v,
Acknowledgment
The author wishes to thank X r . Schaetzle for his assistance.
T
= stoichiometrical conversion number for component j, (v = BJ,) =
residence time, T
Nomenclature
B
=
bl b,
= = =
barometric pressure, ML-IT-2 pressure difference in gasometer, JfL-IT-2 vapor pressure of sealing liquid, .ML-'T-2 c concentration, mol L-2 D = diffusion coefficient, L2T-1 d = diameter, L F = surface area, L 2 k' = l i 0 = chemical rate constant (wall reaction, first order), LT-I kef?' = effective rate constant, LT-' L = length, L n = number of moles nR = number of moles in residual gas Q = amount of heat, cal . R = gas constant, cal mol-' r = radius, L Re = Reynolds number T = absolute temoerature. 0 t = time, T 'b = rate of reaction per unit volume, mol L-3T-l V = volume. La v = linear ga's velocity, L T - 1 IV = rate of reaction per surface unit, mol L-T-' y, = mole fraction of component i ylo = inlet mole fraction of component i
GRLCKLETTER CY
6 {
X q
= = = = =
thermal diffusion ratio thickness of boundary layer, L conversion rate thermal conductivity coefficient, cal L - ' T - W ' kinematic viscosity, L2T-1
literature Cited
Andrussow, L., 2.Elektrochem., 54, 566 (1950). Andrussow, L., Z. Elektrochem., 56, 624 (1952). Andrussow, L., Z. Elektrochem., 57, 124 (1953). Andrussow, L., 2.Elektrochem., 57, 376 (1953). Andrussow, L., Z. Phys. Chem., 199, 314 (1952). Damkohler, G., in "Der Chemie-Ingenieur," 111, Akadem. Verlagsges., Leipzig, 1937, p 359. Endter, F., Chem.-lng.-Techn,, 30, 305 (1958). Endter, F., DECHEMA (Deut. Ges. Chem. Apparatewesen) A%f07L0gr., 33, 28 (1959). Endter, F., et al. (to Degussa), German Patent 1,013,636 (Jan 23, 1958).
Gerdien. H.. 2. Elektrochem.. 39. 13 11933).
Beflin, '1952, p 531. " Wicke, E., Rossberg, M., Chem.-Ing.-Techn., 28, 181 (1956). RECEIVED for review October 6, 1972 ACCEPTED May 25, 1973 Supplementary Material Available. Tables 1-111 and V will appear following these pages in the microfilm edition of this volume of the journal. Photocopies of the supplenieiitary material from this paper only or microfiche (105 X 148 mm, 2 0 X reduction, negatives) containing all of the supplementary material for the papers in this issue may be obtained from the Journals Department, American Chemical Society, 1155 Sixteenth St., K.W., Washington, D. C. 20036. Remit check or money order for $3.00 for hotocopy or $2.00 for microfiche, referring t o code number PRBC-73-444.
A Rate Approach to Design of Perforated-Plate Extraction CoIumns A. H. P. Skelland" and W. 1. Conger Department of Chemical Engineering, The University of Kentucky, Lexington, Kentucky 40606
An attempt i s made to integrate some of the many and diverse studies on droplet phenomena into a coherent design procedure for perforated-plate liquid extraction columns. Equations describing mass transfer during droplet formation, rise, and coalescence, and incorporating relevant hydrodynamics, are used to locate a pseudoequilibrium curve. This curve is used in place of the true equilibrium relationship when stepping off the necessary number of actual stages between the pseudoequilibrium and operating curves on the x-y diagram. The provisional procedure i s written in Fortran IV computer language and the printout gives the number of real plates required for a prescribed separation, the number of perforations per plate, the column diameter, and the cross sectional area of the downcorners. Predictions are compared with all appropriate published values and agreement with fully eligible data (group A) i s substantial.
