INDUSTRIAL AND ENGINEERING CHEMISTRY
1848
advice was offered by members of the research and development depaitment of the Pure Oil Go. The assistance rendered by these sourccs is gratefully acknowledged.
”
=
conditions in which all of the sulfur present in the feed is considered as Sz, and a correction for catalyst fading has been applied
NOR1 ENC L 4TURE
Symbols F = feed rate, gram moles/hour k = reaction velocity constant p = partial pressure 7 = reaction rate V = volume, cc. T I - = catalyst weight, grams R: = conversion, gram moles CSnlgram inole feed Subscripts h = used with V,,/F’ t o denote the effect of the induction
period in the homogeneous reaction c = catalytic reaction e = used with Vs t o denote an effective void volume for the homogeneous reaction G = conditions in the main body of the reactants gas stream h = homogeneous reaction z = conditions a t the surface of the catalyst = used with V t o denote void volume 1 = conditions a t the entrance to the catalyst bed 2 = conditions a t the exit from the catalyst bed 3 = conditions a t the exit from the reactor
Superscripts = conditions in which all of the sulfur prewnt in the feed is considered as S p
Vol. 43, No. 8
LITERATURE CITED
Bacon, R. F., a n d Boe, E. S., ISD. EKG.CHmf., 37, 409-74 (1945). Braune, H., a n d P e t e r , S., .~ulurwissenschaSten, 30, 007-8 (1942). D e Sinio, 1’1.(to Shell Development Co.), U. S. P a t e n t 2,187,393 (Jan. 16, 1940). Fisher, R. 9., a n d Smith, J. N l . , IND.ENG.CHERI.,42, 704-9 (1950). Folkins, H. O., Miller, E., a n d Hennig, H., paper presented before t h e 117th Meeting of t h e AM. CHEM.SOC., Houston, Tex., M a r c h 1950. Hougen, 0 . A, a n d W a t s o n , X. M., “Chemical Process Principles,” Vol. 3, New York, J o h n Wiley 8r Sons, I n c . , 1947. Palmer, G. E., unpublished 11,s. thesis, P u r d u e University (August 1949). Preuner, G., and Schupp, W., 2 . physik. Ch,em., 68, 129-56 (1909). Reinhold, H., a n d Schmitt, K., Ibid., B44, 98-108 (1939). Stull, D. R., IXD. ENG.CHEM.,41, 1968-73 (1949). Thacker, C. M. (to P u r e Oil Co.), U. S.P a t e n t 2,330,934 (Oct. 5 , 1943). Thacker, C. AI., a n d Miller, E., IND.ESG. CHEM., 36, 182-4 (1944). RECEIVED Septeniber 15, 1R50.
Extraction in a Pilot-Unit Spray Tower
-
development
CHRISTIE J. GEANKOPLIS, PAUL L. WELLS,
AND
ELLIS L. HAWK2
OHIO STATE UNIVERSITY, COLUMBUS IO, OH10
Performance data which do exist for spray-type extraction towers are relatively limited in their use, because they are generally applicable only to the specific column for which the data were obtained and not to columns having different lengths, nozzles, and other structural features. The present investigation was undertaken to shed further light on the mechanism of extraction and to answer some of the questions advanced by previous investigators. Data on extraction coefficients were obtained using a pilot-unit size spray tower and the system toluene-acetic acid-water. The method of internal sampling was employed to obtain internal mass transfer coefficients which
were found to be approximately constant and to locate end effects. A large end effect was found a t the continuous phase inlet and it appears t h a t neither the type of system employed nor the direction of solute transfer has any effect on the location of the end effect. A method is proposed for correlating end effects expressed as a fictitious height of column and mass-transfer coefficients. Accumulation of sufficient data using different systems and towers and obtained by analyzing the internal operation of a tower instead of the external operation may enable the obtaining of a generalized correlation of spray tower extraction data.
0
tempted, i t is usually necessary to obtain some pilot-unit data on a replica of the proposed commercial-size tower. Morello and Poffenberger ( 7 ) summarized the small amount of available contemporary data on commercial extraction equipment. They state that the spray tower is perhaps the cheapest and simplest extractor but that it is not used extensively a t present. The performance data which do exist for spray towers are relatively limited in their use since they are generally applicable only to the specific column for which the data were obtained and not to columns having different lengths, nozzles, and other struc-
S L Y a few fundamental studies of mass transfer rates in con-
tinuous solvent extraction towers have been made even though this unit operation has been extensively used in recent years. Extraction is often used to separate components of solutions \Then the conventional unit operations such as distillation or evaporation are too costly or difficult to use. At present there are no reliable methods for predicting the extraction performance of continuous equipment such as spray towers. Before design of a commercial extraction tower can be at1 2
Present address, Marion Industries, hIarion, Ohia. Present addless, Hercules Powder Co., Wilmington, Del.
