Michaels, A. A,, Ind. Eng. Chem. 44, 1922-30 (1952). Nelson, E. T., Walker, P. L., Jr., J . Appl. Chem. 11, 358-64 (1961). Nutter, J. I., Burnet, G., Jr., IND.ENG.CHEM.PROCESS DESIGN DEVELOP. 5 , 1-5 (1966). O’Connor, J. G., Norris, M. S., Anal. Chem. 32,701-6 (1960). Roberts, P. V., Ph.D. thesis, Cornell University, Ithaca, N.Y., 1966. Schumacher, TV. J., Ph.D. thesis, Cornell University, Ithaca, N.Y., 1964. Schumacher, TV. J., York, Robert, IND. ENG. CHEM.PROCESS DESIGN DEVELOP. 6, 321-7 (1967).
Tsuruizumi, A., Bull. Chem. SOC.Japan 34, 1457-65 (1961). Weisz, P. B., Goodwin, R. D., J . Catalysis 2, 397-404 (1963). Wheeler, A., Advan. Catalysis 3, 295 (1951). Wilke, C. R., Chang, P., A.I.Ch.E. J . 1,264-70 (1955). RECEIVED for review February 8, 1967 ACCEPTED July 20, 1967 Prepared from a thesis submitted by Paul V. Roberts in partial fulfillment of the requirements for a Ph.D. degree.
FROTH AND FOAM HEIGHT STUDIES Small Perforated Plate Distillation Column D. A.
R E D W I N E , ’
E. M . F L I N T , 2 A N D M A T T H E W V A N W I N K L E
The University of Texas, Austin, Tex. Foaming studies utilizing perforated 4 X 4 inch plate glass columns, 6 inches in diameter, are reported. A photographic method of evaluating the foam-froth height, using air-water-additive systems, reproducible to h 0 . 2 5 inch was developed using the smaller column and fixed air and liquid flow rates with varying concentrations of: additives. Air-water, air-water-Alconox, air-water-1 -butanol and air-water-3-heptanol were used. Utilizing a 6-inch diameter glass perforated plate column and the same photographic technique, froth-foam data were determined for the distilling systems, acetone-1 -butanol, and methyl ethyl ketone-toluene, maintaining the concentrations within a narrow range of variation and varying the liquid and vapor rates from approximately 400 to 2 2 0 0 pounds per hour using total reflux. This corresponds to an F factor range of 0 . 6 2 to 2.3. Froth-foam heights ranged from 1.4 to 2.5 inches. Relations are presented relating froth density, aeration factor, height, and F factor. Results of a study of the distilling systems show agreement with the air-water data.
FOAM and froth formation is of interest in design of equipment to be used in operations involving mixing and separation of vapor and liquid, such as distillation, absorption, and stripping. Entrainment, priming, and efficiency of contact related to mass transfer between the phases are all affected by the extent of foam and froth formation. Froth has been defined as aeration resulting primarily from vapor agitation of the liquid with which it is being mixed and foam as aeration resulting primarily from physical property (surface phenomena) effects. I n a discussion of tray dynamics, according to Smith (1963), these terms are considered interchangeable to a great degree. Foam formation, in addition to being a function of physical properties of the system, is somewhat related to the method and degree of aeration. Froth bubbles are relatively small in diameter and relatively stable, whereas foam generally consists of larger, more unstable bubbles. There is some agreement that surface tension gradients exert the greatest single effect on foam formation of the variables encountered. When a solute and solvent form a mixture in which there is little change in surface tension, foaming is not expected and the method and aeration effects predominate (Bikerman, 1965). Bainbridge and Sawistawski (1964) reported studies on surface tension systems when frothing occurred and Zuiderweg and Harmens (1958) stated that higher efficiencies were found in the higher surface tension systems when foaming occurred. Foaming systems generally con-
Present address, Enjay Chemical Co., Baytown, Tex. Present address, Humble Oil & Refining Co., Houston, Tex.
