Page 276 - Distillation theory

P1: JPJ/FFX P2: JMT/FFX QC: FCH/FFX T1: FCH
0521820928c07 CB644-Petlyuk-v1 June 11, 2004 20:18

250 Trajectories of the Finite Columns and Their Design Calculation

1 1 1
( η 1 )
a) b) c)
n r2
r 2 2
 L  2  L 
   
' D  V  min x F2  V 
s 2
n s2
n r1
r 1
2  L  1 2  L  1 2
1,2,3 ( η 2 ) 1,2,3   1,2,3  
( )  V  min  V 
x F
s 1
n s1
r 3 n r3
' B  L  3  L  3
   
 V  min x F3  V 
s 3
n s3
3 3 3
( η 3 )
Figure 7.15. Calculation of Petlyuk columns: (a) specifications (in brackets), (b) calculation
of minimum reflux and reboil ratios and product distribution in two-section columns, and (c)
calculation of design variables.
to the quality of the products after transition to rigorous simulation and lead
to nonoptimal design solution. Rigorous models and methods of mathematical
optimization are used in the work (Dunnebier & Pentelides, 1999), but its appli-
cation comes across the difficulties that were mentioned in Section 7.1.
A new simplified method was introduced in the work (Amminudin et al., 2001).
This method is based on preliminary determination of product compositions meet-
ing set requirements to their quality with the help of solution of Underwood
equation system (1948) for the mode of minimum reflux. The number of trays
in sections is determined by means of calculation by method “tray by tray” from
the ends of each two-section column entering into the distillation complex at
the assumption about constancy of molar flows and about the above-mentioned
product compositions. The joining of section trajectories is carried out in a sim-
plified way. Optimal design solution is obtained by means of minimization of
objective function, including energy and capital expenses. Minimization is carried
out by reflux and vapor ratios in each two-section column entering into distillation
complex. This method does not have many of the imperfections of other simpli-
fied methods. It embraces Petlyuk columns, products of which contain not only
one, but also several components. This method besides a number of assumptions
does not take into consideration the general regularities of location of distillation
trajectories, which can lead to “nonjoining” of the calculation trajectories starting
at the ends of two-section columns (see Section 7.3).
We state below a rigorous method of design calculation of Petlyuk columns
and of columns with side sections based on the design calculation of two-section
columns described in Section 7.3.
At design of Petlyuk columns, as of distillation columns and complexes of other
types, the purity of separation products is a set (specified) parameter, while the
tray numbers for all sections n r1 , n s1 , n r2 , n s2 , n r3 , and n s3 (Fig. 7.15) and reflux