SIGNIFICANT DESIGN VARIABLES IN CONTINUOUS GRAVITY DECANTATION KRISHAN D. MANCHANDA AND DONALD R . WOODS Department of Chemical Engineering, McMaster University, Hamilton, Ontario, Canada
The statistically significant design variables for a tall, vertical cylindrical decanter were determined for the separation of coconut fatty acid and water. The significant variables for separating the water from the oil overflow were ratio of height to diameter, total feed flow rate, and temperature, in that order. For separating oil from the water underflow the significant variables were interface location, total feed flow rate, and temperature, in decreasing order of significance. The effect of the feed entering the decanter perpendicularly or tangentially to the side wall, and the interactions of the variables, were not Significant. The crossover in the most significant variables was interpreted to mean that the residence time within each phase was significant. Some comments on these results in the light of existing theory are given. The decanter diameter, the feed drop-size distribution, and the feed concentration were kept constant.
o FUSDAMENTAL basis has been established for the design
N of new or the improvement of existing continuous gravity decanters used to separate concentrated liquid-liquid dispersions. For dispersions in which there is a relatively small amount of dispersed phase, say in a waste-treatment settling basin, a design method based on the time required for the drops to travel to the interface has been reported (American Petroleum Institute, 1963; Brunsmann et al., 1962; Hart, 1947). This is often referred to as the overflow velocity method. A similar approach is also suggested for more concentrated dispersions where the settling velocity was calculated for an assumed typical drop size (Clarke and Davison, 1962; Happel, 1958). When the concentration of the dispersed phase increases, as in extraction units or for the overhead receiver from steam stripping or azeotropic distillation columns, a commonly reported design method is based on a residence time. By this method the equipment size is calculated to allow the mixture a plug-flow residence time of from 5 to 300 minutes, so that the dispersed droplets can travel to the interface and coalesce with their respective pure phases (Oliver, 1966; Perry, 1963; Warner, 1957). These plug-flow residence times are based on experience rather than on theory. Furthermore, this method gives size only and does not indicate the shape or feed and exit configurations. Atkinson and Freshwater (1958) have reviewed the methods for the separation of liquid dispersions. Several research groups have studied the effect of various design and state variables on the separation of specific immiscible systems for concentrated dispersed phases. Ryon, Daley, and Lowrie (1960) studied the separation of kerosine (with 0.1M di-2-ethylhexyl phosphoric acid and 30 grams per liter of tributyl phosphate) and water (with small quantities of U, Fe3+, Al, V, and S02-), and found that the rate of separation was controlled by coalescence. T h e important design and state variables were the flow rate of the dispersed phase per unit cross-sectional area and the temperature. Of some importance were the feed location relative to the interface (for the 6-inch diameter vessel), the wettability of the container walls, and the type of dispersion. The effect of height-diameter ratio was not conclusive. Of no importance were the feed configuration and the degree of mixing in the disperser (the drop-size distribution of the incoming feed was controlled by the degree of mixing in the disperser that produced the feed dispersion from the two pure phases). T h e criteria used for 182
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evaluating these vertical, cylindrical decanters were the concentrations of the entrained fluid in both the overflow and the underflow and the thickness of the dispersion band a t the interface; when it equaled the height of the decanter, negligible separation occurred. The separation of Aroclor-water dispersions in horizontal, rectangular, gravity decanters was studied by Wilke and coworkers (Epstein, 1963; Graham, 1962; Sweeney, 1964). They found that the rate of coalescence controlled the separation. T h e important design and state variables were the total flow rate and the condition of the incoming dispersion [which they characterized by a mixing vessel Reynolds number (Epstein, 1963; Graham, 1962) or an optically measured interfacial area (Sweeney, 1964)]. All runs were made at constant temperature. Of some importance was the feed location above the interface (provided the heavy organic layer occupied a quarter of the decanter depth. The results were independent of the feed location when the organic layer occupied half of the decanter depth). A limited number of experiments indicated that whether the water-oil dispersion was introduced into the water or the oil layer made a marked difference in results. T h e feed concentration (5.4 or 15,0y0) made a difference, and the distance of an impact baffle from the feed pipe affected the results. I n addition, they found that a calculated phase residence time could not be correlated with the criterion of concentration of water in the organic underflow. Graham (1962) suggested that a relationship existed between underflow concentration and a calculated overflow velocity (if the data when the organic phase filled only 1/4 of the vessel are neglected). I n summary, both of the two systems studied in detail were coalescence-controlled and the variables that appeared to be important were feed flow rate, temperature, and interface position. T h e present work reports the results of a statistical analysis to determine the significant design and state variables and the order of importance of these variables. The system studied was distilled water-coconut fatty acid in a tall, thin vertical cylindrical decanter. T h e physical properties are given in Table I. T h e criteria used were the calculated concentrations of immiscible contaminant leaving in both the overflow and the underflow, CFVand C, respectively. T h e five design and state variables studied were feed inlet geometry, total feed flow rate, F, feed temperature, T , interface position relative to the feed inlet I , and height-diameter ratio in the decanter, H. The
Table 1.
