ENGINEERING, DESIGN, AND EQUIPMENT
Stage Efficiencies of liquid Extraction Columns ROBERT E. TREYBAL N e w York Universify, N e w York 5 3 , N . Y.
T
HERE are occasions, in experimental studies of the efficiency of a countercurrent liquid extraction column, when the column used is so long or contains so many stages that the liquid leaving one end of the column will be substantially in equilibrium with the stream entering that end. This may happen particularly when the separation being studied is relatively easy, requiring few stages or transfer units. The accurate determination of the stage efficiency or the height of a transfer unit then becomes difficult if the terminal concentrations of the streams alone are measured. In such cases, it is possible to sample the streams a t positions along the column removed from the “pinch” regions and to determine the extraction efficiencies between sampling points. Particularly in the case of mechanically agitated extractors of the Scheibel(2) or OldshueRushton ( 1 ) design, pulse columns, and others, samplFs withdrawn in this manner are likely to contain some of both insoluble phases, As mass transfer of solute between the phases of the sample will take place during sampling and prior t o analysis, the problem of determining the conditions which exist inside the column from the altered samples arises. The treatment described herewith has been found useful in such cases.
t
Consider the multistage extractor of Figure 1, feed with LR cubic feet per hour of feed solution and LE cubic feet per hour of solvent. The concentrations of extractable solute are XI (feed), X z (raffinate), Y z (fresh solvent), and Y 1 (extract), all expressed as pounds of solute per cubic foot of solution. It is assumed that only the solute is transferred from feed to solvent and that the volumetric flow rates remain unchanged during passage through the tower. The equilibrium distribution of solute is shown in Figure 2. The terminal concentrations a t positions C and D (Figure 1) locate the operating line of Figure 2, where a pinched region is shown a t D. Theoretically it should be possible to enlarge the scale of Figure 2 sufficiently so that the stage efficiency near D can be determined graphically. But the enlarged scale may then represent precisions exceeding those available in the analytical data. Such analytical errors will not influence the graphical determination of stage efficiency in the central parts of the column, however.
EOUIL IDRIUM
CURVE , ,
EXTTRACT LECU FT/HR. V, L 6.SiXUTE/CU. F %
I , 0
FEED LR GU.FT/Ut?. X, L6.SOLUTE/&J.F %
P \
OPERATING LINE SLOPE -- L * / i p
T
X=L8.SOLUTE/CU.F% IN RAFFINQTE
Figure 2. Location of sampling points and determination of stage efficiency
H
C
I RAFFINATE LRCU FT./HR. x2 L B. SOLUE/CU.F~:
Figure 1.
December 1955
Countercurrent extraction column
To determine the stage efficiency for the part of the column between sections a t P and T (Figure I), samples of the streams are withdrawn from the column as shown. It may be desirable to take several samples, which may later be composited, from various parts of the column cross section in order to be certain that the withdrawn streams are truly representative of the liquids flowing past the sections chosen. Inside the column, the liquids passing section P have concentrations represented by point P on the operating line. Immediately upon withdrawal, a twophase sample spontaneously begins to equilibrate and the concentrations change. The sample is then deliberately brought
INDUSTRIAL AND ENGINEERING CHEMISTRY
2435
ENGINEERING, DESIGN, AND EQUIPMENT completely to equilibrium by vigorous shaking, the phases are allowed to settle, and their volumes, E3 (extract layer) and R3 (raffinate layer), are measured. One of the layers (say R3) may then be analyzed for solute concentration X3 and point Q on the equilibrium curve of Figure 2, representing the equilibrated sample, is located. During the sampling and subsequent equilibration, the change in composition of the sampled phases is represented by the following solute balance:
+ RBXP= EsY3 + R3Xs
ESYP
(1)
Equation 2 is represented by line QP (Figure 2 ) , of slope - R3/EI(. Consequently a line of this slope is drawn through point Q to locate P a t the intersection with the operating line. I n similar fashion, point T (Figure 2 ) is located with the information obtained from the sample a t T . The number of ideal stages between points P and T may then be determined by drawing steps between operating line and equilibrium curve in the usual manner (3), and the over-all stage efficiency in this part of the column determined by dividing the number of ideal by the corresponding number of real stages. It has been found, however, in cases where the equilibrium curve shows a marked change of slope, that the Murphree individual stage efficiency is more useful. Assuming that the Murphree efficiency is reasonably constant between sections P and T , the pseudo-equilibrium curve, J M K of Figure 2, is located _ - by trial so that everywhere the ratio of vertical distances .UN/GN is constant, and the number of steps drawn between the operating line and curve J M K equals the number of real stages between P and T (four in the figure). The fractional extract Murphree stage efficiency is then It will be desirable t o repeat the procedure in the region of section H in the column, where the slope of the equilibrium curve is substantially different. If desired, the number of transfer units and the height of a transfer unit between P and T may also be determined in the usual manner.
