Ind. Eng. Chem. Res. 1987,26, 1489-1494
1489
Surface Tension Effects on a Large Rectangular Tray with Small Diameter Holes M a h m o u d M. D r i b i k a * and Michael W. Biddulph Department of Chemical Engineering, University of Nottingham, University Park, Nottingham, U.K.
An extensive series of tests has been carried out on a sieve-tray distillation column. Efficiency results reported earlier for the systems MeOH-H,O and MeOH-n-PrOH, which were obtained on a large rectangular tray with small diameter holes and in the absence of the flow nonuniformities and stagnant zones, were compared. It is shown that the tray efficiencies in the MeOH-H20 system are markedly increased by surface tension effects. T h e effect was mostly concentrated in the higher point efficiencies obtained in the positive system as compared with the neutral system. The effect of surface tension gradients on point efficiencies was found to be a combination of surface renewal effects in the lower composition range, enhancing the mass-transfer coefficients, and increasing interfacial area with increasing composition a t the higher composition region. The enhancement in point efficiencies in the positive system MeOH-H20 was found to be related to the Marangoni index (M). The importance of surface tension effects on the performance of distillation columns has been widely recognized in the chemical engineering literature since the study by Zuiderweg and Harmens (1958). The results from more than 100 publications have been reviewed by Berg (1972). It has often been observed that an increasing or decreasing surface tension in the column internal reflux liquid can exert a significant influence on the interfacial area and consequently affect the plate efficiency. Surface tension gradients can also enhance the mass-transfer coefficients by surface renewal effects and interfacial turbulence (Danckwerts et al., 1960; Ellis and Biddulph, 1967; Sawistowski, 1973). In addition, it has been observed that this effect is closely associated with the flow regime (Bainbridge and Sawistowski, 1964; Fane and Sawistowski, 1969). In general, for plate columns, previous workers on the effect of surface tension have concluded that a t lower vapor velocities, surface tension positive systems have higher efficiencies than negative systems, and a t higher vapor velocities (spray regime), negative systems have higher efficiencies than positive systems. The enhancement factors of the rate of mass transfer due to Marangoni effects has been estimated by Sawistowski (1973) to be on the order of 1.6-3.2 and in mass- and heat-transfer rates by a factor of 1.5-2 (Zuiderweg, 1975). Thus, many previous authors have explained the differences between the behavior of binary systems in terms of their surface tension characteristics. However, most of these conclusions have been drawn from data obtained in small laboratory columns, little information being available concerning larger columns under industrial conditions. Recently, using data from large-scale columns, Zuiderweg (1983) has compared the efficiency results from Fractionation Research Incorporated (FRI), reported by Sakata and Yanagi (1979) on the hydrocarbon system cyclohexane-n-heptane, with the results of Lockett and Ahmed (1983) on the system methanol-water. This comparison was based on system transport properties and tray dimensions. The two sieve trays were reasonably large, of industrial or semiindustrial type. Zuiderweg (1983) related the efficiency enhancement to the Marangoni index (M) and concluded that Marangoni effects markedly increased the efficiencies of the methanol-water system as compared with cyclohexane-n-heptane. Recent publications (Biddulph and Dribika, 1986; Dribika and Biddulph,
* Present address: Al-Fateh University, Department of Chemical Engineering, Tripoli, Libya. 0888-5885/87/2626-1489$01.50/0
Table I. Tray Details of the Large Rectangular Sieve Tray liquid flow path, mm 991 mole diameter, mm 1.8 weir length, mm 83 % free area, % 8 tray spacing, mm 154 outlet weir height, mm 25
1986) on the systems methanol-water and methanol-npropanol have provided data which enable a comparison to be made in terms of the surface tension characteristics. The results were obtained on a large rectangular sieve tray with small diameter holes, the details of the tray being given in Table I. The tray material is typical of that used in cryogenic air separation columns, and details of the equipment have been provided elsewhere (Biddulph and Dribika, 1986). The shape of this tray avoids the problems of stagnant zones and flow nonuniformities which are characteristic of circular, chordal-weir trays.
