ENGINEERING AND PROCESS DEVELOPMENT 8. The probe has a constant cross-sectional area, a constant perimeter, and a constant thermal conductivity 9. The probe has a uniform temperature across any transverse section 10. The probe tip is small compared to the remaining probe surface 11. The gas velocity is sufficiently low (say less than 400 feet per second) so that its stagnation temperature rise is not important Nomenclature
a = transverse cross-sectional area of probe, sq. ft. b = probe length, ft. Cl, C, Ca = integration constants FA = radiation angle factor based on probe area, dimensionless K = radiation emissivity factor, dimensionless h, = convection heat transfer coefficient, B.t.u./hr./sq. ft./” F. h~ = radiation heat transfer coeffitient, defined by Equation 4, B.t u./hr./sq. f t . / ” F. ___ of probe, B.t.u./hr./ft./” F. X. = thermal conductivity m = defined as .\/h,P/(ka), ft.-’ n = defined as . \ / ( % m P m , ft.7’ P = perimeter of tiansveise cross section of probe, ft.
Qc,Q K , Q R T
=
Tr =
TG = TW =
z s c
= = =
= heat flow rate by convection, conduction, radiation, B.t.u./hr. temperature of probe a t location, 2, O R. (units of F. mav of course be used when temperature diffeiences are being calculated) temperature a t tip of probe, R. temperature of gas, R. temperature of enclosing duct or walls, O R. distance along probe from tip, ft. emissivity of probe, dimensionless Stefan-Boltzman constant = 0.173 X B.t.u./hr./sq.
ft./” R.4
literature Cited (1) Assman, R., Veroflentl. Preim. meteorol. Inst. Abhand., 1, 117
(1892). Bolles, W.L., Petiolezm Reliner, 27, N o . 2, 120-6 (1948). ( 3 ) Dahl, A. I., Ibid., 29, No. 3, 115-22 (1950). (4) Emmons, H. W., Elliot Co., Jeannette, Pa., “Development of Temperature Probe, Multishielded Type (1944). (5) Hawthorne, W. R., .I. Inst. Fuel, 12, 64-89 (1939). (6) Howe, E. D., and Boelter, I,. 31. K., “Temperature, Its Measurement and Control in Science and Industry,” pp. 331-41, New York, Reinhold Pub. Corp., 1941. (7) Ingersoll. L. R., Zobel, 0. J., and Ingersoll, -4. C., “Heat Conduction with Engineering and Geological Applications,” pp, 2 1 4 , New York, 1lcGraw-Hill Book Go., 1948. (8) Kern, D. Q., “Process Heat Transfer,” pp, 517-18, New York, YIcGraw-Hill Book C o . , 1950. (9) Kreisinger, H., and Barkley, T. F., U s S.Bur. Mines, BulE. 145 (1918). (10) McAdams, W.H., “Heat Transmission,” pp. 21.9-23, New York, McGraw-Hill Book Co., 1942. (11) Marehall, W. R., Jr., and Pigford, R. L.. “Application of Differential Equations to Chemical Engineering Problems,” pp, 3 8 4 4 , Newark, Del.. Univ. of Del., 1947. (12) Moffatt, E. 11..Instruments. 22, 122--32 (1949). (13) Moore, D . W., Jr., Aeronaut. Eny. Rev. 7, 50.5, 30-4 (1948). (14) ?rlulliken, H. F., “Temperature, Its Alewsurement and Control in Science and Industry,” pp. 778-804, New York, Reinhold Pub. Corp.. 1941. (15) AIulliken, H. F., and Osborn, IT.J., I b i d . , pp. 505-29 (16) l’friem. H., Forsch. Gebiete Ingmieurw., 7, 85-92 (1936) (17) Schmick, H., 2. tech. P h y s , 10, 146-7 (1929). (18) I‘lsamer. 3 . . Forsch. Gehiete Inoenieurw.. A3. 91-8 11932). (19) Waggner, K. J., Ann. P h y s z k . $8, 579 (1896). (20) Wend, LZ.,and Schultze, E , Mztt. W a r m e s t d l e , S o . 92, Ve,.sins (2)
Dezctseher E’isenhultenleute (19261, RECEIVED for review February 19, 3953.
ACCEPTED JIdJr
13, 1Ra3.
