Reduction of a Urea Crystallizer Model by Proper Orthogonal Decomposition and Best-Points Interpolation

Abstract

A reduced model of a urea crystallizer is developed for process control purposes. It is derived from a reference model, which describes the formation of particles in fluid flow and is of very high order. A strong reduction of the system order is achieved by proper orthogonal decomposition (POD). However, it turns out that POD alone does not lead to a satisfactory reduction of the computation time. The reason is the presence of nonlinear terms in the reference model whose evaluation is quite costly in the reduced model. To get a speed-up of the reduced model, the nonlinear terms are approximated by an interpolation technique. The resulting reduced model is 500 times smaller and 100 times faster than the reference model, while the loss of accuracy is marginal.

Model reduction techniques for the simulation of particle populations in fluid flow

“…An efficient alternative, the so-called best point interpolation, is presented in [22]. The results also indicate that a low number of basis functions can capture the overall system behaviour for low Reynolds numbers and sufficiently large diffusion.…”

Modellreduktion von Populationssystemen mit Hilfe von Proper Orthogonal Decomposition

“….., N c erhält man durch Einsetzen der Approximationen in die Bilanzgleichungen (11,12) und Gewichtung des Residuums mit den Basisfunktionen:…”

Automatic model reduction of differential algebraic systems by proper orthogonal decomposition

“…In this work Proper Orthogonal Decomposition (POD) [9,10,11,12] is used for the development of an automatic procedure for model reduction. This method has been successfully applied for numerous problems in the fields of fluid dynamics, optimal control, and for population balance systems like crystallizers [13], [14], and granulators [15]. To put it in other words, the model reduction by POD is a proven approach.…”