I
HENRYK SAWISTOWSKI and WILLIAM SMITH Department of Chemical Engineering, Imperial College, London S.W. 7
Performance of Packed Distillation Columns Conventional methods for expressing performance of packed columns are unreliable
E A R L I E R THEORIES about the mechanism of distillation have limitations and several new mechanisms have been proposed. The work reported here was undertaken to examine the validity of these mechanisms.
Equipment
At first (23) a conventional packed column was used, consisting of a 2-liter flask, a glass rectifying column, 56 inches long and 1 inch in diameter, and a vertical helical coil condenser. The column, lagged with asbestos rope and equipped with a heater to maintain adiabatic conditions, was designed for use under vacuum. It was fitted with two intermediate sampling points for liquid, and three sizes of glass Fenske helices (4, 7, and 10 mm. in outside diameter) ; 1/*-inch glass Raschig rings were used as packings. I n this conventional column, however, the liquid pulsated as it flowed down a packing. I t accumulated in corners formed by the random arrangement of the packing and, when its weight was sufficient to overcome the surface tension forces holding it in position, it ran in a fine stream to another point of accumulation. The process was repeated down the length of the column, the size of the pulses and their occurrence being irregular. T o reproduce this kind of flow in a known and regular way, a second column was constructed (20) and fitted with drop-forming devices (Figure 1). Because it was easier to construct square blocks and to fit observation windows on a flat surface, a column of square cross section was chosen. The blocks were positioned in the column by passing brass rods through holes drilled in the corners of the blocks, spacers on the rods fixing their distance apart. Two spacings were used-Z1/2 and 5 incheswhich will be referred to as close and wide spacing, respectively. The column proper was a square brass tube, 3 feet long and l a / * inches inside dimension, fitted with flanges a t both ends to which glass-to-metal cone adap-
tors were attached. Two smaller glassto-metal cone adaptors served for the introduction of reflux and for sampling purposes. The column was provided with a heating wire, wound a t a variable pitch (the pitch increasing towards the top), to approximate adiabatic conditions. Vapors from the top of the column entered the condenser, the condensate being returned to the column through a flowmeter and a U-tube, the downstream limb of which was fitted with a heater to bring the condensate to its boiling point. The bottom end of the U-tube was provided with a tap for sampling. The connecting piece be-
tween the column top and the condenser was wound with a resistance wire of a heating capacity sufficient to superheat the vapors and thus prevent condensation and rectification. The bottoms from the column were returned to the still through a flowmeter. Asbestos cloth, asbestos rope, and cellular asbestos shapes were used as lagging. The column was operated in four different arrangements. First, either 6 (wide spacing) or 12 (close spacing) Sindanyo blocks were used so that liquid drops formed and fell through the vapor space at regular intervals (stage A). Subsequently, nine glass tubes ( l / 8 inch in outside diameter) were fitted into each
r
A Figure 1. The column was fitted with drop-forming devices made from Sindanyo asbestos blocks
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space between the blocks which were arranged in close spacing. Each tube was inclined at about 25" to the vertical with its top end fixed directly under one of the liquid downcomers, so that drop formation was followed by liquid flow down the tube (stage B). In stage C the space between the blocks was filled with single-turn Fenske helices 1 cm. in outside diameter, with the blocks acting as redistributors. The same packing, without the blocks, was used in stage D. All experiments were performed at total reflux and at three different boilup rates of 10, 20, and 38 cc. per minute. The binary mixtures distilled were carbon tetrachloride-toluene, cyclohexane-toluene and n-heptane-toluene. Equilibrium data of the first two systems were taken from Kirschbaum (70), and for the system heptane-toluene from Bromiley and Quiggle (7). Results and Discussion
The theory that transfer rate of a component between the phases is governed by a concentration gradient is normally applied to all mass transfer processes including distillation (5, 9, 72, 73, 24). I n some theories, however, it is assumed that mass transfer rate is determined by temperature differences between phases (70, 77).