Efficiency Results The results of tray and point efficiencies in the two systems are shown in Figures 1 and 2. The point efficiencies were deduced from matching on eddy diffusion model to the experimental profiles obtained across the tray (Biddulph and Dribika, 1986), and these data are shown in Figures 3 and 4. The tabulated data on compositions and temperatures have been published elsewhere (Dribika, 1986). The results were obtained in the froth regime for both systems. For the MeOH-H,O experiments, the Ffactor was 0.6, while in the MeOH-n-PrOH experiments it was 0.4. Under these conditions the entrainment, predicted by the Fair correlation (Fair and Smith, 1963), was less than 0.2% in both systems, and this value would have had a negligible effect on the efficiencies (Rahman and Lockett, 1981). The temperatures across the tray were found to be very close to the bubble point temperatures. However, the temperatures in the downcomers indicated that slight vaporization was occurring in the two systems similar to previous workers’ observations (Ellis and Shelton, 1960; Lockett and Ahmed, 1983). Discussion In applying the eddy diffusion model to match the composition profiles and deduce the point efficiencies, it is important to note that there are three significant parameters: liquid-phase mixing (Peclet number), the slope of the equilibrium line, and the point efficiency. Figure 5 shows the slopes of the equilibrium lines, similar values applying across the composition range used in the two 0 1987 American Chemical Society
1490 Ind. Eng. Chem. Res., Vol. 26, No. 8, 1987 MeOH-nPrOH MeOH-nPrOH
M.0H-w.t.r
c
160-
3
M.OH-w.fer
1.50 1
m 140
y;"tra;ai '
,
0:3
'
'
'
0:6
Figure 5. Mean equilibrium line slope as a function of composition for the two systems.
0.3
rn
x
.
1
WOH-nPrOH
Figure 1. Tray efficiencies vs. the mean liquid composition across the tray for the two systems.
Figure 6. Liquid-phase diffusion and viscosity as a function of composition for the two systems.
Figure 2. Point efficiencies in the two systems.
75/
..
MeOH-nPrOH MeOH-wafer
1950
l
Position
out
Figure 3. Composition profiles across the tray for the system MeOH-water. 0.9
0.7
0.5
(2f) 0.3
0d
Position on tray
Figure 4. Liquid composition profiles across the tray for the system MeOH-n-PrOH.
systems. The Peclet number was evaluated directly on the same test tray using experiments with water/steam and sodium nitrate solution as the tracer. It is not known to what extent the mixing parameter was influenced by the
I
,
1
,
0.3
s
'
0:6
'
Figure 7. Surface tension and liquid-phase density as a function of composition for the two systems.
physical properties of the system. However, the value obtained for the Peclet number was found to be about 39. This indicates that the conditions were approaching plug flow, and variations in Peclet number in this region due to physical properties would not influence the results greatly. Thus, the higher tray efficiencies obtained in the MeOH-H20 experiments are essentially due to the higher point efficiencies of the MeOH-H20 system as compared with the point efficiencies in the system MeOH-n-PrOH. Because of the similarity of the slope of the equilibrium line, flow regime, and the temperature difference, it is most probable that the higher point efficiencies in the system MeOH-H,O are a function of the physical properties of the system. A comparison of the physical properties, for these polar systems, as calculated by the recommendations of Reid et al. (1977) is shown in Figures 6-9. The surface tension of the mixtures was estimated by the method of Winterfeld
Ind. Eng. Chem. Res., Vol. 26, No. 8, 1987 1491 Table 11. Surface Tension of the Pure Components at Their Normal Boiling Points system surface tension, dyn/cm methanol 18.98 n-propanol 17.7 water 61.06
1
1
7
1
0:3 f ' 0:6 ' Figure 8. Vapor-phase diffusion and density as a function of composition for the two systems. '
2i=-===-I
6
-
nPrOH MeOH
15
10
50
T "C
90
Figure 10. Surface tensions of pure components as a function of temperature.
