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7.5 Design Calculation of “Petlyuk Columns” 251

and vapor ratios in each section are calculated variables (it is convenient to use
r1
s1
r2
instead of them ratios of rates of liquid and vapor (L/V) ,(L/V) ,(L/V) ,
s3
r3
s1
s2
(L/V) ,(L/V) ,(L/V) . Instead of parameter (L/V) for the first column (pre-
fractionator), it is convenient to use the distribution coefficient of flows D /B ,

1 1

where D = D 2 + B 2 , B = D 3 + B 3 , and B 2 + D 3 = S is the side product of the
1 1
main column.
It is expedient to determine the value of optimal distribution coefficient D /B

1 1
at the stage of calculation of minimum reflux mode (see Section 6.8). In particular,
at separation of a three-component mixture, the optimal value of coefficient D /B

1 1
corresponds to the preferable separation (i.e., can be found most easily, see Section
7.3.4). In the general case at separation of a multicomponent mixture, the optimal

value of D /B should be preliminary determined by means of the solution of

1 1
Underwood equation system in the case of sharp separation of a multicomponent
mixture with several distributed components. Then the optimal value of D /B

1 1
should be specified by means of variation of pseudoproduct composition and
minium reflux calculations (see Section 5.6)
s2
s3
The parameters (L/V) and (L/V) can be determined from the condition of
material and heat balances in the second and third two-section columns at chosen
r3
r2
values of (L/V) and (L/V) . Therefore, after exclusion of the above-mentioned
r1
r2
mode parameters, three mode parameters (L/V) ,(L/V) , and (L/V) r3
remain.
Because minimum values of these parameters were determined before at the
stage of calculation of the mode of minimum reflux (see Section 6.8), design their
values should be chosen reasoning from economic considerations taking into ac-
count energy and capital expenditures. This choice is similar to that of optimal
reflux excess coefficient for two-section columns. Along with that, the equality of
vapor flow rates in the second and third columns in the cross-section of output of
side product is taken into consideration.
The main purpose of design calculation is to determine necessary tray num-
bers for all sections at fixed values of mode parameters. At design calculation,
one takes into consideration the equality of compositions at the tray of output
of the side product obtained at the calculation of the second and third columns.
Each two-section column entering into a Petlyuk column is calculated with the
help of algorithms described before for two-section columns. The algorithm of
calculation for splits with a distributed component is used for the first column, the
algorithms for the direct and the indirect splits are used for the second, and the
third columns at separation of a three-component mixture, respectively. At sep-
aration of multicomponent mixtures, the algorithms for intermediate separation
are used.
The calculation of the first column is carried out at set compositions of its
pseudoproducts x D and x B and at compositions at the ends of the column x up =

S and x low = S , corresponding to the maximum concentration in the trays of the
r1 s1
componentintermediatebybubbletemperatureatseparationofthree-component
mixture (see Section 6.8.3) or heavy key component of the side product in point
x up and light key one in point x low at separation of multicomponent mixture (for