Page 266 - Distillation theory

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

240 Trajectories of the Finite Columns and Their Design Calculation

concentrations of non-key impurity components in separation products
and of tray numbers in the section of the column is required.
4. The system of the equations for the componentwise discrepancies of the
material balance in the feed cross-section is solved for the set value of
σ = R/R min , determining the more precise values of little concentrations
of the non-key impurity components in the separation products and of tray
numbers in the column sections. The difference of that from the corre-
sponding step of the algorithm for intermediate splits consists of the fact
that tray numbers in the sections are included into the number of indepen-
dent variables besides the concentrations of the non-key impurity compo-
nents in the separation products. In accordance with that, it is accepted that
the concentration of each component in the feed cross-section is a linear
function not only of the little concentrations of the non-key impurity com-
ponents in the corresponding product, but also of the tray numbers in the
corresponding section:

N r (7.11)
x f −1,i ≈ a i + a i,k+2 x D,k+2 + a i,k+3 x D,k+3 + ··· + a i,n x D,n + a i,N r

N s (7.12)
x f,i ≈ b i + b i,1 x B,1 + b i,2 x B,2 +· · · + b i,k−2 x B,k−2 + b i,N s
The coefficients of these equations are determined in the same way as
in the algorithm for intermediate splits without distributed components.
The system of linear equations of material balance in the feed cross-
section looks as follows:

N r ) + L F x F,i
L r (a i + a i,k+2 x D,k+2 + a i,k+3 x D,k+3 +· · · + a i,n x D,n + a i,N r
N s ) = 0 (7.13)
−L s (b i + b i,1 x B,1 + b i,2 x B,2 +· · · + b i,k−2 x B,k−2 + b i,N s
(i = 1, 2,..., k − 2, k + 2, k + 3,..., n)

5. Specifying Step 4 is to be taken a few times to ensure the set precision. The
column trajectory at quasisharp separation, with the calculation finished,
may be presented as follows:

1 1
x D → qS → x f −1 ⇒⇓ x f ← qS ← x B
r
s
Reg Reg t Reg qsh,R Reg qsh,R Reg t Reg
D r sep,r sep,s s B
6. Steps 1 ÷ 5 are repeated for different values σ = R/R min .
The described algorithm for nonsharp separation and for the modes that are
close to the mode of minimum reflux can be made more rigorous in the same way as
it was described above for the intermediate splits without distributed components.
The content of impurity component k + 1 in the top product and the content
of impurity component k − 1 in the bottom product should be considered while
3
3
2
2
determining points S , S ... N and S , S ... N and by the modified algorithm.
+
+
r r r s s s