14-1
Chapter 14
14.1 Describe a Pareto analysis. When is it used?
Strictly speaking, a Pareto analysis is statistical technique but we use it here in the more
14.2 What is the difference between parametric optimization and topological optimization? List
one example of each.
Parametric optimization focuses on adjusting operating (decision) variables in order to
14.3 What is an objective function? Give two examples of one.
An objective function (OF) is a mathematical relationship that one wishes to minimize
14-2
14.4
Optimal cooling water exit temperature = 39 C
14-3
14.5 – Background simulations from CHEMCAD
14-4
14.5 – Background Information from Chemcad
14-5
14.5: Using previous background information
we find that the value of the products is much
14-6
14.6
14-7
14.7 – Optimum Pipe Diameter
14-8
14.8 – Biological Reactor
14-9
14.9 – Distillation Column
14-10
14.10 – Brine Fouling
14-11
14.11 – Optimal Cycle Time
x= $350
y = $200
V = 7m3
Substituting values into Equation (14.18), we get:
14.12 – Second order reactor – optimum cycle time
2
k
A
B
A material balance at time, t gives: 0
( )
2
A A
B
V C C
Nand for a 2nd order reaction we have
The objective function (OF) can now be written as:
2
0 0
0 0
2 1 1
A A
clean
A A
B A clean
clean
C kt VC
xV y C
C kt C kt
xN yN C
OF t t
Differentiating the OF with respect to t and setting =0 gives
2
1 1 1 1 1 1 1 1 1 1
( )( ( 1) ) (2 1) ( ) ( ) 0
collecting terms we get
clean clean clean
A D E t E t t t E t E t A D t B C