The new separation parameter is obtained using Eq. (3.3)
The new separation parameter is obtained using Eq. (3.3)
The denominator of Eq. (3.40) will be equal to (In SVN, i.e., 8.821/20 = 0.441. The term inside the square root will be equal to iexp 0.441/2.572)2, i.e., 0.3652. Therefore,
(R + 1)(0.6R + 0.34) This gives the quadratic equation
The new reflux flow will be 78.4 lb-mole/h.
A rigorous simulation gave the value R = 1.27 and a reflux flow of 76.0 lb-mole/h.
Caution: The procedure for applying the Jafarey et al. equation (61,62) in this example was empirically developed by the author. It worked in a few examples attempted by the author, but may not work in other cases.
The author strongly recommends that before this algorithm is used for computer control of a multicomponent column, it is first thoroughly tested against the results of a rigorous computer simulation for the column considered. Alternative procedures for extending the Jafarey et al. algorithm for multicomponent distillation are discussed elsewhere (62).
3.3 Nomenclature 3.2.1 English letters
B Bottom flow rate, lb-mole/h b Intercept parameter in Smoker's equation, defined by Eqs. (3.37a and b)
c Parameter in Smoker's equation, defined by Eq, (3.33)
D Distillate flow rate, lb-mole/h
Dr Recovery of a component in the distillate product, given by Eq. (3.12)
F Feed flow rate, lb-mole/h
/} Ratio of component flow rate in the bottom to component flow rate in the feed, Eq. (3.25)
H Enthalpy, Btu/h h Factor in the Smith-Brinkley method, given by Eqs. (3.28a and b)
j Component counter
K Equilibrium constant Eq. (1.1). In Sec. 3.2.7 only, it is the equilib rium constant in the rectifying section
K' Equilibrium constant in the stripping section k Parameter in Smoker's equation, given by Eq. (3.35)
L Liquid flow rate in the rectifying section, lb-mole/h
L' Liquid flow rate in the stripping section, lb-mole/h
L0 Liquid condensed at the condenser, lb-mole/h
M Number of stages below the feed m Slope of the component balance line, given by Eqs. (3.36a and b)
N Number of stages n Number of components
PHK Pseudo heavy key
PLK Pseudo light key q Number of pound-moles of liquid formed on the feed stage when introducing 1 lb-mole of feed
Qc Condenser duty, Btu/h
J? Reflux ratio
S Separation parameter, defined by Eq. (3.3)
Sm,Sn Factors in the Smith-Brinkley equation, defined by Eqs. (3.26) and (3.27)
T,t Temperature, T
tm Average temperature in the stripping section, °F, estimated by Eq.
tn Average temperature in the rectifying section, "F, estimated by Eq.
V Vapor flow rate in the rectifying section, lb-mole/h
V Vapor flow rate in the stripping section, lb-mole/h
X Gilliland's correlation reflux parameter, given by Eq. (3.15)
* Mole fraction in the liquid x^x „ Parameters in Smoker's equation, defined by Eqs. (3.31) and (3.38a and 6)
.Tmt Liquid mole fraction at the intersection of the component balance line and the g-line, given by Eq. (3.34)
xnJx 'K Parameters in Smoker's equation, defined by Eqs. (3.32) and (3.39a and b)
V Gilliland's correlation parameter, given by Eq. (3.16) v Mole fraction in the vapor z Mole fraction in the feed
3.3.2 Greek letters a Relative volatility
Plk/hk Parameter in the Winn equation [Eq. (3.8)]
0 Parameter in the Underwood equation [Eq. (3.10)] eLK Exponent in the Winn equation [Eq. (3.8)]
1 Sum of
3.3.3 Subscripts av Average
DK Distributed key component
DK1.DK2... Distributed key component 1,2...
HK Heavy key component i Component i j Component j
LK Light key component
LNK Light nonkey component(s)
M Minimum mid Middle of the column min Minimum opt Optimum pseudo Pseudo component
S Stripping top At the top of the column u At the conditions differing from bubble point [Eq. (3.18)]
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