August 1951
INDUSTRIAL AND ENGINEERING CHEMISTRY
tural features. This is due to the fact that relatively little is known concerning the mechanism of the extraction process. The first systematic study of spray towers was done by Elgin and Browning ( 2 ) using the system acetic acid-isopropyl etherwater. They found that the mass transfer coefficients were affected by flow rates, direction of solute transfer, and drop size of the dispersed phase. Sherwood and coworkers (9)and Licht and Conway (6)studied extraction from single drops and state that an appreciable amount of extraction took place as the drop left the nozzle. Blanding and Elgin ( 1 ) found that the spray tower should have a funnel-type entrance a t the dispersed phase inlet t o prevent any disturbance of the discontinuous phase in entering the column. Johnson and Bliss (6)state that the most favorable tip diameter a t the dispersed phase inlet was 0.1 inch and that the number of tips should be increased as the dispersed phase flow is increased. In all cases the analyses were made on an over-all basis by analyzing the inlet and outlet concentrations of spray towers Studies of the effect of column length (8, 9) showed that the mass transfer ooefficient increased with increase in column height. Hayworth and Treybal(4) studied drop formation and found that drop size depended upon flow rate through the nozzle, interfacial tension, densities of the liquids, viscosity of the continuous phase, and nozzle size. Geankoplis and Hixson ( 3 )analyzed the internal operation of a tower by employing a movable sampling device t o remove internal samples of the continuous phase during operation of the tower. They determined the concentration gradient throughout the column and located end effects using a tower 1.45 inches in diameter and the system ferric chloride-isopropyl ether-aqueous hydrochloric acid. The concentration gradient inside the tower revealed a very large inlet effect a t the continuous phase inlet to the tower and none a t the dispersed phase inlet. They found that the mass transfer coefficient or (H.T.U.)o W . was approximately constant throughout the tower except at the continuous phase inlet, It appeared to them that the location of the end effect a t the continuous phase inlet may be caused by the inhererit turbulence effect of coalescence of bubbles at the interface or by the fact that the solute was being transferred from the continuous to the dispersed phase. This effect may be a peculiarity of the system used. They also found that the end effect persisted despite radical changes in continuous phase inlet nozzle and column design. T h e possibility that the inlet effect may be negligible in larger sizc columns was suggested. They concluded that a positive method of determining the location of end effects is by internal sampling. In order to shed further light on the mechanism of extraction and to answer some of the questions advanced by Geankoplis and Hixson, this investigation was initiated. A different system, toluene-acetic acid-water, was selected to see what effect the system had on the location and type of end effects. In this system the solute was extracted from the dispersed phase t o the continuous phase instead of the reverse direction employed by the others ( 3 ) . A larger pilot-unit size tower was used t o find out the effect of column diameter on the extraction mechanism and end effects.
a saturator containing a layer of toluene, G, to saturate the ivater phase with toluene. After saturation the water flowed t o a constant head tank, C, and the overflow t o the drain, K. The water, always the continuous phase, entered at the top of the column and flowed out of the bottom of the tower to the drain, L. The toluene, which contained the solute and was always the dispersed phase, was pumped from storage, P, to the constant head tank, B . It entered the bottom of the tower through the copper spray nozzle, D. The toluene leaving the top of the column mas collected for reuse in a drum, 0.
* -'EL -
I
H
.
EXPERIMENTAL METHODS
APPARATUS.The process flow diagram of the spray tower is P t e d in Figure 1. The piping was made of copper or yellow ram because of the corrosive action of the acetic acid solution. The tower, A , was made of glass pipe, 6 feet long and 3.75 inches in inside diameter. The length of the tower between settling sections was 62.5 inches. The bottom of the column was flared so that the inside diameter a t the end was 4.75 inches in diameter and the length of the flared glass section was 4 inches. The constant head tanks, B and C, were glass and the sampling tube, E, was yellow brass. Referring t o Figure 1, the city water, I , was preheated by direct injection of steam, H , t o 25' C. and was demineralized by the cation exchanger, F. Then the water phase was bubbled through
1849
I
! I L - J U
L
it . Ll
E
J
I
I
K
Figure 1.
'
1
Process Flow Diagram
The movable, internal sampling thief consisted of a 5/ia-i~1c11 outside diameter brass tube, E, which extended into the extraction section and occupied 0.2'% of the column 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 without entraining the rising droplets of toluene. The top of the sampling tube was connected t o suction flasks, V and W . The liquid flow was regulated by controlling the suction a t T and throttling the valves a t V or W . The tube was flush against the wall of the tower and its vertical position could be varied. The top end of the tube was fastened to a block which was fitted in a guide. A setscrew in the block, Y , secured the vertical position of the sampler. The internal samples taken in the tower were as shown in Table I.