Concentration difference as a driving force. The theories based on concentration gradients lead to a simple concentration difference as the driving force. The point value for performance of a packed column, E,,, based on overall differences of vapor composition is thus
First, the experimental results were expressed in terms of E O G (Figure 2). The concentration is taken as the arithmetic average of the compositions measured at the top and bottom of the column in mole fractions. The figure
shows that performance of the column, as defined by Equation 1, depends on the mean concentration of the mixture. Some variation is expected, because the use of over-all rather than film-driving forces in evaluating the performance makes KO, (therefore HOGand Eoc) a function of concentration. The relationship between HOG and the film coefhients of mass transfer is G
Hoe = HG f m - H L . L
(2)
I t follows from Equation 2 that H O G is not a satisfactory measure of performance, because it is not independent of vapor-liquid equilibrium relations and will not be constant throughout the length of packing if m varies. The film coefficients are, however, based on film concentration differences, and should be independent of composition, except in so far as the physical properties of the mixture depend on composition. Therefore, when HOGis plotted us. m at total reflux ( G / L = l ) , a straight line should be obtained, the slope of which should equal HL and the intercept on the ordinate axis Ho, Representative results, measured a t total reflux, are plotted in Figures 3A and 3B as H O G against m. There are two ways of choosing the slope of the equilibrium line, m G G or mGL, (79) depending on which film is considered to have the major resistance. Both are used in Figure 3A. The point of zero slope corresponds to a maximum in the value of performance. This maximum in performance is clearly defined in all mixtures studied and its position varies between x = 0.35 and x L= 0.75, depending on the system. For the systems carbon tetrachloride-toluene and heptane-toluene, tangents to the curves at high values of m give negative intercepts on the HOGaxis. Negative slopes a t low values of m are found for all three mixtures. Since the graph of HOG us. m is not a straight line, it appears that HG and H L are not constant, and are there-
fore, indirectly, functions of m. In this case the slope and the intercept of the curve no longer represent the values of heights for the individual transfer units. This may also be seen from the fact that negative slopes and intercepts occur, implying negative coefficients of mass transfer which is meaningless. That the value of film transfer units of a binary mixture varies with concentration has usually been ascribed to change in physical properties of the mixture with concentration. The film coefficients of mass transfer have been expressed in terms of dimensionless groups containing physical properties of the mixture and flow rates of the phasrs; parameters occurring in these equations have been determined experimentally by using wetted-wall columns. By inserting known physical properties of the systems into the: most generally accepted of these correlations for the film units, the theoretical change in their value can be calculated. For this purpose the equation suggested by Pratt (77) was adopted for the vapor phase mass transfer coefficient, KG, and the expression proposed by Chari and Storrow ( 3 ) for the liquid-phase mass transfer coefficient, KL. For a particular arrangement of packing and at a given flow rate, with concentration as the only variable, K~
oI ~ ~ 0 . 6yG-0.42 7
KL
DL0.4SyL-D.16
Brass column. 0 cyclohexane toluene; boil-up, 1 O-grammoles per hour; stage A; wide spacing; A CCIetoluene; bcilup, 10 gram-moles per hour; stage A; wide spacing; nheptane-toluene; boilup, 17 gram-moles per hour; stage B
(4)
The total variation in K L over the whole concentration range was calculated to be about 2570, varying linearly with composition for the systems, cyclohexane-toluene and carbon tetrachloride-toluene. For cyclohexane-toluene it can be represented by K L = A(1.98
Figure 2. Performance depends o n m e a n concentration of mixture
(3)
Using this expression, it was calculated that KG should not vary by more than 5y0over the whole concentration range. For practical purposes KG can thus be assumed constant. Under the same conditions
-
0.54~)
(5)
On substitution of Equations 3, 4, and 5 into the mass balance equation for a differential section of the column, and subsequent separation of variables and integration
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INDUSTRIAL AND ENGINEERING CHEMISTRY
It has been assumed during this integration that a is independent of composition, but this is probably not true in a conventional packed column. However, for the data obtained from the brass column, a can be estimated by observing the frequency of drop formation; it varied by only 2.5y0 over the whole
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/'4
? /2
P
t
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IO
t
sa 06 06 04 02
0
02
O+
06
08
10
12
I*
lZnSS
Figure 3, A and 8. Variation in height of transfer unit with slope of equilibrium line. There are two ways of choosing slope of the equilibrium line, depending on which film is considered to have the major resistance A.