Effect of Tower Height in a Solvent Extraction Tower RICHARD M. KREAGER’ AND CHRISTIE J. GEANKOPLIS O h i o Sfafe Universify, Columbus 7 0, O h i o
T
HE use of solvent or liquid-liquid extraction has increased rapidly in the past decade. Many difficult or expensive separations performed previously b v using the more common unit operationssuch as evaporation anddistillation can now be carried out more efficiently and cheaply by liquid-liquid extraction. Treybal ( 1 7 ) and others ( I f , 18) recently summarized typical industrial equipment and discussed the process variables and the special usefulness of extraction as a separation technique. Trepbal also discussed extraction processes in the petroleum, fat and oil, organic, inorganic, and metallurgical industries. The separation of the rare earth metals by liquid extraction is a useful application There the tedious recrystallizations usually necessary are avoided (5,4, i4,i5). The performance data which do exist for spray-type columns are relatively limited in their use, because they are generally applicable only to the particular tower for which the data were obtained and not to columns having different heights, distributors, and other features. 9 survey of the literature covering liquid-liquid extraction results in the conclusion that the field has
* Present address, B. F. Goodrioh Chemical Co., Avon Lake, Ohio, 2156
been sornen-hat neglected and that some of the informat’ion available is cont’radictory. In studying extraction from single drops, Sherwood, l h a n s , and Longcor ( I S ) used the system benzene-acetic acid-water and found that nearly half the total extraction book place during the drop formatiou. West, Robinson, and hlorgenthaler (19) used the same system and similar equipment but found only about 15 t o 20% extraction during the drop formation. Also, a considerably smaller aniomt of extraction for the whole column was found when compared to Sherwood’s results. Licht and Conway ( I O ) also found results similar to those of Sherwood and of West. Johnson and Bliss (9) st,udied the design of the dispersed phase nozzle and indicated that the optimum tip diameter to use was 0.10 inch and t,hat the number of tips should be incrcased as tjhe dispersed phase flow is increased. Hayworth and Treybal (8) found that drops of uniform size could be obtained from sharpedged nozzles having diameters between 0.059 and 0.31 inch if the linear velocity through the nozzle is less than 0.3 feet per second. Elgin and Browning ( 2 ) found t’hatmass transfer coefficients in
INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 45, No. 10
ENGINEERING AND PROCESS DEVELOPMENT
c
.rt
spray towers were affected by flow rates, direction of solute transfer, and drop size. While studying the flooding rates of spray columns, Blanding and Elgin (1) found that the end design was critical, particularly at high flow rates. Treybal (16) showed that the (H.T.U.)ow varied inversely as the dispersed flow rate to a fractional power. Geankoplis (6) discussed operation of a spray tower and stated that there must be present some mixing of the continuous phase which may be partly due t o the fact that each rising droplet must carry with it an “atmosphere” or surrounding film of the continuous, downcoming phase. On coalescing a t the interface this droplet discharges its atmosphere of continuous phase which may contribute to the end effect. Using a movable internal sampling tube, Geankoplis and Hixson (6) determined the concentration gradient throughout a 1.45inch diameter tower. They found a large inlet effect a t the continuous phase inlet to the tower and none a t the dispersed phase inlet. These results were confirmed by Geankoplis, Wells, and Hawk (7), using a larger diameter, pilot-unit size tower, a different system, and the opposite direction of transfer. Nandi and Viswanathan (18) systematically studied the effect of column height in a spray tower and found an increase of H.T.U. with an increase in column height. At high tower heights the H.T.U. tends to level off as the end effect becomes decreasingly important. The process variables of flow rates, concentrations, types of nozzles, and end designs have been investigated. Most of these investigators have used different column heights in obtaining spray tower extraction data. Very little work has been done in trying to find the effect of column height on mass transfer coefficients. I n order to design extraction spray towers it is necessary to have a generalized correlation of extraction variables which includes column height and end effects. The purpose of the present investigation was to obtain systematic data showing the effect of column height on the mass transfer coefficients and end effects.
qp
To accomplish this the system methyl isobutyl ketone (M.1.K.)propionic acid-water was selected. Internal Sampling and 1.41-Inch Spray Tower Are Used to Study M.1.K.-Propionic Acid-Water System
Process Flow. The process flow diagram of the extraction spray tower is presented in Figure 1. The materials of construction for the tower and accessories were glass for the tower and containers, saran for most of the tubing, and neoprene for the stoppers and one piece of flexible tubing. The methyl isobutyl ketone and water phases were placed in 5-gallon glass bottles A a t a height of about 10 feet above the top of the tower (Figure 1). The solutions from these storage bottles were siphoned a t rates controlled by valves D into constant-head tanks B. The small amounts of overflow were collected in carboys C and were used in future runs. The flow rate of t h e ketone, which was always the dispersed phase, was controlled by needle valve E and the flow of the continuous water phase by valve E a t the top of the tower.
M.1. K. SETTLING SECTION
E XTRAGT ION SECTION
WATER SETTLING-\ SECTION
D O
Figure 2.
Extraction Column
The ketone entered the tower through nozzle F and rose as small droplets up the tower. The water phase entered through nozz1e.G. The height of the interface layer between the ketone and water layers was regulated by an adjustable loop, H. The water and ketone outlet streams were collected in carboys K . Rates of flow were determined by quickly transferring the flows from t h e carboys t o 500-ml. graduates L by means of switching devices M . A glass, movable sampling thief as described by Geankoplis and Hixson (6) was made of a 5-mm. glass tube, P , and extended inside the extraction section. The sampler occupied 1.7% of the tower cross-sectional area. By means of a hook a t the end of the sampler, a sample of the descending water phase was slowly withdrawn by gentle suction without entraining the dispersed ketone phase. Suction was provided a t the sampling flask, T , and the rate of sampling was controlled by valve 2 and the suction at T . The vertical position of the tube, P, which was flush against the wall of the tower, was secured by guide block R in the scale, S. Figure 1 .
