Page 378 - Design of Simple and Robust Process Plants

9.5 Closed Loop Steady-state Optimization 365
9.5.1.3 Fundamental model-based optimization
Fundamental model-based optimization is the most widely used approach, its
advantage being that it forces you to know the process in detail at steady-state condi-
tions, and the dynamic behavior in case of a dynamic optimization. Crucial points
for optimization models include the need to:
. Develop the model in line with the design models (life cycle modeling).
. Develop the model in an equation-based modeling environment with open
equations, to achieve fast responses equipped with an optimizer. The open
form simulators/optimizers are, in concept, characterized by:
± Each equipment is modeled by equations without nested convergence loops.
± Derivatives are calculated.
± All variables are accessible.
± Robust and fast solvers.
± Self diagnostics to identify modeling errors.
. The models to be applied are:
± A set of equations written in residual format f (X)= 0.
± The solution of the model equations is distinct from its formulation.
± Equipped with detailed information about its structure as:
(i)list of equations and variables;
(ii)incidence matrix which variables are in which equations;
(iii)function to return to residual values and derivatives; and
(iv)variables can be fixed or set free:
. Target for an accuracy which is relevant for the objective. To limit the size of
the problem, short-cut approaches might be used for those units that play
neither an essential nor a constrained role in the optimization. Examples for
simplification are:
± the use of splitter boxes for units where energy or solvent consumption are
calculated from the inlet stream,
± short cut simulation for distillation, extraction, stripping absorption
± lumping of trays for columns,
± elimination of small equipment as pumps
. As optimization always means that the process runs against constraints, a
detailed description is required in those areas. A feedback on process param-
eters which are subject to change, such as fouling of heat exchangers, com-
pressor efficiencies, or aging catalyst, are essential when these have a relevant
impact on the performance.
. Reactor models are, in general, essential for the optimal operation due to the
trade-offs between conversion, selectivities, product distribution, and its aging
effect. Exceptions might be reactors running at 100% conversion with a self-
optimizing control on the selectivity. Reactor models might be implemented
as empirical models within a fundamental-based flowsheet model. The model
can be developed based on input and output analysis, although it should cover
the full operational range for the optimization. The operational range is often
larger than originally anticipated for a process without an optimization.