ENGINEERING. DESIGN, AND PROCESS DEVELOPMENT cooperation made possible this research, are gratefully acknowledged.
(0)
Harvey, E. S . ,Whiteley. A. 1-1..anti associates. Ibid., 24, 23-~34 (1944).
( 1 0)
Knapp, R. T., and Hollander, .A,, Truns. Am. Soc. M e c h . Engrs.. 70, 419- 31 (1948).
literature Cited ( I ) Briggs, H., Johnson, J. B., Xason, W. P., J . A c o u s t . Soc. A m . , 19, 664-7 (1947). (2) Fox, F. E., and Griffing, V., Ibid., 21, 352-9 (1949). (3) Fry, F. J., Reo. Sei. Insir., 21, 940 (1950). (4) Fry, W.J., Tucker, D., and associates, J . Acozrst. SOC.Am.. 23, 3 W - 8(1981). (5) Fry, W.J., Wulff, 5'.J., and associates, Ibid.. 22,887-78 (1950). (13) Grabar, P., htti convegno internazionale di ultracustica, Roma, 14-17 Giugno, 1950, pp. 4 8 6 4 7 , iiicola Zanichelli. Bologna, 1951. (7) Harvey, E. N.,Bid. Bull., 59, 306-25 (1930). (Q) Harvey, E, N.,Barnes, D. K.. and associates, J . CelZciZar Comp. P h g s i d . , 24, 1-22 (1944).
(11) Nariiiesco, s., Compt. wntl.. 201, 1187-9 (1935). (12) Mark, H., J . Acovsl. SOC.Anier.. 16. 183-7 (1945). (13) Xeppiras, E. A., and Koltingk. R. E., Proc. Phys.hoe. ( L o n d o n ) . 64B,1032-8 (1951). ( I 4) Kumachi, F., Ordnance liescart~hLaboratory Rept. NORD 7958-27, Aug. 1, 1946. (15) Richards. W. T., Rms. M o d . Phyb., 11, 3&M (1939). (16) Srhmitt. F. O., and Uhlemeyer. B.. Proc. SOC.Ezptl. Biol. X c d . , 27, 826-8 (1930). (17) Khitney, R. h1cL.. and Russell, Lillian A., Food Rescnycit, 16, 205-15 (1981).
RECEIT-ED for review October 15, 1932
.\CCY.PTED
,?, 1:15,$.
Presented ae part of t h e Symposium o n llisinfection and Sanitation befort h e Division of Water. Sewage. and Sanitation Chemistry at thc 122nd 1Icetiiig of the AIERICANCHEMICAL Socn:ru, Atlantic C i t y K . .J.
Distillation in Packed Columns FUMITAKE YOSHIDA, TETSUSHI KOYANAGI, TAKASHI KATAYAMA', AND HARUO SASA12 Department of Chemical Engineering, Kyoto University, Kyoto, Japan
ISTILLATIOS in packed colunins has been the subject of a number of papers. Hovever, most of t,liemhave reported t,he 1I.E.T.P. of small laboratory fractionating columns operated at' total reflux. Relatively € e n investigators have studied packed distillation columns lrom the vien.point of mass transfer. F'urn:cs aiid Taylor ( 4 ) did a eort of pioneer work in this field. They studied the rectification of et,hyl alcohol-n-ater in the enriching section of a packed column 12 inches in diameter at, imious reflux ratios, and they concluded that the major resirtmce to mass transfer was in the liquid film. The corre1:itiou t h p y 01)tairied was {lj
Duncan et al. (aj used a 5-inch cdiimn a8 :in enriching section and correlated HOG values for mcthanol-water and trichloroethylene-toluene systems with the vapor-liquid rat,io and the integral average of the slope of tbc equilibrium curve. Deed et al. ( 2 ) compared the HOL values for carbon dioxide desorption from water with those for isopropyl alcohol-nater rectification in an enriching section, using a G-inch column. Uchida et al. ( 3 )reported the data for methaIiol-n.ater rectification obt,ained at total reflux with a 10-inch column. Bliss et al. ( 1 ) studied the effect of reduced pressures on the rectification of o-dichlorobcnxrne-o-diethylbenzene a t total reflux in a 3-inch column, and conrluded that liquid-film s controlling in of thct marked effect of temper A survey of these papers shoa-s that a general correlation or even a common type of correlation hap not yet been obtained lor packed column distillation and indicates that the factors involved are not so sinq~leas in absorption or desorption. For a given packing, the factors that seem to affect the vapor-film mass , velocity, density, viscosity, and diftransfer coefficient, k ~ are fusivity of the vapor; the factors that are likely to affect thc liquid-film coefficient, k ~ are , velocity, density, vise diffusivity of the liquid. The liquid-vapor interfacial umnbly affected by the type and size of packings, velocity, osity, and surface tension of the liquid, and possibly by vapo? velocity. The importance of the design of the column is shown by the extensive aork of Ryan (B), mho etudied thc effects of 1
2
Present address, Kanazawa University, Kanazavra, Japan. Present address, Toa Gosei Kaaaku Kogyo K . K . , Nagoya, Japan
1756
throughput, packed height, designs 01' liquid distributor, rind packing support on the H.E.T.P. of n 12-inch column operatod a t tot,al reflux, using several kinds oT packings. Besides tliesc factors, the average slope of the vapor-liquid equilibrium c u r v c is considered to be involved in t h r ovcr-a11 coefficients, Rr;a and K L ~or, in the over-all H.T.U.'s-- Le., HOCand H ~ L . Almost JTithout exception, previous experiments wcrr performed in enriching sections or a t tota! reflux. In enriching operation, liquid rate can ncver exceed vapor rate-in other i ~ o r d vapor-liquid ~, ratio is ah-a?-sgrewt,ei th:m unity. Fiirtliw Iiiore, i i i total reflux runs. when vapor and liquid ratm arc cqu:il, the cffects of vapor arid liquid rates (minot be separated. It i. not aurprking that a cwrclat,ion obtained a t total reflux is not applicablr to the general case of varying reflux ratio. Tht, need for data a t various vapor-liquid ratios, especially for stripping operntion, is grrxt. The liquid rates usually met in packed tlistillntion columns are so small that the possibility of liquid c,liannding due to maitlietrihution has to kc considered. Experiments Are Designed to Obtain Very General Correlations
