I
G. V. POTNIS,
H. C. BIJAWAT,'
and 1. K. DORAISWAMY
National Chemical laboratory, Poona 8, India
U p p i n g Column Extraction Efficiency by
Pulse Application
THE efficiency of liquid-liquid extractors is primarily dependent on the degree of turbulence imparted to the system and the interfacial area available for mass transfer. In conventional extractors, the energy for phase dispersion is provided by the density difference between the two phases, but this is usually insufficient to produce the desired turbulence. A number of contactors have been developed in which additional energy for dispersion and agitation is supplied by mechanical moving parts (5, 9, 73-78, 25). I n recent years attention has been focused on columns in which a pulsating motion is imparted to liquids by an external mechanical or electronic device. Internal mechanical parts are eliminated, leakage is minimized, and the pulsator can be isolated, if necessary, from process liquids. Pulsation enhances mass transfer rate and provides flexibile operation. Pulsed columns have been operated satisfactorily with liquids having density differences as small as 0.05 (22). Although pulsed columns use either sieve plates or packing, most investigations reported have dealt with the sieve-plate type ( 7 , 4. 7, 77, 79). The performance of both types has been reviewed (24, 27). I n the earliest study on pulsed packed columns (70), over-all HTLJ was reduced threefold; other workers (26) using the same system and column found that extraction efficiency could be improved almost fivefold. Feick and Anderson (8) found that mass transfer coefficient in packed columns increased considerably under pulsation; they concluded that the predominant effect was to increase the interfacial area of contact Present address, National Carbon Co. (India), Ltd., Calcutta 1, India.
...
- Packed Column The correlation presented can be used to compute the value of HTU corresponding to a given combination of frequency and amplitude. Conversely, it can fix the puIse cond itions necessar y to attain a given value of
HTU by creating a finer dispersion of droplets, rather than to increase film mass transfer coefficients. T h e most detailed investigation on pulsed packed columns was reported by Chantry, Von Berg, and Wiegandt ( 3 ) . HETS values were reduced to one third in a packed column, the best performance being obtained with a combination of low amplitude and high frequency. Pulsation reduced maximum throughput by 5 to lo%, and efficiency was less affected by changes in phase flow rates than in conventional packed columns. Chantry and coworkers have also reported results for a sieve-plate column. Other packed column data have been reported by Thornton (23). Experimental
Apparatus and Materials. The column (Figure 1) consisted of a 30-inch borosilicate glass tube with a n inner diameter of 1.25 inches. The 8-inch long-phase-disengagement section at each end had a n inner diameter of 3 inches The packed height of 11 inches contained 0.25-inch glass Raschig rings having a dry void volume of 71y0 and bulk density of 40 lb./cu. ft. The pack-
ing rested on a Kichrome wire screen (with about 95% free area) fixed just above the lower disengagement section and was confined a t the top by a perforated metallic pressure plate. The end design used was, in general, similar to that employed by earlier investigators (3, 8). Chances of premature flooding a t the packing support were minimized by the large free area of the support. The disperse phase was fed to the bottom of the column through a rotarneter and surge chamber, while the continuous phase entered the top through a flow meter and surge chamber. T h e interface level in the column was controlled by a flexible jack-leg. T h e pulse generator was a variable stroke, reciprocating plunger pump with its valves removed and was connected to the bottom of the column through a mercury seal. Pulse amplitude WBS varied by adjustment of the piston stroke and frequency was changed through a gear unit and pulley system. Pulse amplitude is defined in this investigation as the linear movement of the column liquid between extreme positions. T h e system used was benzene-acetic acid-water, the transfer of solute being from the continuous aqueous to the disperse benzene phase. Solubility relationships show that principal resistance to mass transfer lies in this phase, and hence its dispersion would be advantageous. Acid strength in all runs was about 6% by weight. Equilibrium data for the system were taken from Brown and Bury (2) and the International Critical Tables (72). Procedure. Feed solutions were mutually saturated with respect to water and benzene. T h e column was filled with the continuous phase, and flow rate, pulse frequency, and amplitude were set to the desired values. Benzene VOL. 51, NO. 5