October 1953
Process Plow Diagram
Extraction Tower. A detail of the basic extraction tower is shown in Figure 2. This column was a glass tube 1.41 inches in
INDUSTRIAL AND ENGINEERING CHEMISTRY
2157
ENGINEERING AND PROCESS DEVELOPMENT inside diameter with a flared settling section at, the bottom. The dispersed phase nozzle was placed 2 inches below the beginning of the flared section so that the annular area open to the downcoming x-ater flow was approximately equal to the cross-sectional area of the colunin proper. Three towers with identical end designs m r e used and are shown in Figure 3. Changes in the overall lengths of the towers were made in order to keep the heights of the settling sections as near the same as possible. Decreases in tower height for rxtraction were made by moving the continuous phase nozzle atid the interface from the 8- t,o the 14-inch point or by using the next shorter length tower. The dispersed phase nozzle was kept a t the bottom of the 10" flare in all cases.
was first saturated with water. The exhausted water-acid solution was brought to the desired normality w-it,hpropionic acid. To start a run the ketone valve was opened very slightly t o allow ketone to flow continuously from the nozzle to prevent water from ent'ering this nozzle. The water valve was then opened, and when the interface was a t the correct height bot,h valves were set at the desired openings. The flow rates were checked by collecting t,imed volumes in graduated cylinders and the valves again adjusted to obtain the correct rates. The interface level was maintained a t the tip of the continuous phase nozzle for all runs. Steady-state conditions in the tower were attained after the cont'ents of the tower had changed four t o five times. To obtain internal samples, a purge sample was taken a t a late of 5 ml. per minute. Then a sample of about 25 ml. was collected in another bottle at this same rate, which corresponded to about 2.5% of the total continuous phase flow. This purging and sampling was repeated as the sampler was moved down the tower to the next point. Inlet and outlet samples were taken intermittently during a run and the samples composited. The water and ketone rates were also checked intermittently and average values used. The average temperature of all runs was 0.156"I.D. 75" F. The methyl isobutyl ketone used was technical grade obtained from the Carbide & Carbon Chemicals Corp. Propionic acid, c.P., from Eastman Kodak Co. and C.P. sodium hydroxide from Mallinckrodt 1.13" Chemical Co. were Y) used. D i s t i l l e d "! water was used throughout all the runs. 0.159'I.D. Analytical Analy4 TIPS ses. The amount :-.I of propionic acid in all samples was determined by acidbase titration using Figure 4. Continuous Phase 0.1 N sodium hyNozzle
-r ~~+ 1
M.I.K. S E T T L I N G SECTION, 14" II
ESIWATER Figure 3.
II
J
J
8"
L(
Column Heights and Settling Sections
4
i.
Nozzles. The continuous phase inlet nozzle used in all rune consisted of four tips, each 0 159 inch in diameter (Figure 4). The dispersed phase inlet nozzle shown in Figure 5 permitted t h e number of tips or jets to be varied directly with the flow t o give the same bubble size or interfacial area regal-dks of the dispersed flow. The diagram shows the pattern of tius used for the various ketone rates. The tips to be sealed were blocked by small neoprene stopTable 1. Over-all Transfer Data for Extraction Column pers. The velocity through the tips, as recomNo. Tips mended bv various investigators (8, Q), was kept Over-all Propionic Deliration Flow Rate, Dispersed Methyl constant at 0.27 foot per second for all except the Acid Transfer Rate Sw - n ' Cu. Ft./Hr. Isobutyl Run Height, ( S 4 . Ketone -(Lb. Mole/Hr.) X 103__IY -last two runs. Keeping the bubble size uniform So. Ft. LK Lm Nozzle XW NIT Sav. x 100 cuts down coalescence in the tower proper sincenon7.18 7.75 7.47 I 3.0 28.4 37.9 6 -7.6 uniform size bubbles travel a t different velocities 7.16 6.77 6.97 40.5 -5.5 2 6 2.5 28.5 R.11 6.40 6.25 -4.7 2.0 3 6 28.9 38.6 and bump into each other more often than uniform 4.80 4.78 4.79 40.2 -0.4 1.0 4 6 29.4 3.97 4.16 4.07 0.5 28.5 38.8 -4.7 5 6 ones. The long flare and the perforated glass plate 10.51 10.26 10.39 3.0 2.5 49.1 39.4 6 10 a t the mid-section of the nozzle gave good liquid 9.30 8.38 8.M -10.4 40.4 10 7 2.0 48.0 6.66 1.2 6 . 7 4 6 . 7 0 4 0 . 6 10 8 1 . 0 4 8 . 6 distribution t o all the tips, as was evidenced by 5.37 5.79 -7.5 5.58 10 0.5 48.1 38.9 9 9.10 -2.1 8.91 3.0 39.2 38.8 9.01 10 8 approximate bubble counts from each tip. 8.96 9.51 -6.0 9.24 1OB 3.0 39.8 39.1 8 3.72 Procedure. In all the runs performed the direc3.96 6.3 3.84 15 1.0 4 19.8 39.0 4.82 5.18 -7.2 5.00 40.1 3.0 6 29.2 17 tion of extraction was from the continuous phase 2.34 3.0 2.30 -2.0 27.2 39.0 2.32 6 19 4.29 2.0 4.02 -6.5 40.3 4.16 21 27.7 to the dispersed phase. The spent ketone solution 3.30 2.99 -9 8 3.15 39.4 1.0 23 29.4 6 . 4 8 3 . 0 6 . 1 3 4.0 1 9 . 7 3 9 . 8 6 . 3 1 26 from previous runs was regenerated by washing 8.73 0.1 8.74 3.0 8.74 29.2 39.2 27 first with 2 AT sodium hydroxide solution and then 10.10 10.91 -7.6 40.0 38.4 10 50 3.0 28 twice with distilled water. Any fresh ketone added
,",ok
2158
INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 45, No. 10
~
ENGINEERING AND PROCESS DEVELOPMENT droxide and phenolphthalein as the indicator. All samples were 10 ml. in volume and were mixed with 20 ml. of ethanol prior to titration t o ensure complete miscibility of any organic phase. All titrations were run in duplicate and suitable endpoint blanks were determined,
Table 11. Run No. 1 2 3
Smoothed Data Used to Calculate Internal Mass Transfer Coefficients for Short Tower Sections
4
Theory and Equations. The following equation is usually employed t o calculate the mass transfer coefficient for spray towers if the solvents are relatively immiscible, the distribution law holds, and the concentrations are relatively dilute: -V =. Kwa VACW Im (1) The height of a transfer unit is calculated from Equation 2 :
Lw (H.T.U.)ow = aK ;
.