Physical Properties Density, g./cc. Viscosity, cp. Interfacial tension,- dyneslcm. . .
Solubility, w./w. Oil in water Water in oil
Measured Physical Properties of Coconut Fatty Acid (Oil) Temperature, C. 40 50 60 70
0.8850 6.53
0.8822 5.00
0.8796 3.92
0.8781 3.08
0.00168 i= 2.57, 0.460 & 2.57,
0.00252 0.489
0.00344 0.525
0.00560 0.559
0.00756 0.647
Table II.
Range of Variables Studied Coded Levels
-2 -1 160 200 50 40 O c. 1 inch below I 2 inches below feed inlet feed inlet H 3 .O 3.25 Feed inlet geometry perpendicular or tangential
Variables F T
80
0.880 & 0.25Y0 8.74 3t 1.07~ 30 ' 8.22 3t 27,
Unit Cc./min.
... ...
feed concentration was constant a t 25 volume yo water; the drop-size distribution of the feed was kept constant. T h e diameter of the vessel was not changed. Experimental Approach
T h e Box central composite design used in planning the test conditions facilitated determination of the significance of the variables and their interactions. Two levels of feed inlet geometry and five levels of each of the other four variables were studied. A central composite hypercube design in four dimensions calls for 28 runs-16 at the corners of the four-dimensional cube of =tl level, eight on the axes of the cube at =t2 levels, and four repeated a t the center as shown in Figure 1. T h e variables are listed in Table I1 in both coded and uncoded level form. T h e equipment (Figure 2) had three main sections: feed preparation, test section, and sampling system. I n the feed preparation section correct volumes of water and oil were metered into the disperser that generated a logarithmic-normal distribution of droplets of geometric mean diameter 35.5 microns with a geometric standard deviation of 1.62. T h e
0
+7
240 60 At midpoint
280 70 1 inch above feed inlet 3.75
3.50
flow rate to and the mixing speed of the disperser were kept constant. Part of the mixture leaving the disperser bypassed the test section, so that the flow rate through the disperser was constant even though the flow through the decanter was varied. Photographs were taken of the dispersion leaving the disperser through a square, optical cell of the same bore as the inside of the tubing. T h e test section was a cylindrical glass vessel 4 inches in diameter (9.45-cm. i d . ) and 16 inches high. Two, 4-mm. inlet ports, one straight and another tangential, were fused a t the mid-point of the vessel. The base of the decanter was fixed; the height-diameter ratio was changed by varying the height of the overflow tube. T h e temperature in the decanter was controlled to within 50.1' C. T h e position of the interface in the decanter was controlled by means of overflow tanks and checked by a cathetometer to within 5 0 . 1 cm. Oil from the decanter and the bypass feed both flowed to storage and were allowed to settle. Water from the decanter was discarded. Samples were withdrawn before the overflow tanks to measure the contamination in both the overflow and the underflow streams. The amount of water in oil was determined by titration using Karl Fischer reagent. The concentration of oil in water was found by multiple extraction with benzene followed by evaporation of the benzene. T h e remaining oil was weighed. Details are given by Manchanda (1966).
CODED LEVELS
Run
No.
X I
+I
x2 t1
2 3 4
+1
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5
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4 7
tl
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+I -I -1 -I
9
IO I1 I2 13 14 15 16
+I
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tl
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+I
+I
+I -I +I +I
+I +I
+I +I
-1
-1
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-I -1 -1
-1
+I
-I
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18
-2 0
t2
t2
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28
x.4
tl +I -I -I
-1
19
21 23 24 25 26 27
xn
-I -I
-1 0 0
17
Figure 1 .
