in the design of trickle reactors while Charpentier (1976) and Hoffman (1977) have specifically discussed the hydrodynamics found in such reactors. Studies on pressure drop and holdup and their relationship have been carried out by Larkins et al. (1961), Weekman and Myers (19641, Turpin and Huntington (1967), Charpentier and Favier (1975) and Specchia and Baldi (1977). Little attention, however, has so far been given to beds of small packings (less than 3 mm diameter) which, though of little industrial importance a t present, are essential for biochemical systems where very high Thiele moduli are encountered because of the high enzyme activity and diffusional resistances. Additionally, they are 0019-7882/78/1117-0482$01.00/0
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Ind. Eng. Chem. Process Des. Dev., Vol. 17, No. 4, 1978
explain the variability in results of numerous investigators. Experimental Section Determination of pressure drop data was carried out on a 25-mm i.d. acrylic column packed with glass spheres to heights ranging from 45 to 80 cm (depending on the pressure gradient since the maximum inlet pressure was limited by the available equipment). The liquid (water) and gas (air) flow rate ranges were 1.0 to 10 kg/m2 s and 0.02 to 1.0 kg/m2 s, respectively (0.3 5 Rec I 100; 0.6 I ReL I21). Glass spheres of 0.5,1.0, and 1.8 mm diameters were used. Generally, the experiments were carried out in the trickle flow regime in which the gas phase is continuous and the liquid phase is in laminar flow. The transition and pulsing regimes were reached only at the highest liquid flowrate (10 kg/m2 s) and moderate to high gas flowrates depending on the packing diameter. Initially the packed column was flooded by introducing a very high liquid flowrate to ensure complete wetting of the packing. The liquid flowrate was then reduced to the desired level before the gas flow was commenced. Pressure readings were taken on a mercury manometer for each set of liquid and gas flowrates with the gas flowrate increasing in magnitude until a pre-determined maximum was reached. Sufficient time was allowed for equilibrium before the readings were taken. On reaching the maximum gas flowrate, the gas flow was then reduced to a low (nonzero) level and gradually increased again. This was repeated for various maximum gas flowrates, for various liquid flowrates, and for the different packing sizes. The pressure drop readings were found to be reproducible to within 10% and that of holdup to within 5 % . However, in view of the dependence of these measurements on past history of flow conditions in the bed, extreme care had to be taken to ensure that the bed was completely flooded before the commencement of gas flow. For holdup measurements, the gas and liquid flows were terminated simultaneously by shutting off the respective toggle valves quickly and the column was allowed to drain into a collector. The collector and the column containing the packings were then weighed. By deducting the original weights (dry column, empty container) the quantity of water in the column a t the time the valves were shut off was determined. Results Figure 1shows plots of typical pressure gradients vs. gas flowrates, for each of the packing sizes and for a range of liquid flowrates. Figure 2 is an expanded plot of one set of conditions to show the effect in more detail. In Figure 2, path 0 is followed when the gas flowrate is increased initially from zero with a pre-wetted bed. At any point on path 0 the gas flowrate is the maximum so far experienced by the bed. When the gas flowrate is reduced after reaching a maximum (Gmm,J another path (path 1)is followed where the pressure drop is less than that in path 0. When the gas flowrate is increased or decreased from a point in path 1, it adheres to the same path provided Gmax,lis not exceeded. If the gas flowrate is increased beyond Gmax,lto G m 9 2say, the path followed is an extension of path 0. For all subsequent variations of gas flowrate less than Gmax,2 a new path (path 2) is followed which runs more or less parallel to path 1. It therefore appears that a multiplicity of steady states is possible for beds of small packings. The stability of the various hydrodynamic states was shown by the fact that the pressure drop at any point in the various paths can be retained indefinitely. Runs were left for as long as 24 h
483
1
0 Srnrn
10''
'
'
, ' ' ' . . I
0.1
'
' ' , , . . . I
GAS PHASE MASS VELOCITY
10
(Wrn*/s)
01 10 GAS PHASE MASS VELOCITY (kg/rn2/sl
Figure 1. Dependence of pressure gradient on gas phase mass velocity packing sizes and liquid mass velocities for various values of G,, (---, path followed when G, = 0; -, path followed when G, # 0; A, L = 10 kg m-2 s-l; 0 , L = 6.3 kg m-2 s?; 0,L = 3.0 kg m-2 s-l; W, L = 1.0 kg m-2 s-l).