tain surfactants such as dilute aqueous solutions of alcohols and ketones, while nonfoaming systems consist of the usual hydrocarbon mixtures. T h e air-water system, often used in froth and foam studies, foams less than the nonfoaming systems. Foss and Gerster (1956) and Geddes (1946) considered mass transfer bet\reen the vapor and liquid phases to be a factor related to the height of the aerated liquid above the plate surface in distillation and absorption. The froth height, h,, is used to determine the relative froth density, 6, and the aeration factor, p, for column design. Hutchinson et al. (1949) defined Q, relative froth density, as the ratio of the height of clear liquid on the plate to the height of frothy liquid measured from the same point. T h e term hc is defined as the equivalent clear liquid height that would be present if all of the froth of the tray were collapsed or deaerated. Q =
h 2 h,
They defined aeration factor by
p=-Q+1 2
A number of studies have been made of foaming and froth formation on distillation trays. Mayfield et al. (1952) and Lee (1954) estimated froth height on perforated trays based on measurements in laboratory and plant equipment. Kemp and Pyle (1949) studied foaming on bubble cap trays and Gilbert (1959) and Hutchinson et al. (1949) investigated this problem on both perforated trays and bubble trays using the VOL. 6
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4 OCTOBER 1967
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air-water system. H u n t et al. (1955) studied froth height on perforated trays as a function of gas flow rate with several systems, using a nonliquid flow arrangement. Rennie and Evans (1962) studied froth formation on perforated trays, whose hole sizes ranged from l / 3 2 to l / 4 inch, free area from 0.1 to 8.947,, fixed weir height, column size 3l/2 X 4 inches, and the air-water system. Froth density and bubble size were determined by 7-ray absorption and photographic techniques. Calderbank and Rennie (1962) studied the same system. with the same equipment design, with trays of and lj4-inch holes, free area 1.05 to 8.94%, to determine bubble size as a function of liquid and gas flow rates. Leibson et al. (1956), Davidson and Amick (1956), Hughes et al. (1955), and Benzing and Myers (1955) investigated bubble formation from single orifices using a number of systems. The experimental work has been primarily designed and carried out for either the correlation of foam height or foam density as a function of various designs, flow rates, and system properties or the determination of bubble size and area to enable mass transfer calculations to be made. I n many cases no liquid flow was used and in others the designs were not comparable to those commonly utilized in fractionater and absorber design, both geometrically and in the method of operating the test equipment. T h e present investigation is one of a series to study foam and froth formation to determine foam height and density as a function of a number of pertinent design, operating, and system variables with the purpose of arriving a t design correlations for the prediction of the foam and froth height and density for plant scale engineering design. T o do this, a model which has a flow regime similar to that of commercial equipment should be used to enhance the possibility of scale-up, and the method of determining the foam height should give reproducible results. Both factors were considered in this and related investigations.
meter and onto the top plate, from whence it flowed through a downcomer to another liquid-aligning plate and then to the test plate below, across the test plate, through its downcomer and to the vapor-aligning plate below, and finally to the sump. T h e metered air blown through the column was vented. Samples of the liquid were taken directly from the test plate during the testing period and surface tension was determined on each sample to check the composition which varied over a period of time because of evaporation. Pressure taps above, below, and in the surface of the plate enabled pressure measurements at the three points. T h e test plate characteristics are shown in Table I. Still photographs of the action in the test section were used to determine the average height of the foam and froth formed during a given test. A square glass section above the test plate minimized possible optical distortion caused by curvature of the glass. For the major portion of the tests, steady-state flow conditions of 2500 pounds of liquid per square foot of free column cross-sectional area per hour (72 gallons per hour per foot of weir length) and 500 pounds of air per square foot of free column area (Fc factor of 0.53, or Fh = 6.6) were maintained, to eliminate the possible effects of flow variation on reproducibility of the froth height determinations. T h e photographic procedure involved making 16 exposures a t random 15-second to 1-minute intervals and averaging the froth heights measured from all pictures made during the test run. This technique measured a n average maximum froth height with a n average deviation of 1 0 . 2 5 inch. To determine quantitatively the average height of froth, the contours of the surface shown on the 35-mm. negatives were traced from a n enlarged image projected by a microfilm viewer. T h e area under the traced surface line of froth was measured using a polar planimeter. To determine the averagemaximum height as observed through one side of a square duct, the traced ATM
FILTER
Foam-Froth Height Measurement
Methods of measuring froth height in the laboratory range from visual estimation of the average height of the highly mobile and changing aerated mass using a ruler, to utilization of 7-ray techniques. Since primarily the data used for design correlations were obtained in the laboratory, a variation resulting from the preciseness of the method of measurement could be expected. Observation and measurement of froth heights in industrial equipment are extremely difficult and the quantitative interpretation of the observations has proved generally inconclusive. As an important part of the over-all investigation, it was first attempted to develop a reliable technique, relatively uncomplicated, for measuring froth height and to test the method on systems having different surface tension characteristics. A photographic method was devised which enabled froth height measurements to be reproduced within +0.25 inch on air-water, air-water-Alconox, air-water-1 -butanol, and airwater-3-heptanol systems.
HEAD
MANOMETER
r
I
COLUMN PRESS. MANOMETER
TA PRESS. MANOMETER DIFF.