+2
320 80 2 inches above feed inlet 4.0
0 0 0 0
0 0 0 0 0 0 0 0
tl -1
0 0 0 0 t2
-2 0
0 0 0 0 0
-1
+I -1 +I -1
+I -1 +1
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+I -I 0 0
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0 +2 -2
0 0
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Box method of experimentation in four dimensions Courtesy M. Van Winkle
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f l I D PkWARA7ION
7157 5 I C I I O N
::p
SAMCLING
i 8 b $J&
U!
..______._.____..__..._____._____ j
Figure 2.
Schematic diagram of equipment 1. 2. 3. 4. 5.
6. 7. 8.
9. 10. 11. 12. 13. 14. 15. 16.
17. 18.
19. 20.
O i l storage O i l pump Oil control valve O i l bypass valve O i l rotameter Water storage Water pump Water heater Water control valve Water rotameter Mixing tee Disperser Photomicrographic unit Feed bypass valve Bypass oil storage Test decanter Oil overflow tank Water overflow tank Water in oil sampling O i l in water sampling
w
Dd
A. D.
rc.
---
There is 95% confidence that the population size-distribution did not change throughout the tests. Furthermore, a t and X-test indicated that temperature did not significantly alter the drop-size distribution. For the effect of feed inlet geometry, a statistical test of the replicate runs taken for tangential and perpendicular feed position indicated that the separation of two liquids for tangential feed position is slightly but not significantly better a t the 95% confidence limit than the perpendicular feed position. Now consider the analysis of the remaining variables. T h e remaining variables were F, T,I, H, and their interactions. T h e Student t test, calculated a t 95% confidence level, indicated that
H, F, and T , in that order, were the most important design variables for the separation of water from oil, as evaluated by the entrainment of water in the overflow oil, CUT. I, F , and T , respectively, were the most important design variables for the separation of oil from water as evaluated by the entrainment of oil in the underflow water, C,. Interactions between the variables were not significant for the separation of either water from oil or oil from water. Figures 3 and 4 show the effect of the significant design variables on C, and C, a t various design levels; an increase in T and a decrease in F improve the separation. However, the CALCULATED IMMISCIBLE CONCENTRATION OF WATER IN THE CNFA (C,)% BY WIGHT
Block valve Control valve Analysis Drain Thermocouple Water Oil Water-oil dispersion THE
Results and Discussion
T h e data were statistically analyzed, and the results are discussed in the light of existing theory. Statistical Analysis. T h e data were fitted to four, secondorder empirical equations. One equation related Cw to the four variables, F, T , I , and H for tangential feed flow, and one, for perpendicular feed flow. Similarly, another pair of equations related C, to the variables for each of tangential and perpendicular feed conditions. T h e calculated multiple correlation coefficients, r, are given in Table 111. T h e tabulated value of the correlation coefficient for 13 degrees of freedom and 28 data points is 0.423. Therefore, since the calculated correlation coefficient is much closer to unity and greater than the tabulated value, the fitted correlation represented the data very well. Since a significant correlation was obtained, the relative importance of the different variables was tested. The design and state variables studied were F , T , I, and H. Before they could be tested the constancy of the drop-size distribution of the incoming dispersion and the effect of tangential versus perpendicular feed position were statistically checked.
Calculated Multiple Regression Coefficients
Feed Inlet Geometry
CN
CO
Tangential Perpendicular
0.890 0.899
0.965 0.935
LEVELS Of DESIGN
VARIABTET'
l&EC PROCESS D E S I G N A N D DEVELOPMENT
-
COOED LEVELS OF ----c THE DESIGN VARIABLES
Figure 3. Effect of design variables on calculated immiscible concentration of water in CNFA overflow (CN) at various design levels
-
Height/diameter ratio Flow rate Temperature Feed tangential to decanter wall Feed perpendicular to decanter wall
-------0 0
ALCULATEO IMMISCIBLE CONCENTRATION OF CNFA (Co)xlO:% BY WEIGHT
-2
0
-1
+1
+2
CODED
LEVELS OF THE ESIGN V A R I A B ~
-2
IN WATER
-1
UNDERFLOW
0
+l
+2
C O E D LEVELS OF THE DESIGN VARIABL-
Figure 4. Effect of design variables on calculated immiscible concentration of CNFA in water underflow (C,)a t various design levels
- Interface position
-----
---0 0
164
B
L
-CODED
Table 111.
