INDUSTRIAL A N D ENGINEERING CHEMISTRY
584
Vol. 16, No’ 6
T h e Efficiency of Fractionating Columns‘ By G. Calingaert and F. E. Huggins, Jr. MASSACHUSSTTS INSTITUTE OF TECHNOLOGY, CAMBRIDGE, MASS.
HE efficiency of a fractionating column is defined as the separating power of a definite unit or length, and is measured by comparing its performance with the performance calculated for a theoretical plate column under similar conditions. W. K. Lewis2 has derived a formula to express the efficiency of actual plate columns according to this definition, whereas Peters3 was the first to calculate the efficiency of a packed tower by determining the number of ’ theoretical plates to which its whole length corresponded. The present paper offers an experimental application of this method to the testing of the efficiency of a coke-packed rectifying column under widely variable operating conditions.
T
APPARATUS The experimental apparatusconsisted ,of a coke-filled column, feed liquor being introduced a t the top of the column and the weak liquor or “waste” being withdrawn from the bottom. Steam was introduced a t the base of the column and the product vapors were withdrawn from the top of the column into a condenser. The column was made of black iron pipe, 10 cm. in diameter, packed over 150 cm. with household coke, crushed and separated with square mesh screens, through a screen with 16 mm. between meshes, and over a screen with 9 mm. between the meshes. The column was lagged with 5 cm* of magnesia lagging.
CALCULATION OF EFFICIENCY As will be Seen from the data, the range of concentration of ammonia used was chosen such that Henry’s law holds true. Moreover, the concentration of ammonia is a t all times low enough to allow the substitution of weight concentration for mol concentrations without introducing any appreciable error. The heat of vaporization of even the more concentrated solutions being substantially that of water, no variation of the amount of reflux occurs on account of the variat,ion of Concentration. 1 Received December 22, 1923. Presented before the Division of Industrial and Engineering Chemistry a t the 67th Meeting of the American Chemical Society, Washington, D. C., April 21 to 26: 1924.
* THISJOURNAL,
The amount of heat loss having been determined as corresponding to 0.5 kg. of steam condensed per hour, the amount of overflow can be considered as being constant and equal t o the waste per hour minus 0.25 kg. per hour. Under the conditions thus obtained-namely, (a) constant amount of overflow, ( b ) constant amount of vapor, (c) constant ratio vapor to liquid concentration-it is easy to calculate the performance of the still with varying amounts of vapor and overflow, using the above-mentioned concept of theoretical plate.
THEORETICAL PLATE Calling 0 = amount of overflow, kg. per hour V = amount of vapor. kg. Der hour x = concentration bf the-liquid, grams ammonia per kilogram y = concentration of vapor, grams ammonia per kilogram n, + 1 subscript designating the plates, numbered from the bottom UP t, w = respectively, the top and bottom plate
k e get from an ammonia balance from the ( n the bottom : ox, + 1 = vy, ox,
++
Xn+ 1 ynv/O x , + 1 - x,= x, [ a V / O
Xt
f=
11.8 11.8 11.8
11.7 12.9 12.2 13.0 11.7 12.2 7.2 7.9 8.4 7.9 8.5 8.1 15.7 15.6 16.4 16.1 16.0 20.0 19.0 19.6 19.6 20.0
17.2 14.7 11.8 5.17 7.82 3.19 19.6 4.93 3.48 12.5 9.25 2.96 6.07 15.7 3.19 12.6 6.45 11.3 15.1 14.3 9.26 16.4 9.80 10.1 6.38
= x,
15.1 12.6 9.7 3.05 5.55 1.00
17.4 2.8 1.29 11.0 7.7 1.28 4.47 14.0 1.55 9.8 3.8 8.5 12.1 11.5 6.0
13.25 6.6
6.93 3.0
,
xw
x,
-
+ 1
Xn
- xn
(When the still tested is high enough-i. e., if the number of theoretical plates is, say, above twenty, the quantity x,,+ 1 - Z, in the equation above can be ca,lled the derivative of as regards to n, and the equation becomes
14, 492 (1922).
