MODEL REDUCTION OF PROCESS SYSTEMS USING ORTHOGONAL POLYNOMIALS

Abstract

Usually tray-by-tray rigorous models of separation columns are complex and of a high order. Their application in the field of simulation and optimization is very costly. It is practically impossible to apply modern methods of system theory to design control systems based on such models. Therefore the development of reduced order models is of great use. Present study incorporates the development of reduced order models for process system, which are of great use as rigorous models of separation columns are complex and of a high order. It has made it possible to use this technique in situations where there are a large number of simulations to be performed as in steady state or dynamic optimization, process system interaction analysis, control system synthesis and evaluation. Reduced order dynamic models for absorber and distillation columns are developed using the polynomial approximation method using orthogonal collocation,. technique. The model reduction procedure is based on approximating the composition and flow profiles in the column using different polynomials rather than as discrete functions of the stages. The number of equations required to describe the system is thus drastically reduced. The method is developed using simple absorber system, which is extended to distillation system. The discontinuities in column profiles introduced by feeds are partially removed through suitable redefinition of variables, thus enabling the column profiles to be fitted with a single polynomial across the entire column. The strengths and weaknesses of these reduced order models are explored by taking example of multi-component distillation. Results obtained by reduced order modeling are also compared with those obtained by tray-by-tray rigorous modeling.