OVERFLOW
Flow rate Temperature Feed tangential to decanter wall Feed perpendicular to decanter wall
decreased (with temperature increase) by a factor of about 1.7, concentrations in the effluent streams decreased by a factor of about 1.3. Although Ryon et al. (1960) found a more direct correspondence between changes in viscosity ratio and entrainment concentration, nevertheless the trends are the same.
most significant variable was not the same for both the C , and C, criteria-Le., H was most significant variable based on Cw, whereas Z was the most significant variable based on the C, criterion. Effect of Flow Rate. Both Cw and C, increase with an increase in the total feed flow rate. Epstein (1963), Graham (1962)) Sweeney (1964), and Ryon et al. (1960) reported higher values of Cw with an increase in flow rate. This is to be expected, because higher flow rate meant less residence time within each phase for the drops to settle and coalesce and probably results in an increase in the local turbulence. Effect of Temperature. An increase in temperature produced a decrease in Cw and C, that corresponded roughly to the change in viscosity of the continuous phase with temperature. T h e data in Table IV show that as the viscosity ratio
F a
f a
-INTERFACE SEPbRATlffi FEED FROM EXIT
Effect of Temperature and Viscosity on Separation of Immiscible liquids Viscosity Ratios of Efluent Ratio of Continuous Concentrations Temferature Phase of Water in Oil in Ratio Feed oil, CW water, C, 60/80 1.62 1.47 1.33 40/60 1.75 1.23 1.25
Table IV.
co
co
Figure 5. Significance of interface position and residence time within a phase on separation of two immiscible liquids
A. 8.
0 0
Phase continuity Phase inversion Water
Oil
e X X
e X
.
X
e X
X
X X
t
I
X
I
X
.e * e x h
e n X
x x e
e X X 0
0
I
I
I
5
10 -RESlC€KE
I
I
15 20 TIME IN WATER
I
25 LAYER, MIH.
I
30
Figure 6. Effect of residence time in CNFA layer on calculated immiscible concentration of water in CNFA overflow (C,) 0
X
Feed tangential to decanter wall Feed perpendicular to decanter wall
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Effect of Height-Diameter Ratio, H, a n d Interface Position, I. These were the most significant variables. However, the results are not easy to interpret because the importance of the variable depends on whether the oil layer or the water layer is being discussed. This crossover of significance may, in part, be interpreted as meaning that the residence time within a phase is the most significant parameter. However, the effect of phase inversion may also be significant. Since the vessel diameter is constant, increasing the height increases the total volume of fluid and can increase the volume in the oil phase, if the change in total height has not been compensated for by a change in interface position. Hence the fact that the overflow contamination, Cw,is a function of height may indicate the importance of the residence time within the oil phase. For the water phase, the interface position indicates both the changes in volume of water [and hence the residence time within the phase] and the effect oi' phase inversion. This latter effect occurs because the water dispersed in oil is injected into the oil phase for low interface locations and into the water phase for high interface locations, as indicated on Figure 5 . T h e significance of the interpretation of variables H and I as being measures of the residence time within each phase is shown in Figures 6 and 7. A linear regression of the data for C,, and C, us. residence time in their respective phases indicates that there is a correlation between both CIvand C, and residence time, but the regression accounts for only about 41 and 57% of
the total variance for Cw and C, respectively. Hence, although the residence time within each phase is a very significant design variable, for this work this variable does not account for all the variation; temperature and interface location (partly interpreted as phase condition) are also important. T o check the effect of phase inversion, runs with different phase conditions but the same temperature and roughly the same plug-flow residence time within the water phase are compared in Table V. The result is surprising, in that less contamination occurs when the oil continuous feed is injected into the water layer. However, from Table V it can also be seen that the variation in residence time has more effect on the contamination, C, than changing of the phase conditions. For this system, order of magnitude comparisons between the
~~
Table V. Signiflcance of Interface Position and Residence Time within a Phase on Separation of Immiscible Liquids for 60' C. Residence Time in Water Layer, Min. 77.47 7 7.44 29.3
Phase condition 70by weight
C,,
Continuity
Inversion
Inversion
0.00037 -f 4%
0.00034
0.00010
X
e
x
x e
e X
x e
e X
x .
x
X
e
X
1
X
.
e
.