TABLE I. POSITIONS OF INTERSAL SAMPLER IN TOWER Distance from Top of Extraction Section, Inches 0 (inlet) 3 12 24 36 48 6 2 . 5 (outlet)
Distance from Bottom of Extraction Section, Inches 6 2 . 5 (inlet) 59.5 50.5 38.5 26.5 14.5 0 (outlet)
Details of the continuous flow inlet nozzle are shown in Figure 2. The water entered, b, into an equal pressure section and then flowed through six tubes, d, which were l/s-inch standard pipe and equally spaced in a circle 2.75 inches in diameter. The tubes extended 9 inches into the dispersed phase settling section. The interface level was held constant at the exact end or tip of the continuous phase, inlet tubes. The toluene dispersed phase left the tower a t h. The dis ersed phase nozzle, Figure 3, was a copper funnel 2.94 inches in Jameter, j , and was placed a t the end of the flare to give an annular space between the walls and the nozzle equal to the column cross-sectional area. The settling section, h, was 7 inche8 long and had an inside diameter of 4.75 inches. Details of the nozzle are shown in Figure 4. This nozzIe per-
1850
INDUSTRIAL A N D ENGINEERING CHEMISTRY
Vol. 43, No. 8
T o determine the percentage of saturation of the water by the toluene in the saturator, a 50-ml. sample of water TTas used Toluene was added to the water from a I-ml. graduated pipet until a trace of toluene persisted after repeated shaking. This method does not yield very accurate results for absolute solubilities, but for the purpose for which it was used it gave results which were considered acceptable. By titrating a sample of untreated watw and comparing this with the titration of treated water, an approximation of the relative per cent saturation in the saturator was obtained. TREATMENT OF DATA
SATURATION O F TVBTER B Y TOLUENE. Experimental data from the tests of the laboratory saturator are presented Figure 2. Continuous Phase in Table 11. The superficial velocity Entrance of Column of the water in the saturator was calculated from the water flow and the crossFigure 3. Dispersed Phase mits the number of tips or jets t o be sectional area of the saturator. Entrance of Column varied directlv with the flow to give the The data are plotted in Figure 6 and same bubble size or interfacial area reshow almost a straight line relationgardless of the flow. The diagram shows the spacing of 19 jets for a Row of 19 cubic feet per hour ship on semilogarithmic paper. This curve could then be per square foot. The velocity through the tips in all runs was used to estimate qualitatively the maximum superficial velocthe optimum recommended by Johnson and Bliss ( 6 ) . The ity of water possible for essentially no entrainment of toluene blanks were made inch shorter than the jets t o prevent the in a larger diameter saturator. However, tests to confirm this blanks from obstructing drop formation from the jets. I n order to obtain data t o drsign a suitable toluene saturator should be performed on the larger saturator. It is desirable to for the inlet water phase, experiments were conducted on a small have the bubbles carried part of the way down the column t o scale apparatus, Figure 5 . The metered water was bubbled give a long contact time between the toluene and water. Howthrough a toluene layer and the distance the toluene bubbles were ever, velocities t h a t would entrain toluene out of the saturator entrained in the water phase was measured. These data were used to design the large saturator so that no entrained toluene was should be avoided. carried with the water into the spray tower. Extractlon was performed from the disR U N PROCEDURE. persed toluene phase to the continuous phase for al! runs. The toluene solution was prepared by adding glacial acetlc acid to the spent toluene from the prevlous run. Fresh tap water wa8 used TABLE11. ENTRAINMENT-VELOCITY DATAFOR LABORATORY for all runs and the continuous phase water flow was held constant TOLUENE S.4TURATOR throughout all runs. The rate of flow of each phase was deterDistance Toluene Water Superficial Vel mined by timing measured volumes of each phase. Bubbles Carried Cu. Ft./Sec./Sq. Ft." Run Down Tower, Inches Cross Section or Ft./Sec. After the interface and both flows had been correctly set and the column had reached steady-state conditions, which were found 1 0.0 0.0064 2 1.5 0.0124 experimentally to be the time necessary for the entire contents of 3 3.5 0.0170 the column to change four or five times, internal sampling mas 4 6.0 0.0219 started near the bottom of the column. The average internal 5 7.5 0.0288 6 13.,5 sampling rate was 15 ml. per minute or about 0.8% of the contin0.0693 7 Interface disappears 0.1070 uous phase flow rate. The first portion of internal sample taken a t each position in the tower was used for purging the sampling tube and was discarded. The purging and sampling procedure was repeated as the sampling tube vias moved up the column 2-15/16" -+ during the run. Inlet and outlet samples of the water and toluene phases nere also taken during a run. The toluene stream fed to the column was saturated with water before using. The acetic acid used XTas U.S.P. grade and the toluene R as "nitration" grade purchased from the Barrett Division of the Allied Chemical and Dye Corp. .IO" 17.5" ANALYTIC.4L ANALYSES.The concrntra1 tion of acetic acid in the water phasp was A I determined by an acid-base titration using 1/4" 0.1 AT sodium hydroxide and phenolphthaT lein as the indicator. In determining the concentration of acetic acid in the t o l u ~ n ethe BLANK 0 JET @ same method was employed but two phases were encountered because the standard sodium hydroxide solution was immiscible with the toluene phase. The accuracy of the two phase titration was t e s t d by titrating a known amount of C.P. acetic acid in the 5MM.GLASS water phase alone and the same amount of TUBING acetic acid in the two phase, t o l u ~ n e - ~ ~ a t c r mixture. The r ~ s u l t schecked to n-ithin 0.1 Figure 4. Dispersed Phase Figure 5. Laboratory Model Entrance Nozzle of each other. Toluene Saturator ~
,
ii
T1
August 1951
1851
INDUSTRIAL AND ENGINEERING CHEMISTRY
The large saturator was designed for no entrainment of toluene outside the saturator and tests confirmed this fact. The outlet water from the saturator was analyzed and found to be 71% saturated with toluene. This amount of saturation of the water by the toluene was considered sufficient not to affect the extraction performance or end effects of the spray tower. DERIVATION OF EQUATIONS. To calculate the mass transfer coefficients for spray towers the following equation can be shown to be valid if the solvents are relatively immiscible, the distribution law holds, and the concentrations are relatively dilute:
N = KTUvACTIm
/ O '
(1)
The height of a transfer unit can then be calculated. (H.T.U.)O.T. =
LT KTU
After solving for KTa in Equation 1and substituting this value into Equation 2, the equation can be solved for (H.T. U.)O.T. (H.T. U.)O.T. =
LT VACTlm N
.OOl L 0
(3)
D I S T A N C ~ENTRAINED BUBBLES CARRIED, INCHES
Substituting the values for V and N , there results
Figure 6.