M A Y 1959
645
was introduced into the column, and the interface level and phase flow rates were finally adjusted and held constant throughout the run. T h e column was operated until the composition of the extract and raffinate streams remained constant for a t least 30 minutes. This required from two to three complete changes of the column liquid. Only runs in which acid material balance checked to within 2% were recorded. Standard sodium hydroxide was used for titrating the acid. When benzene was involved in the titration, a large excess of water was added and the titration vessel thoroughly agitated. Periodic checks on the accuracy of benzene titra-
tion were made by diluting the titration sample with ethyl alcohol in place of water. T h e efficiency of extraction was calculated in terms of the height of a transfer unit ( H T U ) . For the case where the solutions are dilute and the system obeys the simple distribution law without much deviation, over-all H T U is defined by the following equation :
Because the distribution coefficient for acetic acid between water and benzene is about 30, major resistance to mass transfer lies in the benzene phase;
"FLOW
METER
EXTRACTION COLUMN
. INTERFACE
LEVEL CONTROL
MERCURY SEAL
f-l
4 ROTAMETER
I
'I EXTRACT
RAFFINATE
PJ SURGE CHAMBER
Figure 1 . The liquid in the extraction column was pulsed by an independently operated pulse generator
646
INDUSTRIAL AND EWGINEERING CHEMISTRY
hence over-all HTU's were based on the benzene phase. When benzene enters the column free of solute, Equation 1 may be written : ( H T U ~ O= B
h
Equation 2 was used to calculate the reported values of H T U . In the following discussion, ( H T U ) o Bis referred to as HTU. Results and Discussion
Several preliminary runs were made to study the mass transfer performance and flooding capacity of the column under conventional and pulsed operation and to fix a suitable packed height. Experiments with a packed height of 25 inches showed that equilibrium had almost been reached and that analyses had to be exceedingly accurate to record minute changes in concentration with varying conditions of operation. At heights between 10 and 15 inches results were satisfactorily reproducible. Accordingly a height of 11 inches was chosen for the main study. T h e perforated pressure plate bearing down on the packing prevented it from becoming linearly displaced and orientated a t higher pulse energies. H T U values were almost quantitatively reproducible throughout the investigation as determined by a series of check runs. With a combined liquid flow rate of about 25 cu. ft./hr./sq. ft. of unpacked area, the unpulsed H T U obtained was of the order of 1 foot. H T U ' s ranging from 1 to 3 feet were reported by Demo and Ewing (6, 20) using a column packed with 0.5-inch carbon rings and substantially the same throughput rates. T h e lower values obtained in the present study are probably due to the small size of the glass rings used. Effect of Pulse Frequency and Amplitude. Flow rates of the acid and benzene phases were maintained at approximately 4.1 and 8.2 cu. ft./hr./sq. ft., respectively, corresponding to about 30 to 40y0 of flooding capacity under unpulsed conditions. Pulse frequencies of 10, 21, 37, 56, 78, and 103 cycles per minute were used a t amplitudes ranging from 0 to 50 mm. (Table I and Figure 2). Runs 41 and 46, and some others not recorded in Table I, were made without pulsation; unpulsed H T U was 6.75 inches. With pulsed operation, a family of curves was obtained as in Figure 2, frequency being the parameter. At 78 and 103 cycles per minute, curves could not be drawn with certainty in the region of the minimum, even though the experimental points are accurate; hence only the points are shown. T h e general pattern was the same at all frequencies investigated, H T U first de-
,PACKED E X T R A C T I O N COLUMN 7
I
I
I
I
I
I
I
I
I
I
I
I
I
I
1
1
1
/
1
Freq., cycles/min.
37
L A = 4 I cu.ft./hr./sq.ft. LB = , 8 . 2
56 (8
78 103 N O pulsaiion
e
4
0
AMPLITUDE,
Figure 2.
= a
24
28
32
mm.