I
0*'3 '
'
Oi6
I '
Figure 9. Vapor velocity based on the bubbling area of tray in the two systems.
et al. (1978). The properties were evaluated a t the mean composition and pressure of the system and the bubble point temperatures. These bubble point temperatures were evaluated taking into account the nonidealities in the vapor as well as in the liquid, the virial equation being used for the vapor phase and the Wilson model being used for the liquid phase. The form of the calculations has been described previously in detail (Dribika et al., 1985). If the physical properties of the vapor phase are compared, the viscosities are similar, but the densities and the diffusivities are slightly different. The higher vapor diffusivities in the MeOH-H20 system influence the vapor mass-transfer coefficient, resulting in slightly higher numbers of transfer units in the vapor phase. The vapor densities in the MeOH-H,O are lower than for MeOHn-PrOH. With the F-factor being higher a t 0.6 as compared with 0.4 in the MeOH-n-PrOH experiments, the vapor velocities were almost double in the MeOH-H20 experiments, as shown in Figure 9. However, the increase in the vapor velocities was found previously (Biddulph and Dribika, 19861, in the MeOH-H20 system, to have an insignificant effect on the efficiencies. The results of Lockett and Ahmed (19831, using a wider range of F-factor, also showed that the effect on the efficiencies was insignificant. However, in the comparison of the physical properties of the liquid phase, it is interesting to see that the surface tension and the viscosities are different in the two systems. The viscosity would influence the diffusivity, but fortunately the estimated values of the diffusivities, using the modifications of Vignes' correlations (1966)which take into account the composition effect as well as the viscosity effect, show that the diffusivities are quite similar in the two systems. Thus, it seems that the most significant difference in the physical properties is in the surface tension.
hfl
mm
I
,
0:3
'
'
0:6
X Figure 11. Froth height in the two systems.
'
'
I t is important to note that the surface tension of nPrOH is slightly less than methanol and much less than water. Table I1 shows the surface tension of the pure components at their normal boiling points, and Figure 10 shows the variation of the surface tension with temperature (Jasper, 1972). Thus, the system MeOH-H20 is highly positive and the system MeOH-n-PrOH is almost neutral, very slightly negative according to the classification of Zuiderweg and Harmens (1958). Therefore, it is probable that the higher point efficiencies for MeOH-H20 result from surface tension effects. The higher efficiencies could be a result of an increase in the interfacial area and/or an increase in the masstransfer coefficients due to surface renewal effects and/or interfacial turburlence. Experimental observations indicate that the froth height in the MeOH-H20 experiments was increasing with an increase in the concentration of methanol, in contrast with the system MeOH-n-PrOH where the froth height remained fairly constant. Figure 11shows the experimentally measured froth heights in the two systems. The increase in the froth height indicates that the interfacial area in the MeOH-H20 system is higher than for MeOH-n-PrOH in the higher composition range of methanol. However, in the lower composition range of methanol, the froth heights are approximately equal, indicating that the interfacial areas are probably similar in the two systems. This is a surprising result since it might be expected that a higher froth height would exist in this composition range of the MeOH-H,O experiments. Similar observations of the variation of the froth height with composition were reported by Hay and Johnson (1960) in the MeOH-H20 system. It is important to note
1492 Ind. Eng. Chem. Res., Vol. 26, No. 8, 1987
0.6/
1.o
1.5 m Figure 12. l/NoGvs. the mean equilibrium line slope for the two systems. 5
Table 111. Vapor- and Liquid-Phase Transfer Units in Both Systems by the Method of the Intercept and the Slope system NG NL MeOH-n-PrOH 1.61 5.83 MeOH-H,O 2.56 12.5
that in this range of composition, the volumetric flow rates of liquid are similar but the vapor velocities are different, being higher in the MeOH-H,O experiments. This would result in a shorter vapor residence time for the MeOH-H,O experiments and would be detrimental to those efficiencies (Haselden and Thorogood, 1964). Since it seems there are no other factors which could significantly influence the efficiencies for the MeOH-H20 system as compared with the MeOH-n-PrOH system, the influence of surface tension gradient causing an increase in the surface renewal and/or interfacial turbulence, and thus influencing the liquid film resistance, is most probably the major cause of the higher point efficiencies in the positive system MeOH-H,O in the lower composition range. The use of the usual assumption of plug flow of vapor, as it passes through the froth, allows the number of overall transfer units in the vapor phase to be calculated: NOG= -(In [1 - E O G I ) (1) From the two-film theory at total reflux, m - =1 - + - l (2) NOG
NG
NL
The variation of 1/NWwith m is shown in Figure 12. The values of N O G of the MeOH-H,O experiments used in Figure 12 were only those calculated from the experiments which showed a similar froth height to the system MeOH-n-PrOH. These values were in the range of composition up to 0.5 mf. MeOH is shown in Figure 11. The values of NG and NL were then determined using the usual intercept and slope method for the two systems, and the results are shown in Table 111. These results indicate a greater number of liquid-phase transfer units in the system MeOH-H,O than in the system MeOH-n-PrOH. By use of these values of N G and NL,the extent of the liquid-phase resistance (LPR) in the two systems was estimated by mNG % LPR = (3) NL + mNG The results are shown in Figure 13. I t is interesting to note that the 70 LPR in the positive system is lower by a difference of about 8% compared with the neutral system MeOH-n-PrOH in the range of the experiments where the froth heights are similar. This is in agreement with the work of Ellis and Biddulph (1967) who studied both negative and positive systems in a pool column with constant
,
,
I
0.3 51 0.6 Figure 13. % LPR for the two systems.
