Ind. Eng. Chem. Process Des. Dev. 1083, 22, 53-58
Hansen, E. M.S. Thesis, InstihMet for Kemlteknk, The Technlcel Univerelty of Denmark, 1982. Jensen, T.; Fredenslund, Aa.; Rasmussen, P. Id.Eng. Chem. Fundam. 1981, 20,239. Kesler, M. G.; Lee, 6. I. h)&ocarbOn Process. 1976, 55, 153. Lenolr, J. M.; Hlpkln, H. G. J . f%m. €ng. Data 1973, 18, 195. Lyderasn, A. L. University of Wleconsln College of Englneerlng Experimental Statlon Report 3 Medison, WI,1955. Pitzer. K. S. J . Am. Chem. Soc.1955, 77, 3427.
53
Rackett, H. 0. J . Chem. €ng, Data 1970, 75, 514. Sullivan, R. F.; Stangeland, B. E. A&. Chem. Ser. 1979, No. 179, 25. Wilson, A.: Meddox, R. N.; Erbar, J. H. OH Ges J . Aug 21, 1978, 76. WHson, 0. M.; Barton, S.T. Research Report 2; Gas Processors Assoclatlon: Tulsa, OK,1971.
Received for review August 28, 1981 Accepted July 14, 1982
Scale-up of Plate Efficiency from Laboratory Oldershaw Data James R. Falr,' Harold R. Null, and Wllllam L. Bolles Monsanto Company, St. Louis, Missouri 63 167
Conditions for commercial-scale testing at Fractionation Research, Inc. (FRI) and other plant situations were duplicated as closely as possible in the laboratory wlth the use of glass and metal Oldershaw columns. A consistent correlation between scales was found, with the indication that point efficlencles may be measured directly with the laboratory equipment. The resutts are especially useful for complex mlxtures and/or when vapor-liquid equilibria are not well defined.
Knowledge of mass transfer efficiency is critical to the design or analysis of a plate-type distillation column. While models for predicting the theoretical stage requirements of such a column have been developed extensively to provide rigorous results, the next step toward column design, the specification of actual stages or plates, may not be taken normally with a high degree of rigor or reliability. The development of reliable predictive models for plate efficiency is still in progress and remains in a fairly primitive stage for separations involving more than two components, large and complex molecules, and highly nonideal solutions. The efficiency of a plate depends upon three sets of design parameters: (1) the system-composition and properties, (2) flow conditions-vapor and liquid flow rates, and (3) geometry-type and dimensions of contacting device. These parameters may be varied more or less independently, although the particular separation at hand will dictate the system, the ratio of vapor to liquid, pressure drop allowance, and so on. The approaches normally used to predict plate efficiency encompass one or more of the following: (1)comparison with a similar commercial installation for which efficiency data are available, (2) use of empirical correlations, and (3) use of theoretical or semitheoretical mass transfer models. The present work proposes that a fourth approach is available, which for some cases may be the most reliable approach direct scale-up from laboratory distillation data, using special tray columns for the bench scale experiments. This work was initiated in the late 1950s at the Monsanto laboratories in Dayton OH. At the time there was developing interest in bypassing expensive pilot plants and going directly from bench scale research to final commercial design. It was also at this time when the program of Fractionation Research, Inc. (FRI) had progressed to a point where efficiency tests of large-diameter sieve trays were being conducted. The results from these tests represented the first reliable and comprehensive performance
* Department of Chemical Engineering, The University of Texas, Austin, T X 78712. 0190-4305/83/1122-0053$01.50/0