Over-all Mass Transfer Data for Column
Inlet and Outlet Concentrations (Lb. Moles Acid/Cu. Ft. X 108)'
5 6 7 8 9 10
10B 15 17 19 21 23 26 27 28 a
In
cw
29.73 30.06 29.90 29.71 30.36 30.50 29.78 29.71 30.06 29.93 29,93 30.36 19.98 9.87 20.37 20.75 30.16 30.08 30.16
out
In
12.21 14.62 15.23 18.71 20.90 5.74 10.58 14.33 17.28 8.67 8.71 20.95 8.85 4.43 11.12 13.71 15.94 9.47 5.79
0 0 0 0 0 0 0
ACwlm X
CK Out
10s 14.50 16.60 17.41 20.40 22.76 11.78 15.20 18.65 20.69 13.38 13.30 19.79 10.20 5.10 12.29 14.78 16.05 12.62 10.58
0
0 0 0 0 0 0 0 0 0 0 0
Over-a11 Transfer Coefficients (H.T.U.)ow, Kwaa ft. 15.90 15.55 16.60 21.75 33.10 27.20 26.86 33.30 50.00 20.80 21.50 17.98 15.12 14.06 15.69 19.75 12.14 21.28 29.44
2.39 2.61 2.32 1.85 1.17 1.45 1.50 1.22 0.78 1.87 1.82 2.17 2.65 2.78 2.58 2.00 3.28 1.84 1.30
Lb. moles per (hr.) (cu. ft.) (Ib. moles/cu. ft.).
(2)
Geankoplis and Hixson (6) showed that if C% is negligible compared to Cw and if the logs of the concentration at different points in the tower are plotted against the linear height, the slope of the resulting line at any point represents the negative reciprocal of (H.T.U.)ow a t this point. In the runs in the present work, however, the C% was an appreciable percentage of CW. Equations 1 and 2 can also be applied t o short sections of the column by treating each section as a small, individual tower The concentration in the dispersed phase can be found by material balance. However, it must be remembered that this calculation assumes that the flow of continuous phase inside the tower is the same as that entering the tower. This has been discussed by Geankoplis ( 5 ) , who states t h a t there may be recircula-
rc)
-
0
IO
x
T I P PATTERNS 0.
S)
O.SO'DIAM
0
BLOCKED OUT
cW =
5
0
i
Z
L K '49.1
10.0x
* 3.0'
LW
39
LK
* 29.1 I
LK '39.1
(-J LK 829.1
tion of the continuous phase. For engineering design purposes the above method should be adequate. Calculations. The method used in calculating the mass transfer coefficients and end effects is essentially the same as that described by others (6, 7 ) . The experimental data obtained from the runs in the spray tower are presented in Tables I, 11, and 111. To illustrate the calculation procedure, the over-all material balance for run l waB calculated as follows:
Nw
4k O . l S ' I . 0 . LK s 2 0 . 0
Figure
5. Dispersed Phase Nozzle and Tip Patterns
October 1953
=
LWA
(CWl
- CWZ)
= 37.9
x
0.0108 (29.73 - 12.21) X
N~ = 7.18 x 10-3 N K = LKA ( C K I - C K Z )= 28.4 X 0.0108 (25.39 N~ = 7.75 x 10-3
N
Nx = Nw + 2
- 0) X
lo-'
= 7.47 X 10-3
INDUSTRIAL AND ENGINEERING CHEMISTRY
2159
ENGINEERING AND PROCESS DEVELOPMENT Table 111. Run No.
Internal Samples of Propionic Acid in W a t e r a t Points inside Tower Concentration .Icid__ In Water Phasr (Lb. F t ) X 103 ___ of -~ _ ~ Moles/Cu. _ _ ____ 5 6 8 12 16 18 ... ... ... ... 17 69 ... ... l7:62 20'72 18'51 19: 81 ... 19:i2 ... ~
1
3
2
3
...
...
... ... 2 i : 24
17'il
16: is
16'51
...
1;:60
...
ii: i 4 ... ... ... ..
...
, . .
... ...
,..
...
22:26
22: 56
...
...
15' 97
...
...
12'36
16:;o
.. ... ...
14.10
...
,..
...
...
...
...
30
24
...
11:29
...
7.56
..
... ...
...
,..
...
... l2:63 10:00 3.34
...
...
l2:83
14:io
...
14 62
20
...
,.. . . I
...
...
2i:QG
...
...
...
These numbers refer t u "inch point."
0
Table IV.