Stagewise columns achieve contact' between two phases in a discontiiiuous maiiner in stages Tvhich may, for example, take the form of bubble-cap plates or perforated plates. Both types of plate are widely used in gas-liquid contacting, such as distillation and gas absorption. I n liquid-liquid extraction the loiyer density difference b e h e e n phases, the higher viscosity of the disperse phase, and the lower iiiterfacial tensions 448
Ind. Eng. Chem. Process Des. Develop., Vol. 12, No. 4, 1973
cause bubble-cap plates to be ineffective, but perforated plates are successful and have been widely used. Skelland and Coriiish (1965) presented a procedure for the design of perforated-plate columns vihich is intended to eliminate the need for experimental determination of stage efficiencies, because these are normally obtained a t substantial cost in time, effort, and money. Furthermore, the applicability
of such efficiencies measured on small-pilot-plant to largescale equipment is al\,.iays a matter of uncertainty. Their procedure consists essentially in using rate equations for mass transfer during droplet formation, free rise (or fall), and coalescence on each illate, to locate a pseudoequilibrium curve. This curve is used in place of the true equilibrium relationship when step!)ing off the desired number of actual stages betn-een tlie pseudoequilibrium and operating curves 011 the 2-y diagram. Thus, although their treatment is in principle valid for both gas-liquid and liquid-liquid systems, i t is evident that grea.ter success is to be anticipated in its application to liquid-liquid systems. This is because the much smaller density difference between phases aiid the substantially higher viscosity of the disperse phase cause the flow pattern to be less turbulent and more nearly predictable for liquid-liquid than for gas-liquid systems. The present study represents a n extensive development of the early outline by Skelland and Cornish, utilizing many relatioii.hips not available a t t,he time of their publicat'ion. .A computer program is presented to implement the tentative desigii procedure, and predictions from the program are compared with all the appropriate published results on perforatedplate extraction columiis. Pseudoequilibrium Curve
Figure 1 shows the nth st'age of a perforated-plate column. The rate of mass transfer into the disperse phase on this stage is as follows, where the agitation resulting from the rising drops causes g* to be constant for a given stage p = KcifAf(lJnbk - Yfjn
+ KdrAr(yn* -
Yr)m
$.
Kd,Ac(yn* -
Yc)m
(1)
This is the sum of the transfer rates during droplet formation on plate n , free rise, and coalescence beneath plate n 1. But
+
(Y,*
--
Yi)m
(Yn* -
Yn)
(2)
and if D does not vary >igiiificantlyover stage n
Inserting these approximations into eq 1
q
=
KdfAf(Yn*- Y n )
I
---
Figure 1 . Plates n column
--Y"tl
+ 1 and n in a perforated plate extraction
1
,EQUILIBRIUM CURVE PSEUDO E Q U I L I ER I U M /CURVE OPE RAT1 NG CURVE
*
Figure 2. Location of the pseudoequilibrium curve and determination of the actual stages
Y,+~ corresponding to a selected pair of yn aiid y,* values (Figure 2). (2) Calculate D, and Dn+l corresponding to g , and the assumed y n + l . (3) Calculate q from eq 5 and 6. Repetition is performed if needed, until the two estimates of q coincide, indicating that the assumed value of yn+l is correct. The pseudoequilibrium curve is constructed in this manner and used with the operating curve t o step off the number of actual perforated plates needed to obtain the required change in composition from y n to gl. (The operating curve is located in the customary !yay [Treybal, 1963al.) Expressions used in this study to evaluate tlie various interfacial areas aiid coefficients in eq 5 for liquid-liquid syst,ems are listed in Tables I and 11. The treatment requires specification of v?; values below the "jetting veloci a t which jets issue from the perforations, ryhere and Meister, 1968) (9)
9 = Dn+iYn+l - DnYn
(6)
and from material balances, if D enters the column a t section 2
Dn+l
I
+
If it is assumed either that only solute (A) is transferred or that solute transfer is accompanied by equimolal countertransfer of solveiit,s between phases
D,
COALESCED D P H A S E (PREDICTABLE THICKNESS)
==
D?(1 -
==
Dn(1 - ~ * ) / ' (-l yn+J
~ p ) / ( l
- Y,)
(7)
(8)
h p p o s e t'hat A f , A,, A,, Kdfr Kdr, and can all be predicted. Then the quantity yn+l corresponding to a given pair of Y, aiid yn* values can he estimated by trial and error as follows, with reference t'o Figure 2. (1) Assume a value of
The authors propose a brief iterative procedure in which a preliminary estimate of d is given by d = ( 6 l . ' ~ ~ g , d ~ / g 4 p ) ~ ' ~ ; this is used for a first est'imate of ON,from eq 9 ; d is then recomputed from the equation for vP in Table I, using Z'N = ; finally o s j is recalculated using this second estimate of d . The overall coefficieiits of mass transfer are compounded from t'lie individual coefficients for the disperse aiid rontiiiuous phases from Table I1 using the familiar relationship
1 ~
Kdf,r,orc
-
1 kdf,r,orc
+ k c fm, r , o r c -__
lvhere subscripts f , r, and c indicate the processes of drop formation, rise, and coalescence, respectively. Effects of Surface Active Contamination
Trace amounts of surface-active impurities. uiikiiowi in structure and coiicentratioii, are frequently present iii commercial equipment'. This leads t o difficulties in interpreting Ind. Eng. Chem. Process Des. Develop., Vol. 12, No.