The influence o f pulse amplitude and frequency showed the same trend a t all conditions investigated
creasing sharply with increasing amplitude to a minimum value and thereafter rising with further increase in amplitude. There exists, therefore, an optimum amplitude for a fixed frequency and set of flow rates. This was also observed ( 3 ) for the methyl isobutyl ketoneacetic acid-water and ethyl acetateacetic acid-water systems. When optimum amplitudes are plotted against corresponding frequencies for benzene-acetic acid-water and for methyl isobutyl ketone-acetic acid-water and ethyl acetate-acetic acid-water ( 3 ) , the data are represented fairly well by straight lines on a semilog plot leading to a general equation of the form:
f
20
16
12
0
+ B log
0,
(3)
where a and /3 are constants dependent on the system, flow rates, and nature of packing. Values of these constants for the three systems are given in Table 11. This correlation, which shows that optimum amplitude is a n exponential function of frequency a t fixed flow rates, is generally valid for pulsed packed columns and enables optimum amplitude to be calculated a t any frequency from only two sets of accurate experiments. For sieve-plate columns a number of investigators ( 7 , 4 )have obtained a correlation between column efficiency evaluated in terms of over-all H T U (or HETS) and the product of pulse displacement and frequency. No correlation which eliminates the frequency parameter has so far been obtained for pulsed packed column. One of the difficulties is apparent in Figure 2 which shows that the value of (HTU),,,. is characteristic of each frequency and tends, in general, to decrease as frequency is increased.
In such cases, certain values of HTU obtainable a t a given frequency cannot be obtained a t some lower frequency regardless of the value of a. O n the other hand, a single-line correlation between H T U and uf implies that under
Table 1.
fixed operating conditions, H T U is a unique function of uf, whatever the individual values of a or f. I n Figure 3, H T U is plotted against uf from the data presented in Table I. Examination of the experimental points
-
Effect of Pulse Frequency and Amplitude Liquid Flow Rates, Cu. Ft./Hr./ Concentration of Sq. Ft. Acetic Acid, Material _____ BenLb. Mole/Cu. Ft. Balance, Run Acid zene Wt. Acid Out No. feed feed" feed nate tract Wt. Acid In 41 46 58 55 56 57 48 45 44 49 47 42 37 40 38 39 43 52 51 50 53 54 63 64 59 62 65 66 67 69 68 a
4.00 4.08 4.10 4.08 4.08 4.08 4.15 4.13 4.10 4.15 4.04 4.08 4.00 4.12 4.07 4.15 4.00 4.08 4.15 4.08 4.08 4.07 4.13 4.10 4.07 3.95 4.10 4.10 4.08 4.08 4.08
7.98 8.30 8.30 8.30 8.20 8.30 8.72 8.20 8.03 8.30 8.30 8.30 7.62 7.74 7.86 8.07 8.45 8.25 8.35 8.30 8.30 8.38 8.20 8.18 8.20 8.14 8.18 8.20 8.20 8.20 8.20
0.0668 0.0662
0.0632 0.0627 0.0667 0.0625 0.0667 0.0625 0.0667 0.0625 0.0667 0.0627 0.0662 0.0623 0.0662 0.0618 0.0662 0.0623 0.0662 0.0625 0.0662 0.0600 0.0668 0.0628 0.0668 0.0630 0.0668 0.0631 0.0668 0.0629 0.0668 0.0630 0.0668 0.0630 0.0667 0.0625 0.0662 0.0618 0.0662 0.0622 0.0667 0.0626 0.0667 0.0625 0.0648 0.0607 0.0648 0.0608 0.0667 0.0625 0.0650 0.0610 0.0648 0.0613 0.0648 0.0608 0.0648 0.0608 0.0648 0.0608 0.0648 0.0609
0.00196 0.00195 0.00206 0.00207 0.00209 0.00202 0.00207 0.00209 0.00204 0.00203 0.00200 0.00216 0.00218 9.00214 0.00214 0.00208 0.00199 0.00208 0.00214 0.00209 0.00200 0.00196 0.00199 0.00199 0.00208 0.00191 0.00192 0.00196 0.00197 0.00196 0.00194
1.005/ 1.0069 1.0025 1.0026 1.0026 1.0056 1.0059 0.9961 1.0004 1.0038 0.9965 1.0064 0.9965 1.0047 1.0034 1.0055 1.0067 0.9991 0.9965 1.0012 1.000 1.0009 1.0004 0.9991 1.0008 0.9963 1.0013 0.9991 0.9986 0.9988 1.0006
on Column Performance
Pulse
F ~ ~ -Pulse
quency, Cycles/ Min.
