Studies on Process Modelling, Simulation, and Control with Applications to Distillation Columns

Abstract

This thesis discusses modelling of industrial plants with focus on distillation. A generic industrial plant (or section of plant) can be abstracted as a set of capacities exchanging extensive quantities through connecting streams. Thus the studied system can be represented as a directed graph, where the capacities are the nodes and the streams are the arcs. A cascade of simplified first-principle models is accomplished by a systematic procedure that combines singular perturbation of the negligible capacities and lumping those capacities with similar dynamics. The proposed procedure is associated with order-of-magnitude assumptions and it is based on simple algebraic operations. Examples are made with the dynamic flash.

Given an introduction to distillation modelling, two dynamic first-principle distillation models are proposed, namely a nonequilibrium model and an equilibrium model. The initialisation of the corresponding DAE (differential and algebraic equations) systems is analysed. The aim is to provide the models with feasible steady-state starting conditions. The used initialisation procedure is based on: (i) a nonlinear algebraic solver to create consistent initial conditions, and (ii) a DAE solver to move from a generic (but consistent) starting point to feasible operating conditions.

To reduce the computation time, it is recommended to use DAE solvers that exploit the structure of the system’s sparsity (tridiagonal blocks matrix in the case of distillation column models). Very frequently, unstructured elements may enter the description. They are common in process control applications, where the states added to the plant description by the integral parts of the controllers introduce unstructured elements in the otherwise very structured Jacobian of the mathematical model. A solution to the handling of “dirty” Jacobians is presented, which is implemented in a DAE solver package available free on internet. This novel DAE solver fully exploits the overall structure of the system’s sparsity, without compromising CPU computation time and precision of the results.

The concern of the computation speed of the dynamic models is particular important in on-line applications such as model predictive control (MPC). To facilitate MPC implementations, it is proposed a self-adaptive approach based on simplified nonlinear models. The proposed methodology yields an MPC that adjusts the dimension of the model according to both the current process conditions and the control objectives. To reduce the size of the model, balanced truncation method is also investigated. When balanced truncation is extended to nonlinear models, it is recommended to consider all the states as balancing outputs in order to accurately reconstruct all the original states.

In addition, to give more robustness to truncation and to obtain smaller models, it is suggested to reduce the nonlinearities of the original model using a static transformation of the variables. In case of distillation column models, logarithmic compositions are a solution.