4, 1973 449
I. Expressions Used to Evaluate Af, A,, and A,.
Table
Ref
At Ar = G a d 2 where no = 4 & d , / T d ~ % ~ l / 2 5 v ~ / 3 6 0 05 1.0 ft/sec; (see also eq 9; ON
d
=
< ON,)
(60~/a)~'~ xugcdN ~
1
vp = F
-__
+
F
+
-
K P C ~ N ~ V N
9AP dzgAp Scheele and Neister TPddN%x2 4.5 ~dN3vx)2pdugc]1'3) 4gAp 49AP (1968) =f[d~(F:v~)~ from / ~ ] Scheele and Meister, 1968.
[(
(The term containing < 10 CP)
po is
neglected when
j&c
Ar
A,
=
(A0
- AD?(H -
hc)$d
(rd2)
UP
where
+
+
A0 = A,, 2AD peripheral band of width wb;when [(4/n)(Apa AD)]"^ 5 0.75 ft, wb = 1/2 pitch, otherwise wb = pitch A,, = nor(pitchj2/3.62, (triangular pitch) A,, = noa(pitcli)2/3.14, (square pitch) Fair (1963) AD = Q ~ U D 53,000Apo.58(d= 5.208 X 10-3ft)0.70 Klee and I,bD = pco.46 PC0.11 Treybal (1986) 0.521(lo-') ugcpdo,4pe0.2 Major and h, = Hertzog
+
+
Klee and Treybal (1956) dt = 7.25 ( gA p ~ A ? ~ ~ ~) , '" H u and Kintner (1955)
Ac A , = Ao
- AD
a T h e following are normally specified:
dN,
H,
Qc,,
Q d 2 , UP;,
pitch
the performance of such plant in terms of experimental and theoretical studies on single drops. Garner and Skelland (1956), Garner aiid Hale (1953), aiid others have shown the rate of mass transfer to be very substantially reduced by the presence of such impurities, because they accumulate a t the interface between the disperse and continuous phases. This inhibits circulation within the drops, changes the pattern of 450 Ind.