El
ROTAMETER
Procedure and Equipment
Measurement Technique. Fractionation column hydraulics were simulated using air as the vapor phase and various water solutions of materials of different surface tension as the liquid phase. The column and accessory arrangement is shown in Figure 1. T h e nominal 4 X 4 inch square test section was located between 2 and 3. The liquid was pumped through a flow526
l&EC PROCESS DESIGN A N D DEVELOPMENT
Figure 1 . ment
Schematic of test column and accessory arrange-
area was divided by the column width. Figures 2 and 3 &OW photograph and the correspondlns traced area from a which the average froth h e g h t was evaluated. Table I1 presents the results of a typical sequence of 16 pictures made a t the higher values of froth height, T h e deviations reported are representative of the degree of variation that occurred in the test section over a typical test period. =he average deviation was 0,59 inch and the standard devialion was 0.76 inch of froth heig-ht. Table I11 shows the results of 56 pictures taken at a fixed liquid and gas rate (C = 500, L = 2500) and liquid concentration with groups of 8 or 16 pictures taken as much as 3 days apart. With the reproducibility of the method established to be well within =t0.25 inch for the four test systems used and
far froth heights ranging u p to about 6 inches, determination of froth heights for distilling systems was the next step,
Effect of VaWr and Liquid Rater on Frothing-Perforated Plate-Distilling Systems Equipment. This investigation was carried out in a 6inch glass-sectioned distillation column. TO provide a clear, unobstructed view of the test tray's action during distilling operations, a 6-inch found piece of borosilicate glass was cut above its beveled end in such a manner that the 6-inch round end fitted into a machined groove '/a inch deep and inch wide in the specially designed test section brass flange. A Teflon tape-wrapped gasket was used both to seal and cushion the glass-metal fitting. T h e test tray was located below the specially constructed flange, which was provided with two taps for samdinn and clear liauid head measurement.
Cr
inch square duct, sq. inches Perforation diameter, inch Tray thickness, inch Pitch, on equilateral triangular centers, inch No. of perforations Free area,
13.7 0.125 0.125 0.250
90
Yo test section cross-
sectional area Downcomer area, yo t a t section cross-sectional area Weir heieht. inch
Figure 2. Scmple photograph of foaming system on test plate
8.1 9.5 0.75
Table II. The Determination of Froth Height for a 26-P.P.M. Deterjlenl-Water Solution Pholo,crafih Foam Height, Dtfermcc from An. NO. Inches Foam Height, Inch 1 4.17 -0.70 2 5.55 +0.68 3 4.21 -0.66 4 5.05 +n.i8 5 4.92 +o.o5 6 5.10 +0.23 7 3.86 -0.99 8 3.98 -0.89 9 4.91 +o.w 10 4.67 -0.20 11 4.45 -0.42 12 5.95 +1.08 13 4.97 +0.10 14 6.33 +1.46 15 5.81 +O .94 16 4.02 -0.85
zce from
Irzh
B
2.84 3 06 2 75 A". 2.88 Average absolute deviation = 0.06 inch Standard deviation = 0.125 inch
C D
Figure 3. Area derived from tracing f o a m surface from photograph
VOL. 6 NO, 4
1.01 . ..
u.u4 -0 18 0 03
OCTOBER 1967
527
Four perforated plates of identical design, whose specifications are shown in Table I, were used in the column. T h e outlet downcomers were the segmental type extending to within ‘/2 inch of the tray surface and the weir height on each plate was 3/4 inch. T h e column, lines, accumulators, and reboiler were insulated. Resistance wire heating around the lines and accessories was used to maintain essentially adiabatic conditions. Internal reboiler heat was provided by three copper sheath immersion-type heaters and resistance wire heating about the bottoms accumulator and reboiler provided additional heat input. Centrifugal pumps provided reflux and column feed flows, metered through two rotameters. T h e piping between the two rotameters enabled some of the overhead product, after the entire overhead product flow had been measured by the first rotameter, to be fed back into the column reboiler as feed for the rectifying section, if so desired. Thus, the total overhead flow was measured by the first rotameter, and metering valves between the first and second rotameters allowed the desired amount of reflux flow through the second rotameter, the remaining overhead product being fed into the reboiler. I n this way, the column served as a rectifying section with the feed rate measured as the difference between the overhead product and the reflux rates. T h e equivalent clear liquid head manometer was constructed in such a way that the system liquid in the glass manometer could be manually purged by nitrogen onto the test plate in order to attain similar liquid compositions both in the manometer and on the tray, thus reducing bubbling in the manometer leg which could lead to errors in measurements. Contamination resulting from rust, corrosion, and other sources was prevented by use of copper, brass, and Teflon in construction of the equipment. Each material was pretested under distillation conditions in the systems selected. A 35-mm. camera with a 10.5-cm. lens