F. Couenne

Bond graph modelling for chemical reactors

In this paper we present a bond graph model of a continuous stirred tank reactor which represents the reaction kinetics as well as the heat and mass transport phenomena in the reactor. The consequences of reticulation of the phenomena and of the systematic use of the power conjugated variables on the formulation of the thermodynamic properties, the reaction kinetics and the energy and mass transport are shown. A classical example of chemical reaction is chosen to illustrate this approach: the equilibrated reaction of hydrogen and iodine in hydrogen iodide.

Model predictive control of a catalytic reverse flow reactor

This paper deals with the control of a catalytic reverse flow reactor. The aim of this process is to reduce, by catalytic reaction, the amount of volatile organic compounds (VOCs) released into the atmosphere. The peculiarity of this process is that the gas flow inside the reactor is periodically reversed in order to trap the heat released during the reaction. This allows use of the reactor in a heat saving mode. The goal of this work is to provide a model predictive control (MPC) framework to significantly enhance the poor overall performance currently obtained through the actual control strategy. It is directly addressed for the nonlinear parabolic partial differential equations (PDEs) that describe the catalytic reverse flow reactor. In the context of the application of MPC to this particular distributed parameter system, we propose a method that aims to reduce the online computation time needed by the control algorithm. The nonlinear model is linearized around a given operating trajectory to obtain the model to be solved on-line in the approach. MPC strategy combined with internal model control (IMC) structure allows using less accurate and less time-consuming control algorithm. Method efficiency is illustrated in simulation for this single-input-single-output system.

Structured modeling for processes: A thermodynamical network theory

We review the use of bond graphs for modeling of physico-chemical processes. We recall that bond graphs define a circuit-type language which root on a thermodynamical consistent definition of its network elements. We present the bond graph basic elements in the light of lumped models arising from chemical engineering. We first illustrate it on the historical example of the diffusion process through a membrane. The examples of a Continuous Stirred Tank Reactor and an adsorption process illustrate how the network structure and the choice of variables ease the reusability of submodels and localize the changes in models to some network elements.

Enthalpy based modelling and design of asymptotic observers for chemical reactors

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.

On the passivity based control of irreversible processes

Irreversible port-Hamiltonian systems (IPHS) have recently been proposed for the modelling of irreversible thermodynamic systems. On the other hand, a classical result on the use of the second law of thermodynamics for the stabilization of irreversible processes is the celebrated thermodynamic availability function. These frameworks are combined to propose a class of Passivity Based Controller (PBC) for irreversible processes. An alternative formulation of the availability function in terms of internal energy is proposed. Using IPHS a matching-condition, which is interpreted in terms of energy-shaping, is derived and a specific solution that permits to assign a desired closed-loop structure and entropy rate is proposed. The approach can be compared with Interconnection and Damping Assignment-PBC, this method however leads in general to thermodynamically non-coherent closed-loop systems. In this paper a system theoretic approach is employed to derive a constructive method for the control design. The closed-loop system is in IPHS form, hence it can be identified with a thermodynamic system and the control parameters related with thermodynamic variables, such as the reaction rates in the case of chemical reactions. A generic non-linear non-isothermal continuous stirred tank reactor is used to illustrate the approach.

Lyapunov based control for non isothermal continuous stirred tank reactor

Abstract In this contribution we apply the approach of passivity proposed by Ydstie [M. Ruszkowski, V. Garcia-Osorio, and B.E. Ydstie. AIChE Journal, 2005] for physico-chemical processes. The originality of this work lies in the fact we consider a thermodynamically nonlinear consistent model for a continuous stirred tank reactor to built the appropriate Lyapunov function for stabilization purpose. Indeed the kinetics of reaction modelled by Arhenius law leads to non linear model with multiple steady state. We propose to stabilize the reactor around the unstable point. In order to apply the Ydstie approach, we assume that the fluid remains homogeneous. This assumption permits to use the concavity property of the entropy function to build the Lyapunov function. We propose feedback laws in order to ensure the closed loop properties of the Lyapunov function. Finally we propose some simulation results.

Port-based modelling of mass transport phenomena

The goal of this article is to present an extension of the port-based modelling approach (bond graphs) which applies to systems subject to heat and mass transfer. The methodology is based on the first principle, conservation laws and constitutive closure relations. The latter are the phenomenological laws relating fluxes and thermodynamic forces. Then instantaneous power conservation appears naturally as a geometric interconnection structure called Dirac structure. The multi-level case (several macroscopic spatial scales) is investigated with the assumption that the spatial scales are separated and may be considered as two distinct phases. In this case, it is shown that both the interconnection coupling within a phase and the multi-level interconnection coupling are Dirac structures.

Thermodynamics based stability analysis and its use for nonlinear stabilization of the CSTR

Abstract We show how the availability function as defined from the entropy function concavity can be used for the stability analysis and derivation of control strategies for non-isothermal Continuous Stirred Tank Reactors (CSTRs). We first propose an overview of the required thermodynamic concepts. Then, we show how the availability function restricted to the thermal domain can be used as a Lyapunov function. The derivation of the control law and the way the strict entropy concavity is insured are discussed. Numerical simulations illustrate the application of the theory to the open loop stability analysis and the closed loop control of liquid-phase non-isothermal CSTRs. The proposed approach is compared with the classical proportional control strategy. Two chemical reactions are studied: the acid-catalyzed hydration of 2-3-epoxy-1-propanol to glycerol subject to steady state multiplicity and the production of cyclopentenol from cyclopentadiene by acid-catalyzed electrophilic addition of water in dilute solution exhibiting a non-minimum phase behavior.

From Brayton-Moser formulation to Port Hamiltonian representation: the CSTR case study

Abstract This paper shows that any thermodynamic potential fulfilling some thermodynamic stability criterion (e.g. the chemical affinity or the ectropy) can be used as a potential function for the dissipative (pseudo) Port Hamiltonian formulation of the non isothermal Continuous Stirred Tank Reactor (CSTR) model. Besides Brayton-Moser formulation is used to obtain some dissipative Port Hamiltonian representation.

Thermodynamic approach for Lyapunov based control

Abstract Abstract This paper focuses on non linear control of non isothermal Continuous Stirred Tank Reactors (CSTRs). The model of the CSTR is thermodynamically consistent in order to apply the control strategy based on the concavity of the entropy function and the use of thermodynamic availability as Lyapunov function. More precisely the stabilization problem of continuous chemical reactors is addressed operated at an unstable open loop equilibrium point. The chosen control variable is the jacket temperature. In this paper we propose a state feedback strategy to insure asymptotic stability with physically admissible control variable solicitations. Theoretical developments are illustrated on a first order chemical reaction.