Page 140 - Plant design and economics for chemical engineers

COMPUTER-AIDED DESIGN 115
is entered into location ~3, and the value 0.3, the fractional conversion, is entered
into location b3. The right-hand side of each equation is entered into the cell
representing the variable on the left-hand side of the equation. The entries into
the spread sheet are indicated by the following table.
a b C d
Mass balances
Reaction: CO + 2H2 -i CH30H
100 0.3
Flow rates, MOL/H
Stream no. c o CH30H
2 (1 - b3)* a3 b3*a3
3 b6 0.0
4 0.0 c6

The results of computation by the spread sheet are (omitting titles)
a b C
3 100 0.3
5 Stream no. CO CH30H
6 2 70 30
7 3 70 0.0
8 4 0.0 30

The solution for the process without recycle has been obtained.
Now the recycle of the unreacted products to the reactor is added, as shown
in Fig. 4-1. The reactor balance equations become
b6 = (1 - b3)*(a3 + b7)
and
c6 = b3*(a3 + b7)
These new equations are substituted in place of the previous ones in the spread
sheet. The separation-step equations are unchanged. The calculations are now
circular, because 66 depends upon 67, which in turn depends upon 66. These
equations will be solved iteratively; that is, the calculations will be repeated until
the values in the table stop changing (within limits). The calculations can be
performed automatically by the spread-sheet software. It is recommended, however,
that the calculations be made utilizing the manual option of the software, at least
initially until it is clear that the calculations are converging. The manual option has
another advantage: It keeps the software from attempting to calculate as the
equations are being entered (such calculation would result in errors because of the
circularity).
If the case without the recycle was solved first, calculations for the case with
recycle can utilize the values from the preceding table for the same feed rate and
conversion. The result of the first iteration is then
b C
6 119 51
7 119 0.0
8 0.0 51