It SccinP hardly posd)le to vary all of these factors in a singlc piwc of cquipnient and with one or two systems. ETon.c!v~~, t,lic~rupcikents ere planned to obtain conclusions th:it, arp a i genri,iil a.n possible. The column T ~ F 15 : cm. in inside diamcto :inti I V ~ Rpacaked with l5-nnn. ceramic! ltaschig rings. Benzcnctoluene vas chosen as the test niisturr because it is an ideal sy&m \\-hose vapor-liquid equilibrium d a h nre well known. Physical propei,tics such as viscosit,y, diffusivity, surface tension, and density do not vary greatly with composition. The relutivc volatility is large, whieh iiialres it possible to vary thc liquidvapor latio--i.e., the slopc~of thc operating line-ovcr a \ r i c h rangr. Ituns m r e made in bvt,li enriching and stripping sections anti a t t,otal reflux. The vapor-liquid ratio was varied from 0.56 to 1.3. The vapor rate raiigcd from 200 to 1300 pounds pcr hour pcr square foot of gross cross section of the column; liquid ratt. r:inged from 120 t o 1500 pourids per (hour) (aquare foot). Column. The apparatu 0jr.n in Figure I. Copper was usrd :L* the material of eoristru The equipment was operated a i d system. It was RO devigricd that the columti could s ( ~ r v either c as an enriching section OT as a stripping Jection or at
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
Vol. 46, No. 9
ENGINEERING, DESIGN, AND PROCESS DEVELOPMENT TOP CONDENSER
THERMOMETER VENT
Figure 1.
V
Apparatus
total reflux. The rate of vapor rising from the electrically heated 10-gallon reboiler to the column bottom was controlled by means of variable autotransformers. The column, 15 em. in inside diameter. was packed vith lz-mm. ceramic Raschig rings to a depth of 54 cm. in most runs. The main reason that such a short packed section waa used was to avoid inaccuracy in the values of the number of transfer units due to "pinching" near the ends of operating lines. The packing was supported by a wire netting of 10-mm. mesh. A triple-tube type of reflux condenser was directly attached to the column top The empty top section of the column, about 1.5 feet high, acted as a wetted-wall type of liquid preheater. The reflux from the top condenser, together with the liquid feed returning from the reboiler in the case of stripping operation, was preheated to its boiling point by the rising vapor before i t reached the reflux trough, where the liquid temperature was taken by a thermometer. The indicated temperature mas within 1" C. of the boiling point as determined by analysis. The preheating of liquid seemed important because true rectification-i.e., equimolal counterdiffusion-would not be performed near the top of the packed section if the liquid temperature was below the boiling point. From the reflux trough the liquid flowed into a round, guttertype liquid distributor with four slot weirs and to the top of the packing in four fine continuous streams. The distributor could be leveled by means of screws, and uniform distribution of liquid was ensured by observation through the sight glasses. The reflux rate was controlled by carefully adjusting the supply of cooling water to the top condenser from a constant head tank. In the case of enriching operation, the residual vapor from the top condenser was condensed as distillate in the multitubular condenser and was returned to the reboiler through a small receiver. Since the receiver had an open vent, operation was carried out substantially a t atmospheric pressure. In total reflux and stripping runs, the total vapor from the column was condensed in the top condenser. In addition, in the case of stripping operation, liquid was returned from the reboiler to the top of the wettedSeptember 1954
wall section through the suction tank, gear pump, constant head tank with an overflow pipe, and a small receiver. Vapor temperatures were measured in the vapor inlet to the column bottom, in the vapor space above the liquid distributor, and in the vapor exit from the top condenser. For the purpose of attaining substantially adiabatic operation, the entire column was enclosed in an electrically heated air jacket, which consisted of two sections. The air temperatures in the upper and lower sections were controlled to approximate the vapor temperatures a t the top and bottom of the column, respectively. Procedure. I t required about 3 hours before steady conditions were attained, as were shown by the constant readings of the thermometers. Flow rates of the liquid leaving the column bottom, the feed entering the top in stripping runs, or of the distiilate in the case of enriching operation were determined by directly weighing the liquid withdrawn froin by-pass cocks for a short period, usually 20 to 40 seconds. This procedure obviously disturbed steady conditions, but tests showed that, if the cocks were opened in proper order, the disturbance lagged somewhat and was negligible in the short period required for the measurements. Immediately after flow measurement, a liquid sample for analysis was taken from the reflux trough. Samples of the bottom liquid, distillate, or of the feed to the top were taken from the liquids withdrawn for flow rate measurements. Analyses. Ana,lysesof the samples were made by the observation of boiling points. This was done by gently boiling about 25 ml. of sample in a 100-ml. flask equipped with a reflux condenser and a thermometer, which was graduated to 0.1" C. and installed just above the liquid level. To ensure reproducibility, two apparatus of t,he same type were used for the same sample. The readings of the two thermometers alvays agreed within 0.1" C. Benzene and toluene, manufactured by Hirohata Iron Works, were of pure grade, and their boiling points, determined with the apparat,us described, were 80.1" and 110.3' C., respect,ively. The apparatus were calibrated with ltnomn mixtures of benzene m d toluene. Vapor compositions at the top and bottom of the column were determined by calculation. In addition, in all the runs vapor samples were taken through a nozzle-type vapor sampler projecting into the vapor line a t the column bottom and pointing downstream. The vapor samples were condensed in a small double-tube condenser. The copper tubing leading to the condenser was heated electrically in order to prevent any condensation. About 60 ml. of liquid sample was collected in 30 to 50
Table 1.