data ever available on commercial scale sieve trays. Accordingly, plans were formulated for scaling down the FRI test data such that parallel laboratory test runs could be made. The program continued over a period of years, first at the Dayton laboratories and later at the St. Louis Research Center of Monsanto. During this time it was encouraging to have reports such as that of Veatch et al. (1960) stating that glass Oldershaw columns had been used successfully in scale-up studies for the Sohio acrylonitrile process or that of Martin (1964))showing that laboratory studies with glass Oldershaw equipment were in good correspondence with plant studies of a high-vacuum solvent-water fractionator. The results of the Monsanto scale-down studies were used to support the successful design of a great many large fractionators, but they could not be disclosed publicly because the FRI data were classified as confidential. Some FRI data were published from time to time, but it was not until recently that any FRI sieve-tray data were released (Sakata and Yanagi, 1979; Yanagi and Sakata, 1981). Thus it is just now possible for Monsanto to share with others its experiences in the scale-up of laboratory distillation data. In the early stages of the present work it was decided that standard, off-the-shelf distillation apparatus should be used, if at all possible. For this purpose the Oldershaw column was selected, and it will be described in the following section. Experimental Work Laboratory Equipment. All of the laboratcry work was done with Oldershaw equipment. The Oldershaw column is essentially a bench-scale sieve (perforated) tray column containing circular downcomers. The associated reflux condenser, reflux trap, feed section, and reboiler components of the total system can be easily assembled with the column through ground-glass joint connections. The column was originally described in a paper by 01dershaw (1941) and is now available from a number of laboratory supply houses. A sketch of a typical Oldershaw section is shown in Figure 1. The usual application is for 0 1982 American Chemlcal Society
54
Id.Eng. Chem. Process Des. Dev., Vol. 22, No. 1, 1983 Table I. Characteristicsof Trays Tested
column i.d., in. tray spacing, in. hole diameter, in. no. of holes hole area, in.l support rod cross section, in.l superficial area, in.l hole/superficial area downcomer area (top), in.l
Figure 1. Oldershaw trays.
distillations carried out at atmospheric pressure and below; for such an application the column is conveniently fabricated from glass and may include Dewar jackets for insulation. When jackets are used, viewing ports permit observation of contacting action on the trays. The glass Oldershaw equipment used in the present work was obtained from the Kontes-Martin Co.(Evanston, IL). Since it was desirable to make scale-down studies of FRI work carried out at pressures above atmospheric,
1-in. glass
2-in. glass
2-in. steel
1.10 1.06 0.036 82 0.079
1.97 1.97 0.035 307 0.295
2.03 2.0 0.043 170 0.247 0.196
0.950 0.083 0.078
3.047 0.097 0.080
3.039 0.081 0.074
metal Oldershaw equipment yas also necessary. This equipment was obtained from Precision Distillation Apparatus Co. (a division of Glass Instruments, Inc., Pasadena, CA). Metal columns are available in a variety of materials; for this work a column of Type 304 stainless steel was used. The metal column plates are fitted tightly into the column as a bundle attached to a central shaft, and thus they differ somewhat from their glass counterparts. The metal columns are not available with vacuum jackets and must be insulated separately. Column sections containing various numbers of trays were used. Dimensions of the trays themselves are shown in Table I. A flow diagram of the experimental distillation SURGE
HEAD PRESSURE
VALVE KEY:
06
THERMOMETER
SVSTEM
110 v
VACUUM GAUGE
REFLUX ADlABATtC TRAP HEAT CONTROL
Liauio SAMPLE BOMB
8 208
VACUUM PUMP
REBOIL HEATCONTROL
Figure 2. Schematic of experimental equipment; 2-in. stainless steel column and auxiliaries.
v
NEEDLE VALVE BALL VALVE TOGGLE VALVE GATEVALVE
Ind. Eng. Chem. Process Des. Dev., Vol. 22, No. 1, 1983 55
Table 11. Systems Investigated
light component cyclohexane cyclohexane isobutane propylene 2-propanol 2-propanol 2-propanol l-propanola a
heavy component n-heptane n-heptane n-butane propane water water water toluene
pressure, psia 3 15 165 165 3.7 7.4 14.7 15
approx top comp., light mtl, % m 85-90 85-90 60-68 41-48 5 5 6 45
re1 volatility 1.67 1.90 1.23 1.17 1.65 1.55 1.49 1.56
University of Texas test system.
