I N D U S T R I A I, A N D E N G I N E E R I N G C H E M I S T R Y
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method, mlieii applied to the conditions a t tlic bottom of the column, mill determine a maximum steam consumption or maximum number of theoretical plates required. If the stripping factor, S, is defined as
s = KT' -L
x,! = mole fraction of component in liquid leaving stripper .re = mole fraction of component in liquid entering strippi
This is the general stripping equation. The first term on the right determines the effect of the composition of the feed and defines the limit to which the composition of any component of the liquid may be reduced when the entering vapor contains none of this component (i. e., x,, + = 0). The second term evaluates the effect of the composition of the entering vapor. The sum of the two terms defines thr composition of the liquid leaving the stripper; since - -AIs- --1- 1 -
S n i l
x - x, ping, tlie ordinate of Figure 1 becomes , and the xe - x,+1 abscissa, tlie -tripping factor S. I n using the chart it should KV Le noted that the stripping factor S = -,L whereas the
absorption factor d =
a derivation similar to the one applied to the absorber lead> to an equation for the composition of the liquid leaving the iiottom plate of a stripper with n plates, where
s o +1
,yn+ I
-s - 1
Equation 15 may Le rearranged:
Vol. 24. No. 5
L KV'
Ordinarily steam is used for stripping, so that x . + thc inole fraction of the component in liquid in equilibrium with the stripping vapor entering the stripper, equals zero, and Equation 16 reduces to
I n this case the value of the ordinate read from Figure 1 represents the fraction of the original content of any coniponent of the oil which is removed by the stripping operation. EVALUATION OF STRIPPINGFACTOR. I n practice it i h customary to express the steam required for stripping a i pounds of steam per gallon of oil. If W repreqents the pounds of steam per gallon of oil, KWM , y = -KV L 18 x 8 3 3 d APPLICATION TO DESIGS Tlie design of the stripping unit usually must be developed in connection with the design of the absorption unit. The quantity of oil required for absorption depends in part upon the completeness of stripping, and the design of the stripping unit depends in part upon the quantity of oil and the completeness of stripping. Economical design usually requires a balance between ab3orbing, circulating, and stripping costs. The absorption and stripping factor methods provide ready means for relating the various factors in these costs.
so thnt
LITERATURE CITED
This corresponds to the plot for the absorption factor (Figure 1) so that the same chart may be used for both absorption and stripping calculations. When used for strip-
(1) Cox a n d Arnold, Proc. Calif. Natural Gasolzne d>soc., 4, Nos 6 a n d 7 (1929). (2) Kremser, SatE. Petroleum News, 43 ( M a y 21, IWO), Proc. CaZJ. Natural Gasolme Assoc., 5 , No 2 (1930)
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V.
Fundamental Design of Fractionating Columns for Complex Mixtures GEORGEGRANGER BROWK, MOTTSOUDERS, JR., AND H, V. NYLAND
A
RAPID and satisfactory graphicalmethod for computing the number of equilibrium plates required in a fractionating column for binary mixtures \vas presented sometime ago by McCabe and Thiele ( 2 ) . A n equivalent method applicable to multiple component mixtures, presented in this paper, has met with only partial succes? until combined with the absorption and stripping factor method of Part IV of this series. This graphical method is substantially a n extension of the method presented by Lewis (1) for the design of natural gasoline absorbers, t o include proper allon aiice for changes in equilibrium conditions due to changes i n the temperature from plate to plate. SOJIESCLATCRE
That part of the column above the feed plate ia indicated as the rectifying column and that part below the feed plate a i the stripping column. The plates are numbered from the top plate of the rectifying column down to the bottom plate of the stripping column. -4"general" plate as denoted by n is in the rectifying columnl and by 5 is in the stripping column. The top plate in the rectifying column will be numbered 1, and the hypothetical plate above the top plate is 1 - 1 or 0. Subscripts indicate the plate of origin of a quantity, as un
incans the inole fraction of the conipoiient under consideration in the vapor rising from plate E, and xn- represents the mole fraction of the component under consideration in the liquid overflowing from plate n - 1. Other symbols are as follows: D
I
