Dynamic Optimization in Process systems

Abstract

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].