Entrainment-Velocity Curve for Toluene Saturator
(4)
runs in the spray tower are presented in Tables I11 to V. The over-all material balance was calculated as follows: For run 5,
Canceling out the flow rates and areas, (5)
Nw
=
ALw(Cw2
- CWI)= 0.0767 N~
The value off(CT) is as follows:
= 8.52
- 0)
X 60.1 (1.846 X
x
10-3
N T = ALT(CTZ- CTI) = 0.0767 X 18.71 (8.76 X N T = 8.80 x 10-3 N = Nw + N T = 8.66 X 10-3
2.63
x lo+)
2
Nw
1
Solving for -in Equation 5 f (CT) (7) Hence, if
f(CT)
is plotted versus the linear height, the slope of the
line at any point is the reciprocal of (H.T.U.)o.r. a t this particular point. I n all cases the values of C*, were less than 1.5% of CT. Therefore, for purposes of correlation Cs can be considered negligible and Equation 6 becomes
- NT X
100 = -3.2%
To calculate the over-all mass transfer coefficients, equilibrium data for the toluene-acetic acid-water system were obtained from LVoodman (10) and used in obtaining the C; values. ACTlm =
(8.76
- 0.10) - (2.63 - 0) X (8,76 - o.lo)
2'310g (2.63
KTa =
~
=
5.06 X IOvs
- 0)
N = VACrhll 0.0767
8.66 X 5.20 x 5.06
x
- 4.27 x lo-' -
LT 18.71 (H.T.U.)O.T.= __ = - = 4.38 KTa 4.27 The over-all mass transfer coefficients are tabulated in Table
Then Equation 7 simplifies to 2.310g CT1 CT2
VI. (H.T.U.)O.T. x
z
Since the inlet concentration CTZis a constant for a run,
This expression is similar to that derived by Geankoplis and Hixson (3). Therefore, if the natural logarithm of the concentration a t different' points in the column is plotted versus the linear height the slope a t any point represents the negative reciprocal of the (H.T.U.)O.T. a t this point. If the line is a straight line the (H.T.U.)O.T.is a constant throughout the column. CALCULATION OF MASS TRANSFER COEFFICIENTS. The experimental data obtained from the
(9)
The experimental Cw values obtained by internal and external sampling are plotted in Figures 7 and 8. The 3-inch point sam~~
~~
TABLE 111. OVER-ALL TRANSFER DATAFOR EXTRACTION COLUMN Flow Rate, Over-all Acetic Acid No. Tips in CU. Ft./(Hr.) Transfer Rate Run Toluene (Sq.Ft.) (Lb. Mole/Hr.) >i 10-8 No. Nozzle Lw LT Nw NT Av.N la 19 15.98 57.9 15.73 15.85 2a 19 15.30 56.0 15.00 15.15 15.70 15.17 2b I9 66.0 14.64 20 19 14.18 14.55 56.0 14.92 26.6 27.1 3" 19 26.9 58.6 25.6 58.6 4a 19 25.7 25.7 26.8 4b 58.6 19 26.0 25.9 40 26.0 26.0 58.6 19 25.9 5 8.52 19 60.1 8.80 8.66 15.27 6 16.20 19 57.1 14.43 55.2 7 25.6 31 26.1 26.7 8 58.6 73 50.2 63.3 68.0 a Sampler removed entirely from column.
Deviation, 1.6 2.0 .7.0 5.1 - 1.9 - 0.4 0.8 0.4 - 3.2 11.1 4.2 -14.8
-
-
-
INDUSTRIAL AND ENGINEERING CHEMISTRY
1852
Vol. 43, No. 8
values of CW from Table VI1 to eliminate scattering of points
TABLEIV.
a
CONCENTRATION OF ACETIC ACID
TOLUENE calculated b y taking differences between closely adjacent points.
IN
PHASE IN C O L U ~ ~
For the short 0.25-foot section, zero inches from the top interface to 3 inches from the top, mass transfer coefficients were calculated. For run 5 , iVw = ALw(Cw2 C w l ) = 0.0767 X 60.1 (0.41 - 0 ) X = 1.89 x 10-3
Concn. of Acetic Acid in Toluene, (Lb. iLIoIe/Cu. Ft.) X 103 Run No. Inlet Outlet l a 14.15 14.15 2a 14.15 2b 14.15 2c 22.80 3a 22.80 4P 4b 22.80 22.80 40 8.76 5 18.08 6 21.72 7 8 23.00 Sampler removed entirely from column.
TABLEV. CONCENTRATION OF ACETIC ACID POIXTS IX COLUMS Run
No.
40 5 6 7 8
0-inch inlet
0 0
0 0 0
IS
-
To obtain the concentration C T in ~ the toluene phase a t the point 3 inches from the top, a material balance was made over the short section of the column.
