Batch Steam .Distillation Nomograph iMELVIN NORD, 244 Broad Street, Mutawan, N. J .
I
N THE theory of batch steam distillation of a volatile component from its solution in a nonvolatile liquid, the following equation (8) appears:
16IS-.
14-This equation applies to the case of a nonvolatile component present in large amount, on the assumption that the volatile component follows Raoult's law. If Equation 1 is to be solved for Bs, a trial and error solution is required. This paper presents a nomographic solution which eliminates trial and error and permits rapid calculations to be made. Let UR define variables SI and SZas
13.-
12I I
--
to
-'
9 .8
Subtrttotirig (3)from (2) gives
7 ..
B -2 BS Compsrisoii of Equation 4 with Equation 1 shows that S I
- 1)
- Sz =
s
(BI
PO - B2) +- EPB -In
6 --
3v &=
SI - s2
Eqiistioris 2 and 3 can be rewritten aa
BI =
F~ ( BI + 0 In
Ba =
(Ba+OIn2) EPB
P
--
4 -.
2)- SI B
-&
or dividiirg both sides of each of these equations by 0,
13
2
14
1.0'"
I5
01
16
P
EP, Figure 1
Equations 8 and 9 are of the form:
f(4 = F(X).+(Y)
+ $(z)
where B1/Oand B,/O, respectively, play the role of variable x in (8) and (9), P / E P Bcorresponds to y, and Sl/O and Sal0 represent L in (8) and (9). Equation 10 is the standard nomographic form for a recurrent variable (1). Thus, we can plot a nomograph consisting of three axes: B/O, S/O, and PIEPB, which can be used once to represent Equation 2, and again to represent Equation 3. The resulting nomograph, Figure l, may be used in either of the following ways: If it is desired to calculate steam requirements for a given change in still composition, draw straight lines between the point on the P / E P a axis and the two known points on the B / O axis. These two lines will intersect the S/O axis at two values, the difference between them representing the desired value of S/O. The steam requirement is found by multiplying this value by 0. If it is desired to determine the number of moles of volatile component Ba remaining in the still after S moles of open steam have been used on a solution originally containing BI moles of volatile component, draw a line between P / E P B and BI/O. The intersection of this line with the S/O axis represents S1/0. Subtract S/O,the ratio of moles of steam used to the number of moles of nonvolatile component, and thus determine &/O, another point on the S/O axis. The line connecting this latter 854
Q
point with P / E P B paases through the desired value of B 2 / 0 . Multiply Bt/O by 0 and obtain the desired value, Bs. Thus, trial and error is eliminated from the solution of Equation 1 by means of Figure 1 . An example of the use of the nomograph is given by the dotted lines which indicate that, if P / E P B = 5.0, BI = 2.0, and SI0 = 3.05, then Bp/O 1.7.
-
S B
O
-
NOMENCLATURE
total moles of open steam used
= total moles of volatile component present in still at any time
= total moles of nonvolatile cdm nent in etiU (constant) = vapor pressure of pure volatiE'component P = total Dreasure B ) actual E = vaporization efficiency = ((PPB) equilibrium pa = partial pressure of volatile component PB
LITERATURE CITED
(1) Perry, J. H.,Chemioal Engineer's Handbook, 2d ed., p. 259 (1941).
(2)
I W . , p. 1389.