-
Run
Internal Samples of Propionic Acid in W a t e r a t Points inside Tower (Smoothed data) Concentration of Acid in Water P&i&b. 5 6 8 10 .. ... 20.3 ... ... .. 20:2 ... 20.3 19: 9 19'4 ... .. 20 174 .. .. ... .. 15:2 ... 17.7 16:s 15:9 ... , . 17:21 .. ... , . ... .. 17.9
___~
Oa 2 3 1 29.73 23.4 .., 2 30.06 21.8 ... 3 29.90 21.7 ... 4 29.71 20.4 5 30.36 21.58 2i.37 6 30.50 20.0 ... ... 7 29.78 20.0 8 29.71 17.6 9 30.06 18.59 18.24 10 29.93 21.2 ... 10B 29.93 ... ... 2 3 . 0 ... 15 30.36 17 19.98 16 0 ... 19 9.87 8.06 , . . 15.5 ... 21 20.37 23 20.75 15.2 ... 26 30.16 24.6 ... 23.7 ... 27 30.08 28 30.16 21.3 ... a These numbers refer t o "inch point." NU.
yo deviat,ion
. \ ' a
-
LVK
22:s
.. ..
s
22:o
... ... ...
14:2
.. ..
14.6
14:6
..
.. ..
X 100 =
= _____
... .., ...
.. .. ..
...
(CWi
- CW;) - Crr;T)
-.
Lw Kwa
x
10-3
=
Nm
=
LwA (Cwi
-
=
14.3
...
1313 13.6
...
.. .. ..
22.1 19.0 15.8
.. .. .. .. , .
...
... ...
11.8 6.19 11.7
,.
...
..
19.4 14.5 10.9
.. ..
.. ..
1014
.. .. ..
..
.. ..
ii:o ..
..
..
..
.,. , . .
...
7.5
...
... ...
36 12.4
.. .. ... ...
5 8
... ... ...
11.3
9.1
10.0 5.37
8.85
... ...
. .
...
16.9 11.0 7.6
...
...
4.%50 , . .
...
15.7 9.4 5.8
= 2.59 x 10-3 = ~ i c - 4( c K ~ - c K ~ ) lop3 = 28.4 X 0.0108 (25.39 - Cm) X 10-3
~w
=
A similar material balance for the section 2 to 10 inche,? fi,orn the interface yields: =
37.9 X 0.0108 (23.40 - 20.30) X = 1.27 X = 28.4 X 0.0108 (16.94 - C K ~X)
SI; = L Y =~ 1.27 X
=
15.90
37.9 = 2.39 15.90 ~
C W ~= ) 37.9 X 0.0108 (29.73 - 23.40) X
2.59 X
By material balance, the C K was ~ calculated from
2160
,.
..
15.2
__.._
14.~50x 10-3
The over-all Kwa and (H.T.TJ.)om values are tabulated in Table 11. The experimental Cw values obtained from internal and external sampling were plotted, as in Figures 6 through 13, and smoothed values read from these curves are tabulated in Table IV. These smoothed values were used to calculate the internal (H.T.U )OW values for short sections of the tower. The smoothing of data mas necessary to eliminate scattering of coefficients calculated by taking differences between closely adjacent points. For the section 0 to 2 inches from the interface for run 1,
Nw
..
..
...
16:3
30 14.0 14 9
Cw:)
i.47 X F Kwa = A 2 ( A C W lm) 0 0108 X 3 X 14.50 X = --
7.18
2.59 X
- (CW2
(CWl (CW?
(29.73 - 12.41) - (12.21 - 0) ACwlm = (29.73 - 12.41) 2.3 log (12.21 - 0 )
(H.T.U.)ow
10:7 11.6
..
14.0
..
.. .. ..
21
C K ~= 16.94 X
-Ca3 2.3 log
..
14: 8 14.5
air1
...
SIC
- i.6
The equilibrium data used in ralculating CE. for the s y d e m methyl isobut,yl ketone-propionic acid-water were obtained from Johnson and Bliss ( 9 ) . To czdculate the over-all mass transfer coefficients for the whole tom ET: ACrplm =
...
hIolea/Cu. F t . ) X 108 12 16 20 .. 16.9 ... 1s:1 1a:4 .. 16.2 18.7 .. ...
5 TOP IO 20 BTM, DISTANCE FROM INTERFACE, INCHES Figure 7. Effect of Inlet Concentration in Water
INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 45, No. 10
ENGINEERING AND PROCESS DEVELOPMENT Table V.
Internal (H.T.U.)OT
Length of Section, Inches10-20 20-30 30-36
2-10
Average
28
3.12 1.80 2.83 3.37 4.05 4.02 1.90 1.40
%Foot Column 3.46 2.07 2.86 4.11 4.83 5.02 2.51 1.68
3.56 2.87 2.10 3.65 2.59 6.24 3.02 1.47
3.26 1.80 2.84 3 72 4.33 4.57 2.20 1.51
2
2 -8 5.00
2.5-Foot Column 8-16 16-24 4.88 5.30
24-30 4.57
5.06
20-24 5.00 2.67 5.22
4 37 2.13 4.42
I 6 10 17 19 26 27
c
(H.T.U.)ow. Ft.
--
Run No.
for Short Column Sections
to Figure 14, the straight portion of the curve was extrapolated until it intersected the ordinate equal to the inlet water concentration. The fictitious height of tower in feet necessary to perform an amount of extraction equivalent to that done by the top inlet effect is distance ZL. The inlet effect a t the dispersed phase inlet was determined in a similar manner and is called Zh in feet. Values of these end effects are tabulated in Table VI.
