Page 174 - Sustainability in the Process Industry Integration and Optimization

CHAPTER 7

Process

Optimization

Frameworks

7.1 Classic Approach: Mathematical Programming

Process system engineering problems, including process synthesis,
are typically considered as optimization problems. The solution or
solutions of these problems are usually generated by solving the
corresponding mathematical models. However, a review of recent
publications reveals various failures in modeling process synthesis
(Friedler and Fan, 2009). An inappropriate mathematical model may
result in a nonoptimal or even an infeasible solution or the model
may be unsolvable because of its complexity. A mathematical model
should be a valid representation of the process, taking into account
all its significant features, and still be solvable.
Process optimization problems are formulated as mathematical
models, where variables correspond to decisions (e.g., the flow rate of
a stream, the amount of heat provided by high-pressure steam) and
constraints correspond to the conceptual model of the system (e.g.,
material balance). Optimization (or Mathematical Programming)
aims to find appropriate values for the variables in such a way
that (1) constraints involving these variables are satisfied and (2) a
specific function—that is, the objective function—of these variables
is minimized (or maximized). The constraints define the search
space, while the objective function is to determine the most favorable
“point” or “points” in this space.
Mathematical models are classified according to the types of
variables (continuous or integer) and constraints (linear or nonlinear).
Therefore, a mathematical model can be linear in constraints and
objective function with continuous variables (i.e., linear programming,
LPR). Similarly, a mathematical model is viewed as a nonlinear

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