Eng. Chem. Process Des. Develop., Vol. 12, No. 4, 1973
droplet oscillation, sets up mechanical barriers to transfer across the interface, and modifies the shape of the drops. The formulation of generalized expressions to account for these effects is prevented by their specific dependence upon structure and concentration of the surface-active contaminant. I n a preliminary and tentative attempt to find some guidance on this matter, however, one may note that in several experimental studies (Garner aiid Skelland, 1956; Garner and Hale, 1953; and Lindland and Terjesen, 1956)) kdr* ivas not reduced by various specific surface-active agents below half the value predicted for stagnant spheres. Additional measurements of t'he effects of cationic or anionic surfactants over a wide concentration range on k d f * , kef*, lid,*, kc,*, kdc*, and k,,* are provided by Skelland and Caeiiepeel (1972). Selection of the appropriate correlations for the disperse and continuous phase coefficients during free rise or fall requires knowledge of whether drops of the relevant size are internally stagnant, circulating, or oscillating. I n a detailed review of the influence of surface-active contaminants on the hydrodynamic and mass transfer behavior of drops, Davies and Rideal (1963) note that internal circulation is inhibited in commercial systems by reduction in drop size and by the use of nonpolar solvents, because of traces of strongly adsorbed impurities. These impurities are less strongly adsorbed a t the interface with polar solvents, which therefore tend to give circulating drops. It was remarked that even large drops of commercial benzene are always stagnant aiid that circulation is reduced in drops 0.5 em in diameter by protein coilcentrations of only 0.0005% when the interfacial tension exceeds 30 dyn, em. The authors noted that the addition of a few per cent of a short-chained alcohol or acetic acid to the dispersed solvent rvill often displace the adsorbed impurity from the iiit'erface, thereby rest'oring the transfer rate to that corresponding to circulating droplets. This remedy seems most likely to prove effective in the case of interfacial films which are only weakly adsorbed. Sustained oscillations of the drops apparently begin when the Weber number ( d . ut2pclugc) reaches a value of 3.58 (Hu aiid Kintner, 1955; Basu 1970! p 86). The influence of surface-active contamination upon this criterion requires investigation. Qualitative determination of the droplet condition in a given system ma>- be achieved in a preliminary glassivare experiment in u-hich small amounts of aluminum particles are insert'ed in the disperse phase aiid the system is then observed with reflected light, (Garner and Skelland, 1956). A Computer Program for the Provisional Design Procedure
The provisional design procedure has been written in Fortran IV language for digital computer applicat'ion, using the relationships listed in Tables I and 11. The data required for its applicat,iori to the provisional design of a column for a specified separation are assembled in Table 111. The computer program listed in Table IT. which will appear in the microfilm edition of this volume of t,he journal, contains many labeled segmeiits to facilitate extension or replacement of individual sections by improved relationships as they become available from further research. The computer printout gives the number of real plates required for a prescribed separation, the number of perforations per plate, the column diameter, and the cross sectional area of the dotviicomers. Comparisons between Predictions and Published Data
The provisional design method in Tables I-IV has been applied to all the appropriate published results on perforatedplate extraction columns. Criteria determining whether or not published data were appropriate for comparison are noted
II. Expressions Used to Evaluate
Table
K d f , Kd,,
and
Kdcn
Ref
Skelland aiid Minhas (1971) Skelland and Hemler (1974)
oscillating drops
i
kd,*
=
k,,"
=
Vermeulen (1953) ; Johnson, et al., (1958) Skelland and Cornish (1963) Skelland aiid Wellek (1964) Ruby and Elgin (1955) ; Treybal (196313) Skelland and Wellek (1964) Garner and Tayeban (1960) Thornt on (1956)
us =
Skelland and hIinhas (1971) Skelland and Hemler (1974) 0 Asterisk signifies low solute concentrations and transfer rates. The coefficients are based on the corresponding areas listed in Table I.