Brass column; Hou vs. maL; cyclohexanetoluene; boil-up rate, 10 gram-moles per hour; stage A; wide spacing HOG vs. mQu; carbon tetrachloride-toluene; boil-up rate, 10 gram-moles per hour; stage A i wide spacing
concentration range. For results obtained from this column (stage A) the assumption is, therefore, justified. The value of the integral in Equation 6 was calculated for a series of results and is plotted in Figure 4 for various values of A/KQ. The value A/KG = 0-Le. KQ = a-refers to the case where only a liquid phase resistance is present; A / K Q = m 4 . e . K L = m- gives a vapor-phase controlled process, and other values of A / K u refer to different ratios of liquid to vapor resistance. According to Equation 6, the value plotted should be independent of concentration. But Figure 4 shows that this is not the case; therefore, it must be concluded that variation in physical properties does not explain satisfactorily the experimental results. This was also the case for the other two binary mixtures. The preceding analysis was based on semiempirical expressions derived by assuming that the two-film theory of Whitman is valid. As far as the other theories of mass transfer are concerned, their film coefficients can be expressed in terms of the same physical properties as were found relevant to the Whitman theory. For example, Kishinevski (72, 73) assumes that the rate of mass transfer is controlled by the degree of turbulence, which extends right up to the interface. I t is, therefore, reasonable to assume that in this case the mass transfer coefficients in the two phases are proportional to some power of the Reynolds number-i.e., to some power of the kinematic viscosity. For the system, carbon tetrachloride-toluene, the kinematic viscosity in the liquid phase is constant, and therefore KL for this system should be constant. However, kinematic viscosity
6.
Glass column packed with '/pinch glass Raschig rings; boil-up rate, 5 to 11 grammoles per hour; n-heptane-toluene
of the vapor decreases almost linearly with mole fraction by about 20%. It follows that Koa should increase with concentration; but it can be shown as before, that this does not result in the performance of the column passing through a maximum. A similar analysis can be made of the theories of Higbie ( 9 ) and Danckwerts ( 5 ) with the same result. Experiments were performed with four different flow conditions in the column: liquid drops forming and falling through the vapor space, forming and flowing down glass rods, and with liquid flowing down a conventional packed column with and without redistributors. In the first two cases, conditions were favorable to regular surface renewal, whereas in the last two cases, random renewal was more probable. Despite the differences in flow pattern, the general trend of the change of performance remained the same as in Figure 2. A change in 6
Figure 4. Variation of aAZ/G with composition. Variation in physical properties does not explain the experimental results satisfactorily
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the efficiency with concentration has also been noted for plate columns (2, 6, 70, 74, 27, 25) and a maximum in the performance has been found for distillation in a wetted-wall column (78). But the way in which the phases flow in a plate column or in a wetted-wall column is quite different from the way in which they flow in a packed column. I t appears, therefore, that many different kinds of equipment with different kinds of flow pattern all produce a similar variation of performance with concentration; it is not likely that variation in performance can be mainly attributed to a difference in the character of the liquid flow. I n connection with equilibrium properties, all theories considered here are concerned only with the mechanism of transfer in the phases. I t is generally assumed that a t the interface, the phases are in equilibrium; thus, there may be a resistance to transfer a t the interface, the presence of which would modify Equation 2 (79). Under certain conditions, interface resistance occurs in liquid-liquid systems (75, 22), but there is no evidence of its existence in other systems. O n the contrary, recent work (4, 7) indicates that it is not present in absorption processes. Temperature difference as a driving force. Performance, E, of a column expressed in terms of temperature driving force ( 7 7) is (7)
Performance expressed on this basis also showed a definite maximum when plotted against concentration. Again, this could not be explained by variation in the magnitude of physical properties affecting individual heat transfer coefficients. Nevertheless, effect of heat transfer between the phases on the mass transfer process is important. Consider a packed distillation column operating at steady state, the rate of I
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Brass column; stage close spacing; cyclohexane- to1 u en e; boil-up rate, 10 grammoles per hour.