~w = 1.89 X
WATER AT
Concentration of Acetic Acid in Water Phdsr, (Lb. Mole/Cu. Ft.) X 103 12-inch 24-inch 36-inch 48-inch 62.5-inch 3-inch outlet point point point point point
... ... .. .. ..
... ... ... 0.'395 0.806 0,308
...
0.'683 1.283 2.219
...
...
... ... ...
....
....
2.23
....
.... .... ....
3.10
...
........
1.271 1.659 2.302 3.16 4.15 5.42 11.64 13.53
=
To calculate the CrZvalue a t the point 12 inches from the top,
ALm ( C W ~ - CWI)= ALT ( C T ~- C T I ) = 0.0767 X 18.71 (CTZ0.0767 X 60.1 (0.61 - 0.41) X 3.95 x 10-3) c T ~ = 4.59 x 10-3 The calculated CT values are given in Table VI11 and plotted in Figure 9. For the short section 3 to 12 inches from the interface,
....
0:847 1.772 2.981
1.89 x 10-3 = A L T ( c T ~ - c T ~ ) 0.0767 X 18.71 ( C T ~- 2.63 X cTZ = 3.95 x 10-3
~VT=
5.78 1.846 3.68 6.04 15.22
ACTh =
- 0.03)(4.59 - (3.95 - 0.02) - 0.03)
=
0.0767 X 18.71 (4.59 - 3.95) X 10-8 = 0.92 X
KTa =
~
N VACT Im
x
0.92
- 0.0767
10-3
3'78
X 0.75 X 4.24 X
The calculated K2.a and (H.T.C.)O.T.values for short sections of the tower are presented in Table IX and are plotted in Figure 10. The averages of the internal (H.T.U.)O.T.neglecting the end effects a t the dispersed and continuous phase inlets were obtained and are given in Table X. If actual rather than smoothed data were used in calculations
i
I INLET C, =.023
L T = 18.9
= 4.24jx
2.3 log (3.95 - 0.02)
N ple in run 7 was too low a concentration and was not plotted in Figure 8 for two reasons: First, this was the last internal sample to be withdrawn near the end of the run and the sample mas withdrawn too hurriedly. This would tend to make the concentration low since water higher u p the tower would be erroneously sampled. Secondly, inspection of Figure 8 shows t h a t it is very unlikely t h a t the run having a n LT of 25.4 would cross the run having a lower rate of 19.2. The smoothed values of these points were obtained from Figures 7 and 8 and the data are given in Table 1'11. These smoothed data were used to calculate the internal ( H . T . U . ) o T and KTa for short sections of the column. This was done by dividing the column into five short sections and calculating the mass transfer coefficient for each section. It was necessary t o use smoothed
(4.59
I
1 I
5 0
~
~
1
,
1
1
1
,
,
1
~
,
,
,
1
,
,
1
1
1
I I
0.
DISTANCE FROM TOP INTERFACE, INCHES Figure 7. Effect of Inlet Concentration of
Acetic Acid in Toluene o n Concentration Gradient i n Continuous Water Phase
.I
1 'M* 20 TOP DISTANCE FROM TOP INTERFACE, INCHES
Figure 8. Effect of Toluene Rate on Concentration Gradient in Continuous Water Phase
INDUSTRIAL AND ENGINEERING CHEMISTRY
August 1951
1853
TABLEVI. OVER-ALL MASS TRANSFER COEFFICIENTSFOR COLUMN Run No. 1 2a 2b 2c 3 4a 4b 4c 5 6 7 8
TABLEVII.
Run No. 2 4 5 6 7 8
0-inch inlet 0 0 0 0 0
0
KTa 5.09 4.86 4.73 4.64 5.95 5.38 5.50 5.52 4.27 3.10 4.77 10.37
( H .T.U.)O.T.
CONCENTRATION OF ACETIC ACID POINTS IN COLUMN
IN
WATERAT
(Smoothed data) Concentration of Acetic Acid in Water Phase, . (Lb. Mole/Cu. Ft.) X 103 3-inch 12-inch 24-inch 36-inch 48-inch point point point point point 0.92 1.21 1.68 2.23 2.87 1.11 1.51 2.20 3.10 4.20 0.41 0.61 0.93 1.26 1.62 0.82 1.21 1.76 2.37 3.10 2.15 3.00 4.10 5.30 ,. 11.3 13.5
.. ..
..
62.5-inch outlet 3.50 5.77 1.90 3.70 6.25 15.50
21 ** c
ITOP
I
I
I
I
I
I
20
40
M.
DISTANCE FROM TOP INTERFACE, INCH
for short sections in run 5, the ( H . T . U . ) O . T .values starting at the top section and going down the tower would have been 3.53, 9.53, 4.48, 5.80, and 16.4 feet. These deviate rather widely from the corresponding values obtained using smoothed data of 4.95, 4.92, 5.72,6.16,and 11.0 feet. DETERMINATION OF ENDEFFECT.To determine the end effects a t the continuous phase inlet the following graphical method was devised: Referring to Figure 11, the straight portion of the concentration-versus-height line was extrapolated until it intersected the ordinate equal to the outlet toluene concentration. The distance 2; is a fictitious height of column in feet necessary to perform an amount of extraction equivalent to the extraction done by the top inlet effect. In determining the inlet effect a t the dispersed phase inlet, the
Figure 10.
