Distillation, Vaporization, and Gas Absorption in a Wetted-W all Column M.
L. JACKSON'
N. H. CEAGLSKE
AND
UNIVERSITY OF MINNESOTA, MINNEAPOLIS, MINN.
Performance data are presented for t h e distillation of the 2-propanol-water system a t total and partial reflux, and for the vaporization i n t o air of water, 2-propanol, toluene, and water f r o m glycerol solutions. A direct comparison of uni- and counterdirectional mass transfer is thus provided and these processes are found t o be similar in so far as the defining equations will permit. A unique type of column construction, and a calculation method, are presented for t h e evaluation of point values of t h e height of a transfer unit. For t h e distillation of 2propanol-water these are observed t o reach a maximum
value over t h e column in most instances. This is considered t o indicate an unexpected effect of composition on t h e mass transfer process. The )D factor correlation is adequate for both distillation and gas absorption In a wetted-wall column, provided t h a t the proper turbulence of t h e gas phase is predictable in terms of t h e friction factor. The Sherwood-von K j r m l n equation likewise predicts mass transfer behavior w i t h good accuracy If t h e correct relationship between eddy viscosity and eddy diffusivity is known. A value for alpha of about 1.15 is indicated for t h e conditions existing in a wetted-wall column.
T
HE problem of separation of a mixture of materials into their respective components has long been of interest in the fields of both chemistry and chemical engineering. The underlying theory in a mass transfer operation is of particular importance in these fields wherein the performance of industrial equipment is to be predicted or evaluated. Quantitative expressions for the rate a t which matter may be transferred between phases are based on the postulation of some mechanism, and the proper testing of these proposals is to be desired. The wetted-wall column has frequently been used for such investigations because the transfer process may be expressed in differential terms and the interfacial area of transfer can be accurately determined. Recently (16, d1,90)it haa been shown for distillation, that negligible liquid flm resistances are encountered in this type of equipment, which therefore permits a direct fitudy of the gas film characteristics, In a wetted-wall column the liquid assumes a wave motion above a critical flow rate, and the absence of a liquid film resistance is attributed to this phenomenon although the exact nature of the flow pattern is not fully understood. Such a wave motion probably does not occur in a packed column, owing to the discontinuities of flow. Finite liquid film resistances have been observed ($1) in such apparatus where, for the same system, they were absent in the wetted-wall column. Mass transfer investigations involving the wetted-wall type of equipment have given results not in complete agreement in all instances. The present work was undertaken to offer a refinement in technique with the expectation that these differences might be reconciled, particularly for the distillation process. A primary objective was the direct comparison of vaporization (transfer of one component in one direction) with distillation (equimolar, counterdiffusion) in the same apparatus. In addition, the available data for distillation under partial reflux are sparse and a study of this type of behavior was included.
Heat transfer. j~ =
(F)"' CG k
(k,)
QPOJM Mass transfer. jn = ~G
a/a
(3) The analogy predicts that j = j / 2 . This has been found to be valid for simple geometric shapes such as tubes, but is not true in general and does not hold for packed columns. Equation 2 is written for gas absorption in terms of the gas film only, and for rectification p , = ~ P. (Throughout this paper only the gas film is considered, because this is the resistance actually being studied in a wetted-wall column.) The definition of k~ in terms of the basic variables is different for the two types of mass transfer usually encountered: Unidirectional transfer of one component
Equimolar, counterdiffusion
D kG' = 2 RTB
(5)
Chilton and Colburn ( 4 ) later introduced the concept of the height of a transfer unit, (Hi), and the number of transfer units, ( N t ) , as a measure of the difficulty of a separation. The pertinent differential equations are integrated over the height of a column to give (Ht)C
= Z/(Nf)Q
(6)
where for gas absorption and vaporization
LITERATURE
In the matter of predicting mass transfer coefficients Colburn ( 6 )extended the analogy between heat transfer and fluid friction as conceived by Reynolds, Prandtl, and others to include mass transfer. Later, Chilton and Colburn (5) summarized these analogies in terms of the j factors: 1 Present
address, University of Colorado, Boulder, C O ~ O .
and for distillation
( H ~ )isG related to the mass transfer coefficients for the two processes by the equations 1188
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
June 1950
1189
the maas transfer process. When written in terms of (H& this equation becomes
The above expressions are written in t e r m of a fictive film having a resistance equal to the combined resistance of molecular diffusion through a laminar film a t the interfaoe and of eddy diffusion in the turbulcnt portion of the stream. The exponent of */a on the Schmidt number is a compromise between the two processes, for molecular diffusion would be proportional to the first power of D,,and eddy transfer to the zeroth power. Recent investigations of velocity gradients for streams in turbulent flow have shown that three zones exist. A layer next to the phase boundary is found to be in laminar flow while the main core is in a turbulent condition. In between exists a buffer zone which is a combination of the two types of flow. Generalized flow distribution curves relating velocity and thickness have been developed. Based on this flow pattern von K & r m h ($8) presented a relationship for heat transfer processes which acoounts for the relative effects of molecular and eddy transfer. Sherwood ($4, $6) has extended these conRiderations to include
'\
This equation involves the term a, whichpelates eddy diffusion to eddy viscosity, and is defined by the equation e=-
CYE
P
A number of investigators have obscrved the maas transfer process in wetted-wall columns. Chilton and Colburn ( 8 ) obtained limited data on the vaporization of water into air in a falling-film tower wherein the jn factors closely checked the values of f/2. Gilliland and Sherwood (11)published extensive data on the vaporization of nine liquids into an air stream. An empirical corrclation was proposed which stltisfactorily represented the data, and later (IO) equally good conformance waa had by expressing the total resistance as the sum of film and core resistances. The data did not closely agree with the j~ factor correlation. Barnet w d Kobe (1) studied the relationships between heat and mass transfer for water vaporization and found the jo factors to approximate the ChiItonColburn line (jo = f/2) but to be somewhat EQUIPMENT high for heat transfer. A STEAM PRESSURE REQULATOR There were published simultaneously (16, 67) 8. REBOILER the results of distillation in two widely differ0. VENTURI METER FOR VAPOR OR AIR 0. U-SEND, 25 DIAMETERS CURVED LENQTH ing types of wetted-wall equipment. Johnstone E. LOWER CALMINQ SECTION, 30 DIAMETERS and Pigford were able to check the j~ factor F, LlOUlD "TAKE-Off" BOX correlation closely on four distillation system 0. SECTIONAL WETTED-WALL COLUMN, 4 1 DIAMETERS H. LlPUlD 'PUT-ON' BOX and concluded that negligible liquid filrn reaist4, UPPER OALMIND SECTION, 14 DIAMETERS ances were encountered. Suroweic and Furnaa K CONSTANT HEAD TANK investigated the distillation of the ethanolL VAPOR CONOENSER M. L l O U l D SUB-COOLER water system and baaed their conclusions on the Y.STORAQE TANK AN0 SIOHT Q A U Q t applicability of the Gilliland-Sherwood correlaO.QEAR PUMP tion to the vapor iilm. Liquid film resistances P. ROTAMETER, LlOUlO T O COLUMN 0. ROTAMETER. LlOUlD TO RESOILLR were reported as amounting to 30 to 40% of R. LlOUlO COOLER the total resistance. 