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406 Chapter 9 Operation Optimization
. An olefin plant is a candidate for CLO.
. An ethylene glycol plant should have off-line optimization.
. A butadiene extraction plant is a candidate for off-line optimization and a sta-
bility and quality control project.
Summary
. A qualitative approach is discussed for the implementation of OO in steps
whereby the ultimate CLO is not considered necessarily as the last step.
. The sequential order of the steps are: reactor modeling, performance meter
implementation, off-line optimization, quality of control, constraint control,
and CLO.
9.8
Appendix
The Optimization Technique based on the Lagrange Multipliers and Analysis of the
Result of a Reconciliation of Measurements versus Modeling Results
The Lagrange optimization technique is also used for the minimization of errors
during data reconciliation and parameter estimation steps. The analysis of the
results is used to develop an estimation of reliability or precision of reconciled val-
ues. A mathematical approach is taken by Heyen (1994)to determine analytically
the precision of the reconciled values. The same problem could be solved by the
application of stochastic technique as a Monte Carlo simulation to calculate the pre-
cision. The mathematical technique is of greater value as it also opens the possibility
to calculate contribution factors and sensitivity coefficients. The analysis is done by
extracting more information from the Jacobian matrix of the constraint equations.
Standard deviations for all state variables, measured or not measured, are related to
the standard deviation of the measurements.
Mathematical development Optimization is expressed as a constraint minimization
problem. The assumption is made that the constraints are linear or linearized.
Notation
X i validated measurement i= 1,m
X¢ i measured value i= 1,m
r i measurement standard deviation i= 1,m
Y j unmeasured variable j = 1,n
h k constraint equation k =1,p
Linear constraints are expressed as:
AX + BY + C = 0
where A is a (p m)constant coefficient matrix
B is a (p n)constant coefficient matrix
C is a (p 1)constant coefficient matrix