- 2.0-Foot Column
2-6 4.04 2.08 4.39
3
I
7 21
2-5 8.76 5.07 10.80 5.33
4
8
15 23
2-3 8.32 4.17
5 0
12-20 4.74 2.13 4.61
6-12 4.35 2.18 4.28
.. .. .. ..
8.68 4.64 10.80 6.84
0.6-Foot Column 3-6 8.43 4.15
.. ..
8.32 4 17
....
-
rr)
0
1.0-Foot Column 5-8 8-12 8.60 8.04 3.50 4.22 10.80 7.87 8.35 6.95
x 3 0
tNLET
30.0 X I d 3
Cw
1 TOP IO 20 30 BTM. DISTANCE FROM INTERFACE, INCHES
rr)
0
Figure
X
9. Effect of Ketone Rate
3
u
LW.39
L K 29.1
I
I
-
rr)
0
TOP 4 8 BTM. DISTANCE FROM INTERFACE, INCHES %
Figure 8.
1
0
Effect of Inlet Concentration in Water
CKe = 12.80 X A C w l m = 14.55 X 10. i 2 7 x 10-3 Kma = 0.0108 X 8/12 X 14.55 X 10-8 37 9 (H.T.U.)op = A = 3.12 12.15
I2*l5
The values of (H.T.U.)ow for the short sections are given in Table V and the averages of these values, neglecting the end effects at both ends, are also given in Table V. End Effects. The end effects a t the continuous phase inlet and dispersed phase inlet were determined graphically using a method similar to that of previous investigators (7). Referring
October 1953
X
TOP IO 2 0 BTM, DISTANCE FROM I N T E R F A C E , INCHES Figure 10.
Effect of Ketone Rate
INDUSTRIAL AND ENGINEERING CHEMISTRY
2161
ENGINEERING AND PROCESS DEVELOPMENT
Table
This end effect may be due to the coalescence of bubbles or t o the discharging of the "atmosphere" of continuous phase surrounding the bubbles when they coalesce. This cocurrent flow of the continuous phase u i t h the iising bubbles would increase the recirculation of the continuous phase and decrease the benefits of true countercurrent flow. The inlet effect can be explained as follows if the extreme case where mixing or recirculation in the continuous phase is 100% efficient is assumed. In this case, the s o l u t r concentration throughout the continuous phase would be constant or uniform.
VI.
End Effects of Column in Terms of Fictitious Height of Column Run 10. ZL, Ft. ZA,Ft. 1
0.83 1.33 1.48 3.20
2 3 4 5 G
0 0.13 0 0 0 0.19 0 0.20
2.90 0.76 0.96
7
2.31 2.12
8
9 10 15 17 19
1.04 2.30 1.00 1 00
21 23 26 27 28
2 25 1,08 0.5G 0.59
Q
0.38
0 0.20 0.63 0 0
1.24
0 0
I
b
0.13
I
End Effect May Be Attributed to Cocurrent Flow of Continuous Phase Surrounding Bubbles
Over-all Material Balances. The average deviation of the over-all material balances for all the runs in the tower is 5% and the maximum is 10.4%. These deviations are reasonably small and should have a negligible effect on calculations of mass transfer coefficients. T o further confirm the fact that internal sampling had a minor effect on the extraction in the tower as shown by others ( 6 , 7 )duplicate runs 10 and 10B were made. Run 10B differed from run 10 in that the internal sampler was removed from the tower. The average moles transferred for both runs check within 3y0 and the over-all (H.T.U.)ow values also check within 30jo0. These errors are within the reproducibility of individual runs. Concentration Gradient and End Effects. All of the runs plotted in Figures 6 through 13 show appreciable end effects a t the t o p or continuous phase inlet. This phenomenon is similar to t h a t reported by previous investigators (6, 7 , 10). Up t o the present time this end effect has been found for a t least three different solvent-solute systems, for column diameters ranging from 1.5 to 3.75 inches, and for extraction from the dispersed to the continuous and from the continuous to the dispersed phase.
50 -
X
I 0
t-
'h
RUN 16
'?---orO-K-
0-0
I--o&
129.1 O-0
LK
X
.W(,
a
m
-
-'----0RUN
0
9
L
lo - 2
8
X
lo
1.0'
- L w = 39 - INLET
Cw
30.0 X
-2
8
0.5'
- L w = 39
=
- INLET
Id3
I
30.0
I
I
*
Cw
5I
=29.1
1
0
s
0
8
3.0'
I
C*
I
5-
2
-
()-
-
0
50
-
m0
rn
x
49.1
The outlct coriccntration would be the same as that inside the to\+er in the continuom phase. On entering the tower, the inlet concentration of the continuous phase would drop immediately t o the average concentration in the continuouq phase. This is similar to one equilibrium stage contact. Hence. a plot of concentration versus column height would show an abrupt drop a t the inlet and then a horizontal line. In theactual caw the mixing is not complete or the cocurrent flow is relatively small, so that the inlet effect would be less and the concentration gradient in the tower grrater. If this hypothesis is correct, it appears that the maximum inlrt effrct that could occur a t the inlet
ENGINEERING AND PROCESS DEVELOPMENT ketone rate, LK, greatly increases the slope of the concentration gradient. The end effect also changes. Similar trends are apparent in Figures 10 through 12. I n these curves the number of tips in the dispersed phase nozzle was increased as the flow was increased in order t o keep the same bubble size. This increase in concentration gradient can be explained b y the fact that the area of contact for extraction is increased and also the turbulence in the tower is increased.