0. REFLUX HEATER Peck and Wagner (61) presented a new mathematical treatment relating gaa and liquid DATA POINTS film resistances, and concluded that the gaa film 1,s. VAPOR SAMPLES f O R OOMPOSITION 2-410. LIPUIP SAMPLES COR COMPOSITION comprised nearly 100% of the total resistance 11. TEMPERATURE OC VAPOR FROM COLUMN, for wetted-wall columns involving rectification. THERMOOOUPLE Similar conelusione were reached using selected 12-19. INSULATION a PIPE WALL T E M P E R A TURES, THERMOCOUPLLS data from the two previous investigations just 20-88. VAPOR TENPLRATURES, THERYOmentioned. The data of Peck and Wagner COUPLE 0 , RE COROe 0 were not compared on the basis of the Chilton23. VAPOR TEMPERATURE IN REBOILER, RESISTANCE THERMOMETER, RECORDED Colburn or Sherwood-von K&rmSnequations. 24. R0,TAMETER LIOUIO TEMPERATURE, SAYK Recently, Storrow (96)applied a unique ap21. VAPOR CONOENSINQ TEMPERATURE, SAME proach to the distillation of methanol-water 86. TEMPERATURE W LlOUlD TO COLUMN, SAMs t Z I B . VAPOR PRESSURE TAPS, COLUMN and ethanol-water systems. Temperature meastB,30. VAPOR PRESSURE TAPS, VENTURI urements were used to determine the composi51. TEMPERATURE O f LlOUlD FROM COLUMH, tions of the vapor phase. It waa concluded NERCURY- #LASS THERMOMCTER NOTE: DOTTED LINES INDICATE INSULATED a that the over-all (&)a was a function of the ELECTRICALLY HEATED SECTIONS vapor composition and hence of column length. The j n factors were 15% above those of Johnstone and Pigford for the ethanol-water system. Westhaver (XI), working in the region of laminar vapor flow, observed that the resistance offered by the liquid film was not a factor for maas transfer in an "open-tube" distillation column. PRESENT OBJECTIVES
Figure 1. Schematie Diagram of Wetted-Wall Column
In attempting to r e b e the technique of wetted-wall investigations, particularly those involving distillation, a number of factors become apparent in the study of previous results. The
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
1190
degree of turbulence in the vapor phase is obviously of prime importance, and evaluation of this item should be possible in a precise manner. End effects may consist of ( a ) the sudden change of relative velocity of the entering gas stream on coming into contact with the liquid on the wall, ( b ) the degree of subcooling of the entering reflux (distillation) below its equilibrium temperature, (e) the absence of wave motion in the liquid a t the top of the column aa it is first introduced onto the wall, and ( d ) the ineffectiveness of separation in the region where the operating line closely approaches the equilibrium line. These end effects become of relatively greater imDortance aa the ratio of column length to diameter"is-reduced. Consideration of the distillation process shows that "PUT-ON' BOX an extreme variation of the operat ing variables over a column can occur if t h e molecular weights of the components are appreciably d i f f e r e n t . Changes of 200 and 300% may be observed in the Reynolds and Schmidt numbers. It is at once apparent that ( H ~ ) Gcan by no means be constant over the height of the column, In gas a b s o r p t i o n such changes are not e v i d e n t , because LIQUID FROM the solute usually comprises only a small percentage of Figure 2. Seotional Features of the total gas presColumn ent. The procedure in distillation has always been to determine ( H L ) oover the entire column and to "average" the variables of density, viscosity, gas mass flow, and the like. This average has usually meant simply the taking of an arithmetic average of conditions a t the top and bottom of the column. The determination of composition a t points along the height of a column would provide information from which point values could be determined. This would avoid the questionable procedure of averaging and would permit the elimination of end effects. It is proposed that point values of (")Q be obtained in the following manner. Substituting Equations 6 and 8 in Equation 10, and writing the expression for a differential height of column,
APPARATUS AND PROCEDURE
Figure 1 represents the column and auxiliary equipment diagrammatically and will serve to relate the component parts and to indicate the flow pattern. The points a t which the data are taken are also shown. The column was constructed of hard copper tubing, 1.505 inches in diameter, and consisted of six l-footc sections. During assembly these sections were aligned with a 2-foot steel bar which had been machined to fit snugly inside the tubing. Each section was joined by an external coupling using soft solder and a nonacid flux. The solder w&s kept from the interior of the column. This method of construction was considered superior to that of using a continuous &foot tube. It provided a method of obtainin a uniform liquid sample and was believed to make possibfe a column deviating less from a straight line. The wetted-wall section was rigidly supported by iron brackets attached to a brick pillar of the building. Vertical alignment wa8 checked by means of a specially constructed plumb bob and deviation from the vertical was considered to be less than l/az inch in 6 feet. This waa confirmed by observing that the flow of liquid down the column wall was uniform throughout and did not progress to any one side. It waa also observed that water wet the column uniformly a t high temperatures and continued to do so when the temperature was reduced. The organic liquids, having low surface tensions, wet the column uniformly at low temperatures. The devices for feeding liquid onto the column, and for removing it, are detailed in Figure 2. The end of the top section was machined to a thin edge, and to this was soldered a he-mesh screen to connect with the upper calming tube. This assured even distribution of the liquid onto the column and served to minimize liquid-vapor contact in the box. The bottom section of the column was soldered to a piece of brass and machined to an expanding cone without a break in the continuity of the wall. This led the liquid off the column into the drainage box through surface tension effects. The end of the inlet tube from the lower calming section was machined to an edge and waa closely spaced to the cone. The ends of each 1-foot section were machined to a 45 angle and a small space between each junction served to collect the liquid sample from the column wall. Prior to the assembly of the main column a test section indicated that any disturbance due to this spacing (none could be observed) had less effect than the waves which the liquid assumed in flowing down the column. The liquid sample was conducted from the spacing through a
-
-
l-l/2'
COPPER TUBIN0
ASBESTOS PAPER NICHROYE HEATINQ WIRE STANDARD 1-114' YA6NESlA INSULATION
TUBE AND LOWER CALMING SECTION
I-VP COPPER TUBINQ THERYOCOUPLE SOLDERED IN NOTCH COPPER PLATE THERYOCOUPLE SOLDERED TO PLATE
Noting that y i = y", since no liquid film resistance is presumed to exist, Equation 13 may be rearranged to give
where (dy/dZ) is the slope of a plot of y versus 2, the height of the y) is the driving force across the film a t the column, and (y' point in question.
Vo1. 42, No. 6
NICHROYE HEATINO WIRE STANOARD 1-114' Y A B N E I I A INSULATION STANDARD 3. YAONESIA INSULATION STANDARD 5 " YA0NESIA INSULATION
WETTED-WALL COLUMN AND UPPER CALMING SECTION
Figure 3.