Total Reflux Runs
2 3 4 5 6 7 8 9 10 11
Molal Composition, Velocity % Benzene Lb.-Mole&f Top Bottom (Hr.)(Sq. Ft.) Packed Height 54 C m . 44.5 13.12 90.7 54.3 87.4 3 67 19.1 9.54 79.9 2 29 49.1 95.5 37.6 79.1 7.18 61.4 7 94 92.0 36.3 15 52 92.0 6 99 82.0 40.8 53.3 4 36 88.8 17.1 2.35 66.5 28.1 3 89 77.5
12 13 14 15 16
70.5 67.3 39.2 44.3 44.3
17 18 19
92.3 90.2 97.4
Run No
T- 1
No of Transfer Units Not NOQ 2.42 1.68 3.45 2.76 2.03 2.18 3.05 2.03 1.83 2.96 2.55
3.46 2.46 3.37 4.48 2.34 2.89 4.10 2.47 2.71 2.49 2.65
Packed Height 4 C m 61.4 17.20 61.4 7.96 32.8 7.22 37.5 3.57 32.5 14.88
0.410 0.270 0.379 0.369 0.671
0.529 0.340 0.296 0.311 0.543
Packed Height 104 C m . 4.33 31.8 5.82 28.4 3 60 55.3
3.30 3.33 2.88
4.34 4.10 5.18
INDUSTRIAL A N D ENGINEERING CHEMISTRY
17s7
ENGINEERING, DESIGN, AND PROCESS DEVELOPMENT minutes. The analyses of the bottom vapor sample checked the calculated compositions xvithin 0.3 mole %. S o vapor sample wrm taken at the top. Column Is Operated ai Total Reflux and As Enriching and Stripping Sections
Tables I, 11, and 111 present the experimental data and calculated results for total reflux, enriching, and stripping runs. For total reflux runs, three packed heights of 54, 4, and 104 em. were used to determine the height equivalent to the end effects above and below the packed section. The packed height was varied by changing the assemblage of t’he column sections. All of the enriching and stripping runs mere made a t t,he packed height of 54 cm. Except for the tot’al reflux runs, where vapor compositions equal liquid compositions, vapor compositions were computed by using material balance relationships, as illustrated below. In order to allow for the difference between the molal iatent heats of vaporization of benzene and toluene, a fictitious molecular weight was used. Based on the true molecular weight of toluene, 92.06, a fictitious molecular weight of 84.06 was as~lgnedto benzene to make the fictitious molal latent heat of pure benzene equal t o the true molal latent heat of pure toluene at atmospheric pressure.
Calculated quantities: Liquid rat)e a t top = 15.15 (14.40) 1b.-moles/(hr.)(sq. ft.) Vapor composition a t bottom = 14.77 X 33.0 - 3.88 X 19.6 = 37.9 mole % benzene 14.77 - 3.88 Vapor composition at top = 14.40 X 69.0 - 5.85 X 18.2 14.40 - 3.85
Consider the general case in Jvhich both liquid and vapor film resistances are involved in inass transfer. By assuming that equilibrium is reached a t the liquid-vapor interface, the following relations are known t o bold:
=a
= -
E- 1 2 3 4 5 6
7
8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37
.
