Ind. Eng. Chem. Res. 1989,28, 1879-1883
1879
Preliminary Design of Sieve Tray Extraction Columns. 2. Determination of the Column Height. Overall Efficiency of Sieve Tray Extractors J. Antonio Rocha,* J. Carlos CBrdenas, and J. Antonio Garcia Instituto Tecnol6gico de Celaya, Departamento de Ingenieria Q u h i c a , Celaya, Gto., Mexico
Experimental data for the overall efficiency in a sieve tray extraction column of 0.246-m diameter were obtained for the systems toluene/acetone/water and methyl isobutyl ketone (MIBK)/acetic acid/water. The results were compared with data generated for the same systems in a 0.10-mdiameter column. I t was found that the overall efficiency decreased when the column diameter increased. By use of the experimental data mentioned above, plus the data from other sources, a correlation for predicting the overall efficiency of sieve tray extractors was obtained by linear regression. The correlation takes into account the column diameter, interfacial tension, plate spacing, and ratio of superficial velocities (or volumetric flow rates) (eq 4). The correlation provides better estimates for the overall efficiency of industrial size contractors when compared with other correlations proposed before. It may be used to estimate the total height of a sieve tray extraction column. The design of sieve tray extraction columns requires basically the specification of two dimensions; the diameter (see part 1) and the height of the column. The latter is fixed when (1)the designer knows the number of theoretical stages needed for the separation, (2) the designer chooses the separation between two plates, and (3) the designer determines the overall efficiency (defined as the ratio of theoretical stages to real stages). Although there are methods for obtaining the height of the column as a function of stage efficiency and methods to predict it (Rocha et al., 1986), the main goal of this paper is to propose a correlation for predicting the overall efficiency for sieve tray extractors from basic data, thus allowing for the estimation of the column height. Previous Work on the Overall Efficiency Treybal(1963), in his classic book, correlated the overall efficiency data reported up to that time. These data as well as other data of more recent researchers are shown in Table I. Most of the data used by Treybal covered column diameters of 0.10 m, with tray spacings ranging from 0.05 to 0.22 m. He proposed the following equation:
Hp5 E , = 0.0057---( U
ud/
Uc)0'42
predicted overall efficiency is higher than 0.30, the overall efficiency will be assumed to be only 0.30, because he observed that it is difficult to get higher values in this type of equipment. Murthy and Rao (1968), using a 0.12-m-diameter column, using plate spacings of 0.15, 0.27, and 0.57 m, and working with the system methyl isobutyl ketonelbutyric acidlwater, compared their data, as well as the data of Garner et al. (19531, with the values predicted by Treybal's equation and observed some overpredictions of the correlation. These researchers proposed a new equation of the same type as Treybal's correlation, but the new one introduced the hole diameter (do) as a parameter. Their equation is U 0.5
Garcia et al. (1988) developed and presented an equation for predicting the overall efficiency. The correlation was similar to Treybal's correlation but included the column diameter. Their proposed equation is (3)
(1)
where Eo is the fractional overall efficiency, Htis the plate spacing in meters, u d / U, is the ratio of superficial velocities (or volumetric flow rates) of the dispersed phase to the continuous phase, and u is the interfacial tension in newtonslmeter. Equation 1 was obtained by using statistical regression of the experimental data and provides clear insight into some of the important parameters involved in overall efficiency: (A) Overall efficiency is directly proportional to the plate spacing and the volumetric flow rate of the dispersed phase. (B) Overall efficiency is inversely proportional to the interfacial tension and the volumetric flow rate of the continuous phase. For developing eq 1, most of the values of ud/ U, ranged from 0.30 to 5.0, Ht ranged from 0.10 to 0.22 m, and interfacial tension ranged from 0.013 to 0.036 N/m. This correlation is often used in industry, but designers say that the equation tends to overpredict for industrial-size extractors. For example, Null (1984) commented that, when eq 1is applied and the numerical value of the
These researchers used the data bank of Table I, reported up to 1984, and a computer simulator (Rocha et al., 1985) for generating their correlation. Basically, this correlation tends to avoid the overprediction characteristic of Treybal's equation when designing industrial-size extraction columns. Experimental Work We trying to test and improve eq 3, carried out experimental runs on a 0.246-m-diameterstainless steel column described in part 1. The two systems used by Rocha (1984) were again used: toluene/acetone/water and methyl isobutyl ketonelacetic acidlwater. The first objective was to study the influence of the column diameter on the overall efficiency. This was possible because Rocha (1984) used a 0.10-m-diameter glass column. Table I1 shows the physical properties and equilibrium data for the systems used, according to Zuiderweg (1978) and Rocha et al. (1986). Because of the constrdction material of the column, it was not possible to observe the drop sizes or flow patterns. This information could help to clarify the effect of the column diameter on the overall efficiency.
