Estimation of Spatial Concentration Profiles in a Plug Flow Reactor using Reduced Dimensional Models

Abstract

Efficient monitoring and control of a plug flow reactor system requires knowledge of temporal variations of spatial profiles of concentrations. However, estimating the state profiles in spatial domain requires discretization of the governing PDEs at a large number of spatial grid points, which results in high order DAE systems. Computational cost associated with solving these DAEs makes them unattractive candidates for development of advanced on-line monitoring and control schemes. In this work, a novel method for reconstructing spatial profiles of state variables is proposed, which exploits the fact that orthogonal collocation based discretization of PDEs employs time-dependent interpolation polynomials as approximate solutions. A reduced-order approximation of PDE system is developed using Lagrange interpolation polynomials and further used to develop a reduced dimensional extended Kalman filter (EKF). States estimated using the reduced-order EKF, in combination with Lagrange polynomials, are used to construct estimates of spatial profiles of state variables. The proposed approach facilitates handling of measurements available from sensors placed at arbitrary spatial locations other than the collocation points. The performance of proposed reduced-order observer is evaluated via simulation studies performed on a benchmark counter-current plug flow reactor system. Analysis of the simulation results reveals that the proposed approach is capable of generating state profile estimates that are comparable to profile estimates obtained using a high dimensional observer with a significant reduction in the computational cost.