hIola1 Velocity, Lb.-lvIoles/ (Hr.) (Sq.Ft.) Liquid Vapor 3.67 7.72 8.64 13.12 7.47 12.55 3.65 8.52 12.32 4.68 4.16 6.40 11.73 7.98 10,72 13.20 13.12 8.88 2.70 3.57 1.73 7.41 4.62 1.83 6.53 1.75 13.18 4.37 5.58 1.69 4.17 12.49 5.82 3.63 4.67 1.40 8.52 5.17 5.80 4.76 3.38 6.32 3.32 2.48 5.96 1.87 13.02 4.31 12.25 4.42 4.07 10.22 3.36 12.56 12.50 5.23 7.60 2.26 11.95 4.36 1.91 4.76 8.86 2.43 12.14 4.84 11.97 4.85 12.63 4.63 2.41 7.26 9.18 7.35
s o . of
Transfer Units A’OL ~ Y O G 2 . 8 8 1.80 2.77 2 . 6 1 3.30 1 . 9 4 3.85 1.64 4.08 1.28 4.3G 2 31 4.30 1 . 9 8 3.47 2 . 8 8 5.14 2 . 7 3 2.82 2 17 3 . 1 7 0.81 3 . 9 6 2 05 2.72 0.82 4 . 1 2 1.59 2.72 0.98 2.95 0.94 2.95 1.99 2.70 0 . 6 8 5.42 1 . 9 7 2.60 1 . 8 8 4.63 1 . 8 7 3 . 2 3 2.14 3.01 0 . 7 2 3.56 1.40 3.14 1 . 3 4 3.34 1 . 5 3 2.83 0.68 3.26 1 . 3 7 3.74 1.07 3.29 1.16 3.43 1.30 3.36 0 . 9 6 3.16 1.24 2.91 1.01 3 34 1 . 0 3 3 26 1 0 5 2 81 2 06
The following is a sample calculation from the data of run 20
of Table I11 (stripping). (Figures in italics designate values based on the fictitious molecular weight.) Measured quantities: Liquid rate at bottom = 11.77 (14.40) 1b.-moles/(hr.)(sq. ft.) Liquid composition a t bottom = 33.0 (91.d) mole % benzene Liquid composition a t top = 61.0 (69.0)mole ’%benzene Feed rate to top = 3.88 (5.85)1b.-moles/(hr.)(sq. ft.) Feed composition = 19.6 (18.2) mole % ’ benzene 1758
&a
-
HOG = H G
m
1
kGa
(Packed height 54 cm.)
R~~ No.
yo brnzene
Choice of Average Slope of Equilibrium Curve Is Important Basis of Interpretation
Enriching Runs
Composition, h f o k ’% Benzene Liquid Vapor T o p Bottom T o p Bottom 8 1 . 3 68.4 51.7 78.5 8 5 . 8 51.5 86.7 6 4 . 3 67.9 48.1 6 5 . 1 31.9 59.0 34.7 65.0 54.5 57.4 36.9 66.2 60.4 6 3 . 5 42.5 60.3 27.6 44.4 14.4 46.2 25.8 7 5 . 6 2 7 . 3 76.7 37.5 71.9 28.4 7 3 . 2 43.9 69.9 3 2 . 0 72.0 43.4 58.9 45.2 6 9 . 0 65.9 51.0 7 9 . 5 70.4 74.0 7 0 . 6 66.8 6 1 . 7 46.9 6 8 . 0 45.0 73.2 65.6 6 8 . 0 46.8 72.2 65.8 54.1 3 4 . 8 60.6 54.2 52.0 71.1 3 6 . 8 73.2 42.3 31.1 53.9 50.6 23.4 12.0 36.2 33.1 13.3 46.3 20.8 44.8 5 2 . 5 38.7 48.0 22.0 63.6 38.2 2 5 . 8 65.7 3 3 . 8 2 3 . 4 4 4 . 3 41.0 6 9 . 8 4 6 . 7 74.2 66.7 72.6 64.8 6 7 . 1 45.1 73.9 64.1 69.6 44.7 59.6 56.0 6 0 . 1 35.9 66.0 55.9 61.0 36.7 55.9 38.3 64.2 59.1 54,5 62.3 5 6 . 5 34.9 56.0 34.4 62.5 54.0 40.1 65.4 60.8 57.0 64.1 55.0 59.0 35.8 30.2 56.4 48.1 51.1 46.2 27.5 52.8 45.8 26 7 50 7 I5 7 41 7 ,d7 2 27.3 67 2 65 3
79.8 (76.6) mole
Bottom vapor compositions given in the tables are calculated values. Molal flow rates of vapor and liquid in the tables are the arithmetic means of the values at the top and bottom. Straight operating lines were assumed in the calculation of the number of transfer units. The error due to this assumption was considered unimportant. AJ the equilibrium data for benzene-toluene system, Mizuta’s data ( 6 ) , Fhich substantially agree with the calculation using Itaoult’s hTT, 1% ere employed.
I
Table It.
=
4- h%
’
-_ . .
m;oa
(3)
k%
+ (mG.v/L.w)HL
H O L = (L.w’?nG.nr) H G
(41
+ HL
(53
H O G = G.vr/Rca
(6;
HOL= L.v/KL~
(7)
There have been a few proposals (4,7 , 8) concerning the kind of average that should be taken for m, the slope of the equilibrium curve. This is an important problem in the case of distillation
~~
Table 111.
Run
so.
