Page 82 - Applied Process Design For Chemical And Petrochemical Plants Volume II

Distillation 71

methods give reasonably acceptable results. Vanwinkle Suggested Procedure
[75] outlines the steps necessary for such calculations.
With current computer technology there are several 1. From Equation &131 expressing 8 and q evaluate 8 by
commercial programs available (as well as personal and trial and error, noting that 8 will have a value between
private) that perform tray-to-tray stepwise calculations up the a of the heavy key and the a of the light key eval-
or down a column, using the latest vapor pressure, K-val- uated at or near pinch temperatures, or at a avg. Sug-
ues, and heat data for the components. This then provides gested tabulation, starting with an assumed 8 value, 8,:
an accurate analysis at each tray (liquid and vapor analy-
sis) and also the heat duty of the bottoms reboiler and Compo- aj xFi/(% - elz
nent xF~ q xFi % - e
aj xFi/(ai - 8)
overhead total or partial condenser. -- - -
Torres-Marchal [110] and [ill] present a detailed a XFa aa XFa “a - ea aa xFa/ (aa - ea) xFa/ (aa -
graphical solution for multicomponent ternary systems ea) *
b
that can be useful to establish the important parameters ea) * xn, ab XFb ab - ea ab xn/(ab - ea) ab xm/(ab -
prior to undertaking a more rigorous. solution with a com-
puter program. This technique can be used for azeotrop- a a m 0 a a
ic mixtures, close-boiling mixtures and similar situations. 0 a m a a 0
An alternate improved solution for Underwood’s y (ea) y’ (ea)
method is given by Erbar, Joyner, and Maddox [113] with Y, VI’, represents function.
an example, which is not repeated here.
Corrected 8 by Newton’s approximation method:
Underwood Algebraic Method Adjacent Key Systems 1721

This system for evaluating multicomponent adjacent (8- 135)
key systems, assuming constant relative volatility and con-
stant molal overflow, has proven generally satisfactory for Repeat the same type of tabular computation, sub
many chemical and hydrocarbon applications. It gives a stituting the corrected 8, for the 8,. If the second cor-
rigorous solution for constant molal overflow and volatili- rected O’, checks closely with €I,, the value of 8 has
ty, and acceptable results for most cases which deviate been obtained, if not, a third recalculation should be
from these limitations.
made using the O’c value as the new assumed value.
Overall Column-Constant a Note that average a values should be used (con-
stant) for each component unless the values vary con-
siderably through the column. In this latter case fol-
low the discussion given elsewhere in this section.
2. Calculate (L/D)kn by substituting the final 8 value in
In arriving at (L/D)min the correct value of 8 is Equation 8-130 solving for (L/D)min. Note that this
obtained from: requires evaluating the functions associated with 8 at
the composition of the distillate product. The a val-
ues are the constant values previously used above.
The “q” value is the same as previously described for the Underwood Algebraic Method Adjacent Key Systems;
thermal condition of the feed. Variable a
Rectifying section only:
For varying a systems, the following procedure is sug-
DXDi (8- 133) gested
vs= 2 * 1. Assume (L/D)min and determine the pinch tempera-
i=l,h,L.

Stripping section only:
ture by Colburn’s method.
2.At this temperature, evaluate a at pinch and a at
age a. As an alternate, Shiras [63] indicates a bvg
i=l,h,H (8-134) overhead temperature, obtaining a geometric aver-
value which gives acceptable results when compared
At the minimum reflux condition all the 8 values are to pinch and stepwise calculations. This suggestion
equal, and generally related: calculates,

ah < 8 < a]