0888-5885/89/2628-1879$01.50/0 0 1989 American Chemical Society
1880 Ind. Eng. Chem. Res., Vol. 28, No. 12, 1989 Table I. Data Sources for Sieve Tray Liquid-Liquid Extraction Columns svstem d,,, m H,, m toluenec/benzoic acid/watero 0.222 0.152 gasolineC/MEK/wateP 0.095 0.076, 0.152 toluenec/benzoic acid/watero 0.092 0.120 kerosene'/ benzoic acid/water" 0.092 0.120 toluene'/diethylamine/water" 0.106 0.152 toluene'/benzoic acid/waterO 0.090 0.076, 0.228 MIBKc/adipic acid/waterb 0.106 0.152 toluenec/benzoic acid/waterbjc 0.050 0.609 0.117, 0.508 diethyl etherc/acetic acid/watei.b 0.219 toluenec/acetone/waterbsc 0.100 0.160, 0.510 0.100 0.160, 0.320 MIBKc/acetic acid/waterbSc toluenec/acetone/watera 0.246 0.2, 0.4, 0.6 MIBKc/acetic acid/water" 0.246 0.2, 0.4, 0.6 oTransfer direction D
-
C. bTransfer direction D
- C. C
reference Row et al. (1941) Moulton and Walkey (1944) Allerton et al. (1943) Allerton et al. (1943) Garner et al. (1953) Treybal and Dumoulin (1942) Garner et al. (1956) Mayfield and Church (1952) Pyle et al. (1950) Rocha (1984) Rocha (1984) present work present work
D. 'Dispersed phase.
Table 11. Equilibrium Data and Physical Properties for the System Used toluene/aceMIBK/acetic property tone/water acid/water equilib (org phase dispersed) Y = 3.358X0.93 Y = 4.25OX1.O5 u, N/m (at low concn) 0.025 0.008 100.16 MW of org phase, mass/mol 92.14 862.0 813.0 p of phase, kg/m3 0.000 56 0.000 69 p of org phase, kg/(m.s) MW of aq phase, mass/mol 18.00 18.00 p of aq phase, kg/m3 992.0 1000 p of aq phase, kg/(m.s) 0.0011 0.0011
In all the runs carried out in this project, the solute was transferred from the dispersed organic phase to the continuous aqueous phase. The sequence in the equipment operation in this project was basically the same as that performed with the 0.10-m-diameter column, reported by Rocha (1984). Experimental Results Tables I11 and IV show the conditions for the experimental runs performed for the systems toluene/acetone-
/water and methyl isobutyl ketonelacetic acid f water, respectively. The conditions for the experimental runs of the previous work have been compiled by Rocha et al. (1985). Correlation for the Overall Efficiency Three-hundred twenty-five points for the overall efficiency as well as the operational parameters, physical properties, and geometric parameters were analyzed by linear regression. Several combinations of dimensionless groups were tried, but none of these gave good results. Most of the time, an equation like the one suggested by Treybal showed better agreement with the experimental data. In the experimental work, it was observed in 1984 and also in this project that the overall efficiency varies with solute concentration. This could be caused by interfacial turbulence (Marangoni effect) or by the decrease of the interfacial tension with the increment of solute concentration or by a combination of both effects. For more concentrated solutions, the experimental overall efficiency is higher. This effect was not used before (at least for the
Table 111. Experimental Results to the System: Toluene/Acetone/Water" mole fraction of acetone bottom run
c'd, m/s
u,, m / s
1 2 3 4 5 6 7 8 9 10 11
0.0043 0.0059 0.0062 0.0067 0.0067 0.0089 0.0103 0.0031 0.0045 0.0055 0.0067
12
Y
top
Y
X
E,,,,
0.0038 0.0039 0.0038 0.0039 0.0042 0.0053 0.0038 0.0057 0.0050 0.0057 0.0062
X Ht = 0.2 m; 2 1 Trays 0.0369 0.0032 0.0307 0.0029 0.0594 0.0088 0.0477 0.0069 0.0648 0.0092 0.0533 0.0103 0.0418 0.0078 0.0434 0.0023 0.0516 0.0039 0.0544 0.0050 0.0514 0.0052