Table 111. Data Required to Use the Computer Program in Provisional Design of a Perforated-Plate Extraction Column flor a Specific Separation.
I\IOLSC, MOLSD (molecular a eights of continuous and dispeise phases), D E X C ( p c ) , T'ISC ( p e ) , D C ( D c ) , D E K D ( P d ) , VISD ( P d ) , D D (Dd), 'm QCl (QcI), QD2 ( Q d d i D 2 (LIZ), OD (&), L-0 (ON), P I T C H (distance between perforatlous), HTH ( H ) , IID (number denoting type of drop; 1 = oscillating, 2 = circulating, 3 = stagnant), HH (number (
~
)
j
indicating direction of transfer; 1 = disperse t o continuous, 2 = contiiiuoub to disperse), 1IP (number specifying pitch geometry; 1 = triangLJar, 2 = square), KT (number shoning v, hether a new system is to be used on the next run; 1 = same system. aiiy othei number = a new s>stem), S D (number of points to be calculated along the pseudoequilibrium cur\ e), Y h 1 (yl), Y.42 (y3), X h l (XI), X.12 (Q), C1, C2 (constants for the equilibrium curve, y = ClzC2), B (l), B (2), B (31, (constants describing the operating curve). a Terms ale a5 they 3ppear in the program, the definitions in parentheses have meaning and units as in the nomenclature at the end of the paper
in Table I-.These ccliisiderations led to the elimination of some! or occasionally all, of the runs in the following papers. Criteria which were unfulfilled for the runs concerned are iiidicated iii pareiithesea iii each case: hllertoii, Strom, and Treybal, 1943 (4, 5 ) ; Garner, Ellis, arid Fosbury, 1953 (4, 8 ) ; Garner, Ellis, aiic. Hill, 1955 (2, 10); Garner, Ellis, and Hill, 1956 (10, 12); Goldberger and Benenati, 1959 (7, 11); llayfield and Church, 1952 (4, 12); Moulton and Walkey, 1944 (4, 6, 9 ) ; Saiidi .aid Gliosh, 1950 (2, 4, 5 , 6 ) ; Pyle, Col-
Table V. Requirements for Applicability of the Provisional Design Program
(1) S o interfacial turbulence phenomena. (2) h-o interference from hydrogen bonding between solute and raffinate as described by Licht and Conivay (1950) aiid Garner, Ellis, aiid Hill (1955). (3) S o surface act'ive contamination. (4) S o jetting or streaming of the disperse phase from the perforations. ( 5 ) All perforations must be operating. (6) All relevant physical properties must be known. (7) All relevant operating conditioiis and equipment dimensions must be known. (8) Drops must coalesce normally beneath each plate. (9) Operation must not be erratic, as when near flooding. (10) Plate-wetting characteristics must ensure good dispersion. (11) Coiitactor must be exclusively of the perforated-plate type. (12) Interfacial tension should be high ( 2 2 5 dyn/cm). burii, and Duffey, 1950 (3, 6, 11); ROW,Koffolt, and Withrow, 1941 ( 7 , 9, 11); arid Treybal and Dumoulin, 1942 (4, 5 , 9). The scarcity of appropriate data compelled use of some measurements which were of very dubious acceptability in terms of the tabulated requirements. I n consequence, the results may be classified into four groups, A, B,C, and D , the last three of which did not satisfy all the criteria of Table V. This means that only group A can be regarded as providing fully eligible data, but examination of results for the "ineligible" groups B, C, and D is nevertheless inst'ructive. (Runs used froin the literature are listed in Table VI.) Ind. Eng. Chem. Process Des. Develop., Vol. 12, NO. 4, 1973
45 1
60
I
Table VI. Runs Used from the Published literature for Comparison with Predictions from the Provisional Design Procedure.
Group A Allerton, Strom, and Treybal (1943), pp 374-375: Kerosene dispersed, and with V , = 24.7, 24.9, 27.2, 75.6, 73.8, 102.0, 103.8, 120.0, 122.2, and 136.0 Eta waterjhr f t z , respectively. Garner, Ellis, and Fosbury (19531, pp 352, 354: D 1 to D11, omitting run D4. Garner, Ellis, and Hill (1955): I1 to 14; J1, H2 to H i . Goldberger and Benenati (1959), p 642: L-I, 2A, 4 h , and 5-1. Row,Koffolt, and Withrow (1941), pp 579-580: 11, 61, 41, 81, lJ, 6J, and 85. Treybal and Dumoulin (1942) , p 711 : A11 23 runs for which temperature does not carry the superscript a, b, or c. Group B Naiidi atid Ghoah (1950) : Part I : Tables 11, 111, and IT. Part 11: Tables I, 11, 111, and ITr. Group C Garner, Ellis, and Hill (1955) : F1 to F4; G 1 to G15. Group D Garner, Ellis, and Hill (1956), p p 226-227: X.11 t o Ah26; CC1 t o CC17. a A total of 178 runs was used from eight different papers.