s- 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
Stripping Runs
(Packed hcight 54 om.) Composition, h f o k % ~ . ~Velocity, ~ l ~ Benzene Lh.-Moles/ Liquid Vapor (Hr.)(Eq. Ft.) Top Bottom T o p Bottom Liquid Vapor 59.2 35.5 7 1 . 0 40.1 9.22 3.23 56.2 34 3 7 0 . 3 40.3 10.37 7.14 79.0 5 4 . 3 8 6 . 1 57.9 14.55 12.35 68.9 47.6 80.3 52.8 13.10 10.01 73.7 48.5 8 2 . 8 62.3 11.89 9.76 70.0 5 2 , 3 80.2 57.3 8.80 6.74 69.8 5 5 . 3 8 0 . 8 61.2 0.85 4.31 6 1 . 1 46.8 74.6 53.8 7.02 4.83 57.2 45.2 7 3 . 8 53.6 10.64 6.32 5 9 . 1 3 9 . 4 74.9 46.0 15.28 10.40 39.4 20.2 5 5 . 1 24.9 14.86 9.39 59.4 31.1 72.1 35.0 15.27 11.67 75.3 40.9 8 2 . 0 43.3 9.82 8.51 75.4 64.8 85.4 71.1 5.74 4.18 61.4 3 8 . 9 7 6 . 1 44.7 11.94 8.55 35.9 14.5 50.3 17.7 16.69 10.92 36.9 1 9 . 1 50.4 23.3 4.41 2.90 70.9 5 2 . 3 83.6 16.55 12.04 58.6 7 4 . 1 5 1 . 8 8 3 . 1 56.2 15.03 12.30 6 1 . 0 3 3 . 0 75.6 37.9 14.96 11.07 7 5 . 0 5 9 . 7 8 6 . 3 65.7 12.54 9 08 4 4 . 5 25.5 60.0 30.8 10.75 6.96 34.6 1 6 . 3 45.7 19.3 7.34 5.11 25.3 14.5 37.7 18.8 9.16 5.23 35.9 19.9 49.2 24.4 13.51 8.66 31.0 1 9 . 9 51.4 2 6 . 2 14.33 7.98 39.2 2 5 . 4 54.2 32.1 4.85 2.88
INDUSTRIAL AND ENGINEERING CHEMISTRY
i No. of Transfer Units NOL
NOG
1.89 2.96 1.78 1.77 1.85 1.40 1.24 1.33 1.46 2.16 2.56
2.54 3.04 2.91 2.89 2.94 2.36 2.29 2.27 2 86 3.51 3.10
2.39 2.16 1.10 2.33 3.08 2.23 1.92 1.68 2.71 1.67 2.46 2.20 1.96 1.99 2.57 1.70
3.11 2.99 2 25 3.50 3.27 2 48 3.56 2.74 4.10 3.42 3.15 2.18 2.17 2.50 3.42 2.23
Vol. 46, No. 9
ENGINEERING. DESIGN. AND PROCESS DEVELOPMENT when the equilibrium line is considerably cuived. The following types of average are considered soundest ( I O ) . For m in Equations 2 and 4
portant part in determining the relative magnitudes of vapor and liquid film resistances. Correlations Show Variations in Individual Film Resisfances
For m in Equations 3 and 5
is the slope of the chord joining points (z$, y%)and (2,y*); is the slope of the chord joining points (G, yi) and (x*,y). These types of average are slightly different from those introduced are ", by Sherwood and Pigford ( 7 ) . plthough (ma)&"and ( m ~ ) ~ sound, neither of them can be computed without the knowledge of interfacial compositions or of the ratio oE individual film resistances. I n cases when only the numbers of over-all transfer unite are known, the use of the following type of average, proposed by Furnas and Taylor ( 4 ) , is more practical. mA
mB
Determination of End Effects. Since the packed height WBB small, it was feared that the mass transfer below and above the packing would account for a subatantial fraction of total mwa transfer. In order to determine the height equivalent to end effccts, total reflux runs were made a t three different packed heights. In Figure 2 the values of the number of transfer units obtained at total reflux are plotted against molal vapor velocity, G,tr, Khich equals molal liquid velocity, LM, on logarithmic coordinates. The correlation obtained is relatively simple. This seems to be related to the fact that many previous investigators obtained simple relationships between H.E.T.P. and throughput a t total relux. 5 4
Equations 8 and 9 reduce to Equation 10 if m~ and m~ are replaced by the slope of the chord joining the points (z*, y) and (2,y*). The value of m defined by Equation 10 lies between those of (m.&. and ( m ~ ) but ~ ~the . , differences are usually within the accuracy of engineering calculation. Therefore, the use of m defined by Equation 10 throughout the present study seems justified.
t' L L 2
0
2, 0.8
0.6
0.4 I
OPERAT ION
mGn /LM I
0 TOTAL REFLUX STRIPPING
I
0.2 I
0.4
I Z
O.?
I
/
Figure.
CM.
I
I
2
4
0
0 1 0
20
30
GMCZLM), LB.-MOLES/O-IR.ICFT~
Figure 2.
Number of Transfer Units at Total Reflux
The ratio of the vapor-film resistance to liquid-film resistance is equal to the ratio of the first to the second terms on the righthand side of any of Equations 2, 3, 4, and 5 . For a given run, the ratio is constant, whether capacity coefficients or H.T.U.'s are employed. However, since the variations of koa and kLa with vapor and liquid rates, respectively, are supposedly greater than those of H Qand H L , thevalues of &a and KLa are considered to vary over wider ranges than HOGand HOL. If it is assumed that the values of HG and H L are in the same order of magnitude, it is seen from Equation 4 or 5 that the value of mG.w/LM plays an im-
September 1954
'
200
3.