---RATES, KG./HOUR--Feed Steam Product
- l] + x,
Introducing in this equation the value of 2, as x,, i t is possible to determine the concentration on the next theoretical plate above it, xw + 1. Repeating the same calculation on that plate and the following ones, it is possible, by a stepwise method, to determine the total number of theoretical plates corresponding with the increase in concentration from the bottom to the top of the still. When enough plates are calculated to find a concentration exceeding that of the top plate, x t , the last fraction of plate is assumed to be proportional to the fraction of the increase in concentration observed-namely,
a l b i d . , 14, 476 (1922).
No. 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 .
+ 1)th p h t e to
Waste
* TABLE I CONCENTRATIONS, G. NHa/Kc. Feed Product Waste
13.9 14.1 13.9 13.8 15.2 14.3 15.2 13.8 14.5 8.7 9.7 10.1 9.5 10.2 9.7 18.5 18.3 19.2 19.0 18.8 23.2 22.1 22.8 22.7 23.3
1.160 1.160 1.133 1.154 0.856 1.031 1,230 1.302 1.200 1.195 1.179 1.154 1.136 1.128 1.102 1.215 0.891 1.107 1.138 1.132 1.117 1.132 1.098 1.078 1.090
0.841 1.076 1.364 4.545 2.025 12.34 0.887 5.448 10.96 0,750 1.143 7.20 1.978 0.664 5.565 1.886 3.674 2.254 1.565 1.460 3.743 1.592 3.370 2.980 7.100
0.00421 0.00405 0.00411 0.00411 0.00391 0,00764 0.00431 0.00421 0.00471 0,00401 0.00601 0.00491 0.00662 0.00461 0.00451 0,00442 0.00420 0.00460 0,00435 0.00450 0,00450 0.00430 0.00480 0.00445 0.00460
Vapor
V 17.0 14.5 11.6 4.92 7.57 2.94 19.4 4.68 3.23 12.3 9.0 2.71 5.82 15.5 2.94 12.4 6.20 11.1 14.9 14.1 9.01 16.2 9.55 9.9 6.13
cg
- 11
+ x,
Overflow
a
V
H. E. T.P.
Volpme Efficiency
13.6 13.9 13.6 13.5 14.9 14.0 14.9 13.5 14.2 8.4 9.4 9.8 9.2 9.9 9.4 18.2 18.0 18.9 18.7 18.5 22.9 21.8 22.5 22.4 23.0
1.25 1.03 0.85 0.36 0.51 0.21 1.30 0.35 0.23 1.47 0.96 0.28 0.63 1.57 0.31 0.67 0.34 0.59 0.80 0.76 0.39 0.74 0.42 0.43 0.27
147 145 129 53.2 74.6 32.4 150 49.5 32.7 I75 120 42.7 117 238 47.6 110 53.2 83.3 123 125 62.7 119 68.1 69.7 40.6
678 789 853 850 820 866
a
Cm.
606
828 796 1110 1048 1238 1582 1208 1278 697 673 588 650 683 546 575 562 552 518.
I
INDUSTRIAL AND ENGINEERING CHEMISTRY
.
June, 1924 which, integrated, gives
_-
-
-
I.
-
1
0 xw 0 However, the integrated formula tends to give low results, mostly when only a small number of plates are considered, and in such case the stepwise method of determining the number of plates must be used.) 240,-
I
I
,?An0 I/AF17R H S N G 70 M R f Z O W - /O
Fro. 1
EXPERIMENTAL DaTA-Data are given below on twentyfive runs, in which the amount of overflow varied from 8.4 to 23.0 kg. per hour, and the amount of vapor from 2.7 to 17.0 kg. per hour. Overflow = slops
Sample Calculation. Run 1 condensate from heat loss 0.50 0 = 13.9 - 13.6
-
2 Vapor = steam used - ‘ / A condensate V = 17.2 - 0.50 = 17.0 2 Concentration on top plate is assumed to be in equilibrium with a vapor of composition of the product. Henry’s law constant is taken as 12.1.4
585
efficiency-the higher the H. E. T. P. the lower the efficiency. Fig. 1 shows the proportionality between H. E. T. P. and the ratio vapor rising to overflow, V/O, over the range investigated-namely, 0.2 to 1.5. This shows that under those conditions-i. e., with an amount of overflow varying from 0.7 to 5 times the amount of vapor-the efficiency of the still investigated was proportional to the reflux a t constant vapor velocity, or inversely proportional to the vapor velocity a t constant reflux. I n other words, the efficiency is proportional to a factor which expresses merely the time of