Height of Transfer Unit a t Points inside Column
intersection of the ordinate equal to the inlet toluene concentration and the extrapolation of the concentration-versus-height line is located. This 2; is negative since this inlet effect causes an amount of extraction less than normal to result. These values are tabulated in Table XI. The theoretical concept of a fictitious height of column was proposed by Yost (11). DISCUSSION
PROVING SAMPLING TECHNIQUE. Geankoplis and Hixson ( 8 ) showed that internal sampling had no effect on the normal overall extraction of their column which was 1.45 inches in diameter. Since the diameter of the tower used in the investigation was
TABLE VIII. CONCENTRATION OF ACETICACID IN TOLUENE AT POINTS IN COLUMN
Run 0-inch No. outlet 2 3.87 4 5.27 5 2.63 6 7.97 7 8.02 8 9.73
(Calculated from data in Table VII) Concentration of Acetic Acid in Toluene Phase, (Lb. Mole/Cu. Ft.) X IO3 3-inch 12-inch 24-inch 36-inch 48-inch 62.5-inch point point point point point inlet 6.60 7.46 8.85 10.50 12.40 14.27 8.65 9.87 11.97 14.69 18.04 22.81 3.95 4.59 5.62 6.68 7.83 8.73 10.49 11.69 13.38 15.26 17.50 19.35 , 12.70 14.55 16.94 19.54 21.60 .. 16.40 18.05 19.55
.
..
...
...
TABLE IX. MASSTRANSFER COEFFICIENTS AT VARIOUSSHORT SECTIONS FOR COLUMN Run
No.
DISTANCE FROM
TOP INTERFACE, INCHES
Figure 9. Concentration Gradient i n Dispersed Toluene Phase
3- t o 12- t o 24- to 36- to 48- to 12-Inch 24-Inch 36-Inch 48-Inch 62.5-Inch Coefficient Section Section Section Section Section KT a 3.14 3.22 3.17 2.22 6.99 ( H . T . U.)O.T. 5.88 5.95 8.50 3.41 KT a 3.96 4.00 3.77 5.65 (H. T . U.)O.T. 4.87 4.82 5.10 KT a 3.78 3.27 3.03 1.70 (H. T .U . b . T . 4.95 6.16 11.0 5.72 KT a 2.70 2.44 2.56 1.55 (H.T.U.)O.T. 6.90 7.63 7.27 12.20 KTa 3.86 3.70 2.15 ( H . T .U.)O.T. 6.90 11.9 6.59 KTa 6.42 4.43 .. (H.T.U.)O.T. 10.47 15.2
...... ..
..
..
INDUSTRIAL AND ENGINEERING CHEMISTRY
1854
Vol. 43, No. 8
Hence, the inlet effect is located at the same position found by HEIGHT OF TRANSFER UNIT INSIDE TOWER Geankoplis and Hixson (3)even though in their investigation the TABLE X. AVERAGE NEGLECTING ENDEFFECTS solute was being transferred in the reverse direction-from the Av. (H.T.U.)O.T., Feet 6.0 5.2 5.5 7.3 6.9
Run NO.
Inlet Conon. of Acetic Acid in Toluene, (Lb. Mole/Cu. Ft.) X 103 14.15 22.80 8.76 18.08 23.00
OF COLUMN IK TERMS OF FICTITIOUS TABLE XI. ENDEFFECTS HEIGHTOF COLUMN
Z& End Effect a t Continuous Phase Inlet, Feet 2.8 2.3 1.8 1.8
Run No. 2 4
5 6
continuous phase t o the dispersed phase. Also, the size of tower and the type of ternary system employed do not appear t o have an effect on the location of the main end effect. Figure 12 shows the great similarity in the type of data obtained from the two investigations. 50
I
ZA,End Effect a t
LDISP. =
Dispersed Phase Inlet, Feet -0.4 -0.2 -0.6 -0.4
I9
XII. EFFECT OF INTERNAL SAMPLING Run No. 1 2a 2b 20 3 4a 4b 4c
Point Sampled None 3 inches 36 inches 60 inches None 3 jnches 36 inches 60 inches
% Deviation of Outlet Concn.
... -1
1 -8
... -4 -3 -2
much larger, a similar check on the validity of the internal sampling technique was made. I n run 1the column was operated with the sampler removed entirely from the tower. I n runs 2a, 2b, and 2c the same conditions as in run 1were used but a sample wm removed a t the 3-inch point in 2a, 36-inch point in 2b, and 60-inch point in 2c. A similar study was made in runs 3, 4a, 4b, and 4c. The data are tabulated in Table XII.
INVESTIGATOR 0
INLET GONG.
AUTHOR GEANKOPLIS AND HIXSON
.I
TOP 20 40 DISTANCE FROM TOP INTERFACf
Figure 12.
E 'M. INCHES
Effect of Direction of Extraction Gradient in Continuous Phase
on Concentration
I
I
TOP BTM. DISTANCE FROM TOP INTERFACE Figure 11. Method of Determining
Column End Effects
The average per cent deviation of the outlet acetic acid concentration in the water when not sampling as compared to the concentration when sampling is only 3%. Since the average deviation in the over-a11 material balance for all runs in the tower is 474, the effect of internal sampling is small and approximately within the experimental error of a run. CONCENTRATION GRADIENTAND ENDEFFECTS.I n Figures 7 and 8 the plots of the log of the concentration in the water phase versus the height from the top of the column show a decided break or inlet effect at the top or continuous phase inlet to the tower.
