Page 35 - Applied Process Design For Chemical And Petrochemical Plants Volume II

24 Applied Process Design for Chemical and Petrochemical Plants

x = liquid mol fraction of a component
y = vapor mol fraction of a component
n = system total pressure, absolute -1 (8 - 41)
y1 = 1 + (a - 1)xl
Partial pressure:
Winn [99] proposes a modification to recognize tem-
(8 - 3) perature variation effects on relative volatility. The
method does not apply to mixtures forming azeotropes or
at conditions near the critical. Kister [94] proposes:
When temperature is constant and at equilibrium for a
homogeneous mixture (such as azeotrope), the composi-
tion of the liquid is identical with the composition of the K1= a12 K2
vapor, thus xi = yi, and the relative volatility is equal to 1.0.

mol fraction of i in vapor phase
Ki = yi /xi, that is, (8 - 9)
mol fraction of i in liquid phase (8-42)

aab = KJh = relative volatility of components a to b (8- 34) a can vary with temperature, so some average a should be
used between top and bottom temperature.
where i = compound identification When blk and plk/hk are constants at a fixed or constant
r = reference compound
pressure, but evaluated for the light (1) and heavy (h) keys
at top and bottom temperatures, their relationship is [94] :
As previously discussed, the charts of K values are avail-
able, but do apply primarily to hydrocarbon systems. Ref- at fmed pressure (8 - 43)
erence 79 presents important other data on K value rela- Plk/hk = &k/(&k)bk,
tionships. See Figures 84A and 84B for charts with Winn's equation reduced to Fenske's at blk = 1.0 and
pressure effects included (not ideal, but practical charts).
Plk/hk = alk/hk (8-44)
a1,2 = KdK2 = P1/n (8-35)
Example 84: Determine Minimum Number of Trays by
For multicomponent mixtures [79,59] :
Winn's Method (used by permission 1991)
The minimum number of trays necessary to debutanize
the effluent from an alkylation reactor will be calculated.
The feed, products, and vapor-liquid equilibrium costants
where 1,2,3,4, . . . are components in a multicomponent
mixture of the key components at conditions of temperature and
a112 = relative volatility of component 1 with respect to pressure corresponding to the top tray and reboiler are
component 2 shown in Table 8-1.
"312 = relative volatility of component 3 with respect to The constants f3 and b are evaluated using Equation
component 2. 843 as follows:

0.94 = p (0.70)b
3.55 = fi (3.00)b

Divide to solve for value of b. Then:

3.78 = (4.29)b
b = 0.913
= 1.301

For a binary system with constant relative volatilities: By use of Winn's Method [99] for product rates:

b (;) 1-b
,
V+l= (+) (2) for liquid overhead product (8 - 45)