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A/Ka = 0 ; A/ka = m (equivalent to and plotted as ZEou vs. x )
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Figure 5. Temperature-concentration relationships. Thermal distillation may account for the discrepancy between mass transfer theories and the results obtained in this work
mass transfer being specified in some way by concentration differences between the bulk phases and the interface. I n the vapor phase the less volatile component is moved to the interface preferentially and carries Tvith it the latent heat of vaporization. At the interface this heat is transferred preferentially to the more volatile component and is carried back into the bulk vapor phase. If the latent heats are equal and there is equimolal transfer, there will be no net transfer of energy by this source. Even when these conditions are not met, net transfer of energy will be small. Temperatures of the bulk phases are determined by the rate of heat transfer between the phases. Consider Figure 5. I n the length of column Az, the vapor will remain at its boiling point only if an amount of heat equal to the specific heat of the vapor times A t G is transferred to the liquid. Likewise the liquid will remain a t its boiling point only if it receives from the vapor an amount of heat equal to its specific heat times AtL. But there is no reason why the amount of heat rejected by the vapor should equal that required by the liquid. Also there is no reason why the over-all heat transfer coefficient should have a value such that a t the temperature difference available. At, the requisite amount of heat will be transferred. Magnitude of the heat transfer coefficients will depend mainly upon the state of turbulence of the moving phases, and will not be related in any direct way to the rate of mass transfer. There are two possibilities. If the rate of heat transfer is small, then insufficient heat is removed from the bulk vapor to keep it a t its condensation point, and it will superheat (8, 76). A41so insufficient heat is supplied to the bulk liquid to keep it a t its boiling point and it will subcool. Under such conditions, mass will be transferred between phases not a t their condensation or boiling points, and the temperatures of the phases will
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change through the column in a way represented by the dotted lines 5‘5‘ (Figure 5). O n the other hand, if the rate of heat transfer is high, the vapor will cool to its condensation point and the liquid will heat to its boiling point, Beyond this stage, heat transfer will cause condensation in the bulk vapor and evaporation in the bulk liquid. Under these conditions additional mass transfer by thermal distillation will occur in the bulk phases. Consider conditions at the interface between the bulk phases. Temperature will be the boiling point of the mixture at the interface, and the composition of this mixture will be determined by the rate of mass transfer through each phase. But if the temperature of the interface is determined in this way it does not follow that the rate of heat transfer in each phase will be equal; for there is no reason why the film heat and mass transfer coefficients should correspond in such a way as to ensure this. In this case, ivhcn the rate of heat transfer through the vapor phase is greater than that in the liquid phase there will be evaporation a t the interface. A more likely condition is condensation at the interface, because the ratio of heat to mass transfer rates will usually be greater in the vapor