7. Steady State Process Optimization

The chapter deals with the formulation and solution of chemical process optimization problems based on models that describe steady state behavior. Many of these models can be described by algebraic equations, and here we consider models only in this class. In process engineering such models are applied for the optimal design and analysis of chemical processes, optimal process operation, and optimal planning of inventories and products. Strategies for assembling and incorporating these models into an optimization problem are reviewed using popular modular and equation-oriented solution strategies. Optimization strategies are then described for these models and gradient-based NLP methods are explored along with the calculation of accurate derivatives. Moreover, some guidelines are presented for the formulation of equation-oriented optimization models. In addition, four case studies are presented for optimization in chemical process design and in process operations.

The previous six chapters focused on properties of nonlinear programs and algorithms for their efficient solution. Moreover, in the previous chapter, we described a number of NLP solvers and evaluated their performance on a library of test problems. Knowledge of these algorithmic properties and the characteristics of the methods is essential to the solution of process optimization models.

As shown in Figure 7.1, chemical process models arise from quantitative knowledge of process behavior based on conservation laws (for mass, energy, and momentum) and constitutive equations that describe phase and chemical equilibrium, transport processes, and reaction kinetics, i.e., the “state of nature.” These are coupled with restrictions based on process and product specifications, as well as an objective that is often driven by an economic criterion. Finally, a slate of available decisions, including equipment parameters and operating conditions need to be selected. These items translate to a process model with objective and constraint functions that make up the NLP. Care must be taken that the resulting NLP problem represents the real-world problem accurately and also consists of objective and constraint functions that are well defined and sufficiently smooth.