Ampli. tude, Mm.
(H TU)on, In.
0 0 10 10 10 10 21 21 21 21 21 37 37 37 37 37 37 56 56 56 56 56 78 78 78 78 78 103 103 103 103
0 0 4.0 10 18 36 4.0 6.0 22 30 44 5.0 6.4 9.4 14 40 50 2.0 4.0 8.0 22 32 2.0 4.0 5.0 9.0 14 1.0 3.0 4.0 6.0
6.75 6.60 5.80 5.73 5.55 6.10 5.51 5.45 5.76 5.87 6.15 5.10 4.95 5.23 5.15 5.73 6.40 5.61 4.95 5.36 6.35 6.52 5.56 5.60 5.65 6.38 6.25 5.88 5.78 5.88 6.03
Concentration of acid in benzene feed was zero.
VOL. 51, NO. 5
M A Y 1959
647
I
I
1
I
I
I
I
I
I
1
I
-\
f
i
System: Benzene-acetic acid- water 4.1 cu.ft/hr,/sq.ft.
LA
= 8.2
L,
.-c
0'
-
m
0
3
I-
I
Freq.,cycles/min. 5 10
0
21
c)
37
e
56 70
0
103
0
@3
NO Dulsalion
0
4
0
400
1200
800
1600
2000
a x f , mm. rnim-1
Figure 3. The minimum in this plot sets a limit on the pulse energy that can increase efficiency and defines a condition of optimum operation
No
0
pulsation
Freq. = 37 cycler/min. Amp. = 8 rnrn.
0
Freq. 78 cyciedrnin. Amp. = 2 5 rnrn.
0
Acid r a t e : 4 . 2 5 cu.ft./hr./sq I t .
I
Table II.
LB
System Benzene-acetica acid-water
LA 4.1
8.2
Ethyl acetate-b acetic acidwater (3)
4.2
8.4
Methyl isobutylb ketone-acetic acid-water (3)
8.0
8.5
a
HTU.
648
I
I
Constants for Equations 3 and 6 Packing 0.25-inch glass Raschig rings 0.25-inch Dorcelain Raschig rings 0.25-inch porcelain Raschig rings
* HETS.
INDUSTRIAL AND ENGINEERING CHEMISTRY
01
P
9
125
-103
76.5
94
-70
184
160
r 6.92
11
10
20
12.25
S
-150.0
-42.5
-103
reveals that because of the variation of (HTU),,,. with frequency, the latter cannot be eliminated as parameter within the range of uf values from about 100 to 350, but on either side of these limits a single-line correlation is approximately valid. Unfortunately, the range of pulse energy where frequency appears as parameter corresponds in part to the most useful region of column operation. It might thus appear that in cases where (HTU),,, is almost independent of frequency, a single-line correlation between H T U and uf should be possible over a wide range of uf values. This is not necessarily true; although (HETS),,, was virtually independent of frequency from 29 to 78 cycles per minute for ethyl acetate-acetic acid-water ( 3 ) , a singleline relationship between H E T S and uf could not be obtained. T h e minimum in the plot of H T U us. uf sets a limit on the pulse that can result in increased efficiency and defines a condition of optimum operation. At low and medium pulse energies, imparted turbulence reduces droplet size with a consequent increase in interfacial area of contact and degree of coalescence and redispersion, leading to increased efficiency. Beyond this stage, backmixing becomes predominant and reduces efficiency until a t still higher pulse energies the column floods because of excessive holdup of the dispersed phase. Correlation of Pulse Characteristics and HTU. Figure 2 shows that a given extraction efficiency can be achieved with various combinations of pulse amplitude and frequency. For methvl isobutyl ketone-acetic acid-water ( 3 ) . amplitude was inversely proportional to the square of the frequency a t an H E T S value of 7 inches. When this correlation is extended to other H E T S values, the relationship does not always hold satisfactorily, nor do the present data conform. O n the other hand, the exponential relationship between pulse frequency and optimum amplitude (Equation 3) suggests that a similar relationship might exist between frequency and amplitude a t a fixed value of extraction efficiency. A family of parallel straight lines is obtained when frequency is plotted against the logarithm of the amplitude with H T U as parameter. The data of Chantry ( 3 ) for methyl isobutyl ketoneacetic acid-water and ethyl acetateacetic acid-Lvater can also be correlated in this manner. Thus a t any fixed value of H T U or HETS, pulse frequency and amplitude are related as follows: f
=
p
+ slog n
(4)