and 52-mm. polarizing filter was used for recording the best section tray action. A square fluorescent lamp with an opal glass was used behind the test section to eliminate shadows. Dual polarizing light sources with filters lighted the front of the test section. All compounds comprising the binary systems distilled were at least 99 mole yo reagent grade material. Experimental and literature refractive indices for the compounds are compared in Table V. Vapor-liquid equilibrium data for the acetone-butanol system were reported by Brunjes and Furnas (1935) and for the MEK-toluene system by Steinhauser and White (1949). T h e method of Pitzer et al. (1955a, b) was used for vapor density calculations for the MEK-toluene system, and the acetone-butanol liquid physical properties were obtained from Ling and Van Winkle (1958a, b). Procedure. The column was operated over a range of flow rates from 80 to 410 pounds per hour of liquid. For each of the two binary systems studied the test tray liquid composition was adjusted to be greater than 70 mole yGof the heavy component. Only one series of four data points was taken in which the tray liquid composition was less than this. T h e column, performing as a rectifying section, was gradually heated until the desired liquid and vapor rates were obtained. After 45 minutes to 1 hour of steady-state operation, the first series of pictures and column samples was taken. After another 30-minute interval another series of pictures and samples was taken, and the heat input was then adjusted for the desired flow rate for the next data point. Immediately prior to each series of pictures, samples Lvere taken of the overhead product and tray liquid. T h e samples were sealed, cooled, and stored for later analysis in the refractometer. Also, prior to the pictures, manometer readings from the three manometers were observed and recorded. Often, because of the fluctuations inherent in the equivalent clear liquid head measurements for a column of this size, values were taken a t random time intervals and were averaged to determine a representative value for this pressure measurement. A microfilm projector was used to project the image of each negative onto a horizontal plane. The liquid perimeter \vas 528
l&EC
PROCESS DESIGN A N D DEVELOPMENT
Table IV. Test Tray Specifications Column diameter, inches 6.00 Cross-sectional area, sq. foot 0.1882 Active (bubbling) area, sq. foot 0.1168 Free area, yc cross-sectional area 7.72 Downcomer area, % cross-sectional area 9.09 Perforation diameter, inch 0.1563 Pitch/diameter, equilateral triangular centers 2.80 IVeir height, inch 0.75 18.0 Test section tray spacing, inches 109 Number of perforations Total perforation area, sq. foot 0.0145 Table
Exptl. Lit.
V. Refractive Indices of Pure Components (Temperature, 25’ C.) Butanol MEK 1.3971 1.3764 1 ,3563 1 ,3974 1 ,3763 Acetone 1 ,3560
Toluene
1.4915 1 ,4939
traced from the projected images with the foam or froth surface included in the tracing and excluding separated droplets of liquid as froth or foam. A polar planimeter was used to determine the enclosed area scaled to its actual size. T h e actual froth height was obtained by dividing the actual liquid area by the test section length. Once a series of froth heights was obtained, and the refractometer analysis on the samples indicated that the column was operating a t steady-state conditions, averages for each series of pictures were obtained and recorded along with the compositions and manometer readings. Experimental Results
The experimental data taken during this study and the calculated correlation parameters are recorded in Table VI. The tabulated liquid and vapor rates are those for the test tray. Since the rotameter recorded the top tray product and reflux flows, constant molal overflow was assumed for calculation of the test tray’s vapor and liquid rates. Discussion
T h e residual pressure drop across the perforated tray, h,, was calculated by the method of Hunt, et al. (1955).
hi
= h,
f
hdp
f hi
This term expresses the energy necessary to form bubbles and generate turbulence. T h e total pressure drop is also expressed in Smith’s book by ht =
hdp
+ $(Lf L J
tvhich represents the sum of the dry tray pressure or ori5ce pressure drop plus the pressure drop resulting from passag:: of the vapor through the aerated liquid on the tray in term i of inches of clear liquid. The dry tray or orifice drop was calculated by the method of Kolodzie and V a n Winkle (1957). T h e vapor F factor was based on the active or bubbling area of the perforated tray; thus,
The liquid rate parameter, L ’ j q , is defined as the volumetric froth flow rate per foot of lveir length xvhich is calculated as the clear liquid flow rate per foot of weir length divided by the froth density. Effect of Vapor Rate on Froth Height, h p The froth height was found to increase slowly with increasing vapor rates a t the lower vapor F factors. but more rapidly with increasing vapor rates a t higher F factor values. Figure 4 illustrates this trend. The F factor is used as a vapor rate-correlating factor
Table VI.
