T H E JOURNAL OF IAVDUSTRIAL AND ENGINEERING CHEMISTRY
476
Vol. 14, Yo. 6
SYMPOSIUM O N DISTILLATION Papers presented before the Division of Industrial and Engineering Chemistry a t t h e 63rd Meeting of t h e American Chemical Society. Birmingham, Ala., April 3 t o 7 , 1922.
The Efficiency and Capacity of Fractionating Columns By W. A. Peters, Jr. E. I. D U
PONT
DE NEMOURS & CO., WILMINCTON, DELAWARE
HE capacity of a fractionating column is defined as a measure of the amount of vapor and liquid which can be passed countercurrent to each other in a column without causing the column. to load or prime. The efficiency is defined as the separating power of a definite unit or length of the column and is measured by comparing its performance with the performance calculated for a thcoretically perfect plate column under similar conditions.
T
the number of plates in the calculated theoretical column divided by the height of the filled column in any units chosen gives a measure of the efficiency of the filled column. We have found it. convenient to measure the reciprocal of this efficiency, which will be called the "height of equivalent theoretical plate," or H. E. T. P. SIEVE Tup8-h example will be given as an illustration of the method.
N
:I
PLATECOI~UMNS The theoretically perfect plate column has been defined by Professor Lewis and from his definition it follows that Y n
Xn+1 =
-Yc(1-
P)
(1)
P
where
X, + 1 Yn
Y,
the equivalent latent heat fraction of the low boiling l)thplate. material in the liquid on the (n = equivalent latent heat fraction of the low boiling material in the vaporizing from the ltth plate. = equivalent latent heat fraction of the low boiling material in the distillate. =
+
By equivalent latent heat fraction is meant the heat required to volatilize the amount of low boiling material in 1 lb. of the mixture on or above the given plate divided by the latent heat required to volatilize one pound of this mixture. Expressing the compositions in this way simplifies the calculations. p = the ratio of the heat required to volatilize the liquid run back divided by the total latent heat in the vapor passing up through any horizontal cross section of the column. This is also often called the reflux ratio. These relations are of course true only when radiation and changes in heat content of the liquid are neglected over the section of column considered.' Formula 1 gives the relation which must exist between the compositions of the vapor rising from one plate, the liquid refluxing from the plate above, and the heat balance in the theoretical column. If p, Y, and Y , are known, X,+ can be determined, Y, will then be fixed, according to the definition of the theoretical column, and thus the composition of the liquid and vapor at every point in the theoretical column will be fixed. (Fig. 1.) To compare an actual column with the theoretical column, then, it is necessary to run the column on some given mixture and to measure p , Y, and Y,. The theoretical column which will give the same values for Y, and Y, with the same value for p is then calculated, and the number of plates so calculated divided by the number of plates actually employed to make the separation gives the efficiency factor, K, of the actual column. If the column tested is a filled column, 1
If p
0
-Yn).
R,+l Formula 1 may be written R n +, -
V,(Y,
R,
Yn--Xn+i
+,+v,'
PIC.
1-DIICRAM
THEORETICAL COLUMNFOR MATRRIALS EQUAL LATENTHEATS
O F PLATSS OF
WITH
EXAMPLR The column tested was a 28411. diameter sieve plate column with twenty-eight plates separating acetic acid and water. The following d a t a were obtained: Vapor from still Distillate Liquid on top plate
70.8 per cent water 98.52 per cent watei 98.14 per cent water (from curve) Steam condensed in coil 19q0 Ibs. per hr. Distillate 200 Ibs. per hr. The latent heat of acetic acid will be taken as 90 and t h a t of water a s 540. 7 0 . 8 X 540 Then Y s (vapor from the still) = = 0.935 70.8 X 540 29.2 X 90 98.52 X 540 Y C (distillate) = = 0,998. 98.52 X 5 4 0 + 1 . 4 8 X 9 0 Total heat in vapor passing up column (available heat in 1980 Ibs. steam condensed under pressure at 500 P. C. t J . per lb.) = 990,000 P. C. U. Heat t o vaporize 200 Ibs. of distillate containing 98.52 per cent water and 1.48 per cent acetic acid = 108,000 P. C. U. 108 000 Then p = 1 = 0.8'5 990,000 0,935 - 0.998 (1 - 0.89) = 0.927 Hence x1 0.89 which calculated back to actual percentage is 67.8 per cent water. From the known relations between t h e compositions of the vapor and liquid phases of acetic acid and water mixtures at equilibrium, t h e value of Yi for X I = 67.8 per cent is found to be 76.1. Xz,etc., are then calculated in the same way, until finally XI^ is found to be 98.1. The results of the calculations are shown in Table I.
+
-
Of course the work can be simplified by expressing all compositions and amounts as equivalent heat fractions and drawing all curves in the same terms, just as for some pur-
T H E JOL'RNSL OF INDCSTRIAL A N D ENGIIVEERl.VC CHE.IIISTRY
June, 1922
poses it is found conveiiient to express relationships in terms of molal fractions, or Formnla 1 can he so written that conrpositions and amounts are espressed in act.ual percentagcs and ponnds in which case it becomes:
x,,,= Y"I,