the B-rich layer be 2 pounds, analyzing yz weight fraction of solute C, and that of the A-rich layer be U pounds, analyzing ZU. Points U and Z , representing these, lie a t the ends of a tie line of Figure 3, as shown. Point M , representing the average composition of the entire sample, is located on the tie line through a solute material balance. (3)
A line through 0 and M must then intersect the binodal curve a t W and V, corresponding to conditions inside the tower prior to sampling. The corresponding point on the operating line a t ( X W ,y ~ is) then located, and the Murphree stage efficiency for the section of the column between the point of sampling and the solvent entrance is determined in the manner described above and shown in the figure.
Mx/m.
‘8
XR
xW
XK
XF
x : WT FRACTION SOLUTE tN R A F F N A E
c
Figure 4.
Determination o f stage efficiency
The general techniques described here are applicable t o any mass-transfer device involving two heterogeneous phases, including gas, liquid, and solid streams, although the details of bringing the withdrawn samples to equilibrium would necessarily differ for systems including nonliquid phases. Acknowledgment
The cooperation of the Metals Research Laboratories, Union Carbide and Carbon Corp., in permitting publication of this report is much appreciated. Figure 3.
Construction for a two-phase sample
The technique is readily adapted to cases where the quantities of the liquids in contact change on passage through the extractor. Figure 3 represents a typical case. Here feed F is brought in contact with solvent B to produce effluent extract E and raffinate R. The symbols represent flow rates in pounds per hour and simultaneously locate the corresponding compositions on the phase diagram. Point 0 represents the operating point (S),and any line OJK radiating from 0 intersects the two branches of the binodal solubility cprve a t concentrations of solute C, xg in the raffinate and ?JJ in the extract, corresponding t o a fixed level in the extractor. In this manner the operating line of Figure 4, which here shows a pinch a t the extract-effluent end, is located. Let a two-phase sample be withdrawn from the column in the manner described earlier. After equilibration, let the amount of
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Nomenclature
E = extract layer of sample, cu. feet L = rate of liquid flow, cu. feet per hour R = raffinate layer of sample, cu. feet U = raffinate layer of sample, pounds X = solute concentration in raffinate, pounds per cu. foot x = solute concentration in raffinate, weight fraction Y = solute concentration in extract, pounds per cu. foot. y = solute concentration in extract, weight fraction 2 = extract layer of sample, pnunds literature cited (1)
Oldshue, J. Y . , and Rushton, J. H., Chem. Eng. Progr., 48, (1952) .
297
(2) Scheibel, E. G., I b i d . , 44, 681, 771 (1948). (3) Treybal, R. E., “Liquid Extraction,” McGraw-Hill, New York, 1951.
RECEIVED for review May 18,1956.
INDUSTRIAL AND ENGINEERING CHEMISTRY
ACCEPTED August 29, 1955.
Vol. 47, No. 12
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