Method of Buffering Column against Heat Loss
June 1950
INDUSTRIAL A N D ENGINEERING CHEMISTRY
1191
stant for various compositions. Table I summarizes the data on which these conclusions are baaed. The 2-propanol used was of high purit and waa distilled once with the e n d discarded. The boiling point range ws9 81.35-81.45' C.?t a pressure of 734 mm. of mercury, which compares mth the literature value (2) of 81.35' C. at the same i-mure. The refractive index a t 20' $was 1.3771 compared to 1.3776 from the literature (28). The refractive indexes of mixtures of Zpropanol and p 0.003 water were determined with a Zeiss immersion refractometer and this calibraP z tion waa used for a11 subsequent evaluations of composition. The density and viscosity of these liquid mixtures were REYNOLDS NUMBER OF GAS PHASE determined a t several temperatures. The values were extrapolated to the boilin Figure 4. Friation Factors for Swtional Wetted-Wall Column point and were used for calculating liqui8 surface velocities. Viscosities of the vapor mixtures were calculated by -& hole in the coupling and thence to a sam le cooler. The collecsuming additive roperties of the pure components on a mole tion rate wm regulated by small needle v&es. fraction basis. #he viscosit of %propanol vapor was extraThe rate of va r flow waa measured by a calibrated Venturi polated from experimental d t a (17, 18) using the Sutherland meter using a gfferentia~water-toluene manometer for low equation ($8). rates, and a water manometer for the higher rates. The pressure leads from the meter to the manometer were heated electrically, which in combination with air traps prevented Condensation Table I. Heat Content of 2-Propanol-Water Vapor during the distillation runs. The aa phase passed through a UMlxturet above 80" C. bend of 25 diameters and a strai&t section of 30 diameters to provide calming before entering the test section. For distillaMole Frsction in Liquid B.t.u./Lb. Mole of Vapor tion, the vapor was generated in a reboiler heated b steam 0.0 18 100 under regulated pressure. This waa condensed for relux and 0.1 17'300 0.2 17'400 feed in a water-cooled condenser of the &ell and tube type. For 0.4 17'200 vaporization air was supplied by a heavy-duty blower and the air 0.6 17'400 stream from the column waa vented to the outside atmosphere. I .o 17:440 The li uid from the surge tank passed through the constanthead tan% before going to a calibrated rotameter and onto the column wall. For distillation at partial reflux a second rotamFor va orization both %propanol and water were employed eter served to split the condensate and feed a portion of the individuAy, so that a direct comparison could be made for these stream directly back to the reboiler. compounds in counter- and unidirectional diffusion. The % The calming sections and vapor tubas were heated electrically propanol was essentially similar to that employed for distillation, to prevent condensation, and the column roper was buffered except that it waa used without the ends removed. It was against heat loss. The method is indicates in Figure 3. The replaced frequently, because analysis showed that it tended to column and portions of the u per and lower calming tubes were pick up water from the air. Toluene and glycerol solutions were arranged in four sections. &&rent input to each section was also used and were prepared from C.P. grade reagents. The adjusted to give corresponding readings on the thermocou le viscosity of air-water mixtures at various humidities is available This waa considered aa adequate to provide for negligille (9). E%%v!a inasmuch aa the temperature of the liquid phase on the Procedure. In distillation the vapor and liquid rates were equalwalls didnot vary a preciably. ized by maintaining a constant level of li uid in the surge tank, Temperature reaiinga at the points indicated were recorded Adjustments were made in the column tfeaters to provide for either aa potentiometer reading of thermocouples on a Microadiabatic operation. The column was assumed to be operating a t mix instrument, or aa resiatance thermometer readings on multidynamic e uilibrium when successive samples gave the same compoint Ta liabue reoorders. Thermometers (0.1 ") were used for position. %he column sampling devices were then ad'usted to wet and 8ry tem rature readings of the exit as (vaporizatiqn) collect liquid a t the rate of about 10 drops a minute. '$his slow and for the liquigoming from the column walf Inlet humidity rate waa necessary to revent an upset of equilibrium operatin of the air for the vaporization procw waa determined by a sling conditions. The t o t 2 sampling rate comprised 0.5 to 3.Od psychrometer which had been calibrated to assure the correct of the liquid reflux rate. Readings of flow rates and temperstemperature readings. turea were taken simultltneously with the collection of the samples Pressure tapa for determining the head loss of the as phase over the period of test, which amounted to about 0.5 hour. passing through the column were placed immediate$ before Representative data were considered aa having been obtained and after the test section (see Figure 2). The distance between when the various items remained essentially constant. these taps waa 74.5 inches and the,length of column exposing For va rization the procedure was somewhat different. interfacial transfer area waa 72.25 inches. The presaure dro The humi%y of the inlet air was determined for all instances, was determined by a micromanometer using w!ter for the fluicf and for water eva ration the exit humidity waa obtained from Readinga were indicated by contact of a platinum needle a wet and dr b u g tem ratures. These thermometers were proaching the water surface from an off podtion. The nee& placed directfy in the o u t E stream and care waa taken to wure and water completed a circuit with a source of 110-volt alternating that the wet bulb reading was correct. The rate of water current and a neon glow lamp. evaporation was ehecked by noting the rate of fall of the liquid level in the surge tank. This method was also used to determine Systems and Physical Properties. In order to determine vapor the vaporization rate of the other liquds. Re resentative data compositions from liquid compositions for distillation, it is ne?& over a period of at least 20 minutes were use: for the baais of wry that the operating line be sccurately defined. Thie necbssithe calculations. tates that the molar flow of each phase be constant within narrow PRELIMINARY INVESTIGATION limits, and hence that the molar latent heats of vaporization be The question of gaa stream turbulence appears as a major nearly equal. The 2-propanol-water system meets these requireconsideration in predicting mass transfer behavior. The effect ments. Calculations based on the vapor pressures of various of the liquid surface velocity on the turbulence of the vapor mixtures (18, 28) employing the method of Othmer ($0)show haa been variously treated, some investigators choosing to ignore that the latent heats of the two components are very nearly the it and others treating the liquid aa being in true viscous flow. same. The total heat content of the vapors is practically con-
I N D U S T R I A L A N D ENGINEERING CHEMISTRY
1192
60
I 0
Figure 5.
I
I
I
I 2 3 4 5 FEET FROM BOTTOM OF COWMN
0.4
6
Instantaneous Values of Operating Variables, Run IW-28
It has been shown (8) that the liquid surface velocity departs from that for viscous flow a t a Reynolds number of about 30 and then increases above the expected value. Because the range of this investigation was limited, a method was developed and applied to the present apparatus for determining liquid surface velocities at higher flow rates, The method is based on the actual momentum loss experienced by the gas stream in contact with the liquid film. The detailed results are to be reported elsewhere, but the essential conclusions are that the effect of the falling liquid film is to increase the gas velocity by an amount equal to the surface velocity, and that the actual momentum loss of the gas phase corresponds to this velocity. The liquid surface velocity is shown to reach a constant value of about twice the average liquid velocity. The friction factors as determined for the sectional column are prasented in Figure 4, and agree well with the expected values from the literature for smooth tubing (299). However, in the region below Reo SOOO, the data exhibited inconsistent behavior, whether approached from the turbulent or viscous flow zone, The spread of the data in this region is indicated in this, and succeeding figures, by two dotted lines.
reflux, that the composition of the liquid arid vapor streams be identical at any point. This requirement is met within experimental limits, as may be observed by inspection of Column5 X b and u b for compositions a t the bottom of the column. The vapor and combined reflux and feed rates should be the same, and the difference between them is expressed as a percentage of the average. Run IW-17 was without reflux on the column walls and gave a check on the sampling technique. Of the runs omitted from the table, all were for the purpose of determining the friction factor of tl-ie mixed vapors flowing. This was unsuccessful because of the uncertainty in the densities of the gas phases involved. End Effects. Certain phenomena which occur at either end of the test section may cause departure from typical behavior. First of all, the vapor entering the column experiences a sudden increase of relative velocity on coming into contact with the liquid surface. The percentage increase will vary with the rate of flow, but in any case is significant and a period may be necessary for the vapor to assume its proper turbulence. A second effect may arise because the reflux enters below its boiling or equilibrium temperature. Partial condensation of the vapor will occur on contact with the undercooled liquid and a change in the flow rates of both phases will result. For the present system this change in flow rate may be estimated as about 4% for 12" C. below the boiling temperature. The values for the changes in the vapor flow rate would be equal to, or less than, those for the liquid depending on the reflux and feed rates. Thirdly, the assumption of a negligible liquid film resistance at the extreme top of the column may not be valid. It is probable that the absence of a liquid film resistance in wetted-wall columns is related to the phenomenon of wave formation (8, 16). It was observed in the present instance that the liquid did not assume this wave motion for about the top 6 inches of the column. Inspection of the y versus Z data for various runs shows that in many cases a break does occur in this section. This may be attributed to both wave motion and reflux subcooling effects. A fourthend effect can he observed in cases where the operating line closely approaches the equilibrium curve. This can occur a t either end of the column, and in such instances the driving forces become very small. This results in a small change of composition and introduces the likelihood of a large error in the calculations for (Ht)o, Inspection of the data for Run IW-9
Table I I .