1
interfacial area. Their results indicated that a higher number of liquid-phase transfer units existed in the positive system as compared with the negative systems. In further experiments by Biddulph (1966), on the spreading velocity using the system MeOH-H,O, a greater spreading velocity was observed a t the higher values of the surface tension driving force (in the lower composition range of methanol), and this spreading velocity was decreasing with a decrease in the surface tension driving force (in the higher composition range of methanol). In the neutral systems which they investigated, there was no spreading, while in the negative systems some repulsion of eddies was observed. The authors concluded that the higher efficiencies found in the positive system as compared with the negative system may be due to differing surface renewal effects in the positive and negative systems influencing the liquid film resistance. It is also interesting to note that the values of NL and NG can provide an estimate of the enhancement of the mass-transfer coefficients by the Marangoni effect. We define the individual number of transfer units in the usual way by NL = kLahfA/L (4) NG = kgahfA/ V
(5)
For the liquid phase, eq 4 is applied for the two systems and it is noted that the froth heights and liquid volumetric rates are similar in the lower composition range, dividing gives NL1
kL1
-=-
kL2 where subscript 1 refers to the MeOH-H20 system and subscript 2 refers to the MeOH-n-PrOH system. Substituting the values of NL into eq 6 gives k L 1 = 2.1432~2 (7) Since the liquid diffusivities are similar, the form of eq 7 indicates that the rate of mass transfer in the liquid phase in the positive system is more than double that in the neutral system MeOH-n-PrOH, presumably because of the Marangoni enhancement. For the vapor phase, applying the same steps when using eq 5 and noting that U, = V/A gives NL2
NG1
-=--
k€!l ug2
NG2
kgZ ugl
Substituting the values of
(8) NG
and U , into eq 8 gives
Ind. Eng. Chem. Res., Vol. 26, No. 8, 1987 1493 However, since the vapor diffusivities in the MeOH-H20 system are higher than in the MeOH-n-PrOH system, the enhancement in the vapor mass-transfer coefficient given by eq 9 cannot all be due to the Marangoni effects. In order to estimate the extent of the enhancement, the vapor mass-transfer coefficients in the two systems were expressed by the penetration theory as n \ 0.5
where * indicates a Marangoni free-vapor mawtransfer coefficient. The vapor contact time is defined as roughly equal to the duration of the gas in the two-phase layer:
t=
(h-W / U g
(11)
-30 X
Figure 14. Marangoni index and surface tension gradient as a function of composition for the two systems.