0.0222 0.0200 0.0315 0.0264 0.0290 0.0317 0.0283 0.0212 0.0291 0.0235 0.0265
0 0 0 0 0 0 0 0 0 0 0
0.024 0.023 0.047 0.044 0.052 0.060 0.042 0.017 0.022 0.036 0.033
13 14 15 16 17 18 19 20
0.0030 0.0045 0.0073 0.0087 0.0091 0.0095 0.0085 0.0093 0.0035
0.0041 0.0038 0.0038 0.0036 0.0042 0.0038 0.0040 0.0040 0.0026
Ht = 0.4 m; 1 2 Trays 0.0027 0.0769 0.0079 0.0563 0.0075 0.0418 0.0056 0.0299 0.0028 0.0563 0.0098 0.0593 0.0086 0.0528 0.0081 0.0893 0.0102
0.0260 0.0421 0.0363 0.0295 0.0216 0.0363 0.0352 0.0341 0.0512
0 0 0 0 0 0 0 0 0
0.030 0.057 0.061 0.056 0.036 0.081 0.074 0.070 0.063
21 22
0.0040 0.0085
0.0040 0.0045
Ht = 0.6 m; 9 Trays 0.0286 0.0015 0.0453 0.0054
0.0194 0.0279
0 0
0.029 0.075
do = perforation diameter = 0.004 7625 m. Dispersed phase = organic phase. Mass-transfer direction: dispersed phase
phase.
-
continuous
Ind. Eng. Chem. Res., Vol. 28, No. 12, 1989 1881 T- A-W
PRESENT WORK
6 '
I
/
/
EO
QD/QC
Figure 1. Variation of the overall efficency with volumetric flow rate, at different plate spacings. System: toluene/acetone/water. (+) Ht= 0.20 m; (a) Ht= 0.40 m. MIBK-A A - W
/
CALC
ai
Figure 3. Parity plot for the overall efficiency between experimental data and data calculated by using the correlation proposed in this work. Column diameter = 0.246 m. (X) Toluene/acetone/water; (0) MIBK/acetic acid/water. TREYBAL
w X 0
W
3
2
l t
t 01
'5
f ,
, 1'0
,
,
,
,
1'5 2'0 QD/QC
,
, 2'5
/
,
3'0
Figure 2. Variation of the overall efficiency with volumetric flow rate, at different plate spacings. System: MIBK/acetic acid/water. (0) H,= 0.20 m; (@) Ht= 0.40 m.
authors) in estimating the efficiency. One way to take the concentration into account is to consider its influence over the interfacial tension value; higher concentrations lead to lower interfacial tension values, and this provides higher efficiencies. For developing the new correlation, the values of the interfacial tension were corrected (taking the concentration as the average between the bottom and the top of the column). For the systems used in this project, Zuiderweg (1978) presented plots of interfacial tension versus solute concentration. For other systems, the method of Pliskin and Treybal (1966) was used to estimate the value of interfacial tension as a function of solute concentration. By use of the corrected interfacial tension (u), the correlation obtained is
Within the experimental data studied in this work, the hole diameter showed no appreciable influence on the overall efficiency. It is believed that the correlation should give good results for plate spacings below 0.60 m, which cover the range of plate spacings used in industry. Analysis of the Results and Comparison with Other Correlations The standard results of higher efficiency for higher plate spacings were obtained and are show in Figures 1 and 2 for toluene/acetone/water and MIBK/acetic acid/ water,
Of',
,
,
,
,
,
,
,
,
,
,
iviiBn/ acetic acia/ water.
respectively. 'l'he increase in efficiency tends to damp at high values of plate spacing, but the effect of higher efficiency is observed at the range of plate spacings used in industry (0.200.60 m). Also the standard result of higher overall efficiency for systems of lower interfacial tension is clear by comparing Figure 2 versus Figure 1or directly in Figures 3-6 which present parity plots where experimental and predicted overall efficiencies are compared.