SJ
DISTILLATION RESULTS
Because of the voluminous nature of the distillation data, only the more significant results are tabulated here. The detailed operating data and all calculated results are available (14). The following development ia used in presenting the results: (a) accuracy of the data, ( b ) end effects, (e) instantaneous (&)a values, (d) point jn factors, and (e) over-all jn factors. An evaluation of the distillation process in terms of the Sherwoodvon Khnirn equation is included in the discussion of vaporisation. Figure 5 shows instantaneous values of the operating variables for a typical run. The extreme variation of the Reynolds and Schmidt numbers is to be noted. Also indicated are the comQ be positions and driving forces from which the point ( H ~ ) may bbtained. Accuracv of Data. Table I1 provides an indication of the accuracy l f the data. A material balance necessitates, for total
Vol. 42. No. 6
Run IW-4 IW-6 IW-7 IW-9 IW-10 IW-12 IW-13 IW-14 IW-15 IW-16 IW-17 IW-18 IW-19 1"-20 JW-21 IW-23 IW-24 IW-25 IW-26 IW-27 IW-28 IW-29 IW-30 IW-31 IW-32 IW-33 IW-34 IW-86
Flow Rates and Terminal Compositions for Distillation of 2-Propanol-Water System
ReEux Ratio Total Total Total Partial Total Partial Total Total Partial Total
Flow Rate
zb
0.001 0.072 0.020 0.006 0.136 0.184 0.070 0.155
0.110
0.170 0.367 Par&l 0.027 Partial 0.053 Total 0.007 Total 0.003 Total 0 215 Partial 01038 Total 0.119 Partial 0.029 Total 0.002
Total
Total Partial Partial Partial Partial Psrtid Partial
0.081 0 073 0'006 0:106 0.042 0.011 0 025 0.156
yb
0.005 0.071 0.033 0.114 0.137 0.234 0.096 0.161 0.170 0.179 0.367 0.078 0.138 0.008 0.006 0 214 01203 0.119 0.132 0.016 0.090 0 080 01133 0.166 0.177 0.184 0.331 0.223
Lb. Mole/H&r
% iff^^^^^^
Reflux 0.832 1.605 0.692 1.112 1.126 1.243 0.358 0.833 1.513 0.968
in Rates -1.7 -3.7 -1.0 -0.3 -1.1 -1.5 -0.5 -1.2 -3.2 -1.0
z: 0.231 0.329 0.342 0.292 0.386
Vapor 0.818 1.547 0.685 1.800 1.114
0.405 0.414 0.392 0.351 0.398 0.367 0.310 0.381 0.260 0.240 0.416 0.402 0.355 0.347 0.496
1.550 0.356 0.825 2.645 0.958 2:075 2.410 2.030 1.944 1093 1:OlO 1.861 1.908
1:502 1.907 1.996 1.347 1.113 0.558 1.929 1.308 0.126
0.427 0 372 0'302 01397 0.367 0.335 0.369 10.437
0.370 0 706 01738 2.240 2.160
0.353 0.703 0 426 11890 1.336 2 73 2 76 2.47
...
.
,, ,,, , ,
.
Feed
.. .
..,
0:693
...
0.330
. .. . ..
1:iiS 01364 0.568 0:489
01442
0:6iO ,.
.
.
.
O:& 0.486 0.886 1.390 2.93 0.636
...
-4.3 -2.7 f1.7 f5.7 -1.8 4-1.0 -3.6 -0.5
...
+4.7 f0.4 t3.3 -6.9 -3.3
...
.. ....
INDUSTRIAL AND ENGINEERING CHEMISTRY
June 1950
. 3b
I
I
I
0.1 0.2 0.3 0.4 Y MOLE FRACTION OF ISOPROPANOL IN VAPOR
-
I
1193
the usual belief” solvent vapors in air at conasntrations of 1 to 6% are “appreciably” associated. His conclusions were based on ’a gaseous refractivity method. Poht J’D Factors. In order to reduce the uncertainty of ( H ~ ) at Q either end of the oolumn, which arises in taking the tangent of the curve at these positions, “point” values of the jn factor and the Reynolds number were determined for each 1-foot section. The ( H ~ ) used Q for this purpose was obtained by graphical integration over these narrow limits. Likewise, the Schmidt and Reynolds numbers were 4culated as an average over each section, usually an arithmetic averwe being Dermissible. Two different j D f a c t o r s e r e ckculated, aa shown
O5
in Table V for Run IW-28, depending on whether the Schmidt number was evaluated Figure 6. Some Point (HJQValues a t main stream conditions or at film conditions. For the latter an arithmetic average of the Schmidt number at main stream and given in Table I11 indicates that the effectivenessof the lower interface conditions was used. section (0-1) is about nil. The correct average value of ( H ~ ) Q Values of these point factors a t main stream conditions are over the column is 8.06, and the value obtained in the usual manner, based only on end conditions, would be 6.73, which is appreciably in error. Table 111. Separation Data for Run IW-9 In the treatment of the data those sections were eliminated from consideration wherein the end effect was likely to be large. The z Y Au W~)Q 0 0.114 scattering of the data of certain investigators may be attributed 0.002 1 0.116 to the presence of a large proportion of these end effects. 0,018 8.23 Point ( H ~ ) Q Values. Typical values of the point ( H ~ ) Q are 2 0,134 0.039 8.55 given in Table IV. The slope of the composition versus height 3 0.173 0.043 7 84 plot was read from a large scale plot by means of a prism 4 0.216 tangent meter which was considered as having sufficient ac0.039 8 04 6 0.255 curacy (M),Equation 14 was applied and the calculation pro0 037 7 69 oedure is outlined in the table. Some typical results are plotted 6 0.292 in Figures 6 and 7 . Table IV. Point (H& Values for Run IW-28 The expected behavior of a gradual decrease of ( H ~ ) as Q predicted by the j D factors (dotted lines in Figures 6 and 7 ) is not z Y Y* Y dddZ (HL)Q 0.0 0.090 0.412 0.1240 3.38 observed. Rather, in many instances the ( H ~ ) Qreached tl 0.5 0.144 0.385 0.0907 4.24 maximum when these were plotted against the mole fraction of 1.0 0.181 0.362 0.0632 6.74 1.6 0,212 0.339 0.0570 5.94 the vapor. It may be significant that this maximum in many 2.0 0.239 0.316 0.0535 6.91 0.286 0.292 0.0510 5.73 instances corresponds to a vapor composition lying between 0.2 2.5 3.0 0.292 0.269 0.0570 4.72 and 0.3 mole fraction. This would lead to the conclusion that 3.6 0.322 0.243 0.0583 4.17 4.0 0.350 0.213 0.0630 4.11 (&)o is a function of the composition in a manner not accounted 4.6 o m 0.197 0,0486 4.06 0.398 0.179 0.0420 4.26 for by the underlying theory. The work of Storrow ($6) s u p a.0 0.6 0.418 0.164 0.0380 4.30 ports this observation for the systems methanol-water and 6.0 0.436 0.150 0.0341 4.40 ethanol-water. The effect of composition, as distinguished from column height, could not be evaluated because of the limited composition range encountered. A speculative explanation might be that some association of the vapors does occur. Havilicek ( I d ) stated that the specific heat of water 9 vapor near saturation is higher than when t slightly superheated, and he suggests “coagf gregated multiple molecules’’ as an explanation. Eyring (7) presented a method for determining the molecular weights of saturated vapors by an effusion method which he considers as acE curate to 1%. He concludes for the pure vapors TOTAL REFLUX of water, methanol, ethanol, and %propanol that association does not occur. In contrast, Maass (19) cites a method for obtaining molecu& lar weights from vapor density measurements z4 which was considered accurate to 1 to 10,OOO. It was stated that there is definite evidence for association of methanol and ethanol vapors in 0 0,I 0.2 0.3 0.4 0.5 the region immediately above srtturation. LikeY - MOLE FRACTION OF ISOPROPANOL IN VAPOR wise, Craven ( 6 ) has stated that “contrary to Figure 7. Some Point (H’)QValues
...