xvhere and s are constants. The former is dependent on the value of H T U or HETS while the latter has the same value for all straight lines of the family.
PACKED EXTRACTION COLUMN I t is now possible to formulate a general equation relating pulse characteristics to H T U or HETS. When fi in Equation 4 is plotted against the corresponding value of H T U or HETS on rectangular coordinates, a straight line is obtained which satisfies the equation
p
= g(r
- HTU)
12
I
I
I
I
I
I
I
I
I
0
No pulsation
Freq. = 37 c y c l e s h i n . Amp. 8 mm.
e
(5)
\\.here q and r are constants. (HETS may be substituted for HTU in Equation 5 wherever appropriate.) Substituting for p in Equation 4 : f
=
q(r
- HTU)
s 10%
(I
(6)
Values of the constants q, r , and s for benzene-acetic acid-water, ethyl acetate-acetic acid-water, and methyl isobutyl ketone-acetic acid-water are given in Table 11. I t is necessary to define the limits within which Equation 6 is valid. At a fixed frequency, the upper limit of amplitude occurs when a = a,, ( a , is obtained from Equation 3) : H T U calculated from 6 then corresponds to Equation (HTU),,, . The lower limit of amplitude can be fixed as follows. Theoretically, both f and a are zero when H T G = (HTU).,. Equation 6 does not apply under unpulsed conditions, but HTU as calculated from this equation equals (HTU),, a t definite positive values of f and a. If the frequency is fixed, H T U = (HTU),, when a = uUp. Hence a t a given frequency. Equation 6 can only be used for amplitudes greater than uUp. The amplitude aUp is generally quite small so that there is little improvement in efficiency (less than about 5%) over the unpulsed value a t amplitudes lower than uup. At any frequency, the limits of validity of Equation 6 can be defined as follows: (HTU),,
> ( H T U ) 2 'HTU),,,
e
5 -
a 0
I
I
I
I
I
I
I
1.2
0.8
0.4
I 1.6
I
2.0
PHASE FLOW R A T I O , L,/L,
Figure 5. Column performance is well demonstrated here-HTU values for the pulsed column do not change significantly over a range of flow rate ratios
For ethyl acetate-acetic acid-water ( 3 ) , Equation 6 represents the experimental data with an average error of about 8%. For methyl isobutyl ketoneacetic acid-water ( 3 ) , the agreement is good for frequencies u p to 78 cycles per minute. Beyond this frequency, experimental data in the correlation range are meager, and a reliable check is difficult, but it is believed that Equation 6 will hold with sufficient accuracy a t higher frequencies also. Effect of Liquid Flow Rates. Table I11 summarizes runs made to determine the effect of continuous phase rate on efficiency. T h e disperse phase rate in
these runs was held constant a t 12.45 cu. ft./hr./sq. ft. Without pulsation H T U passed through a minimum a t a relatively low continuous phase rate, as has also been reported by other investigators (27), while under pulsation it was almost insensitive to changm in continuous phase rate; this enables the pulsed column to be operated effectively in the region where conventional operation is least efficient. T h e effect of varying the disperse phase rate from 2.42 to 19.9 cu. ft./hr./ sq. ft. for both pulsed and unpulsed columns a t a constant low continuous phase rate of 4.25 cu. ft./hr./sq. ft. is
or aUp
\Yithin these limits, Equation 6 can be used to compute the value of H T U corresponding to any given combination of pulse frequency and amplitude. Conversely, it can fix the pulse conditions necessary to attain a given value of H T U . I t can be used with Equation 3 to calculate the maximum efficiency obtainable a t a given pulse frequency and set of flow rates. For benzene-acetic acid-water, experimental and calculated values of H T U checked to within about 5%. A reliable check of Equation 6 when is possible only H T U = (HTU),,,. when (HTU),i, has been experimentally established with certainty. I n general, the use of Equation 6 for this system is quite reliable,
Table Ill.