1882 Ind. Eng. Chem. Res., Vol. 28, No. 12, 1989 Table IV. Experimental Results to the System. Methyl Isobutyl Ketone/Acetic Acid/Water" mole fraction of acetic acid run 1 2 3 4 5 6 v
8 9 10 11 12 13 14
15 16 17 18 19
Y
X
EW,
0.0038 0.0039 0.0042 0.0037 0.0044 0.0042 0.0042 0.0039 0.0037 0.0040 0.0040 0.0040 0.0041
bottom Y X H , = 0.2 m; 21 Trass 0.0708 0.0118 0.0120 0.0687 0.0159 0.0793 0.0120 0.0486 0.0151 0.0643 0.0121 0.0501 0.0289 0.1191 0.0160 0.0744 0.0063 0.0435 0.0130 0.0586 0.0152 0.0602 0.0105 0.0407 0.0129 0.0516
0.0026 0.0025 0.0062 0.0089 0.0180 0.0079 0.0161 0.0075 0.0012 0.0064 0.0112 0.0088 0.0097
0 0 0 0 0 0 0 0 0 0 0
0.212 0.220 0.200 0.194 0.160 0.205 0.248 0.215 0.162 0.195 0.240 0.220 0.220
0.0040 0.0040 0.0042 0.0040 0.0040 0.0040
Ht = 0.4 m; 12 Trays 0.0491 0.0028 0.0306 0.0053 0.0423 0.0074 0.0479 0.0102 0.0455 0.0109 0.0386 0.0093
0.0020 0.0038 0.0053 0.0055 0.0055 0.0052
0 0 0 0 0 0
0.310 0.230 0.280 0.345 0.325 0.420
m/s
U,, m/s
0.0042 0.0044 0.0064 0.0069 0.0098 0.0086 0.0077 0.0057 0.0036 0.0066 0.0080 0.0084 0.0081 0.0042 0.0049 0.0058 0.0066 0.0069 0.0070
ud,
top
0 0
a d o = perforr ion diameter = 0.004 7625 m. Dispersed phase = organic phase. Mass-transfer direction: dispersed ph se phase.
Table V. Average Relative Deviation for Each Correlation equation dev, % Treybal (1963) 57.6 Murthy and Rao (1968) 84.2 Garcia et al. (1988) 40.4 proposed (present work) 30.1
Effect of the Diameter on the Overall Efficiency. Figures 3 and 5 and 4 and 6 show that for both systems higher efficiency is obtained for small diameter columns. Figures 3 and 5 show how the proposed correlation (eq 4) fits the experimental data for both systems and both column diameters. It is clear that the correlation works better for bigger column diameters and that it underpredicts the overall efficiency for small columns when high interfacial tension systems are used. Figures 4 and 6 show how Treybal's correlation (eq 1) fits the experimental data, again for both systems and both column diameters. Here it is observed that the correlation overpredicts for bigger columns, and this gives good predictions for small columns using high interfacial tension systems. It can be said that, when comparing Treybal's correlation (or Murty and Rao (1968)) and the correlation proposed in this work (or Garcia et al. (1988)), the overall efficiency prediction is a function of two factors: interfacial tension and column diameter. From the analysis of Figures 3-6, it can be inferred that each correlation has a range of application, which is summarized in Figure 7. When the average relative deviation av re1 dev =
[
iEo,exp
- Eo,pred
E0,exp
'1
(5)
av
is applied to all the experimental points of the data bank,
-
continuous
TREYBAL
4 ~-
a
z
0
W
3.--
2 -1 --
TU, W ' .
,
lo
,
,
,
,
2
1
I3 EO
1
4
5
6
CALC
Figure 6. Parity plot for the overall efficiency between experimental data and data calculated by using Treybal's correlation. Column MIBK/acetic diameter = 0.10 m. (X) Toluene/acetone/water. (0) acid/water. t,
