Enthalpy based modelling and design of asymptotic observers for chemical reactors

Abstract

This article proposes to consider the basic thermodynamics based formulation of the energy balance equation for chemical systems with a limited number of simplifying assumptions. The objective is to show, via the design of one typical mass and energy balance state observer, how such design can be modified by considering the proposed thermodynamically based model formulation. The objective is also to emphasise the difference and the links between the energy balance-based temperature equation largely used in process control. The design of the asymptotic observer is illustrated with two examples: one CSTR in liquid phase and another one in gaseous phase.

Keywords:

• thermodynamics
• enthalpy
• (bio)chemical process
• reaction invariants
• state observation

Acknowledgements

This article presents research results of the Belgian Network DYSCO (Dynamical Systems, Control, and Optimization), funded by the Interuniversity Attraction Poles Programme, initiated by the Belgian State, Science Policy Office. The scientific responsibility rests with its authors.

Notes

Notes

1. A typical case of dependent reactions are equilibrium chemical reactions where there are indeed two reactions with the same stoichiometric coefficients and two distinct reaction rates of opposite signs. It is worth noting that it can be assimilated as one single reaction whose rate is the difference between the reaction rates of both reactions and which can then be either positive or negative.

2. For the sake of simplicity, the design with (28) will not be explicitly detailed since it is exactly the same as the one presented here.