50
rr)
-
0
BTM.
X
DISTANCE FROM INTERFACE Figure 14. Method of Determining Column
0
TOP
3 10
End Effects
tillation tower. The end effect at the discontinuous phase entrance is small, as seen in Table VI. Inspection of Figure 6 shows that the concentration gradient lines have approximately the same slopes in spite of different inlet concentrations. Figures 7 and 8 show similar trends. Since the slope is related t o the (H.T.U.)ow, the inlet concentration has little effect on the (H.T.U.)ow over the range of concentrations studied. Flow Rates. I n Figure 9 for the 36-inch tower, increasing the
-
A
4
c
0
2 . 3.0' 2 - 2.5' 2.0'
z-
x 2 - 1.0' e Z = 0.5'
t
.5
5
TOP 4
8 12 16 20 2 4 28 32 BTM. DISTANCE FROM INTERFACE, I N C H E S Figure 16. Effect of Column Height
I
I
L W -39
LK ~ 2 9 . 1
I-
I
I I I I I I I I ( I I I I ( I I I I 8 12 16 20 2 4 28 32 BTM.
t
TOP 4
D'STANCE Figure 15.
October 1953
1
1
INTERFACE, INCHES Effect of Column Height
I
0.6
I
I
0.8
l
l
1.0
I
I 2
LK'LW Figure 17.
Effect of Flow Rates on (H.T.U.)ow for Overall Column
INDUSTRIAL AND ENGINEERING CHEMISTRY
2163
ENGINEERING AND PROCESS DEVELOPMENT
I
I
61
20
I
4
c w = l o x 10-3
INLET
TO
30x10-3
% 0
?
?
=r
Y
W
c3
a
I
0.4
I
2
0.6 0.8 1.0
I 4
l
a w >
l 6
a
Z, FT. Figure 18.
Effect of Height on (H.T.U.)ow for Overall Column
I
I V
0.4
I
0.6
I
l
l
1
I ~
OB 1.0
2
4
LK ' L W Figure 20.
t
I
Effect of Flow Rates on Average (H.T.U.)ow with End Effects Eliminated I
IV
INLET
c w = I Ox
10-3T O 30
x
s INLET C w @ 3 0 x 10-3 o 20 x 10-3
1.0
0.4
2
0.6 0.8 1.0
4
6
810
2 , FT. Figure 19.
Correlation of Operating Variables for Over-all Tower
If the number of tips is kept constant while increasing the ketone rate, as in Figure 13, the increase in rate is more effective in increasing the concentration gradient when compared to Figure 9 where the optimum number of tips recommended by Johnson and Bliss (9) was used. This is contrary t o what was expected, since more uniform bubble size should result in less coalescence and larger areas for extraction. Considerably more work should be done in this field. Tower Height. Figures 15 and 16 show that for a given iiilet concentration the data for different column heights fall approximately on one general line. These results show that, with other factors constant, the amount of extraction for any tower height can be predicted with an accuracy sufficient for design purposes if internal concentration data for only one tower height are available. Or if external or over-all concentration data are available for two column heights, the same method may be used. 2164
0.4
0.6
OB 1.0
2
Z, FT. Figure 21.
Effect of Height and Flow Rates an Average
(H.T.U.)ow with End Effects Eliminated Process Variables Are Correlated for Over-all M a s s Transfer Coefficients
Figure 17 shows a log-log plot of the over-all (H.T.U.)ow versus L K I L w . I n this case, LWvaried only about 7% but other investigators (16) have shown that mass transfer data %ill correlate against LK or LKILw. The lines for different tower heights are approximately parallel. In Figure 18 the same data are plotted against tower height and show that for a given LK the (H.T.U.)ow increases with column height.
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
Vol. 45, No. 10
ENGINEERING AND PROCESS DEVELOPMENT
I
Using the slope of the lines in Figure 17, the data were correlated as indicated in Figure 19. T h e graph shows t h a t the over-all (H.T.U.)ow levels off at high tower heights. This is to be expected, since the end effect should have a negligible effect a t large values of tower height. The line can be represented by the equation (H.T.U.)ow = 2.34 ( L ~ / L w ) - o . 8 7(1.59)-1/2 (3) The average deviation of the experimental d a t a from this equation is d ~ 4 . 6 7and ~ the maximum deviation is 13%. Hence, this equation represents the data almost within the experimental accuracy of the individual runs. End Effects Eliminated. The data in Figure 20 are plotted in amanner similar t o Figure 17, except that the average (H.T.U.)ow with end effects eliminated is used. The slope of these lines is somewhat greater than in Figure 17. Figure 21 shows the effect of tower height on (H.T.U.)ow with the end effects eliminated. T h e exponent of the (LKILw)factor is greater and is 1.15 instead of 0.87. Also, the (H.T.U.)ow decreases as the column height increases. The height to diameter ratio for the tower may be an important factor, since at high values of this ratio more truly countercurrent action is probably obtained and this should lead t o a lower (H.T.U.)ow inside the column. This decrease appears t o be masked in Figure 19 where the e?d effect is included in the over-all (H.T.U.)ow. I n Figure 22, Zc, 2, and (H.T.U.)ow are correlated. I n this graph the Zc or efficiency of the end effect increases with an increase in (H.T.U.)ow. Proposed Design Procedure. T o predict the column performance using the system methyl isobutyl ketone-propionic acid-water and tower design similar t o the present investigation, the following method could be used with over-all extraction coefficients: Set t h e amount of extraction t o be performed andselecttheflow rates. Assume a tower height, 2, and obtain t h e value of (H.T.U.)ow from Figure 19 for this 2 and these flow rates. Using t h e above mass transfer coefficient and extraction t o be performed, calculate the tower height, 2, necessary. If the 2 calculated does not check t h e 2 assumed, assume a new value of 2 and repeat the above steps.