As R o d d be expected the concentration-versus-height plot for the disperjed toluene phase in F i p r e 9 shows the same inlet effect a t the top as Figures 7 and 8. The concentration gradient is approximately a straight line except at the top where a large inlet effect occurs and at the bottom where the line curves down slightly. Instead of a positive inlet effect being evident a t the dispersed phase entrance, a negative effect occurs--i.e., the extraction is less than normal or the (H.T.U.)o T. is greater. This might be explained by the fact t h a t in flaring the last 4 inches of the tower, the water phase by-passed the rising bubbles for the last 4 or 5 inches of the tower. The average 2; of the values in Table X I is about 5 inches. I n the majority of the runs made by Geankoplis and Hixson (9) in a tower with no flare a t the dispersed phase inlet, no end effect was evident at this i d e t point. If the large end effect a t the top is due to the coalescence of bubbles, then coalescence of bubbles in the middle section of the spray tower may be a desirable thing which may more than offset the loss in surface area. T h a t is t o say, coalescence of two bubbles in the middle section may act as a small interface. Inspection of Figure 10 and Table I X shows that the ( H . T . U.)O.T.is approximately constant throughout the column except near the dispersed phase entrance where the (H.T.U.)O.T. increases. CORRELATION OF (H.T.U.)o.w. AXD ENDEFFECTS. Data in Table XI11 were obtained by applying the method shown in Figure 11 of determining 2; t o t h e data of Geankoplis and Hixson
INDUSTRIAL AND ENGINEERING CHEMISTRY
August 1951
G
G .u
N I-W 1
Z_
-
-DATA O f GEANKOPLIS
2 I.2-
F
-
v
-
z 0
1855
A N D HIXSON
II
I
0 DISPERSED PHASE ETHER RATE,
AVERAGE ( H.T.U.)o.w. FOR COLUMN WITH INLET EFFECT ELIMINATED
Figure 13. Effect of Dispersed Phase Flow Rate on Inlet Effect a t Continuous Phase Inlet
(3). The data were plotted versus dispersed phase ether rate and are shown in Figure 13. This shows a definite correlation between the inlet effect, Zd, and rate; and a t zero rate the Zd appears t o be zero. This curve is independent of inlet concentration and appears t o have more utility than the correlation of end effects presented by other investigators (3)which depends on concentration.
Figure 14. Relation between Height of Transfer Unit in Column and Inlet Effect
Set the amount of extraction to be performed. Select a dispersed phaser ate and obtain the Z& Z;, and average (H.T.U.)O.T. with the end effects eliminated from the correlations. Solve for KTUusing Equation 2. Then using Equation 1 solve for the apparent column height, Z'. Then solve for the actual column height, Z, in Equation 11. Z' = 2;
TABLE XIII. ENDEFFECT OF COLUMN IN TERMS OF FICTITIOUS HEIGHTO F COLUMN
[Data of Geankoplis and Hixson (5)I
Run No. 27, 30 28 29 31, 32 33 34 35 36 37 38 39
40 41 42 43 ~.
44 45 46
Zh, End Effect a t Continuous Phase Inlet, Feet 0.49 0.52 0.35 0.48 0.56 0.50 0.50 0.30 0.28 0.50 0.64 0.61 0.30 0.47 0.31 0.43 0.54 0.63
Av. (H.T.U.1o.w. in Column with End Effect Eliminated, Feet 0.69 1.5 3.9 0.65 0.69 0.63 1.10 2.8 2.3 1.04 0.75 0.70 2.1 1.1 5.2 2.6 1.04 0.70 .
The end effect or 2 ; plotted against the average (H.T.U.)o w for the tower with the inlet effect eliminated is shown in Figure 14. This shows a relationship between the efficiency of extraction in the tower and the efficiency or magnitude of the top end effect. Hence, it appears t h a t factors such as bubble size and diffusion which affect the extraction in the column proper also affect the extraction performed by the end effect. To correlate extraction PROPOSED CORRELATION PROCEDURE. data the end effects in the form of 2; and 2; and the average height of transfer unit in the tower could be used. Accumulation of sufficient data from different systems correlated in the above manner may lead t o a generalized correlation of extraction spray tower data. T o predict the column performance using the above correlation, the following method could be,wed: ,
+ 2 + zf,
(11)
The actual height of the column t o use is 2. It should be noted that Zg has a negative value. NOMENCLATURE
interfacial area per unit volume of extractor, square feet/cubic foot A = cross-sectional area of column, square feet CT = concentration of solute in phase T , pound moles/cubic foot C*, = concentration of solute in phase T which would be in equilibrium with concentration in opposite phase, pound moles/cubic foot CW = concentration of solute in phase W , pound moles/cubic foot aCTlm = log-mean values of CT - CT*fer the two terminals of column (H.T.U.)o T = over-all height of transfer unit based on phase T , feet (H.T.U.)o W. = over-all height of transfer unit based on phase W , feet KTU = over-all extraction coefficient based on phase T, pound moles/(hour)(cubic foot)(pound moles/cubic foot) k. = constant LT = flow rate of phase T,cubic foot/(hour)(square foot) LW = flow rate of phase W ,cubic foot/(hour)(square foot) N = amount of solute transferred, pound moles/hour N T = amount of solute transferred in phase T, pound moles/ hour NW = amount of solutetransferred in phase W , pound moles/ hour V = effective volume of extraction column, cubic feet Z = effective height of extraction section of tower, feet (actual distance between tips of water nozzle and tips of toluene nozzle) Z' = apparent height of extraction section of tower, feet Z& = fictitious height of column equivalent t o continuous phase inlet effect, feet 2; = fictitious height of column equivalent to dispersed phase inlet effect, feet
a
=
Hayworth, C. B., and Treybal, R. E., Ibid., 42, 1174 (1950). Johnson, H. F., and Bliss, H., Trans. Am. Inst. Chem. Engrs., 42,
Subscripts 1,2 = ends of tower or section of tower C = continuousphase D = dispersedphase
T
=
Vol. 43, No. 8
INDUSTRIAL AND ENGINEERING CHEMISTRY
1856
331 (1946).