Run Class 1-I -I I -111 -1V 2-1 -I I -111 -1V 3-1 -I I -1V
-V 4-1 -I I -111
-1V 5-v -VI -VI1
L , Lb./Hr. 312 265 174.4 91.4 198 146 128 100 194.3 83 82 101 125 86 105 149 74.3 102 135
7-1 -I I -111 8-IV
V , Lb./Hr. 31 2 309 301 284 21 1 197 191 184 208 179 102 107 132 122 124 161 143 147.5 156
306 355 407 320 256 226 290 268 315
-V -VI 9-VI1 -VI11 -1x
308 360 41 0 324 259 230 297 276 320
Experimental Results and Correlation Parameters
h,, In. 2.115 2.05 1.94 1.81 1.596 1.576 1.616 1.585 1.72 1.615 1.42 1.469 1.504 1.435 1.482 1,650 1,500 1.555 1.65
FAA 2.02 2.00 1.97 1.87 1.332 1.245 1.212 1.172 1.33 1.15 0.642 0.67 0.839 0.781 0.79 1 .oo 0.911 0.935 0.973
hc 6 P 10 x L 1 / $ ht 1 . 1 5 Equivalent clear liquid manometer not 1.34 installed for this series of runs 1.20 1.12 0.121 0.97 0.28 0.64 0.44 0.075 0.53 0.88 0.34 0.67 0.072 0.50 0.31 0.66 0.75 0.086 0.41 0.26 0.63 0.63 0.157 0.38 0.22 0.61 0.70 0.078 0.31 0.19 0.60 0.70 0.056 0.37 0.26 0.63 0.53 0.069 0.38 0.26 0.63 0.70 0.091 0.36 0.24 0.62 0.37 0.054 0.40 0.28 0.65 0,50 0 27 0.64 0.069 0.40 0.44 0 21 0 60 0 126 0.35 0.49 0.40 0 635 0 049 0 27 0.45 0.34 0 62 0 082 0 22 0.45 0 096 0.41 0 62 0.47 0 25
1.935 2.192 2.45 1.94 1.76 1.68 1.792 1.754 1.914
1.72 2.00 2.30 1.79 1.42 1.28 1.64 1.52 1.77
0.95 1.05 1.55 1 .oo 0.93 0.89 1 .oo 0.98 1.06
0.35 0.39 0.40 0.39 0.34 0.34 0.42 0.45 0.39
0.18 0.18 0.18 0 20 0 19 0.20 0 23 0.25 0.20
0.59 0.59 0.59 0 60 0 60 0 59 0.62 0.63 0.61
0.283 0.326 0.374 0.265 0.218 0.187 0.205 0.172 0,253
Xtmy
soh
0.88 0.86 0.76 0.78 0.05 0.03 0.03 0.03 0.04 0 04 0 02 0.01 0.09 0.04 0.02 0 01 0 03 0 03 0 01
0.94 0.97 0.95 0,90 0,59 0.51 0.47 0.39 0.61 0.44 0.41 0.41 0.71 0.59 0.56 0.48 0.38 0.39 0.39
0.22 0.15 0.17 0.17 0.14 0.12 0.07 0.06 0.05
0.64 0.54 0.57 0.59 0.55 0.55 0.39 0.37 0.33
because it indirectly includes pressure effects in vapor rate calculations. Earlier a.ir-water studies by Foss and Gerster (1956) showed that the total vapor rate rather than the vapor rate through the perforations was the fundamental variable in froth height correlations. T h e line of Figure 4 represents a second-order least squares fit of the experimental data. T h e second-order fit has the value 0.933 as the sum of the absolute values of the deviations for the 24 plotted data points, indicating a fairly good statistical fit of the experimental data. However, the liquid rate was not a constant factor for the data, and all the test tray liquid compositions of Figure 4 were in the 0.01 to 0.25 mole fraction mor#-volatile component range. I n quantitative terms the equation
h,
=:
1.57(v)O.212(L)0.120
describes the froth height as a function of liquid and vapor rate reasonably well. T h e largest deviation of calculated data point from the corresponding experimental data point was 0.26 inch froth height, and the average of absolute deviation was 4.4%, indicating a reasonable description of the data by this correlation. From the correlation, a t a constant liquid rate, a fourfold increase in vapor rate \vi11 result in a 46% increase in froth height, or the froth height is proportional to the vapor rate raised to the 0.272 power. However, of the 24 data points used in this correlation, all 1 5 of the acetonebutanol data points wei:e in the 0.10% mole fraction acetone range. I t is in this concentration region that the acetonebutanol system liquid properties change most rapidly with concentration. Effect of Vapor Rate on Froth Density, 6. Figure 5 illustrates the effect of the vapor F factor on froth density. T h e upper curve is the data of Foss and Gerster (1956) for a value for h, h,, = 5.6 inches, and the intermediate curve represents their data for h, h,, = 1.9 inches. These curves resulted from data taken on the air-\\-ater system. T h e lower curve represents a second-order least squares fit on the experimental data of this study. T h e weir height in this study
+
+
0.5
I .5
1.0
2.0
2.5
F~ A Figure 4.
Foam height vs. active area F factor
was 0.75 inch, and the h,,, as calculated by the modified Francis formula using the Bolles (1956) correction for segmental downcorners, ranged from 0.064 inch for an F factor cf 0.642 to 0.204 inch for a n F factor of 1.332. Thus, the lower curve, which is for data derived from this experimental study, could be thought of as representing a n h, h,, = 0.81 to 0.88 inch of liquid for F factors up to 1.33. For F factors greater than 1.33 the curves merge. This postulation of the addition of a third h, h,, parameter to the Foss and Gerster froth density correlation seems to be consistent with their previous experih,, parameters, using the air-water mentally determined h, nondistilling system.