G ,
0
7 I
600
L~B~'AHR,)(
I
BOO 1000
'
2000
FT:)
HOG versus Vapor Rate with Liquid Rate a5 Parameter
4 L - 4 1 1 '
=4
)
I
The height equivalent to end effects was determined by making cross plots from Figure 2 a t various throughputs with the number of transfer units as ordinate and packed height as abscisfia on a rectangular scale. The height equivalent to end effects is shown as the intercept on the horizontal axis, which ranged from 2 to 5 cm. However, since this height was small relative to the packed height of 54 cm. and it was not clear how the end effects were affected by vapor and liquid rates, no allowance for end effects was made in the calculation of H.T.U.'s or capacity coefficients. Correlation for H.T.U. The use of the H.T.U. has the advantage over the use of capacity coefficients in that the former has a simpler dimension of length, although they are easily interchangeable with each other. Furthermore, the range of variation of H.T.U. is, in general, smaller than that of capacity coefficientcl. Several correlations were tried for H.T.U.'s, but the one shown in Figure 3 seems to have more general applicability than the others. Referring to Figure 3, Hoc values for all the runs, including enriching, stripping, and total reflux runs, were plotted
INDUSTRIAL AND ENGINEERING CHEMISTRY
1759
ENGINEERING, DESIGN, AND PROCESS DEVELOPMENT against average vapor inass velocity on a logarithmic scale. Liquid rate was varied a t random, but the trend with liquid rate 6s shown by the graph. The numerals written beside the data points indicate average liquid rates in 100 pounde per (hour)(square foot) rounded to one or two significant figures. For instance, 12 indicates average liquid rate of about 1200 pounds per (hour) (square foot). Solid curves drawn through the points represent various liquid rat'es. HOGvalues for the stripping and total reflux rum slightly decrease with increasing vapor and liquid rates and, a t total reflux, when vapor rate equals liquid rate, Hm values have a relatively siniple relationship with throughput, as shown by the broken curve. I n enriching operation, in which vapor rate always exceeds liquid rate, HOGvalues increase rapidly with decreasing liquid rate or in rate. This trend in enriching operation is in qua1it:Ltive accord with the results of previous investigators on enriching operationLe., Duncan et al. (5)and Furnas and Taylor (4)> who noticed a marked effect of vapor-liquid ratio or of liquid rate on HOG or KQU. Hoi?vever, some of the runs of those investigators show far greater values of HOG. This is possibly due to thc fact that both of those previous experiments were performed in longer packed sections. With a long packed sect'ion, because of the pinching a t the end of operating line, slight error in the drtermination of vapor composition results in considerable error in the calculated values of ~ V Oand, C consequently, of HOGor Kea. Usually, liquid composition can be analyzed with fair :iccurac.y.
,I
80 r 60-
-
1
TOTAL REFLUX STRIPPING
I
I
!
8
40 816
I
present data are concerned, liquid-film resistance is relatively large in enriching operation and vapor-film resistance is relatively large in stripping operation, because of the variation of mG,$f/L,v. However, in practical columns having both enriching and stripping sections, the situation possibly could be the reverse-that is, mG,v/L, could be greater than unity in the stripping section and less than unity in the enriching section. Only a slight effect of m is noticeable in Figure 3. This could be explained by the €act that, since the operable range of composition in the preaent experirnenta was limited by reflux ratio, t,he value of m was not completely independent of the Jope of the operating line, L,I~/G.I~. It icl likely that the very rapid increase of Hoc's in Figm,e 3 a t a vapor rate of about 1100 pounds per (hour) (square foot) is caused by loading or flooding. Calculation showed that this could hsppen. Correlations for Kgc and K L ~ The . statement coiiceriiing the relative magnitudes of individual film resistances becomes c ~ e n more dear when over-all caparity coefficicnts, KGUand &,a, are correlated. The reason seems to be that Kca and KLUvary ovei' wider ranges than HOGand H O L ,rcspectivcly. I n Figure 4 the values of KGUare plotted against molal velocity of vapor expressed in pound-moles per hour per square foot ot' gross cross-sectional area of the column on logarithmic coordinates. The numerals beside the data points indicate mold liquid rates in pound-moles per (hour) (square foot) rounded to one or tn-o significant figures. Data points for all the runs in which mG.v/L.w values are less than unit'y-most of the stripping and total reflux runs in t8hepresent experimenQ-lie along a straight line; all the points representing t'he runs where rnG.~,/L,,f values are great,er than unity-all the enriching runs in the present experiments--scatter and lie be lo^ the straight line if they are plotted on the graph. It appears that vapor-film resistance is controlling in runs in which ttzGIIfiLMvalues are leaa than unity. Hoiwvei, probably the truth is that vapor-film resistance is relatively large but not 100% in those runs and the straight line in Figure 1 expresses the combined effect of vapor and liquid rates. It is coriceivahle that liquid rate affects the liquid-vapor interfacial area, a, as well as t,he liquid-film coefficient, k ~ .At any
I I
2
G, Figure 4.
4
6 0 1 0
20
30
, LB:MoLEs/(HR.)( F T . ~ )
Over-all Coefficient, &a, Vapor Rate, GX
versus Molal
The trend shown in Figure 3 seems to imply that both liquidand vapor-phase resistances are involved in the mass transfer in packed distillat,ion columns, and that the relative magnitudes of individual film resistances vary mainly with vapor-liquid ratio, or by the value of mCM/LJv. A study of the data reveals that, aa shown in Figure 3, the values of mCM/L,vare greater than unity (1 to 4) in most of the enriching runs, less than unity (0.5 t'o 1.0) in the stripping runs, and near unity (0.7 to 1.5)in the total reflux runs. This fact, together 6 t h the trend shon-n in Figure 3, seems to validate the assumption that H G and H L are in the same order of magnitude. Probably the truth is that, so far as the
1760
I
L
I
2
4
6
8 1 0
20
3
L ~ LB;MOLES , /(HR.)(FT.~) Figure 5 .
