Computational strategies for the optimal operation of large-scale chemical processes

This dissertation deals with the development of computational strategies that enable the implementation of sophisticated first-principles dynamic models in on-line chemical process operations. During the last years, it has been recognized that first-principles models can lead to a tighter integration of the decision-making hierarchy and, consequently, to an increased process performance. The development and implementation of model-based applications involves the extensive use of parameter estimation, state estimation, data reconciliation, model predictive control, and real-time optimization techniques which require the solution of optimization problems constrained by differential and algebraic equations (DAEs). As models of increasing sophistication are considered, the computational complexity of these problems becomes a crucial obstacle. In this work, we present strategies targeted towards this issue. The strategies are based on simultaneous full-discretization approaches and sparsity-exploiting interior-point nonlinear programming (NLP) solvers. In addition, they make use of classical numerical linear algebra techniques and NLP sensitivity concepts. We first derive strategies for large-scale parameter estimation including standard leastsquares and advanced errors-in-variables formulations. Here, we exploit the multi-set structure of these problems inside the NLP solver and derive strategies to extract large-scale covariance information directly from the Karush-Kuhn-Tucker (KKT) matrix. In addition, we establish connections between the numerical properties of the KKT matrix, second order optimality conditions and observability in order to verify the uniqueness of the estimates through the NLP solver. We then derive on-line synchronization strategies for moving horizon state estimation (MHE) and nonlinear model predictive control (NMPC). These strategies are based on an advanced-step principle which allows to accommodate large-scale dynamic models in on-line environments. Here, we use the dynamic model to predict the future state and measurements, use this information to solve reference problems in between sampling times, and correct these solutions on-line using NLP sensitivity. This predictor-corrector type strategy allows to minimize the on-line computational time by at least two orders of magnitude and to decouple the MHE and NMPC problems solved in background. We establish rigorous bounds on the loss of optimality, sufficient stability conditions and connections with traditional strategies such as Riccati-like regulators and Kalman filters. Finally, we implement the proposed computational strategies in the state-of-the-art NLP solver IPOPT and demonstrate the concepts through small-scale case studies. Scale-up and computational performance are demonstrated in a large-scale low-density polyethylene tubular reactor process. In this process, we use a detailed first-principles reactor model to derive an economics-oriented operational framework able to improve its overall profitability.