+
+
+
VOL. 6
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529
0.70
0.65
B 0.60
I 0
I I I I
, , , . , , ,
, , , ,
0.5
I I I I
1.0
1.5
7
2.0
2.5
0.5
1.0
2.0
1.5
2.5
F~ A Figure 5. factor
Relative froth density vs. active area
F
Both the first- and second-order least squares fits show good agreement with the air-water curve a t F A A values greater than 1.33. T h e sum of the absolute values of the deviations was 0.653 for the first-order fit, and 0.651 for the second-order fit, indicating fairly representative fits for both trials, statistically. T h e froth density approachts 0.18 as a limiting value compared to the value of 0.25 resulting from air-water studies. I t would also appear that for F factors greater than 1.75 there is little change in the froth density. This 1.75 value corresponds to an active area column vapor velocity of 4.07 feet per second. Effect of Vapor Rate on Aeration Factor, p. Figure 6 compares the air-water data and the data from this study as fitted by both first- and second-order least squares fits. The aeration factor approaches a n asymptotic value of 0.519 with increasing F factor values, which is consistent with the froth density limiting value. Effect of Volumetric Froth Flow Rate on Froth Height, h,. Figure 7 includes the experimental data points and the curves resulting from a second-order least squares fit. The froth height increases with increasing L ' / $ values more slowly a t the lower values of L ' / $ than a t the higher values. Since froth density decreases rather rapidly at lower froth heights (corresponding to the lower F factor values), the rapid increase of L'/$ with small changes in h , is to be expected. As the froth density nears its limiting value, which occurs a t F factors a b m e 1.33, the froth height becomes more clearly a function of clear liquid rate. At an F factor of 1.33, the froth height is 1.68 inches of liquid, which corresponds to a volumetric froth flow rate of 0.0155 cu. ft./ft.-sec. At volumetric froth flow rates greater than 0.01 55, the froth height decreases less rapidly with increasing froth rate. T h e same effect of volumetric froth flow rate on froth height was also found in a series of air-water bubble-cap studies by Gerster et al. (1959). I t was concluded from the air-water study that liquid rate has very little effect on froth height, and this study substantiates the conclusion. For points of a relatively constant vapor rate, the increase in froth flow rate has very little effect on froth height. An example of this would be data points 2-11 and 3-1, in which a change of 25% in the experimental L'/+ range resulted in a 7% change in the experimental froth height range. 530
I&EC
P R O C E S S DESIGN AND DEVELOPMENT
FA A Figure 6. Aeration factor as a function of active area F factor
0.04
0.03 0.02
0.01
0.005
2.0
IN5
2.5
hf Figure 7. Volumetric froth rate as a function of froth height
Correlation of froth height as a function of clear liquid and vapor rate resulted in the afore-mentioned equation. From this eqhation it can be seen that froth height is proportional to the clear liquid rate in gallons per minute raised to the 0.120 power, or, for a constant vapor rate, a fourfold increase in clear liquid rate results in a n 18% increase in froth height. Effect of Equivalent Clear Liquid Head on Froth Height, h p T h e equivalent clear liquid head values determined in this experimental study are plotted in Figure 8 along with the plate pressure drop, dry plate pressure drop, and the residual plate pressure drop term, all in inches of water a t 80' F. T h e equivalent clear liquid head, or dynamic liquid head, exhibits the trend normally expected of the static liquid head according to MacMillan (1960). Measurements of equivalent clear liquid head in this study was obtained by a section of copper tubing inserted through a brass ring into the column beneath the test tray and flared into the center hole of the tray. During the distilling operations the system liquid actually filled the glass manometer tube and the other leg of the equivalent clear liquid head manometer.
1.5
h I .o 0.5
0 1.4
2.0
1.5
2.4
hf Figure 8. Relation between equivalent clear liquid head and froth height 1. 2.
3. 4.