Under Pulsation HTU Was Almost Insensitive to Changes in Continuous Phase Rate
Liquid Flow
Run No. 93 94 95 102 100 99 98 101
W 97
Rates. Cu. Ft./Hr./ Concentration of Sq. Ft. Acetic Acid, B ~ ~ - Lb. Mole/Cu. Ft. zene Acid Acid RaffiExfeed" feed tract feed nate 0.96 2.20 10.65 4.25 1.75 14.35 17.85 1.75 10.50 13.85
12.45 0.0653 12.45 0.0653 12.45 0.0653 12.45 0.0653 12.45 0.0652 12-45 0.0653 12.45 0.0653 12.45 0.0652 12.45 0.0653 12.45 0.0653
0.0473 0.0550 0.0631 0.0598 0.0529 0.0634 0.0638 0.0529 0.0630 0.0634
0.00148 0.001 70 0.00173 0.00169 0.001 92 0.00202 0.00201 0.00191 0.00 198 0.00201
Material Balance, Wt. Acid Out Wt. Acid In 1.0103 0.9893 0.9988
...
1.0210 0.9980 0.9982 1.0205 1.0000 0.9984
Pulse F ~ ~ pulse -
quency, Cycles/
Amplitude,
Min.
Mm.
0 0 0 0 37 37 37 78 78 78
0 0 0 0
8.0 8.0 8.0 2.5 2.5 2.5
(HTUIOB,
In. 8.60 7.58 8.29 7.8 5.57 5.80 5.94 5.57 6.00 5.88
Concentration of acid in benzene feed was zero.
VOL. 51, NO. 5
MAY 1959
649
HTU = height of transfer unit, inches Table IV.
Run NO. 83 82 80 79 78 84 85 86 87 91 90 89 88 a
Liquid Flow Rates, Cu. Ft./Hr./ Sq. Ft. BenAcid zene feed feed” 4.28 4.25 4.25 4.25 4.25 4.25 4.25 4.25 4.25 4.25 4.25 4.25 4.25
Concentration of Acetic Acid, Lb. Mole/Cu. Ft. Acid RaffiExfeed nate tract
2.87 0.0653 5.35 0.0653 13.25 0.0653 17.00 0.0653 19-90 0.0653 2.92 0.0653 5.15 0.0653 12.45 0.0653 20.60 0.0653 2.42 0.0653 5.08 0.0653 12.25 0.0653 20.8 0.0653
0.0640 0.0630 0.0598 0.0590 0.0580 0.0638 0.0620 0.0596 0.0561 0.0640 0.0625 0.0590 0.0560
Material Balance, Wt. Acid
Pulse
Wt. Acid In
quency, Cyc1es/ Min.
out
Pulse Amplitude, Mm .