phase. Thus, heat transferred between the phases goes mainly to alter their temperature as they pass through the column. When the rate of heat transfer is high some thermal distillation may occur in the bulk phases, but when it is low, the vapor is not necessarily a t its condensation point, nor is the liquid necessarily at its boiling point. Also thermal distillation will probably occur at the interface itself. Mass transfer by thermal distillation is additional to that taking place under the control of a concentration gradient-Le. contact distillation. This extra mass transfer, normally included with and ascribed to contact distillation, may partly account for the discrepancy between the mass transfer theories and the experimental results obtained in this work. Acknowledgment
The authors wish to thank J. M. Coulson, D. M. Newitt, and J. F. Richardson for their encouragement of this work. Nomenclature
A
D E G
= = = =
H K L
=
2
=
INDUSTRIAL AND ENGINEERING CHEMISTRY
= =
constant diffusion coefficient performance of column molal rate of flow of vapor unit cross-sectional ai ea column height of transfer unit mass transfer coefficient molal rate of flow of liquid unit cross-sectional area column total height of packing
a
=
h
=
m
= =
mGG
meL =
t
=
x,y =
z
=
y
=
v
=
interfacial area per unit volume of column heat transfer coefficient slope of equilibrium line slope of equilibrium line used with H O G when vapor resistance is controlling; djle/dx slope of equilibrium line used with HOGwhen liquid resistance is controlling; (ye - y ) / (2 - .*) temperature bulk concentration of the more volatile component in liquid and vapor phase respectively, mole fraction height of packing molar latent heat kinematic viscosity
Subscripts. B = bottom of column G = vapor phase L = liquid phase 0 = over-all value T = top of column e = equilibrium value i = interface value Literature Cited (1) Bromiley, E., Quiggle, D., IND. ENC. CHEM. 25, 1136 (1933). (2) Byman, L., Keyes, D. B., Univ. Illinois Eng. Exptl. Sta. Bull. 328, 1941. (3) Chari, K. S., Storrow, J. A., J . Afifil. Chem. 1, 45 (1945). (4) Cullen, E. J., Davidson, J. F.: Trans. Faraday Soc. 53, 121 (1957). (51 Danckwerts. P. V., IND. ENG. CHEM. 43, 1460 (1951). (6) Garcia, J. O., Anales real. soc. espaii. Jis.y guim. 48B,449 (1952). (7),Harvey, E. A., Ph.D. thesis, University of London, 1958. (8) Haselden, G. G., private communica-
tion. (9)-Higbie, R., Trans. Am. Inst. Chem. Eng. 31, 65 (1935). (10) Kirschbaum,
E., “Distillier- und Rektifiziertechnik,” 2nd ed., Springer Verlag, Berlin, 1950. (1 1) Kirschbaum, E., VDZ-Beih. Verfahrenstech. No. 1, 15 (1943). (12) Kishinevski, M. K., Zhur. Priklad. Khim. 24,542 (1951). (13) Kishinevski. M. K.. Pamfilov. A. V.. ‘ Ibid., 22, 1173’(1949).’ (14) Langdon, W. h4., Keyes, D. B., IND.ENG.CHEM.35, 464 (1943). (15) Lewis, J. B., Chem. Eng. Sci. 3, 248, 260 11954). e, R. A., Ph.D. thesis, University 3n, 1956. , H. R. C . , Trans. Inst. Chem. (1951). A. K., Smith, W., J . Inst. Petrol. 44, 137 (1958). (19) Sawistowski, H., J . Imp. Cvll. Chem. Eng. Soc. 9, 73 (1955). (20) S.awistowski. H., Ph.D. thesis, University of London, 1955. (21) Shilling, 6 .D , Beyer, G. H., W;itson, C. C., Chem. Eng. Prvgr. 49.128 (19513). 122) Sinfelt. J. H Drick amer, H. G., ‘ j . Chem. khys. 23, 1095 (1955). (23) Smith? !W,, Ph.D. thesis, University of London, 1953. (24) Whitman, W. G., Chem. 4Y M e t . Eng. 29, 147 (1923). (25) Wijk? 1%’. R., Thijssen, H. A. C., Chem. Eng. Sci. 3, 153 (1954).
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RECEIVED for review April 10, 1958 ACCEPTED September 12, 1958