Over-all Coefficient, KLa, versus Molal liquid Rate, f.$f
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
Vol. 46, No. 9
ENGINEERING, DESIGN, AND PROCESS DEVELOPMENT I V
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DEED ET A L . ~
were chosen for the only reason that the greatest number of runs were available with that packing. Furnas and Taylor noticed little effects of the size and type of packing. In Figure 6 only the data in which mGM/L,M values are greater than unity are plotted. About two thirds of both sets of data satisfy this condition. The same type of correlation that is shown in Figure 5 is applicable to other systems, provided that ~ G M / L isM greater than unity. The data of Furnas and Taylor show considerably smaller values of KLUfor given values of LM. One explanation for this is that liquid distribution was somewhat poorer in Furnas’ column, since the packed section was a8 high as 9 feet. However, the question arises whether or not it is theoretically sound to use molal rate as the criterion of liquid velocity. Molal rate is more 00 60
40
se
l l
20
0.6
n
X
0,6
2
0.4
m
n
G
IO
L
a
a
6
x
z
2 4
2
5
AI
-
rate, the straight line in Figure 4 could be used as a practical correlation for the case in which m G M / L M is less than unity. The values of HOUeasily could be obtained by dividing GM by Koa-Le., the value of the abscissa by the corresponding value of the ordinate in Figure 4. A correlation of KLUversus molal liquid rate, LM,is in remarkable contrast with the correlation of Koa versus GM. Figure 5 is such a pIot on a logarithmic scale. The numerals beside the data points give vapor rates in pound-moles per (hour) (square foot) rounded to one or two significant figures. All of the runs in which mGM/LM values are greater than unity-all of the enriching runs and few total reflux runs in the present experimentsfall roughly on a straight line; the runs in which rnGM/L.W values are less than unity-most of the stripping and total reflux runs in the present study--scatter and show smaller values of KLU, if they are plotted in Figure 5 . It appears that the liquid film offers major resistance when ~ G , M I L , M is greater than unity, in qualitative accord with the conclusions of Furnas and Taylor ( 4 ) or of Bliss et al. ( 1 ) . However, this again seems to be matter of comparison. Probably, the straight line in Figure 5 expresses the combined effect of liquid and vapor rates, but the line is considered useful as a practical correlation in case in which m G M / L M is greater than unity. The effect of m would be apparent from Figure 5, if the values of m were noted on the graph. At higher liquid rates, KLUvalues are greater, the greater the values of m. This is reasonable from Equation 3, provided that rePistances of both films are involved. Correlations of KLCC versus L.$f were also tried using two sets of reliable data, both of which were obtained in enriching columns or a t total reflux. In Figure 6, KLUvalues calculated from the data of Deed et al. ( 2 ) on isopropyl alcohol-water with ‘/Z-inch Raschig rings and those from the data of Furnas and Taylor ( 4 ) on ethyl alcohol-water with 1-inch Berl saddles are plotted against the molal liquid rate, L.w>on logarithmic coordinates. I n using the Furnas-Taylor data, the data for 1-inch saddles September 1954
5
Y
2
BENZENE-TOLUENE 15-mm RINGS
I 0.8 0.6 0.4
ETHANOL- WATE R I” SADDLES
0.2 )
60 8 0 100
L
Figure 7.
200
,
400
6 0 0 8 0 0 1000
2000
LBAHRXFT~I
Comparison wi h Data of Other Investigators, KLa versus f
convenient to use in that it is substantially constant throughout a column, and such a plot as Figure 5 or Figure 6 has the advantage that it gives the values of H o t immediately. On the other hand, mass liquid rate is more proportional to actual linear velocity of liquid than is molal liquid rate. It is not inconceivable that KLUis more affected by mass liquid rate than by molal liquid rate, in case liquid-film resistance is predominating. In Figure 7 KLUvalues from the two sets of previous data as well as from the present study are plotted against mass liquid rate, L, expressed in pounds per (hour) (square foot). The arithmetic averages of the values a t the top and bottom of the column were used as values of L. The present data and the Furnas-Taylor data are in good accord. Whether or not this is mere coincidence could be elucidated by further investigations. In interpreting the data of Furnas and Taylor, if liquid-film resistance were really conti olling, KLUfor all the runs could have been correlated against L/r. The tact that m IS in the brackets in Equation 1 seems to imply that liquid-film resistance WRS not. 1 0 0 ~ oin their experiments Their correlation includes runs in which mGnf/LM is less than unity.