-
f
i
I
1’
;
INDUSTRIAL AND ENGINEERING CHEMISTRY
1194
Val. 42, No. 6
the average deviations being .t4.5% with maximum deviations of about 10%. The behavior a t partial reflux is seen to be comparable to that a t total reflux. The data of Johnstone and Pigford (16) for the distillation of four systems in a 1.17-inch diameter column were converted to the jD factor basis and are compared with the present values in Figure 10. These data are presented as over-all values based on end conditions. The Reynolds number is essentially that relative to the liquid film and the Schmidt number is for main stream conditions. The agreement 0.001 with the present data is very good. IO00 2000 4000 6000 IC000 20000 4O0006ooOolOOOOO The data of Peck and Wagner (91) inREYNOLDS NUMBER OF GAS PHASE volving three distillation systems in a Figure 8. Point Values of j d Factor 2.07-inch column were not presented to Dlstlllatlon of 2-propanol-wrter show mass transfer behavior in terms of the j D factors. Calculations to this basis were made from the original data and the results are given in Figure 11 as over-all values a t main stream conditions. In all cases the points lie considerably above the Chilton-Colburn line and the previous data. In addition, although the 2propanol-water and methanol-water systems correspond, the acetone-water system is somewhat different. The inlet vapors were in a high state of turbulence, because they were introduced into the bottom of the column through the side entrance of a tee fitting. Suroweic and Furnas (97) distiIled ethanol-water and concluded that an appreciable liquid film resistance waa present, REYNOLDS NUMBER OF GAS PHASE but this was considered to be in error (21). Accordingly, the data as published were Figure 9. Over-All Values of j d Factor recalculated to the jD factor basis for the Dlstlllatlon of 2-propanol-water gas film. Figure 11 shows the data so treated to lie considerablv above the Chilton-Colburn line and quite apart from any of the preceding plotted in Figure 8. A very similar distribution is obtained at investigations. These data were obtained in a column 12 inches film conditions which averages about 10% lower. The solid line indicates the value of f / 2 as determined for the column and the general agreement with the Chilton-Colburn theory is to be noted. Table VI. Over-All Performance Data for Distillation of Over-All Factors. Even with the variation of the point 2-Propanol-Water ( H ~ ) observed, Q the j o factors, when based on integrated averages Reflux Seotiona SubcoolErnof the Reynolds and Schmidt numbers, give consistently good (jD)Q Run ing, C. ployed W e ) @ (Sc)/ ( H t ) Q x 102 results. The over-all performance data, corrected for end IW-4 1 1-6 0.936 0.761 7.24 0.418 0.295 7,100 effects, are given in Tables I1 and VI, and the j~ factors are IW-6 7 0-5 0.794 0.621 8.26 0.325 0.275 16,170 IW-7 4 0-6 0.784 0.625 6.24 0,426 0.366 7,580 plotted in Figure 9. Again, the solid line indicates the ChiltonIW-9 5 1-6 0.748 0.625 8.06 0.319 0.283 18,600 01 1 % -' 4 0-6 0.687 0.558 7.06 0.344 0.299 13,820 Colburn relation to friction and the dotted line is for the experimental values at film conditions. The agreement of the data IW-12 5 0-5 0.610 0.527 8.16 0.296 0.268 20,680 IW-13 1 0-6 0.675 0.563 4.98 0.483 0.428 4,820 at main stream conditions with the Chilton-Colburn line is good, IW-14 5 0-6 0.662 0.557 6.34 0.374 0.333 10,580
Table V. Z 0
z y 0.081 0.090
1
0.172 0.181
2
0.230 0.239
3
0.282
0.292
4
0 341 0.350
5
0.389 0.398
6
0.427 0.436
Point j D Factors for Run IW-28 (Sc)Q
(Sdf
(Ht)O
(jD)Q
(iD)f
(Re)Q 3520
0.880 0.674
4.28
0.00669 0.00561
0.764
0.611
5.92
0.00441 0.00380
4080
0.691 0.572
5.52
0.00442
0.00395
4560
0.633 0.541
4.18
0.00551 0.00495
5060
0.583 0.513
4.09
0.00533 0.00490
5520
0.546 0.492
4.35
0.00479 0.00448
5940
IW-15 IW-16 IW-18 IW-19 IW-20 IW-21 IW-23 IW-24 IW-25 IW-26 IW-27 IW-28 IW-29 IW-30 IW-31 IW-32 IW-33 IW-34 IW-35
7 4 8 12 9 9 0 2 8 5 6 1 1 2 4 3 5 1 6
1-5 0-6 0-6 0-5 1-6 3-6 0-6 0-6 0-5 0-6 1-6
0-6 0-6 3-6 0-5 0-6 2-5 5-6 0-6
0.742 0.654 0,777 0.742 0.863 0.771 0.632 0.650 0.734 0.719 0.659 0.683 0.753 0.735 0.690 0.680 0.684 0.588 0.634
0.616 0.553 0.623 0.601 0.668 0.678 0.538 0.554 0.591 0.591 0.555 0.569 0.600 0.601 0.672 0.573 0.573 0.515 0.540
8.52 6.53 9.02 7.45 8.24 8.08 7.16 7.08 7.68 8.12 2.60 4.62 6.33 7.14 7.74 8.30 8.83 9.30 7.73
0,300 0.360 0.293 0.343 0,343 0,348 0.321 0.331 0.331 0.309 0.908 0.524 0.405 0.356 0.315 0.291 0,274 0,236 0.293
0.265 0.321 0.253 0.299 0.289 0.298 0.288 0.297 0.286 0.270 0,810 0.464 0.351 0.312 0.278 0.260 0.244 0.216 0.268
28,140 12,340 21,550 25,960 18900 17:820 14,380 12,440 20,590 21,030 1,790 4,780 7,910 8,100 25,800 25,080 46,100 72,150 35,740
June
19s
I N D U S T R I A L AND E N G I N E E R I N G C H E M I S T R Y
in diameter and 11 feet high.
1195
Calming
of the inlet vapor stream was not proa
P
vided, because the column was situated directly over the reboiler. The differences of these last two groups of data may be explained, in part a t least, by consideration of end effects and of turbulence in the enteringgas phase. In both instances calming of the gas phase was not provided and the turbulence would therefore be greater than for normal flow. This v) 0 DATA OF JOHNSTONE AN0 PIWORD, DI8TILLATIOW I T TOTAL RLfLUX would result in larger friction factors and correlations higher than for I 1 Ill 0.001 “normal.” The actual friction factors 1000 2000 4000 6000 10000 20000 4oooO WOO0 KKK)o are not available for these columns and REYNOLDS NUMBER OF QAS PHASE a comparison of the Chilton-Colburn Figure 10. Over-Ail I d Factors for several ~nvestigatorr theory under these conditions is not possible. In addition, both of these investigations employed columns having process is similar to that for distillation, except in the region relatively low ratios of column length to diameter. This would for Reynolds numbers below 6000 where the results are inresult in a greater proportion of end effects and in the greater conclusive. scattering of the data observed. For the Suroweic and Furnas data, most runa were for very low compositions in the liquid phase The vaporization data agree in general with the observations a t the bottom of the CofUmn. The o p e r a h line closely aPof Barnet and Kobe, and of Chilton and Colburn, both of which proaches the equilibrium line in this region and introduces the poswere for the evaporation of water into air. They do not, howsibility of a large error. ever, closely check the vaporization data of Gilliland and Sherwood. The data of the latter, when calculated as j~ factors and VAPORIZATION AND GAS ABSORPTION corrected for liquid surface velocities, lie about 10% above the Chilton-Colburn line for water and about 25% high for the Data on the vaporization of toluene, 2-propanol, and water were obtained using the same column as for distillation. As with previous investigations (1,fZ) it was considered that Table VII. Performance Data for Vaporization of Water into Air the driving force could be represented by a log mean partial pressure difference, Air Liquid Air
3
A
TemDera-
W
(15)
The j D factors were obtained by applying Equation 2, using the gas mass velocity computed a t the average of air stream conditions a t the top and bottom of the column. The Schmidt numbers employed are given in Table I X and are the accepted values (11 ). For each component the liquid flow rate was maintained a t a nearly constant value for that series of determinations. Reynolds numbers of the gas phase were corrected for liquid surface velocities as follows: water 1.5 feet per second, 2propanol 1.0 foot per second, toluene 1.7 feet per second, and glycerol solutions 0.9 foot per second. For density and viscosity of the air stream, the concentration of diffusing component was neglected and these properties were evaluated a t the average water humidity. The significant data for vaporization are given in Tables VI1 and VI11 for every other run, and the results are plotted in Figures 12 and 13. It is a t once apparent that the jn factors closely approach the values of f/2 for the column, and that the v a p o r i z a t i o n
Temoers-
W-2 W-4 W-6 W-8 W-10 W-12 W-14 W-16 W-18 W-20 W-22 W-24 W-26 W-28 W-30 W-32 W-34 W-36 W-38 W-40 W-42 W-44 W-46 W-48 W-50 W-52 W-54 W.56 W-58 W-60 W-62 W-64 W-66 W-68 W-70
33.0 28.8 28.4 29.1 29.9 29.1 28.8 29.1 32.6 33.8 34.1 27.0 28.8 30.9 31.3 32.7 30.3 31.8 28.2 35.1 35.2 32.2 26.4 34.2 33.0 32.9 33.0 29.5 31.3 32.6 33.6 29.5 41.5 42.5 40.2
29.0 23.9 25.0 26.4 26.8 27.2 27.8 27.5 28.1 28.6 29.2 28.1 28.0 28.3 27.5 24.4 23.3 24.5 27.2 27.2 25.3 25.3 22.5 27.5 26.4 25.3 25.0 27.2 27.5 28.1 44.7 41.7 45.3 44.1 44.2
27.1 18.1 22.3 23.5 24.1 25.2 26.2 26.3 21.4 21.7 20.8 25.9 24.5 23.2 22.3 18.6 17.2 17.7 19.4 20.8 20.2 18.6 18.0 21.4 20.8 19.9 18.7 21.9 22.3 21.4 39.6 35.2 45.9 43.0 40.6
0-1 G-2 0-3 G-4 G-5 0-6 G-7 G-8
53.9 52.8 51.4 50.0 49.1 48.6 48.1 48.0
52.4 52.3 51.6 51.2 50.5 49.3 49.8 49.3
44.8 42.6 4L.0 39.4 38.2 37.3 36.4 35.6
29.5 28 6 25:O 26.4 26.8 27.2 27.8 27.5 26.9 27.5 27.8 28.1 28.0 28.3 27.5 21.7 20.6 22.0 24.4 25.6 25.3 23.6 20.6 24.7 23.6 22.5 22.2 24.4 27.5 26.9 55.8 57.0 56.5 56.1 57.2
Humiditv.