X
I
I 2
4
1
I
I
a
6
-RESIDENCE
TIME
IN
CNFA
10 L A Y E R , MIN.
I
12
Figure 7. Effect of residence time in water layer on calculated immiscible concentration of CNFA in water underflow (C,) X 186
Feed tangential to decanter wall Feed perpendicular to decanter wall
l & E C PROCESS D E S I G N A N D D E V E L O P M E N T
settling rates and the coalescence rates and the presence of a clean interface (instead of a dispersion band) suggest that sedimentation rather than coalescence was the controlling mechanism for separation. T h e overflow contamination could not be theoretically predicted from the inlet drop size distribution and on the assumption that the upward oil velocity was the uniform across the cross section. Conclusions
I n tall cylindrical decanters: T o separate water from coconut fatty acid (CNFA) the significant design variables are, in the order of decreasing significance, height-diameter ratio, total feed flow rate, and temperature as judged by the criterion of the concentration of immiscible water in the oil overflow. To separate CNFA from water, the significant design variables are, in the order of decreasing significance, interface position relative to the feed inlet, total feed flow rate, and temperature as judged by the criterion of the concentration of immiscible oil in the water underflow. Whether the feed was injected perpendicularly or tangentially to the side of the vessel did not significantly affect the concentrations in either underflow or overflow. T h e interactions among the variables were not significant for either separation. T h e improved separation in both phases with increase in temperature substantiated the findings of Ryon et al. I n this work, however, viscosity ratio did not bear so close a relationship to the entrainment ratio as Ryon et al. found. T h e improved separation in both phases caused by a decrease in flow rate substantiates the findings of Ryon et al. and Wilke and coworkers. T h e crossover in the most significant variable (height-diameter ratio for water from oil, and interface position for oil from water) was interpreted to mean that the residence time within each phase is the most significant design variable for the separation of either immiscible fluid. A significant correlation exists between the entrainment concentrations and the residence time within each phase. Since this is a tall, thin decanter, the concentration of water droplets leaving in the overflow should be theoretically predictable from the feed drop-size distribution, the feed concentration, and the upward velocity of the rising oil. However, the theoretical model of a uniform plug-flow rising oil and a settling
velocity calculated from the Hadamard-Rybczynski equation (1911, 1912) could not predict the observed results. Calculations suggested that sedimentation is controlling rather than coalescence; this was substantiated by the absence of a dispersion band at the interface. Ac knowledgrnent
We are grateful to the Ontario Research Foundation and the National Research Council, Grant A 2101, and McMaster University for financially supporting this work. Procter and Gamble (Canada), Ltd., donated the fatty acids. C. M . Crowe helped us with the statistical analysis. Nomenclature
C, = calculated immiscible concentration of oil in water underflow, % by weight CW = calculated immiscible concentration of water in oil overflow, 7 0 by weight F = total feed flow rate, cc./min. H = ratio of height to diameter, dimensionless Z = interface position relative to feed inlet, dimensionless T = temperature, O C. Y = multiple correlation coefficient literature Cited
American Petroleum Institute, New York, “Manual on Disposal of Refinery Wastes,” Ser. 6, Vol. 1, 1963. Atkinson. E.. Freshwater. D. C.. Brit. Chem. Enp. 3. 554 119581. Brunsmann, ’ J. J., Cornelissen,’ J., Eilers, H.: J.‘ Water Poliution Control Fed. 34 (Nol), 44 (1962). Clarke, L., Davison, R. L., “Manual for Process Engineering Calculations,” 2nd ed., McGraw-Hill, New York, 1962. EDstein. A. D.. M.S. thesis. Universitv‘ of California Radiation ‘Laboratorv. 10625. Jan. 14. 1963. Graham, R.’ J., M.S. thesis, ’University of California Radiation Laboratory, 10048, Feb. 5,1962. Hadamard, J., Compt. Rend. 152, 1735 (1911); 154, 109 (1912). Happel, J., “Chemical Process Economics,” p. 251, Wiley, New York. 1958. Hart, w. B., Petrol. Processing 2, 282, 471 (1947). Manchanda, K . D., M. Eng. thesis, McMaster University, 1966. Oliver, E. D., “Diffusional Separation Processes, Theory, Design and Evaluation,” p. 375, Wiley, New York, 1966. Perry, J. H., ed., “Chemical Engineer’s Handbook,” 4th ed., p. 21-18, McGraw-Hill, New York, 1963. Ryon, A. D., Daley, F. L., Lowrie, R. S., Oak Ridge National Lab., Rept. 2951 (Oct. 5, 1960). Sweeney, W. F., University of California Radiation Laboratory, Rept. 11182 (Jan. 20, 1964). Warner, B. F., “Scale-up of Chemical Plant Processes,” p. 70, Institute of Chemical Engineers, London, 1957. RECEIVED for review February 27, 1967 ACCEPTED November 24, 1967
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