# Integrated Chemical Process Optimization: NLP Strategies Based on Multi-Scale Engineering Models

Lorenz T. Biegler*

The development of efficient algorithms for Nonlinear Programming (NLP) and Mathematical Programs with Complementarity Constraints (MPCCs), along with large-scale optimization modeling platforms has led to powerful strategies for process optimization. Nevertheless, these strategies continue to be challenged by the development, application and integration of multi-scale models. The state of the art for chemical process optimization deals with lumped parameter and equilibrium-based models; NLPs and MPCCs formulated for this task can often be addressed with efficient solvers. On the other hand, there is a growing need to integrate these process models with multiple time and length scales that include molecular dynamics, complex fluid flow, population balances and nonlinear dynamic systems. Addressing this integrated optimization problem requires model reduction strategies that still guarantee convergence to the optimization problem defined by the Original Detailed Models (ODMs). To address this multi-scale process optimization task, we extend well-known trust region frameworks for ROM-based optimization to chemical processes that incorporate multiple reduced models (RMs), often derived from physics-based reductions and engineering shortcuts. We further develop a strategy that minimizes frequent recourse to ODM evaluations, using the concept of $\epsilon$-exact RMs. Convergence properties of this approach are discussed and numerous process examples are presented that demonstrate the effectiveness of this strategy.

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Plenary Lecture