Fre-
1.0008 1.0025 0.9906 1.0042 0.9906 0.9999 0.9989 1.0050 1.0076 1 .OW4 0.9990 0,9904 0.9978
0.00191 0.00188 0.00169 0.00167 0.00149 0.00198 0.00200 0.00200 0.00198 0.00199 0.00203 0.00202 0.00198
shown in Figure 4, which is based on the data of Table IV. T h e efficiency of the pulsed column is not entirely uninfluenced by the disperse phase rate, but the effect is much less than in the unpulsed column where H T U increases with increase in benzene rate. For a nonpulsed column a similar behavior a t approximately the same continuous phase rate (3.52 cu. ft./hr./sq. ft.) was observed by Demo and Ewing (6, 20). Thus, a t a low continuous phase rate the effect of pulsation is greater a t higher disperse phase rates. Pulsation a t 37 cycles per minute and 8-mm. amplitude reduces conventional column HTU almost linearly with increasing disperse phase rate; a t a benzene flow rate of 20 cu. ft./hr./sq. ft. the pulsed column is almost twice as efficient as the conventional column. Obviously column performance can be better demonstrated by plotting HTU as a function of phase flow ratio (Figure 5). H T U values for the pulsed column do not change significantly over a sevento eightfold range of the ratio of the two rates, while for the unpulsed column H T U is markedly high a t low values of
0 0
0
0
0
0
0 0
0 0 8.0 8.0 8.0 8.0 2.5 2.5 2.5 2.5
37 37 37 37 78 78 78 78
6.74 6.05 8.24 8.90 10.15 6.13 5.80 5.60 5.40 5.97 5.56 5.87 5.40
T h e present column is to be operated a t acetic acid and benzene flow rates of 4.1 and 8.2 cu. ft./hr./sq. ft., respectively, and a t a pulse frequency of 50 cycles per minute. Calculate the optim u m amplitude, the minimum attainable H T U , and the value of HTU at a n amplitude 50% lower than optimum. Solution : Optimum amplitude (a,) is calculated from Equation 3 which for the benzene-acetic acid-water system may be written f = 125
- 103 log a,,
7d.5 (6.92
- HTU) 150 log 5.35
HTUmi,, = 4.84 inches (HTU),,, = 6.75 inches. this value in Equation 6 : 50
=
76.5 (6.92
-
6.75)
Substituting
-
150 log u p
u p = 0.57 mm.
This is the approximate amplitude below which pulsation is not likely to produce any practical improvement in efficiency. T h e limits of validity of Equation 6 under the given conditions are, therefore, 5.35 2 a > 0.57; a,/2 = 2.68 mm., and this amplitude lies within the foregoing limits. Substituting in Equation 6 : 50
=
76.5 (6.92
-
HTU)
-
150 log 2.68
H T U = 5.42 inches. Nomenclature a
LAILB.
Illustrative Problem
=
an
a.P
C
c*
AC
f
h
iNDUSTRlAL AND ENGINEERING CHEMISTRY
ft./hr. /sq. ft.
SVBSCRIPTS (HTUIOB, In.
At f = 50 cycles per minute, a, = 5.35 mm. The minimum value of H T U will occur when the column is operated at optimum amplitude. To obtain (HTU),in., Equation 6 is used. Substituting in Equation 6: 50
= superficial liquid flow rate, cu.
q, r, s = constants of Equation 6 a, p = constants of Equation 3
Concentration of acid in benrene feed was zero.
650 ’
= constant of Equation 4
Variations in Disperse Phase Rate Have Much Less Effect on the Pulsed Column
pulse amplitude (distance between extreme positions of the pulse), mm. pulse amplitude for minimum HTU at a given frequency, mm. pulse amplitude a t which (HTU) = (HTU)., in Equation 6 concentration of acetic acid, 1b.-moles/cu. ft . equilibrium concentration of acetic acid in any phase corresponding to a given concentration in the other, 1b.moles/cu. ft. concentration driving force pulse frequency, cycles/minute effective height of column, inches
A
= = min. = Im = o = ti@ = 1 = 2 =
B
acid phase benzene phase minimum log mean over-all unpulsed inlet conditions outlet conditions
literature Cited
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RECEIVED for review April 5, 1957 -ACCEPTED May 13, 1958