I
I Gmox.1 Grnqx.2 01 10 GAS PHASE MASS VELOCITY (kgirn45)
Figure 2. Dependence of pressure gradient on G,, and presence of wetting agent: d, = 1 mm, L = 1.0 kg m-2 s-l ( 0 ,G = G,, no with Teric 160; 0,path 1, G, = 0.63 wetting agent; A, G = G,, kg m-2 s-l; path 2, G,, = 1.05 kg m-2 s-l; A, G,, = 0.63 kg m-* s d with Teric 160).
without any appreciable change in pressure drop being observed. Effect of Liquid Flowrates and Packing Size on Pressure Drop. The pressure drop-gas mass velocity plots on a log-log scale give a straight line for the low liquid
484
Ind. Eng. Chem. Process Des. Dev., Vol. 17, No. 4, 1978 0 20 1
1 mm diameter pocking Liquid Wose moss v e b c i w = 1
0.01
0 !q/m2/5
I
1
01 GAS PHASE MASS VELOCITY 1kg/m2/s)
10
Figure 4. Dependence of total liquid holdup on. ,G ,
~
10
~~
1167
R'c ~~0167
100
i
L
Figure 3. Comparison of data with those of Turpin and Huntington , A, d, = 1 mm, G,, = 0.77 kg m-2 (1967): A, d, = 1 mm, G =; , G s-l; e, d, = 1.8 mm, G =; , G , 0,d, = 1.8 mm,, G , = 1.83 kg m-2 s-l; - - -, Turpin and Huntington correlation.
flowrates with the 1mm and 1.8 mm packings, while those for the smallest packing show curvature at all flowrates. In all cases, however, the paths followed when the gas flowrate is reduced from a nonzero maximum run approximately parallel to each. The effect is not observed for high liquid flowrates when the pulsing regime is reached. If the data are plotted in the manner of Turpin and Huntington (1967) (Figure 3), it can be seen that the friction factors are in general larger for the smaller packings than for those used by Turpin and Huntington. Additionally, it is evident that the friction factors are significantly higher for a preflooded bed (solid points) than for one where G is less than ,G (hollow points). Effect of Wetting Agents. Some runs were carried out with Teric 160, an IC1 wetting agent, added to the liquid phase. At a concentration of 0.002 % the surface tension a t 20 "C was reduced to 38 dyn/cm from 70 dyn/cm. Little change in the characteristics of the multiple hydrodynamic states was observed although the pressure drops of all paths were increased slightly (Figure 2). Attempts to obtain a lower surface tension by using higher concentrations of Teric 160 failed because of the onset of foaming, which resulted in a many-fold increase in pressure drop. Holdups in the Various Hydrodynamic States. Figure 4 shows the effect of the history of operating conditions on the total holdup expressed as the volume of liquid phase per unit volume of empty column. If the column had been operated a t a higher gas flowrate, the liquid holdup (h,) was greater than the holdup (htJ obtained otherwise. The higher the maximum gas flowrate experienced, the greater was the increase in holdup. In the same manner as for the pressure drops, the effect on liquid holdup appears to be greater for higher values of ,G and for smaller packing diameters and is not observed a t all at high liquid flowrates when the pulsing regime is reached. The effects of packing size, liquid flowrate, and ,G are illustrated in Figure 5. The effect is measured in terms of the ratio ht/ht,. Discussion For small packings, the distance between packing surfaces in the packed bed is small and surface tension
. . . .
I
I
0.1
1
.o
mox
1.0 0.1
1.0
GIGm o x
Figure 5. Effect ,of, G packing size, and liquid flowrate on liquid holdup: top-effect of G,, L = 1kg m-2 s-l, d = 1 mm; 0,G, = 1.05 kg m-2 s-l; 0, G,, = 0.52 kg m-2 s d ; A, &= , = 0.22 kg m-* center-effect of packing size, L = 1kg m-2 s-l,, G , = 1 kg m-2 s-l; e, d = 1.8 mm; U, d, = 1 mm; A, d, = 0.5 mm; bottom-effect , = 1 kg m-2 s-l, d, = 1 mm; 0,L = 3 kg m-2 of liquiiflowrate,, G s-l; 0,L = 1 kg m-2 s-l.