If mass transfer coefficients with end effects eliminated and Zd values are to be used, proceed as follows: Set the amount of extraction t o be performed and flow rates and assume a value of 2 as before. Obtain the (H.T.U.)ow
IO I
0
6
z
0
n
6 ,
4
A cd
0.5’ 1.0’ 2.0; 2.5
0
3.0’
N 4
e
-0
N Y
A
2
I I
2
4
6
A V E R A G E (H.T.U.), Figure 22.
October 1953
8
IO
from Figure 21 and then the value of 2; from Figure 22. Using t h e above (H.T.U.)ow and t h e extraction t o be performed, calculate t h e apparent tower height, Z’, needed. Then from the following equation calculate 2, the actual height: 2’ = 2; 2 z:, (4) The value of 2; can be assumed as zero. If the Z calculated does not check t h e 2 assumed, repeat the steps using a new value of 2.
+ +
Nomenclature
a A
CK
= interfacial area per unit volume of extractor, sq. ft./cu.
= cross-sectional area of column, sq. f t . = concentration of solute in phase K , Ib. moles/cu. f t .
ft.
CW* = concentration of solute in phase W which would be in
equilibrium with concentration in opposite phase, Ib. moles/cu. f t . C m = concentration of solute in phase W , lb. moles/cu. f t . ACw Im = log mean values of C w - CW* for the two terminals of column 2 = effective height of extraction section of tower, ft. 2’ = apparent height of extraction section of tower, f t . 2: = fictitious height of column equivalent t o continuous Dhase inlet effect. ft. 2; = fictitious height of dolumn equivalent t o dispersed phase inlet effect, ft. (H.T.U.)ow = over-all height of transfer unit based on phase W , fC
1U.
Kwa
W , Ib. moles per (hr.) (cu. ft.) (Ib. moles/cu. f t ) LK = flow rate of phase K , cu. ft./(hr.) (sq. ft.) L w = flow rate of phase W , cu. ft./(hr.) (sq. ft.) N = amount of solute transferred, lb. moles/hr. N K = amount of solute transferred in phase K , lb. moles/hr. N W = amount of solute transferred in phase W , lb. moles/hr. V = effective volume of extraction column, cu. f t . Subscripts 1, 2 = ends of tower or section of tower C = in continuous phase D = in dispersed phase K = in ketone phase W = i n water phase = over-all extraction coefficient based on phase
Literature Cited (1) Blanding, F. H., and Elgin, J. C., Trans. Am. Inst. Chem. Engrs., 38, 305 (1942). (2) Elgin, J. C., and Browning, F. M., Ibid., 31,639 (1935). (3) Fischer, W., and Bock, R., 2. anorg. u. allgem. Chem., 249, 146 (1942). (4) Fischer, W., and Chalybaeus, W., 2. anorg. Chem., 255, 79, 277 (1947). (5) Geankoplis, C.J., IND.ENO.CHEM.,44, 2458 (1952). (6) Geankoplis, C.J., and Hixson, A. N., Ibid., 42, 1141 (1950). (7) Geankoplis, C. J., Wells, P. L., and Hawk, E. L., Ibid., 43,1848 (1951). (8) Hayworth, C. B., and Treybal, R. E., Ibid., 42, 1174 (1950). (9) Johnson, H. F.,and Bliss, H., Trans. Am. Inst. Chem. Engrs., 42, 331 (1946). (10) Licht, W.,Jr., and Conway, J. B., IND.ENG. CHEM.,42, 1151 (1950). (11) Morello, V. S., and Poffenberger, N., Ibid., 42, 1021 (1950). (12) Nandi, S. K., and Viswanathan, T. R., Current Sci. ( I n d i a ) , 15, 162 (1946). (13) Sherwood, T. K., Evans, J. E., and Longcor, J. V. A., IND. ENG.CHEM.,31, 1144 (1939). (14) Templeton, C. C.,J. Am. Chem. Soc., 71,2187 (1949). (15) Templeton, C. C., and Peterson, J. A.,Ibid., 70,3967 (1948). (16) Treybal, R. E.,“Liquid Extraction,” p. 324, New York, McGraw-Hill Book Co., 1951. (17) Trevbal. Ibid.. DD. 346-93. (18) V o i Berg, R. L.: and Wiegandt, H. F., Chem. Eng., 59, 189 (1952). (19)West, F. B., Robinson, A. C., Morgenthaler, 20 A. C., Jr., Beck T. R.,and MeGregor, D. K., IND. ENG.CHEM.,43,234 (1951).
Effect of Height of Column on Average (H.T.U.)ow with End Effects Eliminated
RECEIVED for review December 17, 1952.
INDUSTRIAL AND ENGINEERING CHEMISTRY
ACCEPTED RIay 20, 1953.
2165