system, showing a metal column in the test position, is given in Figure 2. All efficiency tests were made at total reflux, in keeping with the test approach at FRI. Information on setting up Oldershaw equipment is available from the vendors of the equipment. Articles by Biribauer et al. (1957), Mead and Rehm (1967), the Economides and Maloney (1979) also provide valuable background in Oldershaw test installations. Systems Studied. The test systems are described in Table 11. Not all of these systems have been covered by published FRI data and thus the total scale-up picture cannot be disclosed. On the other hand, some additional scale-up data taken at The University of Texas are included to extend the presentation. Composition ranges and representative relative volatilities are shown in Table I1 and are for general information only. Care was taken to use the same volatilities and composition ranges for the corresponding large- and small-scale tests. Commercial Scale Equipment. The FRI tests were run in a 4.0-ft diameter column containing eight to ten single crossflow sieve trays, each with a segmental weir 2.0 in. high by 37.0 in. long, and a spacing between trays of 24 in. The perforations in the trays were of 0.5 in. diameter. Two ratios of hole area to bubbling area were used: 0.083 (Sakata and Yanagi, 1979) and 0.137 (Yanagi and Sakata, 1981). The general layout of the equipment has been described by Silvey and Keller (1966, 1969). As mentioned earlier, all FRI tests were run at total reflux. The efficiencies reported by FRI are overall column efficiencies and include the effect of entrainment, weeping, and liquid mixing patterns. The University of Texas work was carried out in an 18-in. diameter column containing three sieve trays, each with 0.25-in. diameter holes occupying 12.8% of the bubbling area. Weir height was 2.0 in. and tray spacing was 18 in. Details of the equipment are given in the theses by Anderson (1974) and Garrett (1975) and in the papers by Anderson et al. (1976) and Garrett et al. (1977). Total reflux efficiencies were reported. Data Analysis Overall column efficiency is defined by E , = N,/Na (1) Murphree vapor efficiency is defined by
Since all FRI testa were at total reflux, L/V = 1. Also, the composition ranges over the FRI column were such that the average value of the slope of the equilibrium line, m, was close to unity. Thus, it could be assumed that Ew = E,. Point efficiency for tray n in a column is defined by
The relationship between overall and Murphree vapor efficiency is given by E, = In [ l EMv (X - l)]/ln X (3) where X = mV/L (4)
F, = U B ~ $ ~ (11) Note that the 2-in. metal column calibrated satisfactorily with the l-in. and 2-in. glass columns. Figures 4 through 7 show Oldershaw data for the cyclohexaneln-heptane, isobutaneln-butane, and propylene/ propane systems. Also shown are the corresponding
+
If the liquid and vapor are completely mixed on the tray EMV = Eov (6) If the liquid moves across the tray in plug flow, and the vapor rising through the tray becomes completely mixed before entering the tray above (7) Equations 6 and 7 represent extremes not true for the FRI data, and corrections for partial mixing were made through the use of a diffusion-type mixing model. This model, which employs an eddy diffusion coefficient, is described in several references (for example, the AIChE manual (1958) and Perry's Handbook (1973)) and will be only summarized here. The efficiencies Ew and E , are related by (8) Ehlv/Eov = f ( X , E,,, Pe)
w
Pe = -
DEf~
(9)
For eddy diffusion the correlation of Barker and Self (1962) was used D E = 0.013U,1.44 + 0.025h~- 0.061 (10) The functional relationship indicated in eq 8 has been presented graphidly in many references; a convenient one is in Figure 18-27 of Perry (1973). This model assumes that the vapor is totally mixed between trays. Such an assumption is believed to be approximately true for the FRI column since its diameter is twice its tray spacing. The FRI efficiency data were converted from overall column efficiency to point efficiency according to eq 1-10. Results The results of the laboratory work are shown in Figures 3-7. Figure 3 shows column calibration data as well as pressure effects on efficiency, using the 2-propanol/water system. The abscissa parameter is the superficial F fador
Ind. Eng. Chem. Process Des. Dev., Vol. 22, No. 1, 1983
56
I
0
OLDERSHAW, 1 1 . 2 ATM.