Group d comprised high interfacial tension systems which largely coiiformed to the specifications of Table V. The group consists of 65 runs corresponding to eight sets of data from six different papers. Resulk for group A are summarized in Table VI1 and plotted as individual and averaged values respectively in Figure 3. The overall average error between the number of perforated plates predicted by the program and the number actually used to achieve the measured separation is - 18.67,. The corresponding average absolute error n-ithout regard to algebraic sign is 22.47,. Figure 3 shows that about 90% of the data are within +33% of the relatioiiship nactual = npredicted/ (1 - 0.186). The fact that the program underestimates the actual plates used by ail average of 18.6% is consistent with the probable presence of trace amounts of surface-active impurities in the six experimental studies which provided these 65 runs. Gamer, Ellis, and Fosbury (1953), for esample, attributed their decline in extraction with continued recycling of raffiiiate to the accumulation of surface active contamination in the system. Group B consisted of systems which in the present contest exhibited "imperfect" operation. About 83% of these data also involved mild hydrogen bonding between raffinate and solute. The group comprises 54 runs Trith dilute solute by Kandi and Ghosh (1950) in a nine-plate, 1.75 in. i.d. column with 36 or 72 holes per plate. About 83% of the runs transferred acetone from Tvater to benzene or to kerosene of unspecified molecular weight, The remainder transferred benzoic acid from benzene to water. The authors indicate that some perforations n-ere iiot, functioning in much of the study, arid there are implications of jetting or streaming in some runs. The iiiterference from hydrogen bonding referred to here \vas described by Licht and Conwag- (1950) and by Garner, Ellis aiid Hill (1955). They postulate that transfer of solute out of a solvent, to ~ l i i c hit adheres by hydrogen bonding 452
Ind. Eng. Chem. Process Des. Develop., Vol. 12, No. 4, 1973
I
I l l l l l l
m
1 1 ' .
l " l l " @
v
I
I
overoge values f o r e o c h o f 8 se!s o f d a t o ( t o ! o l runs.651
individual Y O I U ~ S for 8 sets of d o l o itotol runs.65) a n u m b e r s s h o w overlopping p o i n t s
@
0'
n u m b e r s show r u n s overage
I
'"predicted: nac!uoI
t l I l / '
.8 I
I
2
I
I
4
I
l l l l l
6
8 10 1
I
I L / I
15 20 2
I
4
I
l l l l l
6
8 IO
I
20
1-1 40
*OC1"01
Figure 3. Comparison between actual and predicted numbers of plates required for the 65 separations in group A (Table VI1 gives some relevant details): 4, data of Allerton, Strom, and Treybal ( 1 943); 0, data, of Garner, Ellis, and Fosbury ( 1 953); 0,data of Garner, Ellis, and Hill ( 1 955); V, data of Goldberger and Benenati (1 959); A, data of Row, Koffolt, and Withrow ( 1 941); D, data of Treybal and Dumoulin (1 942)
occurs much less readily than from a solvent t o which it is linked by the relatively weaker van der TT'aals forces. Thus, when transferring diethylamine in alternate directions between toluene and water, Garner, Ellis, and Hill (1955) found the transfer rate from toluene to be several fold greater than from water. The hydrogen bond betvieen acetone and water is probably considerably weaker than that between diethylamine and water (Pimentel, 1972; Pirnentel and 11IcClellan, 1971) but is certainly significant. The overall average error between the actual and predicted numbers of plates for the 54 runs of group 13 was -30.47, and the average absolute error was 36.6%. The corresponding average errors obtained for the combined runs of groups -1 and B together were -23.9 and 28.8%, respectively. Group C comprises 19 runs by Garner, Ellis, and Hill (1955) on a system with strong hydrogen bonding between raffiiiate aiid solute. In this study diethylamine was transferred from wat,er to toluene a t the relat,ively slow rate described above. The column dimensions were as listed in Table VII. The number of plates was consistently underpredicted for these 19 runs, the overall average error beiiig - 62%. The explanation by the authors in terms of retarded transfer due to strong hydrogen bonding betrreen diethylamine and water may be retained here. Group D consisted of 40 runs on a low interfacial tension system in which adipic acid was transferred from methyl isobutyl ketone to Tvater. I n this study by Garner, Ellis, and Hill (1956) each phase was dispersed in turn, using the column described in Table VII. The overall average error and the average absolute error between actual and predicted iiumbers of plates were t 6 8 . 5 arid 6970,respectively, corresponding to overestimation of the plates required. The direction of this result suggests that the effects of int'erfacial tension may be inadequat,ely represented by the present formulation. .I further limitation 011 the present provisional program, then, is its restriction to high interfacial tension systems. This is perhaps related to the fact that txo-thirds of the data leading to the expressions for k ~ and * k d , * ivere for high u , while the correlations for kCf* and kcc* were obtained esclu-
Table VII. Summarized Comparison between Actual and Predicted Plates Required Separations in Group AC
Ref
Systema
Direction of transfer
No. of perfor ations per plate
Perforation diameter, in.