0.0104 0 0046 0:0039 0,0044 0.0046 0.0037 0.0041 0.0046 0.0058 0.0059 0.0058 0.0060 0.0056 0 0054 0.0043 0,0056 0.0046 0.0039 0.0051 0.0061 0 0057 0,0044 0,0044 0.0079 0.0069 0.0060 0.0054 0,0091 0.0043 0.0058 0.0128 0.0126 0.0128 0.0120 0.0121 I
I
0.0206 0 0 06 0:0t38 0.0155 0.0161 0.0157 0.0153 0.0155 0.0147 0.0151 0.0145 0.0174 0.0169 0.0167 0.0166
0.0113 0.0103 0.0109 0.0122 0.0139 0.0136 0.0116 0.0110 0.0139 0.0128 0.0124 0.0117 0.0149 0.0151 0.0149 0.0556 0.0497 0.0655 0.0624 0.0567
34.0 33.8 27.3 24.7 21.1 18.1 13.7 11.4 66.9 71.5 86.5 17.9 25.1 37.2 40.4 91.9 91.8 85.0 97.7 102.3 105.6 102.7 49.7 84.8 84.6 85.7 84.5 83.9 40.4 66.8 58.9 76.4 22.4 34.3 45.2
0.454 0.632 2.56 2.89 1.230 1.830 2.09
0.421 0.398 0.384 0.402 0.413 0.375 0.324 0.328 0.341 0.338 0.348 0.388 0.885 0.388 0.397 0.300 0.316 0.336 0.299 0.330 0.340 0.316 0.364 0.296 0.286 0.333 0,328 0.328 0.372 0.353 0.340 0.321 0.366 0.384 0,330
8,400 8.850 7,320 6,570 5,910 5,170 4,210 3,670 20,400 17,300 20,700 5,140 6,780 9,530 11,100 23,000 21,800 20,400 23,200 24,200 25,000 24,300 12,400 20,200 20,400 20,500 20,100 19,900 10,300 16,400 15,300 19.400 6,580 9,260 11,800
0.709 0.874 1.004 1.084 1.194 1.223 1.356 1.383
0.346 0.358 0.849 0.316 0.293 0.293 0.272 0,246
4,450 5,690 6,840 8,140 9,580 10,500 12,010 13,100
0.357 0.214 0,283 0.275 0.252 0.223 0.161 0.129 0.618 0.684 0.782 0.213 0.293 0.436 0.474 0.570 0.550 0.624 0.711 0.831 0.871 0.768 0.344 0 536 0.524 0.568 0.553 I
0.506
VAPORIZA,TION ERCIMG L Y C OL ~ RSOLLWIONLI
55.6 56.2 56.7 57.2 58.0 56.4 57.1 57.6
0.0136 0.0137 0.0139 0.0141 0.0138 0.0135 0.0132 0.0134
0.0548 0.0521 0.0500 0.0465 0.0440 0.0415 0.0400 0.0384
17.5 23.1 28.2 34.0 40.2 44.3 51.2 56.1
INDUSTRIAL AND ENGINEERING CHEMISTRY
1196
1000
2000
4000 6000 10000 20000 40000 Woo0 100000 REYNOLDS NUMBER OF GAS PHASE
Figure 11. j d Factors Calculated from Data Appearing in Literature
Vol. 42, No. 6
uted to the presence of a small liquid film resistance, inasmuch as the liquid Reynolds number was of the order of 60. This is in the region where the wave motion is not completely established and hence some liquid film resistance is conceivable. Johnstone and Pigford reported the absorption behavior of two systems. One of these checks the Chilton-Colburn line closely, but the other system was considered to be in error. It was also reported (16) that the absorption of sulfur dioxide from air-gas mixtures with sodium hydroxide solutions gave values slightly lower than those expected from the Chilton-Colburn relation.
Distillation at total reflux EDDY VISCOSITY AND EDDY DIFFUSIVITY
The present vaporization and distillation data were compared with the a ( H t ) ~ values calculated from Equation 11. In all cases the predicted values of a ( H t ) ~ were 15 to 20% lower than those actually observed. These values were based on the only experimental value of alpha available, which was reported (&5) for the transfer of water between the two opposite faces of a narrow rectangular duct. I t might be expected that alpha, which relates eddy diffusivity to eddy viscosity and is defined by Equation 12, would have a different value for transfer in a wettedwall column. Eddy diffusion is essen1000 2000 4000 boo0 loo00 20000 4oooo60000KXKWX) tially a mixing process which arises from REYNOLDS NUMBER OF GAS PHASE the turbulent condition of flow. For the Figure 12. j d Factors for Vaporization of Water into Air rectangular duct, the mass transfer process has an effective component in only one direction, whereas the friction loss involves 0 009 components of mixing for all three co,0.008 ordinates. The value of alpha reported .- 0.007 for these conditions was 1.6. 0.006 In contrast, mass transfer in a wetted?0 0005 wall column has components in two di8 0 004 rections and involves the total wall area. It should therefore more nearly correspond 0003 to the process for the loss of momentum, u) z and it is to be expected that alpha would a have a different and unique value for a 0002 Ithis transfer pattern. In fact, it is v) stated (16) that if the processes involvv) a ing the transfer of both mass and 5 0 001 momentum were physically identical, then 1000 2000 4000 6000 10000 20000 40000 60000 100000 E and ap would be the same, and alpha REYNOLDS NUMBER OF GAS PHASE wou1.l be unity. Figure 13. j d Factors for Vaporization of 2-Propanol and Toluene into Air Based on these considerations, values of alpha were calculated by inserting the experimental values of a ( H t ) ~ ,(f), and (SC)Qin Equation 11. The results are presented in Table IX organic liquids. The friction factors for this column were refor the present and other data. A comparable value of alpha is ported as being a few per cent above the expected values, but this obtained for the various systems and processes, and a weighted is not sufficient to account for highjn factors. average would be 1.15. A limited amount of data was obtained for the desorption of water from glycerol solutions of approximately 48 weight % ’ CONCLUSIONS concentration. The partial pressures of water over the glycerol For the particular case of mass transfer in a wetted-wall solutions (fa,17) were interpolated for temperature by the use column the processes involving unidirectional diffusion and of a Duhring plot. The results are reported in Table VII, and, equimolar counter transfer are analogous to the extent permitted when plotted, would fall about 15% below the line representing by Equations 4 and 5 if the physical properties are evaluated at the value of f/2 for the column. This difference may be attrib-
2
INDUSTRIAL AND ENGINEERING CHEMISTRY
June 1950
Table VI I t . Performanoe Data for Vaporlzatiion of 2-Propanol and Toluenie into Air Air
Temperature, C. Bottom Top
Run
Liquid Temperature, O C.