contact between liquid and vapor. Another expression of efficiency, which is also due to Peters, is the volume efficiency, or the capacity of a given volume of the column to effect the fractionation of a given amount of material. The H. E. T. P. indeed refers only to the capacity of effecting separation, regardless of the amount of material treated. It is obvious that the desirability of operating a still under a given set of conditions is proportional to both the fractionating efficiency and the capacity of the equipment. Therefore, the volume efficiency, which is given in Fig. 2, is the H. E. T. P. multiplied by the section of packing necessary to handle 1 kg. of vapor per hour. Here again a low volume-efficiency factor will correspond to a high efficiency. As can be seen from the plot, a high volumeefficiency factor corresponds t o a high value of 1/0, or, in other words, the optimum operating conditions over the range investigated correspond to the use of a high amount of reflux. These results seem to be in conflict with the conclusions of Peters that the H. E. T. P. is independent of the overflow a t constant vapor velocity, but it must be remembered that this statement was restricted to the range 0.8 to 1.0 for the ratio overflow per vapor, thus only one-twentieth of the one covered here. The variation of H. E. T. P. in that range observed by the authors amounts to only 20 per cent, as compared with a sevenfold variation over the total range. /G 00
0
fACTOR ” PACKLD RECnr/MG COLUMN
“VOLUNE EFf/C/€#CY
- 0.0694 12.1 Concentration on successive theoretical plates from the bottom up (12.1)(17.0)(0.00421) + o,oo421 = o,0676 .Tu f 1 = 13.6 x i = - 0’841 -
0.968 ~t Xw + 2 - XU + 1 Fraction of theoretical plate above (w
X, + 1
+ 1)th:
= 0.0018
Number of theoretical plates = 1.02 Height for equivalent theoretical plate, the still being packed with coke over 150 cm: - - - 147 cm. = H. E. T.P. 1 02 Volume efficiency = H . E. T. P. multiplied by that cross section through which 1 kg. of vapor passes per hour. (H. E. T. P.) d Z - 678 4V
DISCUSSIOX For n convenient interpretation of the results, the efficiency is expressed here as “height of equivalent theoretical plate” (H. E. T. P.), as was first suggested by Peters. It must be borne in mind that this term is in fact a reciprocal of the 4
Calingaert and Huggins, J . A m . Chem. SOC.,45, 915 (1922).
RLC/PROCHL OF W€RFL OW FIG.2
-YO
CONCLUSIONS I t can be seen from the above that the efficiency of a packed distilling tower can readily be tested under widely varying operating conditions, by using it as a stripping column for dilute ammonia solutions. The stepwise method of determining the number of plates must be used when the column is short, the integrated formula applying when the number of plates equals at least twenty.
. ,
586
INDUXTRIAL A N D ENGINEERING CHEMISTRY
The data thus obtained can be applied to any other distillation problem. Whereas, the a c t u d efficiency will differ with the mixture which it is desired to fractionate, the variation of efficiency with operating conditions will be substantially independent of that factor.
Vol. 16, No. 6
ACKNOWLEDGMENT Thanks are due to W. K. Lewis under whose direction this investigation was conducted, and to W. H. McAdams and W. A. Peters, Jr., for valuable suggestions concerning the interpretation of the data.
T h e Determination of Manganese in Water by t h e Sodium Bi sm IIt h at e M et h od'j2 By W.D. Collins and Margaret D. Foster
u. s. GEOLOGICAL SURVEY,
DEPARTMENT OF THE INTERIOR, 'WASHINGTON, D.
