Page 39 - Chemical engineering design

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CHEMICAL ENGINEERING
The variables selected as design variables (fixed by the designer) cannot therefore be
assigned as output variables from an f node. They are inputs to the system and their edges
must be oriented into the system of equations.
If, for instance, variables v 3 and v 4 are selected as design variables, then Figure 1.11
shows one possible order of solution of the set of equations. Different types of arrows
are used to distinguish between input and output variables, and the variables selected as
design variables are enclosed in a double circle.
v 3 v 4

f 1 f 2 f 3 f 4 f 5

v 1 v 2 v 5 v 6 v 7

Design variables (inputs)
Inputs
Outputs
Figure 1.11. An order of solution

Tracing the order of the solution of the equations as shown in Figure 1.11 shows how
the information flows through the system of equations:
1. Fixing v 3 and v 4 enables f 3 to be solved, giving v 1 as the output. v 1 is an input to
f 1 and f 2 .
2. With v 1 as an input, f 1 can be solved giving v 2 ; v 2 is an input to f 2 and f 4 .
3. Knowing v 3 , v 1 and v 2 ,f 2 can be solved to give v 5 ; v 5 is an input to f 4 and f 5 .
4. Knowing v 4 , v 2 and v 5 ,f 4 can be solved to give v 6 ; v 6 is an input to f 5 .
5. Knowing v 6 and v 5 ,f 5 can be solved to give v 7 ; which completes the solution.
This order of calculation can be shown more clearly by redrawing Figure 1.11 as shown
in Figure 1.12.

v 3 v 5
v
3
v v v v
f 3 1 f 1 2 f 2 5 f 4 6 f 5 v 7
v
v 4 2
v 4
Figure 1.12. Figure 1.11 redrawn to show order of solution