Plate spacing, in.
Downcomer diameter, in.
Column diameter, in.
No. of runs used
for the 65
No. of plates used
Average no. of plates predicted
11 9.9 KeroseneFrom 51 4 . 7 5 0.1875 2 X 0 . 4 8 5 3 . 6 3 10 benzoic organic acid-water phase 6 0.125 1 4 TolueiieFrom 8 . 627b 7.3 10 59 organic diethylaminephase water From 6 0,125 1 4 Garner, Ellis, and Water59 11 8 7.1 organic diethylamineHill (1955) phase toluene From 15 0,046 0.497 2.718 1 1 Toluerie4 Goldberger and organic benzoic Benenati (1959) phase acid-wa t er 6 0,12-event, the restriction t o high u is certainly in the range of niuc71i industrial interest. This is because high iiiterfacial teiisioii t e n s are considered desirable to f:icilitate phase sepnration and the avoidance of stable emulsions (Treyhal, 1963, 1) 131 : Treylid, 1968,p 413414: Perry, 1963, 1.1: 1) 41).
More quantitative design iiiformat,ioii is clearly needed I u c h plienonieiia as droplet detaclimeiit after growth, drop size distribution. droplet coalesceiice arid redispersion during free 1i.e or fall, iiiterf‘ncial turbulence, iioii-Sentoniaii properties. interactions such as those on k,, for swarms of I;t:igiiaiit a i i d oscillating drops, coalescence mechaiiisms a t the plane coalescence interface, surface active contamination, ociated with the direction of transfer, a i d the infiueiicr of plate-netting chnracteriqtic,s on the effectiveness of dispcwion.
oil
Nomenclature
Conclusions
I t must not be tliought that the procedure outlined here for the desigii of pe .forated-plate columns is presented as tlie final form of treatment. Indeed, mniiy of the siniplificatioiis involved become apparent from an esamiiiatjoii of t h r revie\T- by Oliiey and Xiller (1963). The program must lie regarded as I)rovisioiial, because it is clear that eslirei~ioiis for some phase.: of the process are at present arai1:ihle only i i i iiiteriin form. Figure 3A empliasizez that, eveii with the l ~ * of t correlatioiis, ertr:ictor desipii is iiot very 1,rec’ise. X fr:Lniexork> lion-ever, is tleliiieatecl n i i d areas iieediiiy refiiieiiieiit :IIY aplinreiit. I’or tleaigii purpose> relatiniislii1)4 Ixi.etl 011 rori.elntioii of ezl)erinieiital data are pmhalilj- to he liret’erred for wine time to come. .Uthougli > u c h eml)iricd esl)res&ii< leave nia11:- q u e h m s uiiaiis~eredTT itli regard to iiiecliaiiisni, they iiewrtlieless represeiit nieamrenieiits apiiii?t n-1iic.hfurther t lieoretical developiiieiits caii be tehtetl.
=
;1D
cross sectional area of downcomer, ft2
-If = total surface of ?todrops a t detachment,, Et2 Alf,,=lrJ= total interfacial area between two consecutive plates for the stages of drop formation, free rise (or fall), and coalescence, respectively, fte -40 = cross sectional area of entire column, ft2 Ad
=
L4pz = area of perforated zone per plate, i t ? 1) = molar flow rate of disperse phase, lb mo1,’lir D,,, DIiTl = molar flow rates of disperse phase a t plates n aiid j z I , re.pectively, in a stagewise column, Ib mol hr D , = molecular diffusirity of :elute in the pliase under conderntion, ft?.hr D2 = molar flow rate of dis1ier.w phase entering the column: 111 mol hr cl = droplet diameter, ft (I, = interiial diameter of nozzle, orifice, or perforation, Et d, = traiisitioii value of d, ft IChem. Eng. Sei., 2, 157 (1953). Garner, F. H., Skelland, A. H. P., Ind. Eng. Chem., 48,.51 (1956). Garner, F. FI., Tayeban, >I., Anal. Reale Soc. Espanola Fis. Qicin,., Seri‘c B, Quint. Tonio LV7I (H), 479 (1960). Goldberger, W. >I., Benenati, K. F., Ind. Eng. Chcm., 51, 641 (IQ33.