'(I
DATA OF S M U C K , 2 0 . 4 ATM
0.80
I
I
20
40 PERCENT
I
I
I
60
80
FL003
Figure 7. Efficiency of 2-in. stainless steel Oldershaw column compared with point efficiency of 10-ft commercial column; propylenelpropane system.
z
0.80 *
w
c "
I
1
0
OLDERSHAW, 0 . 2 0 ATM.
A
FR:,
A
F R I , 0 . 2 7 ATM, 14'7 OPEN
1
I
0.27 ATM, 8., OPEY
0 OLDERSHAW, '(I ao
20
60
PERCENT
0.20
2O
4c PERCENT
60
80
FLOOD
Figure 8. Efficiency of 1-in. Oldershaw column compared with point efficiency of 18-in. column; 1-propanol/toluene system.
OLCERSHIW, 1 . 0 A I M . F R I , 1 . 6 3 ATP.,
1 ,O ATM
S I E V E TRAY
80
FLOOD
Figure 4. Efficiency of 1-in. Oldershaw column compared with point efficiencyof 4.04%FRI column; cyclohexaneln-heptane system.
0 A
18 IN
I
I
I
I
I
,A5 ,+'
8': OPEN
/+'
+'
I
>
I
f
A
3 a0
1
5c
FEPCEYT
c >
0 u
0
OLDERSHAW, 1 1 , 2 A I M .
A
F R I , 1 1 . 2 ATM.,
A
F R I , 1 1 . 2 A T M . , 14'
0.80-2
0:
FLOOD
>
z v
-"-
'
A
L
0.50
-
8 ' . OPEN
A -0-040 A
OPEN
A
A AA-
-8s-& -
A
20
40 PERCENT
60
d/
,/+L
:?
02 n
a3
Figure 5. Efficiency of 1-in. Oldershaw column compared with point efficiency of 4.04 FRI column; cyclohexaneln-heptane system.
w
ISOPROPANOLIWATER PRESSURES)
I
760 mm iig
I
4:
23
" "
1
eo
FLOOD
Figure 6. Efficiency of 2-in. stainless steel Oldershaw column compared with point efficiency of 4.04% FRI column; isobutaneln-butane system.
data from FRI, converted to point efficiencies. Since no data on propylene/propane from FRI are available, published efficiency values by Smuck (1963) are included in Figure 7. The Smuck values were converted to point efficiencies, but it should be noted that the test column
0
I 6
I 12 TRAY S P A C i N G ,
I 18
I 24
I 3c
INCHES
Figure 9. Flooding characteristics, Oldershaw tray columns: (A) 2-propanol-water, 760 mmHg, 1 in.; (v) 2-propanol-water, 380 memmHg, 1 in.; (A)2-propanol-water, 190 mmHg, 1 in.; (0) thylcyclohexaneln-heptane,760 mmHg, 2 in. (Cooke, 1967); ( 0 ) methylcyclohexaneln-heptane,760 mmHg, 4 in. (Cooke, 1967); (+) points from commercial correlation (Fair, 1961, 1963).