The liquid holdup on the tray was calculated by using the recent correlations of Bennett et al. (1983), which were obtained on small diameter hole sieve trays with outlet weir heights ranging from 0 to 25 mm. These values were found to be similar in the two systems. Substituting eq 11 into eq 10 and applying the resultant equation for the two systems gives
Substitution of the values of D, and U, into eq 12 gives
kgl* = 1.987kg2*
(13)
Dividing eq 9 by eq 13 and noting that the vapor masstransfer coefficients in the system MeOH-n-PrOH, given by eq 9 and 13, are expected to be similar because of the absence of Marangoni effects in this system, gives
kgl = l.86kgl*
(14)
Thus, the enhancement of the vapor mass-transfer coefficients due to surface renewal effects is of a similar order of magnitude to that for the liquid-phase mass-transfer coefficients. These results agree with those of Sawistowski (1973), who stated that the presence of Marangoni effects will increase the mass-transfer coefficients several times over the values predicted on the diffusional basis of the film theory or penetration theory. These effects will enhance the overall mass-transfer coefficient in the vapor phase by a factor of about 2. This would result in a higher number of transfer units, and thus higher point efficiencies, in the positive system as compared with the neutral system in the lower composition range where the interfacial areas are similar. In the higher composition range, the influence of surface renewal effects would be decreased, as reported by Biddulph (1966), due to the spreading velocities in the positive system being decreased with an increase in the concentration of the methanol. This would most probably result in similar values of the 70LPR in the two systems, but the surface tension effects would influence the interfacial areas where the froth height is increased. Thus, the enhancement in the higher composition range would be mainly due to the interfacial area for mass transfer, causing the number of overall transfer units in the vapor phase to be higher for the positive system than for the neutral system. This would result in higher point efficiencies for the system MeOH-H20 as compared with the system MeOH-n-PrOH, as measured in the column. It is also possible to relate the efficiency enhancement by the Marangoni effect in a quantitative manner to the M-index as suggested by Hovestreydt (1963) and Moens
0.3 X 0.6 Figure 15. Enhancement of point efficiencies over the AIChE prediction method.
(1972) and used successfully by Zuiderweg (1983). Figure 14 shows the surface tension gradients as well as the Mindex values calculated approximately by
In order to estimate the efficiency enhancement, the AIChE method of point efficiencies, as outlined by Fair and Smith (1963),was applied to represent the "Marangoni free" point efficiencies since the method does not allow for surface tension effects. It is also important to note that the AIChE method is based on an eddy diffusion model without allowing for any flow nonuniformities and stagnant zones. These effects are also absent in this work because of the tray format. The point efficiencies predicted are shown in Figure 2, and it can be seen that the predicted values in the two systems are quite similar and significantly lower than those measured, even in the neutral system MeOH-n-PrOH. The reason for this is probably that the method does not account for small hole size sieve trays (Swanson and Gerster, 1962);Biddulph and Dribika, 1986). The ratios of the observed efficiencies over the AIChE values are shown in Figure 15. The efficiency enhancement was then found by dividing the ratio in the MeOHH 2 0 system by the ratio for the MeOH-n-PrOH system, thus including the effect of the hole size as well. The results are plotted vs. the M-index and shown in Figure 16. It can be seen that the enhancement of point efficiency in the positive system is strongly dependent on the M-index. This agrees with the Zuiderweg (1983) findings in alcohol-water systems. Conclusions From this study it can be concluded that the higher efficiencies reported earlier, in the MeOH-H20 system as compared with the efficiencies of the MeOH-n-PrOH system, obtained on a large rectangular tray with small diameter holes and in the absence of the flow nonuni-
1494 Ind. Eng. Chem. Res., Vol. 26, No. 8, 1987
Greek Symbols p = vapor-phase density, kg/m3 pL = liquid-phase density, kg/m3
151
wL = liquid viscosity, CP u =
1.3
U'
surface tension, mN/m
= surface tension gradient, mN/m
Literature Cited 2
4
8
M Figure 16. Enhancement of point efficiency by the Marangoni effect in the MeOH-H,O system.
formities and stagnant zones, are probably due to the enhancement of the MeOH-H20 efficiencies by Marangoni effects. The enhancement in point efficiencies in the positive system MeOH-H20 was found to be related to the Marangoni index (M). It therefore seems reasonable that these effects should be included in efficiency predictions.