Bottom
Re nolds VaDOri~i~ of zation Gas $0 Rate Rate Phase Top Lb./H& ' Lb./H&r X 103
do.
[-SO
27.9 30.0 32.5 35.8 30.4 28.0 23.6 26.6 25.4 28.0 31.1 28.6 32.4 34.0 34.5 29.8 29.6 28.8 30.0 31.1 27.9 23.8 21.6 24.1 22.4
28.3 27.8 28.3 27.8 26.4 23.9 22.5 23.6 22.6 24.6 24.2 23.6 26.7 26.7 25.3 24.4 29.4 26.7 28.1 26.9 27.2 25.8 23.3 24.9 22.2
24.5 21.1 20.3 18.8 18.2 16.4 18.0 18.0 16.8 17.4 14.8 13.8 16.7 16.9 17.2 15.2 21.3 18.3 18.7 17.0 21.3 21.5 19.3 20.4 16.4
28.3 27.8 28.3 27.6 26.4 23.9 22.5 23.6 22.6 24.5 24.2 23.6 26.7 26.7 25.3 24.4 29.4 26.7 28.1 26.9 27.2 25.8 23.3 24.9 22.2
T-2 "-4 T-6 T-8 T-10 "-12 T-14 "-16 "-18 T-20 T-22 T-24 T-26 T-28 T-30 T-32 T-34 T-36 T-38 T-40
33.5 30.6 31.2 26.2 26.6 25.3 28.9 27.2 30.9 28.8 24.8 25.1 25.2 26.2 28.8 27.0 29.8 33.1 28.6 24.8
28.1 22.8 26.1 22.5 23.1 20.6 23.1 22.5 22.8 23.1 21.7 21.7 24.7 25.3 27.1 26.7 26.9 26.7 23.1 21.7
18.6 16.2 19.4 15.5 18.1 16.3 16.2 17.5 17.0 18.0 17.0 17.0 21.6 22.2 21.3 22.2 18.5 19.3 18.1 17.0
28.1 22.6 26.1 22.5 23.1 20.6 23.1 22.5 22.8 23.1 21.7 21.7 24.7 26.3 '27.1 26.7 26.9 26.7 23.1 21.7
1-2
1-4
1-6 1-8 1-10 1-12 1-14 1-18
1-18
1-20 1-22 1-24 1-28 1-28 1-80 1-32 1-84 1-36
1-38
1-40
1-42 1-44 1-46 1-48
11.07 19.61 25.2 29.9 34.2 38.4 14.30 20.9 24.1 26.7 62.7
77.7
58.2 48.3 82.8 48.1 18.28 25.7 31.2 39.9 12.63 10.93 11.20 10.83 19.47
0.625 0.928 1.366 1.376 1,598 1.462 0.484 0.817 0.864 1.185 2.13 2.51 2.25 2.00 3.04 1.767 1.064 1.264 1.525 1.665 0.584 0.458 0.402 0.413 0.657
0.392 0.358 0.426 0.378 0.418 0.393 0.345 0.391 0.386 0.448 0.351 0.350 0.341 0.368 0.326 0.361 0.445 0.439 0.400 0.364 0.435 0.338 0.337 0.330 0.364
3,280 5,270 6,670 7,660 8,670 9 050 4,050 5,600 6,330 6,950 15,300 18 500 14'200 11'900 19:900 11900 4'970 6:720 8 020 9:980 3,660 3,240 3 320 3:240 5,205
2.28 2.63 2.12 2.44 0.748 2.11 2.52 1.652 2.37 1.460 1.776 0.570 0.680 0.608 1.187 0.532 3.36 2.50 1.598 1.687
0.397 0.358 0.376 0.302 0.413 0.369 0.318 0.391 0.363 0.387 0.430 0.365 0.381 0.374 0.388 0.393 0.339 0.373 0.373 0.373
12 100 18'600 12'500 2O:SOO 10,800 16,300 19,700 11 400 17:000 9,970 11 700 4:410 4,810 4 430 7:060 3,780 20,600 14 100 10:800 11,700
1197
The d ~ e r e n c e sbetween various investigations involving distillation in wetted-wall columns may be attributed, in most instances, to end effects and to the condition of turbulence in the entering gas stream. The relation between eddy viscosity and eddy diffusivity a p pears to be unique for ?,he type of flow involved in a wetted-wall column. A value of a = 1.15 would enable the Sheiwoodvon K h & n equation satisfactorily to predict mass transfer behavior for the present and certain other data. ACKNOWLEDGMENT
The authors wish to thank A. J. Flynn for obtaining the data on vaporization. NOMENCLATURE
a
A B
interfacial transfer area per unit volume, (sq. feet)/ (cu. foot) = interfacial ares for mass transfer, sq. feet = effective film thickness for mass transfer, feet = specific heat, (B.t.u.)/(lb.)(O F.)
=
TOLUENE 47.2 75.6 48.8 83.6 41.4 65.1 79.9 43.8 68.4 37.8 44.8 13.78 15.52 13.82 25.3 11.08 84.2 56.2 41.4 44.8
main stream conditions. Performance may be satisfactorily predicted by the use of the jD factors, providing that the correct turbulence of the gas phase is known or may be evaluated. For distillation systems there is indicated an effect of composition on the mass transfer process which is not accounted for by the usual mass transfer expressions. However, it appears that the effect of changing composition on mass transfer coefficients may be ignored when calculations are based on terminal conditions alone according to usual procedures. ~~
Table IX. Values of a Computed from Equation 11 No. of Range of Date Average, Schmidt Re nolds
System and Investigator 2-Propanol-water Water-air 2-Propanol-air Toluene-air
Points
(I!
No.
P R ~ B ~DATA NT 27 1.11 0.60-0.86 0.60 62 1.16 1.60 32 1.00 1.86 29 1.04
JOHN~TONE AND P I Q S O ~ 0.65 Toluene-Bbhylsne dichloride 31 1.15 0.54 Ethanol-water 17 1.18 0.72 Acetone-chloroform 5 1.45 0.65 Benzene-toluene 13 1.10 3 1.51 0.69 Ethylene dichloride-benzene Water-sir
BARNETAND KOBE 29 1.24
0.60
(&)a
zn JD
k
= height of a transfer unit based on the gas film, feet = j factor for heat transfer, dimensionless = j factor for mass transfer, dimensionless = thermal conductivity, (B.t.u.)(feet)/(hour)(sq.
foot)
( " F.)
mass transfer coefficient, (lb. moles)/(hour)(sq. foot) (atm.) L = length of transfer section, feet M = mean molecular wei ht of gas phase, (lb.)/(lb, mole) M L = molecular weight oftiquid, (]be)/ Ib. mole) (Nt)o = the number of transfer units base on gas film p , pi = partial pressure of diffusing component in the gas phase for main stream and interface conditions, atmospheres Apm = log mean partial pressure driving force across gas film, atmospheres pol = mean partial pressure of nondiffusing component in the gas film, atmospherea P = total pressure, atmospheres R = gas constant, (cu. feet)(atm.)/(lb. mole)( O K.) (Re)@= Reynolds number of gas phase, dimensionless (SC)O,(Sc)* (SC)~ = Schmidt number, (w/&), a t main stream, interface, and mean film conditions, dimensienleea 7' = temperature, OK. V = average gas phase velocity relative to the liquid surface, feet/second w = rate of mass transfer, Ib./hour y, yc, y * = mole fraction of the more volatile component in the gas hase at main stream, interface and equilibrium con&ions 2 = height of column measured from the bottom, feet a = proportionality constant for eddy diffusion and viscosity e = eddy vlscosity, (Ib.)/(foot)(sec.) p = molecular viscosity (lb.)/(foot)(sec.) p = density, (Ib,)/(cu. i m t ) ko
=
6
608.