contained a combination of sieve and valve trays. The column diameter was 10 f t and there was double crossflow of liquid. Figure 8 shows the University of Texas data for the toluene/l-propanol system. In this case the same investigators ran both the large- and the small-scale tests. In order to correlate the small and large column throughputs, the abscissa in Figures 4-7 is "percent flood", defined as F,, operating % flood = (12) F,, flood x 100 This is the first key to the scale-up method. Since the data are plotted on the basis of a "reduced" F factor (approach to the flood point), some means for estimating a flooding condition of an Oldershaw column is useful. Figure 9 shows an approximate correlation based
Ind. Eng. Chem. Process Des. Dev., Vol. 22, No. 1, 1983 57
on reported flood data as indicated plus an extrapolation of the flood capacity chart for larger equipment (Fair, 1961, 1963). This permits estimating the maximum vapor rate for the Oldershaw column, but it is recommended that the Oldershaw flood point be determined experimentally. Discussion of Results An examination of Figures 4-8 shows that over the region of practical interest (50 to 85% of flood) the commercial point efficiency was always either equal to or slightly higher than the Oldershaw column efficiency. Agreement was best a t about 60% of flood where one would expect serious problems of weeping and entrainment to be absent from properly designed sieve trays. The differences between the two sets of FRI efficiency data (8% and 14% open area cases) is undoubtedly due to weeping, it being difficult to prevent weeping of larger open area trays across the entire range of operation. The recent work of Chan and Fair (1982) indicates that an even better agreement between the Oldershaw and FRI data would be obtained if the large column weir setting were 1in. instead of 2 in. The important point is that the Oldershaw column appears to be measuring the point efficiency of the commercial tray, and this is the second key to the scale-up method. The several assumptions implicit in the comparison of small and large trays should be noted, for they may well serve as limitations on the scale-up method. The computation of the larger scale point efficiency is based on a diffusion-typemixing model for the liquid phase (and eddy diffusion coefficients obtained from rectangular simulation test trays), absence of retrograde flow, and complete mixing of the vapor between trays. The FRI data were limited to 2-in. weirs and 1/2-in.perforations. The differences in the reported efficiencies of the FRI data sets simply underscores the fact that the geometry of the commercial scale contacting device must be taken into account. Nevertheless, the agreement of the computed point efficiencies with the measured Oldershaw efficiencies lends some new credence to the deduction procedure, since one would expect a close approach to the point efficiency in a small contactor such as the Oldershaw. It is of interest to speculate why the point efficiencies are similar in magnitude. The point efficiency may be expressed in terms of transfer units Eo,= 1 - e-" (13) Accordingly, for equal point efficiencies (N0,)l = ( N 0 V ) Z (14) where subscript 1refers to the Oldershaw and subscript 2 refers to the commercial column. Utilizing transfer definitions (KO,) l@l (2,) 1 - (Kov)2aZP2(Zf)z (15) (GM) 1
(GMM)2
Now, G M = U&,/M,, and for equivalent compositions and operating conditions (KO,) lal(Zf)l - (Ko,)zaz(zf)z (16) KJJl
W J 2
For the same approach to flood, a reasonable approximation is (2,)1 / (TS) 1 = G f ) 2 / ( TS), (17) On the basis of the definition of approach to flood (eq 12), and combination with eq 16 and 17
Comparing the FRI and l-in. Oldershaw geometries gives (TS),/(TS), = 24. The ratio of flood velocities (Figure 9) is about 3. Finally, then
