Page 158 - Plant design and economics for chemical engineers

132 PLANT DESIGN AND ECONOMICS FOR CHEMICAL ENGINEERS

Example 4 Computational order for styrene process. A styrene process flow
diagram is shown in Fig. 4-5. From this flow sheet it is apparent that there are two
recycle streams in this simple process: the unreacted ethylberizene is recycled and
mixed with the fresh feed and the reactor effluent is recycled back to the heat
exchanger.
Solution. The use of the calculation-ordering algorithm described above is
demonstrated here. Starting with the styrene feed stream, follow the arrows and
list the operations in the order encountered. The equipment numbers in order are,
1 2 3 2
Observe that the number 2 recurs, establishing that there is a recycle and that it
includes operations 2 and 3. These operations are combined into one unit, label it
10. All operations within a loop must be solved together (usually by iteration).
While following the streams, if an output stream is followed that is not a feed to
another operation, e.g., SO8 from operation 5, check for another output from that
operation (there is one-S09) and follow it. Continue listing the operations
encountered:
1 10 4 5 6 7 8 1
Here the number 1 reappears, so another recycle loop has been found. This loop
includes all the operations in this list. Note that the first loop, unit 10, is “nested”
within this new loop. All the listed operations can now be combined into one new
unit, label it 11. At operation 8, stream S14 was followed, it returned to operation
1; if stream S15 had been followed instead, operation 9 would have been
transferred to the calculation list-the same result as obtained later. The choice of
which output to follow first has no fundamental effect on the result except to
perhaps change the calculation sequence. Continue following the outputs (there is
only one from unit 11, S15) and listing the operations encountered:
11 9
The outputs from operation 9 are not feeds to any process dperation, so 9 is
removed from this list and placed in a calculation list. This leaves only unit 11 in
the process list and its output now is not a feed to any other operation (9 has been
removed). Thus, operation 11 is now removed from the process list and added to
the calculation list ahead (to the left) of what is already there. The calculation list
is now
11 9
and nothing remains in the process list. The computation sequence is from left to
right, so unit 11 is computed first and then operation 9 is computed.
One stream in each recycle loop must be chosen as the tear stream for that
loop. It is the one to be assumed, checked for convergence, and iterated. There is
not an unambiguous guideline for this choice, nor is it usually critical which stream
is chosen. If there is one for which it is easier to make a reasonable initial
estimate, probably it should be selected. The actual recycle stream is often selected
as the tear stream.
A decision must be made whether the two recycle loops, units 10 and 11, are
to be converged simultaneously or separately. Simultaneous convergence, as
illustrated by Fig. 4-8a, is approached by checking and reestimating both tear
streams once in each iteration. Separate convergence proceeds by converging the