LITERATURE CITED 4000-72000 6'000-25'000 6:000-20:000 6,000-20,000 7 000-26 000 4'000-12'000 10:MH)-241000 15,000 13,000-23.000 2,200-18,300
(1) Bsrnet and Kobe, IND. ENG.CHEM.,33,376 (1941). (2) Brunjes and Bogatt, Ibid., 35,255 (1943). (3) Chilton and Colburn, Ibid., 26,1183(1934)., (4)Ibid., 27,255 (1935). (5) Colburn, Ibid., 22,967(1930). (6) Craven, Proc. Phus. Soc. (London), 57, 97 (1945). (7) Eyring, J. Am. Chon. SOC.,50,2398 (1928). ENG.CHEM.,33,885 (1941). (8) Friedmand and Miller, IND. (9) Gamson, Thodos, and Hougen, Tmm. Am. Inst. Chem. Enpra., 39, 10 (1943). (10) Gilliland, IND. ENG.CHEM.,30, 506 (1938). (11) Gilliland and Sherwood, Ibid., 26 516 (1934).
1198
INDUSTRIAL A N D ENGINEERING CHEMISTRY
(12) Havilicek, Engineming, 129,1 (1930). (13) International Critical Tables, Vol. 111, pp. 291, 293, 310,311, New York, McGraw-Hill Book Co., 1928. (14) Jackson, h.1. L., Ph.D. thesis, University of Minneaota, 1948. (15) Johnstone and Pigford, Trans. Am. Inst. Chem. Engrs., 38, 25 (1942). (16) Kalinske and Pien, IND.END.CHEM.,36,220(1944). (17) Landolt-Bornstein, “Physikalisch-Chernische Tabellen,” Eg IIb, p. 1338, 1931; Suppl. 111, Pt. 1, p. 186, 1937; Ann Arbor, Mich., J. W. Edwards. (18) Lange, “Handbook of Chemistry,” 6th ed., pp. 933, 1590, Sandusky,Ohio, Handbook Publishers, 1944. (19) Maass et al., Can. J. Research, 2, 388 (1930); 4, 283 (1931); 5, 436,442(1931); 6,428(1932). (20) Othrner, IND.ENC.CHEM.,32,841 (1940). (21) Peck and Wagner, Trans. Am. Inst. Chem. Engrs., 41, 737 (1 945).
Vol. 42, No. 6
(22) Perry, “Chemical Engineer’s Handbook,” 2nd ed., pp. 308, 613,792,New York, McGraw-Hill Book Co., 1941. (23) Richards and Room, Science, 71,290 (1930). (24) Sherwood chapter in “Fluid Mechanics and Statistical Methode
in Engineering,” Bicentennial Conference, Philadelphia, University of Pennsylvania Press, 1941. (25) Sherwood and Woertz, IND.ENQ.CHEM.,31, 1035 (1939). (26) Storrow, J . SOC.Chem. Id., 66,41,73 (1937). (27) Suroweic and Furnas, Trans. Am. Inat. Chem. Engrs., 38, 86 11842). -_,. I__
(28) Von K&rm&n, Ibid., 61,705 (1939). (29) Walker, Lewis, McAdams, and Gilliland, “Principles of Chemical Engineering,’’ 3rd ed., p. 443, New York, McGraw-Hill Book Co., 1937. (30) Westhaver, IND. ENC.CHEM.,34,126(1942). RECEIVED November 30, 1949.
Fractional 0.
F. ASSELIN’ UNIVERSITY
AND
T h e effect of returning reflux in solvent extraction processes involving four or five components was lnvestlgated. Two of these were t h e essentially immiscible solvents, water and n-amyl alcohol, and two of the others were the compounds in a mixture to be separated. When a fifth component was used, it served as a separating agent between the other two solutes. The effect on the fractionation achieved caused by varying the relative amounts of the two solvents, t h e total concentration of the two compounds in the feed, and the composition of t h e feed on a solvent-free basis was also observed using a five-stage countercurrent extractor. A stagewise graphical method of calculation i s presented which permits t h e computation of the results of such extraction processes when reflux is employed. The position of a so-called “reflux line” relative t o the equilibrium curve enables one t o estimate very quickly the course which the extraction will follow. Calculations for complete extraction units are presented which indicate t h a t the equilibrium relationships of t h e system must meet certain conditions, if reflux Is t o be very effective. Its use is of greatest advantage with systems employing a flfth component as a separating agent.
A
FRACTIONAL liquid extraction process is one in which an immiscible liquid solvent preferentially extracts one of two or more solutes from the liquid in which they are dissolved. One of the better known commercial examples of this type of process is the Duo-Sol method for refining lubricating oils (6). The purification of certain of the less common metals and the production of iron-free alumina by fractional solvent extraction have also been described (6,IO). Commonly only a few extraction stages are used, but when two highly purified products are desired, a larger number will be required. A large number of stages may be justified in the fine chemicals industry for the separation of valuable materials which are difficult or impossible to separate by other means. A case in point is the separation of thorium from the rare earth elements by fractional solvent extraction (2). The number of stages required in a difficult separation should be kept to a minimum. The most commonly used method of decreasing the number of equilibrium contacts required in distillation consists in returning reflux. Saal and van Dyck (12) were the first to discuss in detail the close analogy betaeen dis1 Preaent
E. W. C O M I N G S
OF ILLINOIS. URBANA. ILL.
address, Humble Oil & ReBning Company, Baytown, Tex.
tillation and extraction and the implications of returning reflux. Their paper was concerned only with threecomponent liquid systems and is not applicable, except in its broadest principles, to the four-component systems encountered in the fractionation of two solutes by means of two immiscible solvents. Scheibel (13) discusses fractionations which employ such four-component systems but makes no mention of the use of reflux. The present investigation shows the effects of returning reflux and presents a method of calculating the course of the extraction when reflux is utilized. EQUIPMENT AND OPERATION
A five-stage extraction system was used in reference to a packed column because it provided a more de&ite number of equilibrium contacts and permitted sampling at definite, intermediate stages. The latter is important when the equipment is used to follow the course of extraction in a system for which complete equilibrium data are not available. Each stage consisted of a ear ump, a mixing column 1 inch in diameter b 2 feet, paeke8 wit{ 0.125-inch glaas beads, and a settling chamger similar in design and construction to that used by Knox et al. (8). The settling chambers were made from 1liter Florence flasks and were provided with a fixed solvent overflow arm and an adjustable arm with rubber tube connections to control the level of the liquid interface. Piping was a/a-inch streamline copper pipe and connections to glms were made with rubber tubing. The provision for reflux consisted of a mechanical reflux splitter, a spray-type extraction column 1 inch in diameter b 5 feet and a glass evaporator similar to Kemmerer’s desi n (7‘f The evaporator was equipped with liquid level control fevices to maintain conatancy of operation, Figure 1 shows an over-all flow diagram of the apparatus. Aqueous feed enters the extractor at one end, proceeds countercurrently to the alcohol through five extraction stagw, and is then split into two streams, one of which is withdrawn as purified product and the other is sent to the evaporator to provide reflux. Thick liquor from the evaporator I stripped of part of its solute content by fresh solvent in the spray column. The aqueous raffinate from the column is recycled to the evaporator and the alcohol extract bearin the reflux is sent to. the extractor. All the solute which enters t f e evaporator IS ultimately transferred to the alcohol phase and returned to the extractor as re flux. The concentration of each solute in the evaporator will adjust itself so that this will be accomplished, irrespective of the efficiency of the spray column or the rate of thick liquor recirculation. Thus, the composition of solutes on a solvent-free basis is the same in the aqueous stream, leaving, and in the alcohol, entering, at one end of the extractor.