Thus the Oldershaw column provides a volumetric coefficient of about eight times that of the FRI column. It would not be prudent to speculate further on a quantitative basis, but observations of the aerated mixtures of the two scales shows a much finer dispersion on the Oldershaw trays, as might be expected from very small holes and relatively low velocities. Penetration theory would suggest much shorter exposure times at the small scale, and this plus the probable enhanced area per unit volume lends support to the general magnitude of the volumetric mass transfer coefficient ratio indicated in eq 19. Scale-up Procedure Based on the research reported here, the following scale-up procedure is recommended: (1) Run the real system in the Oldershaw column. (2) Determine the 01dershaw flood point. (3) Establish Oldershaw normal operation for about 60% of flood. Case A. Good Vapor-Liquid Equilibrium Data Available. (4A) Run the Oldenhaw at total reflux, taking compositions top and bottom. (5A) Compute the required number of theoretical stages and the Oldershaw overall column efficiency Eo,. (6A) Assume Oldershaw Eo,= Em = E,. (7A) Assume commercialE, = Oldershaw E, (8A) Estimate commercial E,, using liquid mixing model. (If this is regarded as too involved, then a conservative assumption would be to take commercial E, = Eo,. (9A) Compute required actual column plates. Case B. Good Vapor-Liquid Equilibrium Data Not Available. (4B) Run the system in the Oldershaw and find by test the combination of plates and reflux that gives the desired separation. (5B) Assume that a commercial column with the same reflux ratio and number of plates will make the same separation. (6B) If the commercial column is large in diameter, the number of plates may be reduced somewhat by estimate of the liquid crossflow enhancement of efficiency (i.e., Murphree efficiency greater than point efficiency. Limitations of the above procedure must be recognized, as discussed in the preceding section of this paper. Conclusions On the basis of the research reported here, one may conclude that a bench-scale Oldenhaw column can be used to obtain an approximation of the point efficiency of a system to be separated by distillation. If the system is multicomponent and not well-defined, for example a complex, boiling-range mixture, the Oldershaw is thus useful in providing direct data for scale-up without going through intermediate steps of vapor-liquid equilibrium analysis and theoretical stage calculation. The Oldershaw equipment is easily available and readily assembled. It can be operated continuously as part of a bench-scale demonstration unit and thus provide operating experience as well as point efficiency information. The weak link in the scale-up procedure is probably the conversion from point efficiency to Murphree tray efficiency, but the results here provide some support to the eddy diffusion approach for making the conversion. Acknowledgment A number of people participated in the laboratory work of this project. The authors wish to recognize the con-
58
Ind. Eng. Chem. process Des. Dev. 1983, 22, 58-87
tributions of R. C. Binning, D. C. Boyce, L. J. Breuklander, D. Cova, S. D. Koban, A. C. Pauls, and especially R. A. Murray. Nomenclature a = interfacial area for mass transfer, ft2 ft3 DE = eddy diffusion coefficient for liqui flow, ft2/s Ew = Murphree tray efficiency, vapor concentration basis, fractional E, = overall column efficiency, fractional E,, = point efficiency, overall vapor concentration basis, fractional F, = superficial vapor F factor, (ft/~)(lb/ft~)’/~ GM= vapor molar mass velocity, Ib-mol/(s-ft2) hL = liquid holdup on tray, in. KO,= overall mass transfer coefficient, vapor basis, lb-mol/ (s-ft2-atm) L = liquid molar rate, lb-mol/s m = slope of equilibrium line M, = molecular weight of vapor N , = actual plates in column No, = number of overall vapor transfer units Nt = theoretical stages P = pressure, atm Pe = dimensionless Peclet number fL = average residence time of liquid on tray, s TS = tray spacing in column, in. U, = vapor velocity through active, or bubbling, area, ft/s Us = vapor velocity based on total, or superficial area, ft/s U,, = superficial vapor velocity at flood point, ft/s V = vapor molar rate, lb-mol/s W = length of flow path, ft zf = froth height on tray, in. Y = vapor mole fraction Y* = vapor mole fraction in equilibrium with exit liquid
d