Nomenclature A = bubbling area, m2 a = interfacial area per unit volume of dispersion, m-l B = enhancement of point efficiency over the AIChE prediction C = enhancement of point efficiency by the Marangoni effect D, = vapor-phase diffusivity, m2 s DL = liquid-phase diffusivity, m / s Em" = Murphrfee tray efficiency EOG= overall vapor-phase point efficiency hf = froth height, m hL = liquid holdup, m k , = vapor-phase mass-transfer coefficient, m/s k,* = vapor-phase mass-transfer coefficient based on the penetration theory, m/s kL = liquid-phase mass-transfer coefficient, m/s L = liquid flow rate, m3/s LPR = fraction liquid-phase resistance M = Marangoni index, mN/m m = mean slope of the equilibrium line across the tray NG = number of vapor-phase transfer units NL = number of liquid-phase transfer units Noc = number of overall vapor-phase transfer units t = contact time, s U, = vapor velocity based on the bubbling area, m/s = vapor flow rate, m3/s X = average liquid mole fraction across the rectangular tray y* = equilibrium vapor mole fraction with X
4
Bainbridge, G. S.; Sawistowski, H. Chem. Eng. Sci. 1964, 19, 992. Bennett, D. L.; Agrawal, R.; Cook, P. J. AZChE J . 1983,29(3), 434. Berg, J. C. Recent Developments in Separation Science; Chemical Rubber Co.: Cleveland, OH, 1972; Vol. 11, p 1-31. Biddulph, M. W. Ph.D. Thesis, 1966, University of Birmingham. Biddulph, M. W.; Dribika, M. M. AZChE J. 1986, 32, 1383. Danckwerta, P. V.; Sawistowski, H.; Smith, W. Znt. Chem. Eng. Symp. Ser. 1960,6, 7. Dribika, M. M. Ph.D. Thesis, University of Nottingham, 1986. Dribika, M. M.; Biddulph, M. W. AZChE J. 1986, 32(11), 1864. Dribika, M. M.; Rashed, I. G.; Biddulph, M. W. J. Chem. Eng. Data 1985, 30, 146. Ellis, S. R. M.; Biddulph, M. W. Trans. Inst. Chem. Eng. 1967,45, T223. Ellis, S . R. M.; Shelton, J. T. Znt. Chem. Eng. Symp. Ser. 1960, 6, 171. Fair, J. R.; Smith, B. D. Design of Equilibrium Stage Process; McGraw-Hill: New York, 1963. Fane, A. G.; Sawistowski, H. Znt. Chem. Eng. Symp. Ser. 1969,32, 1:8. Haselden, C. G.; Thorogood, R. M. Trans. Inst. Chem. Eng. 1964,42, T81. Hay, J. M.; Johnson, A. I. AZChE J. 1960, 6, 373. Hovestreydt, J. Chem. Eng. Sci. 1963, 18, 631. Jasper, J. J. J . Phys. Chem. Ref. Data 1972, 1, 4. Lockett, M. J.; Ahmed, I. S. Chem. Eng. Res. Des. 1983, 61, 110. Moens, F. P. Chem. Eng. Sci. 1972, 27, 275. Rahman, M. A.; Lockett, M. J. Znt. Chem. Eng. Symp. Ser. 1981,61, 111. Reid, R. C.; Prausnitz, J. M.; Sherwood, T. K. The Properties of Gases and Liquids, 3rd Ed.; McGraw-Hill: New York, 1977. Sakata, M.; Yanagi, T. Znt. Chem. Eng. Symp. Ser. 1979,56,3.2/21. Sawistowski, H. Chem.-Zng. Technol. 1973, 45(18), 1093. Swanson, R. W.; Gerster, J. A. J . Chem. Eng. Data 1962,7(1), 132. Vignes, A. Znd. Eng. Chem. Fundam. 1966,5, 189. Winterfeld, P. H.; Scriven, L. E.; Davis, H. T. AZChE J . 1978,24, 1010. Zuiderweg, F. J. Chem. Eng. Res. Des. 1983, 61, 388. Zuiderweg, F. J. 79th National Meeting of The American Institute of Chemical Engineers, Houston, March 1975, B9. Zuiderweg, F. J.; Harmens, A. Chem. Eng. Sci. 1958, 9, 89. Received for review March 12, 1986 Accepted March 6, 1987