Total troy pressure 'drop, ht, inch water Dry plate pressure drop, hdp, inch water Equivalent clear liquid head, h,, inch water Residual pressure drop, hR, inch water
T h e perforations immediately around the center tap hole were not blocked off, as suggested by MacMillan as a requirement for true static liquid heads. Arnold et al. (1952) also observed fluctuations in their liquid head measurements resulting from the turbulence on the plate, but considered that they obtained reasonable average dynamic liquid head readings. Investigation of the residual pressure term, h,, shows that it starts from a maximum value of 0.12 inch of water a t the lowest experimental data point, and decreases to -0.05 inch of water a t the highest experimental data point. A possible interpretation of this trend is, assuming the equivalent clear liquid head trend to be correct, that more energy is needed to form bubbles and cause turbulence at low froth heights, and therefore a t lower F fa'ctors, than a t higher F factor values. This phenomenon could possibly be interpreted to mean that a cellular froth or foam (existsa t the lower F factors, and as the F factor increases along with the froth height, a mobile foam, or froth, begins to predominate, and the energy needed to form bubbles of froth is less than the energy needed to form the cellular froth, or foam, a t the lower F factor values. If the equivalent clear liquid head curve had shown the trend expected of the dynamic: liquid head as defined by MacMillan, the h, term would be expected to increase gradually with increasing F factor, thiis perhaps signifying a n interplay of kinetic energy effects between the equivalent clear liquid (dynamic liquid head) term and the residual pressure term, h,. Arnold et al. (1952), Foss and Gerster (1956), and Mayfield et al. (1952) have shown that merely attempting to define the plate pressure drop in terms of only the dry plate pressure drop and the static liquid head leads to predicted values which are, in some cases, up to 25T7 less than their experimentally determined values, leading to the conclusion that a complicated, dynamic liquid behavior near newly forming bubbles is responsible for the observed discrepancies. Conclusions
Prior investigators use'd o n their test tray liquid head manometers that measured a liquid head defined as a dynamic head by MacMillan, rather t:han the true static liquid head on the tray. A clearer indica.tion as to whether equivalent clear liquid (dynamic head) or static liquid head is the more signif-
icant term in tray dynamics correlations would greatly aid future investigators, since different sources weigh one definition more heavily in their correlations than the other. Sources of experimental error include the pressure effect of the nitrogen blowback and the inherent fluctuation of the measured liquid head o n the plate. At the maximum nitrogen flow the blowback contributed 0.01 inch of water to manometer readings, which was an insignificant amount with respect to the recorded pressure readings. T h e reported plate liquid head readings are considered to be accurate to fO.10 inch of system liquid because of the tray's dynamic action during operation. I t can be generally concluded that: Froth height is affected more by total vapor rate than by liquid rate, and froth heights increase more rapidly for increasing vapor velocities a t higher F factors than for lower values. Both froth density and aeration factor decrease rather rapidly with increasing vapor velocities a t the lower F factors, but approach limiting values of 0.18 and 0.59, respectively, with vapor velocities a t higher F factors. T h e photographic technique employed in this study gives reliable results, and the maximum reliability range of 1 0 . 1 5 inch of liquid is conservative. T h e rather low values of froth height a t low F factor, and increased ratio of h,lF factors, tend to support the conclusion that a cellular foam or froth is formed a t low vapor rates, finally, only froth exists a t the higher F factor values. Nonfoaming systems differ from foaming systems a t high vapor rates, in that the froth height of the nonfoaming systems increases with increasing vapor rate, while the foam height of foaming systems decreases with increasing vapor rate. At constant vapor rates, froth height is proportional to the clear liquid rate raised to the 0.120 power, and a t constant clear liquid rates froth height is proportional to the vapor velocity raised to the 0.272 power. Results of this study corroborate previous air-water studies in derivations of froth density and aeration factor as a function of the F factor. Nomenclature
cross-sectional area. sq. ft. area of downcomer, sq. ft. F factor, based on column free cross-sectional area = U P 2 5 F factor, based on active area = A - 2 A d equivalent clear liquid height, in liquid equivalent dry plate or orifice pressure drop, inches water average froth height, inches froth height, individual measurement, inches height of crest over weir, inches liquid residual pressure drop, inches water total pressure drop, inches height of weir, inches liquid rate, pounds/hr. liquid rate across plate, cu. ft./sec.-foot weir number of determinations vapor velocity based on active area, ft./sec. vapor rate, pounds/hr. aeration factor relative froth density summation density of vapor, pounds per cu. ft. Acknowledgment
T h e authors acknowledge gratefully the support of the National Science Foundation in the form of a grant to carry out this work. Also appreciation is expressed to the Ethyl Corp. for fellowship support of one of the authors. VOL. 6
NO. 4
OCTOBER
1967
531
literature Cited
Arnold, D. S., Plank, C. A., Schoenborn, E. M., Chem. Eng. Progr. 48, 638 (1952). Bainbridge, G. S., Sawistawski, H., Chem. Eng. Sci. 19, 992 (1964). Benzing, R. J., Myers, J. E., Znd. Eng. Chem. 47, 2087 (1955). Bikerman, J. J., Ind. Eng. Chem. 57, 56 (1965). Bolles, W. L., Petrol. Process. 11, 64 (1956). Brunjes, A. S., Furnas, C. C., Znd. Eng. Chem. 27, 396 (1935). Calderbank, P. H., Rennie, J., Trans. Znst. Chem. Engrs. 40, 3 (1962). Davidson, L., Amick, E. H., Jr., A.Z.CI1.E. J . 2, 337 (1956). Foss, A. S., Gerster, J. A., Chem. Eng. Progr. 52, 28j (1956). Geddes, R. L., Trans. A.Z.CI2.E. 42, 79 (1946). Gerster, J . A , , et al., Chem. Eng. Sci. 10, 243 (1959). Gilbert, T. J., Chem. Eng. Sci. 10, 243 (1959). Hughes, R. R., Handlos, A. E., Evans, H. D., Maycock, R. L., Chem. Eng. Progr. 51, 557 (1955). Hunt, C., Hanson, A. N., Wilke, C. R., A.Z.CI2.E. J . 1, 441 (1955). Hutchinson, M. H., Buron, A. G., Miller, B. P., Los Angeles Meeting, A.I.Ch.E., May 1949.