T
HE sodium bismuthate method for the determination of manganese in water has been recommended for a number of years in authoritative publications3which refer back to a paper on the subject published by Weston4 in 1907. A study of the method with reference to the saving of time and reagents resulted in the adoption of the procedure given below. The discussion is based on about one hundred experiments on the effects of various modifications of details of the method. METHOD Use 100 cc. of water or a sample small enough to contain less than 1 mg. of manganese. Add 10 cc. of dilute nitric acid (1 part strong acid to 3 of water), 1 cc. of concentrated sulfuric acid, and heat in a beaker on a hot plate until most of the sulfuric acid has been driven off. Cool, take up with about 50 cc. of water and 20 cc. of dilute nitric acid through which air has been bubbled to remove oxides of nitrogen. Add 0.10 gram of sodium bismuthate, stir for 1 or 2 minutes, allow the excess of bismuthate to settle, and filter through an alundum crucible or a Gooch crucible with a mat of ignited asbestos which has been washed with permanganate solution. Dilute the filtrate to a definite volume and compare with standards. To prepare the standards measure out appropriate volumes of standard permanganate solution, add to each the quantity of nitric acid used for the samples, and make to the same volume. DISCUSSION Evaporation of the sample with nitric and sulfuric acids insures the removal of chloride and of organic matter. By stopping the evaporation just short of dryness the manganese sulfate is obtained in an easily soluble condition. It is well to evaporate nearly all the sulfuric acid, because the shade of the permanganic acid is not the same in sulfuric acid and in nitric acid solutions. The usual directions call for the use of 40 cc. of nitric acid (1to 3 ) . This quantity assures a concentration of acid within the range found by Cunningham and Coltmans to be the best. Unless special care has been taken to remove all the lower oxides of nitrogen from the acid, the color will fade more rapidly with this concentration than with less nitric acid in the solution. I n a series of tests with 1.0 mg. of manganese and 0.10 gram of sodium bismuthate, the full color was developed with 2 cc. of nitric acid (1to 3 ) in a volume of 50 cc. and nearly 90 per cent with only 0.5 cc. of acid. With small quantities of acid appreciable quantities of manganese will be precipitated after several hours. I n a series of tests with quanReceived January 22, 1924. Published by permission of the Director, Geological Survey. I Am. Pub. Health Assoc , Standard Methods of Water Analysis, 1912, p. 49; 1917, p. 49; 1923,p 51; Assoc. Official Agr. Chem., Methods, 1920, 0. 36. 4 J. 4 m . Chem. SOC., 29, 1074 (1907). 6 THIS JOURNAL, 16, 58 (1924). 1 2
c.
tities of aerated acid ranging from 5 to 40 cc., the full cblor was developed in all samples, but the loss on standing was least with 20 cc. of acid. Manganese precipitated in the solutions containing less acid and the color faded more in those with more acid. Older directions call for the use of 0.5 gram of sodium bismuthate. According to the results of Cunningham and Coltmans this is enough bismuthate for 19 mg. of manganese. A series of tests using from 0.50 to 0.025 gram of bismuthate with 5 cc. of nitric acid (1 to 3) for 1 mg. of manganese in a volume of 50 cc. showed no difference in color G t h from 0.50 to 0.075 gram of bismuthate. With 0.050 gram bismuthate the color was 85 per cent of the standard. Taking 0.10 gram of bismuthate as the minimum makes an appreciable saving of reagent in examining any large number of water samples. The experiments reported were made with bismuthate from a lot that contained 83 per cent of NaBi03, determined as recommended by Cunningham and Coltman.6 A lot received later contained only 68 per cent of NaBi03. Practically all directions call for double treatment with bismuthate. This is necessary if the sample, when first treated with bismuthate, contains material that will be slowly oxidized by the permanganic acid after filtration from the bismuthate. If a water sample is treated as directed in the method given above, there will be no such material left and the heating to destroy the permanganic acid color is an unnecessary step which wastes time and bismuthate. When large quantities of manganese are determined in samples containing unoxidized material, some manganese may be precipitated. Directions for steel analysis provide for the solution of this precipitated manganese with the aid of a reducing agent such as sulfur dioxide, sodium thiosulfate, or sodium bisulfite. That this precipitation has rarely occurred in water analysis is indicated by the persistence of the direction to use ammonium or sodium bisulfate for this purpose. If precipitation of manganese a t this point in the analysis had taken place many times, the misprint probably would have been corrected. Cunningham and Coltman6 confirm the statement of Blumc that sodium bismuthate oxidizes manganese perfectly to permanganic acid, so that a solution of potassium permanganate of known strength is as useful as a manganese sulfate solution for the preparation of standards. There is no advantage in reducing the manganese in a permanganate solution with oxalic acid in the presence of sulfuric acid and then using this manganese sulfate for the preparation of Btandards with nitric acid and bismuthate. The usual precautions in preparation and preservation of the permangsnate standard solutions must be observed and a fresh standard solution should be made rather than trust one that has been kept for a long time. 6
J . A m . Chem. Soc., 54, 1379 (1912).