Licht, W., Jr., and Conway, J. B., IND.EKQ. CHEW,42, 1151 (1950).
toluenephase
W = waterphase
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. BI., Ibid., 31, 639 (1935). (3) Geankoplis, C. J., and Hixson, A. N., IND. ENG.CHEM., 42, 1141
Morello. V. S..and Poffenberaer. N.. Ibid.. 42. 1021 (1950). Nandi, S. K., and Viswanathln, T. R., Current Sci. (Indid), 15, 162 (June 1946). ENQ. (9 1 Sherwood, T. K., Evans, J. E., and Longcor, J. V. A., IND.
CHEM., 31, 1144 (1939). (10) Woodman, R. M., J . Phys. Chem., 30, 1283 (1926). (11) Yost, J. R., M.S. thesis, University of Pennsylvania, 1949. RECEIVED December 16, 1950.
(1950).
EngF-iYring
Heat Transfer and Heat Release
in Fluidized Beds
p*cess
development' I NORMAN
L. CARRI
A N D NEAL R. AMUNDSON
UNIVERSITY OF MINNESOTA, MINNEAPOLIS 14,
MI".
T h i s paper is a portion of an investigation into the interaction of fluids and solids i n fixed, moving, and fluidized beds in which the main concern is the operation carried on in the bed. This particular investigation was begun with the idea of determining in a theoretical way the temperature relations in a fluidized bed, depending upon the Bow and mixing assumptions. Formulas have been derived relating operating variables and physical parameters for heat transfer and heat release for two cases. The first assumed t h a t the conductivity in the solid might be a limiting factor, while in the second case conduction in the solid was neglected. I t is shown
for the case of heat transfer alone that for particles of the size ordinarily encountered in fluidization practice the two cases give almost identical results. With the assumptions made of random motion of particles in the bedand complete mixingof the fluid, the simple case discussed above is sufficient for design purposes. This offers a simplification which materially diminishes the calculations and should further aid the experimenter in the determination of heat transfer coefficients between the fluid and the particle. This work is being continued i n order to determine the effect of other fluid and solid mixing assumptions.
M
ticles from the bed presents a problem Those solution can bwt be obtained from considerations of probability. This problem has been discussed in the previously mentioned paper oE KaTten and Amundson (6). If solid is admitted to a bed containing S pounds of solid dt a rate of w s pounds per hour, the fractional part of an element, dm = wad+, introduced a t time Q = 0 still residing in the bed a t time 4 is given by - %?s@ __ e 8
EAT transfer and the release of heat in fluidized catalytic beds is a major factor in the design of these reactors as well as in their operation. In spite of the importance of this probleiii little is available in the literature either from an experimental or theoretical point of view. The problem of mass and heat transfer between particles and the fluid has been considered by Wilhelin and hIcCune ( I $ ) , Resnick and White (II), and Kettenring, Manderfield, and Smith (6). Kalbach ( 4 ) considered chemical reactions in fluidized beds from an over-all standpoint, while Carr and Amundson ( 1 ) and Kasten and Amundson ( 5 ) discussed reversible chemical reaction and adsorption, respectively, in fluidized beds. Experimental work on chemical reaction systems has been presented by Lewis, Gilliland, and McBride ( 7 ) and Len-is, Gilliland, and Reed (8). A great deal of other work is being done but reports have not been made. I n this paper the problem of heat release and heat transfer is considered from a theoretical point of view. It is supposed that a fluidized bed is simultaneously fed with a fluid stream and a solid stream. Effluent streams of fluid and solid are withdrawn a t the same respective rates a t which they were admitted. The solid is assumed t o be in the form of small uniform spheres of constant diameter which enter the reactor in a continuous fashion much in the manner of a fluid. Because their size is small and because the rate of solids circulation is usually large, this assumption is probably valid. If it is assumed that the particles in a fluidized bed are in completely random motion the withdrawal of these par1
Present address, Illinois Institute of Technology, Chicago, Ill.
and the amount of this element still in the bed a t time Q is given by -W S 9 __ (1) w,e S d~ Integration of this expression over all past time
should give the total mass of solid S in the bed. This it does. If one wishes to obtain the average residence times of particles in the bed the weighted mean of the time must be considered as
;Jmw,ee-
-Wad
S
de
This gives on integration by parts, S/wB,which is usually called the nominal holding time for such a reactor.