INDUSTRIAL AND ENGINEERING CHEMISTRY
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'ENGINEERING, DESIGN, AND PROCESS DEVELOPMENT Correlation of Koa with G,Mwas also tried, using some of the ,data of Deed et al. ( 2 ) and Furnas and Taylor ( 4 ) in which mGM/L.>f is less than unity. About one third of their data satisfy this condition, although they were obtained in enriching or total reflux runs. Both sets of data fall roughly on two st,raight lines parallel to that in Figure 4. However, the Furnas-Taylor data show smaller values of Koa, while the data of Deed et al. show greater Kaa for corresponding values of GM. Naturally, the differences in physical properties should be taken into account before a definite statement is made conccrning the comparison among different systems. However, with 8ysteme usually met in distillation, physical properties such :is the Schmidt numbers of vapor and liquid phases are, in general, of the same order of magnitude. The effects of the size and type of packing prescrit anothi:r problem, although Furnas and Taylor conclude that tlw csffi.rt'? are negligible. Correlations M a y Be Useful for Design Purposes with Proper Allowances
Although the authors do not cltiiai that the correlations presented in this paper generally are applicable for packed column distillation, they could give some clue in case pilot plant data are lacking. For injtance, design procedure could be as folloivs: On an x - y diagram, draw operating lines for enriching and stripping sections. and Calculate the values of the numbers of transfer units. XOG X O L ,for both sections. Determine the values of mGni,/L,v using Equation 10. For the eection where mG,w/Lx is over unity, obtain the value of R L a and of H O Lby the use of Figure 5, Figure 6, or Figure 7 . For the section where mG,w/L.v is less than unity, use Figure 4 to obtain the values of Koa and HOG. The packed heights of both sections are obtained as the products of H.T.U.'s and FOGor Nor,.
It ie recommended that ample allonranee be made in using the correlations in this paper for design purposes, since the good liquid distribution obt,ained in this experiment,al column hardly is expected in large industrial columns. It is also recommended that, a packed section higher than 5 or 6 feet not be used. If necessary, t,he packing should be divided into two or more sections, with a liquid distributor at the top of each section. The choice of proper column diameter is important'. If a column of too large diameter is used, good liquid distribution is hardly expected. Conclusions
I n view of the experimental data on the distillation of the benzene-toluene syetem covering enriching, total reflux and stripping runs, it seems that the relative magnitudes of individual film resistances in packed distillation columns vary, depending on the value of mG.,f/L~f. In case mG,v/L,vis greater than unity, liquidfilm resistance appears to be relatively large, and when mGaf/L.w is less than unity, vapor film seems to offer relatively large resistance I n the former case a plot of KLa versus L,cr or L and, in the latter case, a plot of KGa versus G.11 give practical correlatione foi the estimation of over-all coefficients or H.T.U.'s.
1762
However, their uses are limited in that physical properties of systems are not included. General correlations involving physical properties of systems would not be obtained until the splitting of over-all resistance into individual film resistances is made possible by some means. Acknowledgment
This work was supported in part by the Science Research Fund of the Ministry of Education, Japan. The authors are grateful to Nippon Kagakukikai Seizo Co. for constructing the apparatus and to Hirohata Iron Works for donating the sample. They also thank several students for their assist'ance in the experimental work. Nomenclature
= active interfacial area per unit volume, sq. Ct.,/w.ft. = average mass vapor velocity, lb.i(hr.)(sq. ft.) = average molal vapor velocity, 1b.-moles/(hr.)(sq. ft.) = height of individual vapor-phase transfer unit, f t . =
height of individual liquid-phase t'ransi'er unit, Et.
= height of over-all vapor-phase transfer unit, ft. = height of over-all liquid-phase transfer unit, ft.
over-all coefficient based on vapor composit,ion, Ib.moles/(hr.)(sq. ft.)(unit 4 y ) = vapor film coefficient, 1b.-moles/(hr.)(sq. ft.)(unit, Ay) = over-all coefFicient based on liquid composition, 1b.moles/(hr.)( sq. ft.)( unit Az) = liquid film coefficient, 1b.-moles/(hr.)(sq. ft.)(unit Az) = average mass liquid rate, lb./(hr.)(sq. ft.) = average molal liquid rate, 1b.-moles/(hr.)(sq. ft.) = average elope of equilibrium curve = slope of chord joining points (56,yi) and (z, .y*) = slope of chord joining points (26,yi) and (z", y ) = average value of VZA, defined by Equation 8 = average value of m ~defined , by Equation 9 = number of over-all vapor-phase transfer units = number of over-all liquid-phase transfer units = mole fraction of more volatile component in liquid = mole fraction of liquid in equilibrium with vapor of composition y = x and y a t interface, respectively = mole fraction of more volatile component in vapor = mole fraction of vapor in equilibrium with liquid of composition z = packed height, em. = liquid viscosity, Ib./(hr.)(ft,) =
literature Cited Bliss, H., E a h a y a , 1.Si.,a n d Friuch, N. W., Chem. Eng. Progr.,
48,627 (1952). D e e d , D. W., Schutz.
P.W.,
and Drew,
T. B., IND.ENG.
CHEY..39, 766 (1947). Duncan, D. W-., Koffolt, J. H., a n d Withrow, J. R., Trans. Bm. I n s t . Chem. Engia., 38, 259 (1942). Furnas, C. C., a n d Taylor, A I . L . , Ibid., 36, 135 (1940). Miauta, A I , , J . SOC.Chem. I d . , J a p a n (in J a p a n e s e ) , 37, 22 (1934).
Ryan, J. F., P h . D . thesis, Pennsylvania S t a t e College, 1953. Sherwood, T. K., a n d Pigford, R. L., "Absorption a n d Extract i o n , " 2nd ed., p. 125, McGraw-Hill, S e w York, 1952. Simon. M.J., a n d Govinda R a u , SI I s n . E m . CHEM.,40,93
(1948). Uchida and associates, Chern. Eng. ( J a p a n , ) ,11, 53 (1947). Yo?hida, F.. D.Eng. thesis. K y o t o University. 1950. RECEIVED for reviev January 4 1 S 5 i .
INDUSTRIAL AND ENGINEERING CHEMISTRY
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JIay 4, 1954.
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