Performance of reduced distillation models in dynamic real-time optimisation
Systematic methods and tools for managing the complexity
Process Simulation & Optimization - II (T4-9b)
Keywords: dynamic real-time optimization, model reduction, aggregated models, distillation
The interest in dynamic real-time optimization (DRTO) using first-principle nonlinear models for distillation columns has grown recently. Compared to decentralized control systems and linear model predictive control schemes, DRTO covers a broader range of operating conditions and allows the prediction of optimal transitions like e.g. load changes. Furthermore, a profitable and flexible operation is ensured by the usage of economic optimization objectives in DRTO. However, the solution of optimization problems with nonlinear, possibly stiff models carries a substantial computational load, which restricts the usage of these models in real-time applications. For this reason, research currently focuses on reducing the complexity of the models as well as developing efficient algorithms for solving dynamic optimization problems in real-time. In this work, the computational load of reduced and rigorous distillation column models are compared when applied in a real-time optimization algorithm for receding horizon control.
The reduced models are obtained by applying a well-established tray aggregation method (1). In the present study, a binary model of a distillation column with constant tray hold-ups and one material balance per tray is used. This method has been successfully extended to more complex distillation models recently (2). Although the method is physically intuitive and yields low-order reduced models, the question whether these models give a computational advantage over non-reduced models has to be answered taking into account the complete dynamic optimization procedure. This is because the efficient solution of a model with a certain structure crucially depends on suitable numerical integration and optimization techniques.
Taking this fact into account, the reduced and the full model are compared in terms of computational load and accuracy of the predicted control trajectoies in an online optimization scenario, where simulated disturbances in the feed require repeated optimizations of the control trajectory on a moving horizon. It is found that the computational load of the reduced model for the optimization is reduced due to the lower dynamic order of the model. However, the present study shows that in order to use a reduced model in a computational advantageous fashion, care has to be exerted regarding its implementation and the selection of the real-time optimization configuration.
(1) J. Levine and P. Rouchon: Quality Control of Binary Distillation Columns via Nonlinear Aggregated Models, Automatica, Vol. 27, No. 3, 1991, pp 463-480.
(2) S. Khowinij et al.: Dynamic compartmental modeling of nitrogen purification columns, Separation and Purification Technology, Vol. 46, 2005, pp 95-109.
Presented Tuesday 18, 08:45 to 09:05, in session Process Simulation & Optimization - II (T4-9b).