plays an important role in determining the microstructure of the liquid phase. Whereas in beds of larger packings the liquid phase trickles down the bed in drops and films, the flow in beds of small packings is more likely to be in the form of channels in which the liquid phase completely bridges the space between the packing surfaces. Under such circumstances, the tortuosity of the gas flowpath can vary quite substantially depending on the orientation of the liquid bridges. If the gas phase is considered to flow in a number of tortuous paths in which the true average velocity is u, then the superficial gas velocity G is given by
The overall pressure drop A p l Z is related to the pressure gradient 6 in the flow path by
-AP_
z - 76
Ind. Eng. Chem. Process Des. Dev., Val. 17, No. 4, 1978
If the gas phase is laminar, then 6 is proportional to u / a 2 where
(3)
485
than in terms of liquid holdup. This explains why the effect on holdup was not observed with respect to 1.8-mm packings even though it was significant in terms of pressure drop. Conclusions
By assuming ideal gas behavior, it follows that for given G (C - hJ2P(Ap/Z)'i3 7 = (4) N This is consistent with experimental observations and may be explained as follows. For a pre-wetted bed in which the gas flowrate is being increased from zero, the initial orientations of the liquid bridges are quite random. As gas flowrate is increased, bridges in directions transverse to the general flow of the gas tend to be broken down leaving those intact which are in the flow direction. The density of flowpaths N is increased and the length of the gas flowpaths, that is the tortuosity, is reduced. In view of the high surface tension effect in beds of small packings, this flow pattern is stable and the lower tortuosity and higher N are retained even when the gas flowrate is reduced. For a given G, A p l Z and P are observed to be lower which is consistent with (4). However, when the liquid flowrate is high and turbulence generates random changes in liquid and gas flowpaths any ordered pattern of liquid bridges is unstable, and the effect is no longer observed. Similarly, in beds of large packings, the surface tension effect is low and no large variation in tortuosity is possible. If surface tension were to play a major role in stabilizing various hydrodynamic states, then the addition of wetting agents should have the same effect as increasing packing sizes. That this was in fact not observed does not necessarily mean that the explanation provided above is invalid. It is possible that the decrease in surface tension induced by the surface active agent was not sufficient to cause a change in stability which is observable experimentally. It is also possible that the addition of wetting agent altered the flow regime so that film flow was more predominant rather than channel flow. This would certainly explain the observed increase in pressure drop. From eq 1to 4, it may be shown that the overall pressure drop Ap/Z is inversely proportional to ( t - hJ2.Thus, the effect is more easily observable in terms of pressure drop
For two-phase cocurrent flow in beds of small packings, a multiplicity of steady states is possible. Pressure drop is a function not only of the flowrate, properties of the phases and packing size, but also of the maximum gas flowrate experienced by the bed. Nomenclature
a = characteristic diameter of gas flow path, m G = gas mass velocity, kg m-2 s-l G,, = maximum gas mass velocity experienced by column,
kg m-2 s-l h, = total liquid holdup for G < G,, h,, = total liquid holdup for G = G,, (Le., path 0) L = liquid mass velocity, kg m-2 s-l N = number of flow paths per unit cross sectional area of packed bed P = absolute pressure, Pa ( A p / Z ) = pressure gradient in column, Pa m-l ReG = gas-phase Reynolds number based on packing diameter ReL = liquid-phase Reynolds number based on packing diameter u = real average gas velocity, m s-l Z = reactor length dimension, m Greek Letters 6 = pressure drop along flow path, Pa m-l t
= column voidage
p = 7
gas density, kg m-3
= tortuosity factor
Subscript 0 = refers to path 0 Literature Cited Charpentier, J. C., Chem. Eng. J . , 11, 161 (1976). Charpentier, J. C., Favier, M., AIChE J., 21, 1213 (1975). Hoffman, H., Int. Chem. Eng., 17, 19 (1977). Larkins, R. P., White, R . R., Jeffrey, D. W., AIChE J . , 7, 231 (1961). Satterfied, C. N., AIChE J . , 21, 209 (1975). Specchia, V., Baldi, G., Chem. Eng. Sci., 32, 515 (1977). Turpin, J. L., Huntington, R. L., AIChEJ., 13, 1196 (1967). Weekman, V. W., Myers, J. E., AIChE J., 10, 951 (1964).
Received for review October 17, 1977 Accepted June 8, 1978
Degeneracy of Decoupling in Distillation Columns Azmi Jafarey and Thomas J. McAvoy' Department of Chemical Engineering, University of Massachusetts, Amherst, Massachusetts 0 1003
An interacting control system may be internally decoupled through the use of noninteracting manipulative variables. Application of this concept to dual composition control of a binary column (9= 1) leads to the unexpected result that the conditions for half-decoupling of either loop are effectively the same. This degeneracy very closely approximates the column material balance and makes lt impossible to completely decouple the system. The findings appear to be of general validity and afford insight into the success of the Shinskey material balance control scheme.
In recent years, an increasing significance has been attached to the steady-state control of industrial processes (Ellingsen, 1976; Lee and Weekman, 1976). Several tools are now available which aid in determining steady-state 0019-7882/78/ 1117-0485$01 .OO/O
control strategies for multivariable systems. These concepts have found a natural application in the design and implementation of control algorithms for distillation. The most successful of the syntheses has been the material @ 1978 American Chemical Society
