Dynamic Optimization in Process Systems

Abstract

Dynamic models describe many operations and processes that take place in several disciplines, including chemical engineering, economics, ecological engineering, management of communications services and aeronautics, among others. Many processes and applications in the chemical industry are intrinsically dynamic. Such processes include the operation of batch and semibatch reactors, intensively used for the production of specialty chemicals, pharmaceutical and high-value products, and polymers. For continuous processes, dynamic optimization is used in the design of distributed systems, such as plug flow reactors and packed distillation columns; as well as in the determination of optimal trajectories in the transition between operating conditions and in handling load changes. For model building of dynamic systems and model validation with experimental data, parameter estimation also requires dynamic optimization. Moreover, process control problems in chemical engineering as an example of online applications require dynamic optimization, especially in the case of multivariable systems that are nonlinear with input and output constraints. In particular, nonlinear model predictive control and dynamic real-time Mathematical models describing dynamic optimization problems involve large sets of partial differential algebraic equations, with constraints on control and state variables, leading to infinite-dimensional problems. The development of robust numerical strategies, together with the increasing computational capacity has paved the way to the formulation and solution of dynamic optimization problems within key applications in chemical engineering. Therefore, dynamic optimization has become an important tool in current industrial operations and decision-making processes.This chapter provides a general description of dynamic optimization problems and available numerical methods. These methods can be broadly classified as indirect or variational approaches and direct approaches, which can be further divided into sequential and simultaneous. In direct methods, the problem is discretized and the infinite-dimensional nature of the dynamic optimization problem is transformed into a finite-dimensional problem. Available software for both approaches is mentioned and briefly described. Finally, two typical examples in process and ecological engineering are presented. The first problem is the dynamic optimization between two operation states in a continuous stirred tank, which is solved with sequential and simultaneous strategies in gPROMS [1], and IPOPT [2] within AMPL [3], respectively. The objective is to minimize the transient between both steady states. Numerical results are presented for increasing discretization degree, with comparison of number of variables in the nonlinear problem and computational time. Different objective function weights are also explored. The second example is a parameter estimation problem for a water quality model that includes phosphorus cycle through phytoplankton, phosphate and organic phosphorus dynamics. The model is solved with a simultaneous approach with IPOPT [2] in GAMS [4].