Kemp, H. S., Pyle, Cyrus, Chem. Eng. Progr. 45, 435 (1949). Kolodzie, P. A., Van Winkle, M., A.Z.Ch.E. J . 3, 305 (1957). Lee, D. C., Chem. Eng. 179 (May 1954). Leibson, I., Holcomb, E. G., Cacoso, A. G., Jacmic, J. C., A.Z.Ch.E. J . 2, 296 (1956). Ling, T. D., Van Winkle, M., J . Chem. Eng. Data 3, 82 (1958a). Ling, T. D., Van Winkle, M., J . Chem. Eng. Data 3, 88 (1958b). MacMillan, W. P., J . Imp. Coll. Chem. Eng. Sot. 13, 64 (1960-61). Mayfield, F. D., Church, W. L., Green, A. C., Lee, D. C., Rasmussen, R. W., Znd. Eng. Chem. 44, 2238 (1952). Pitzer, K. S., J . Am. Chem. Sot. 77, 3427 (1955a). Pitzer, K. S., Lippmann, D. Z., Curl, R. F., Jr., Hu gens, C. M., Petersen, D. E., J . Am. Chem. Sot. 77, 3433 (1955bY. Rennie, J., Evans, F., Brit. Chem. Eng. 7, 498 (1962). Smith, B. D., “Design of Equilibrium Stage Processes,” McGrawHill, New York, 1963. Steinhauser, H. H., White, R. R., Znd. Eng. Chem. 41, 2912 (1949). Zuiderweg, F. J., Harmens, A,, Chem. Eng. Sci.9, 89 (1958). RECEIVED for review February 20, 1967 ACCEPTEDJuly 24, 1967
S I M U L A T I O N OF THE H E A T l T R A N S F E R P H E N O M E N A I N A R O T A R Y KILN A L L A N SASS
U . S.Steel Applied Research Laboratory, Monroeville, Pa.
A simplified model of the heat-transfer phenomena occurring in a rotary kiln has been developed. The correlations used for the various modes of heat transfer encountered in a kiln are presented. In this study, the influence of simultaneous chemical reactions has not been considered. The model was tested with data collected from a cement kiln and a kiln used for preheating iron ore. The outlet solids temperature for both cases was 1300’ F. and the inlet gas temperature was approximately 2000” F. The predicted kiln lengths were in error by only 7 and 15%, respectively. This was far superior to the results obtained from existing correlations.
A
LTHOUGH rotary kilns are used in many areas of the chemi-
cal and metallurgical industries, very meager information has been published concerning the design and scale-up of these units. This lack of information is partially due to the complexity of the heat and mass transfer phenomena which can occur in these units. I n this study, we have considered a very simplified model of a kiln and have developed the general equations and heat transfer correlations which predict the heat transfer rates fairly accurately. This development can therefore be used as a n aid in kiln design. T h e influence of simultaneous chemical reactions has not been considered in this study. Description of Model
Heat transfer in kilns is a complicated phenomenon, inasmuch as heat is transferred simultaneously by conduction, convection, and radiation between bodies that have time-varying temperature distributions. I n such situations, a solution can be developed only by considering a simplified model of the heat transfer processes. A schematic cross section of the kiln model is shown in Figure 1. T h e equations describing the process were based on the assumption that a t a given cross section in the kiln, the gas, solid, inner-wall, and outer-wall temperatures are not functions of their radial position in the kiln. For the solids, this assumption is equivalent to stating that the material is well mixed. Imber and Paschkis (1962) have shown that this assumption is more accurate than assuming that the solids are not well mixed and that a temperature gradient exists in the charge a t a given cross section. 532
I&EC PROCESS D E S I G N A N D DEVELOPMENT
For generality, a kiln which is being fed wet solids has been considered. I n this situation, the kiln can be considered to consist of three sections. I n the first, the wet solids are heated to the boiling point of the entrained liquid. T h e solids then enter the second region in which liquid evaporates at constant temperature until the feed is completely dry. I n the third region, the dry solids are heated to some desired temperature and then are discharged from the kiln. Development of Differential Equations. In the first region of the kiln, the wet solid is heated to the boiling point of the liquid by the hot gas. I t is assumed that no vaporization occurs in this region. In the equations presented below, the following heat-transfer paths have been considered : 1, Gas to solid. 2. Gas to inner kiln wall. 3. Inner kiln wall to solid. 4. Conduction radially through the kiln wall. 5. O u t e r kiln wall to ambient air. When these various modes of heat transfer are considered, the following equations result:
dT, 1 _- _ _[az(Tg - Ts) dx C,Gs
+ a~(T2a- TJI
d 5 - 1 [a2(Tg- T J +,al(T, dx C,G, ~
T, =
- 7dI
+ C Y ~ ) [ C+Y ICYSTS] T , + a4~~5Ta
(CY,
T,’
=
+ +
C Y ~ T , a5Ta CY4
CY5
(1)
(2)
(3) (4)