Greek Letters X = ratio of slopes of equilibrium and operating lines
p
= density, lb/ft3
Subscripts L = liquid n = tray n (or stage n) v = vapor 1 = small scale 2 = commercial scale
Literature Cited American Instltute of Ctmmlcal Englneers, “Bubble Tray Design Manual”, New Ywk. 1958. Anderson, R. H. M.S. Thesis, The Univsrslty of Texas, Aucltin, TX, 1974. Anderson, R. H.; Ga~&t,G. R.; Van Wlnkle, M. W. Ind. Eng. Chem. process Des. D e w . 1976, 15, 96. Barker. P. E.; Self, M. F. Chem. Eng. Scl. 1962, 17, 541. BkJbauer, F. A.; Oakley, H. T.; Porter, C. E.; Staib, J. H.; Stewart, J. Ind. Eng. them. 1957, 49, 1673. Chan, H.; Falr, J. R. Paper presented at AIChE Meeting, Anaheim, CA. June 1982. Cooke, 0. M. Anel. 0. 1967, 39, 286. Economldes, M.; Maloney, J. 0. A I C E Svmp. Ser. No. 783 1979. 75, 80. Falr, J. R. Pebo/chsm. Eng. 1961, =(IO), 45. Fak, J. I?.In Smith, B. D. “Dedgnof Equ#lbrlum Stage Processes”; McGrawHa: New Ywk, 1963; Chaptsr 15. Garrett, (3. R. Ph.D. MsecKtetkn, The Univeslty of Texas, AwrUn, TX, 1975. Qarrett,0. R.; Andereon, R. H.; Van W l e , M. W. Ind. Eng. Chem. Roces.5 L b . D e v . 1977, 16, 79. Mertin, H. W. Chem. Eng. Rug. 1964, 60(10), 50. Mead, R. W.; Rehm, T. R. Chem. Eng. Prog. Symp. Ser. No. 70, 1967, 63, 44. Olderehew, C. F. Ind. Eng. C b m . , A n d . Ed. 1941, 13, 265. Perry, R. H.; Chitton, C. H., Ed. ”chemicel Engineers’ Handbook”; McGrawHill: New York, 1973; sectkn 18. Sakata. M.; Yanapi, T. I . Chem. E . Symp. Ser. No. 56 1979, 3.2121. Slhrey, F. C.; Keller, 0. Chem. €ng. Rug. 1966, 62(1). 68. Slkey, F. C.; K e k , G. I . chsm.E . Symp. Ser. No. 32 1969, 418. Smuck, W. W. Chem. Eng. Rog. 1963, 59(6), 64. Veatch, F.; Callahan, J. L.; Idol, J. D.; MHberger, E. C. Chem. Eng. Prog. 1960, 56(10), 65. Yanagl, T.; Sakata, M. Paper presentedat AICM Meeting. Houston, TX, Apr 1981.
Received for reuiew September 21, 1981 Accepted July 2, 1982
Lamella and lube Settlers. 1. Model and Operation Woon-Fong Leung. and Ronald F. Probsteln Department of Mchanlcal Engineering, Massachusetts Institute of Technology, Camb-,
Massachusetts 02139
The three-layer, stratified viscous channel flow model of Probsteii, Yung, and Hicks for lamella settlers is generalized and applied to evaluate the performance of cocurrent flow lamella settlers and countercurrent flow tube settlers. For topfeeding lamella settlers a subcritical mode in which the feed layer expands down the channel and a supercritiii mode in which it contracts are confirmed. The mode obtained depends, respectively, on whether the clarified layer thickness at the outlet is less than or greater than about half the channel height, with the exact value dependent on the ratio of the solids fraction in the feed to that in the sludge. I n the bottom-feeding countercurrent flow tube settler there is shown to exist only a subcritical mode. Data from experiments on bench-scale Plexiglas settlers show that for a given settler angle and slurry concentration the efficiency of the supercritical mode is always higher than that of the subcritical mode. The efficiency decreases for both modes as the settter angie and slurry concentration are increased. The efflclency decrease with settler angle is sharp and results principally from flow instability.
Introduction Lamella settlers (Forsell and Hedstrom, 1975) are high-rate sedimentation devices consisting of inclined parallel plates stacked to form into which a s l ~ n y is fed for gravitational separation. Typical dimensions of *Address correspondenceto this author at GulfResearch and Development Co., Pittsburgh, P A 15230. 0196-4305/83/1122-0058$01.50/0
a conventional lamella plate are 150 cm wide by 240 cm long with channel spacings of 4 cm and settler angles between 45 and 60’ (Culp et d . , 1978). In each lamella channel partidea in the influent sediment toward the lower wall Of the channel. The settled sludge slides downward and is removed as the underflow. The downward movement of the feed slurry and sludge, which is commonly referred to &8 “cocurrent flow” (Ward, 1979), induces an upward flow of the clarified effluent. For most lamella 0 1982 Amerlcan Chemical Society