Hu,PI,‘Kintner, It. C., AIChE J . , 1, 42 (1953). Johnson, A . I., Hamielec, A . E., Ward, I).j Golding, A,, Can. J . Chrm. Eng., 36, 221 (1958). Klee. 4.J.. Trevbal. R . E.. AIChE J.. 2. 444 il9.56). Licht, W., Con&y, J. B., ind. Eng. &e&, 42, 1151 (1950). Lindland, X. P., Terjesen, 8.G., Chrnz. Eny. Sci., 5, 1 (1956). l l a j o r , C. J., Ilertzog, I?. It., Chem. Eng. Progr., 51, KO. 1, 17-5
-
i1 Qi.i\ ,,. I
llayfield, F. I),, Church, JV. L., Ind. Eng. Chcm., 44,2253 (1952). lloulton, 11. rV.j IValkey, J. E., Trans. Anier. Inst. Chena. Eng., 40. 695 119341 Sanrh, S. Ghosh, P. K., J . Indian Chcm. Soc., Ind. .Yews Ed., 13, 03, 103 (1950). Olney, li. H., lIiller, 13. P.,in “3Iodern Cheniical Engineering,” ri. Acrivou, Ed., Vol. 1, Keinhold, Sew York, X.Y., 1963, pp
&.I
vi)-i ‘20 ,/.,
Perrv, 1:. H., Chilton, C. H., Kirkpatrick, S.D., Ed., Chemical Eigineering Handbook, 4th ed, lIcGraw-Hill, Xew York, \-.Ti.. - . , 1QW -Pimentel, G. C., private communication. Pinlentel, G. C., ~IcClellan,A . L., Annu. Rea. Phys. Chem., 22, 3.70 (1971). Pyle, C., Colburn, A . P.,Duffey, H. lt., Ind. Eng. Chcm., 42, 1042 (19T,C). l t o ~ S. , B., Koffolt, J. H., JVithrow, J. R., Trans. Amer. Inst. C h o n . Eng., 37, 559 (1941). Iluby, C . L., Elgin, J. C., Chcm. Eng. Progr. S y m p . Ser., 51, F o . 16, 17 (10.5,5). Scheele. G. F.. 1Ieister. R . J.. AIChE J . . 14. 9 11968). Skelland, A . H. P., Caenepeel, C. L., d f C h h J:, 18,’1153 (1972). Skelland, .A. H. P., Cornish, A . 11. H., AIChE J., 9 , 73 (1963). Skelland, A . H. P., Cornish, Ai.11. H., Can. J . Chem. Eng., 43, 302 (196.5). Skelland, A . €I. P., Heniler, C. L., to be published; also Hemler, C. L., Ph. 1). Thesi3, Vniveriitp of Xotre Dame, 1974. Skelland, -4.H. P., JIinhas, S.S., AIChE J . , 17, 1316 (1971). Skelland, A. H. P., JVellek, 11. lI.,AICkE J . , 10, 491, 759 (1964). Thornton, J. D., Chtrn. Eng. Sei., 5, 201 (1956). Treybal, R. E., “Liquid Extraction,” 2nd ed, 1IcGraw-Hill, Yew York, S . T . , 196:3, (a) p 260, ( b ) p 480. Trevbal, 11. E., “1Iass Transfer Operations,” 2nd ed, lIcGrawHill, SeTv York, S.Y., 1968. Treybal, I?. E., Dumoulin, F. E., Ind. Eng. Chcm., 34, 709 11942). Vermeulen, T., Ind. Eng. Chem., 45, 1664 (19.3). ~
11~ci:rv~:ofor review October 16, 1972 ACCEPTED >larch 30, 1973 Table IV will appear following these pages in the microfilm edition of this volume of the journal. Single copies may be obtained from the Business Operations Office, Books and Journals Division, American Chemical Society, 11.55 Sixteenth St., S.W., Washington, 11.C. 20036. Remit check or money order for S3.00 for photocopy 01 52.00 for microfiche, referring to code number PliOC-73-448.
