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In this paper, we investigate the stability analysis and the feedback stabilization design problem for multiphase chemical systems using a nonequilibrium thermodynamics formalism. We first present a compartmental model for multiphase systems far from thermodynamic equilibrium. The modeling framework allows us to describe irreversible multiphase systems as a differential-algebraic equation (DAE) system. The differential part of the model corresponds to macroscopic balance equations. The algebraic system of equations represents the interface thermodynamic subsystem that occurs between bulk phases. Integrating the DAE model is equivalent to fixing the degrees of freedom prescribed by the Gibbs phase rule. A linear stability analysis and numerical simulations for the resulting differential-algebraic model are presented. We stabilize the system by fixing the pressure to a constant value. Following this result, we present a feedback structure that fixes the pressure of the system using the proposed modeling framework.

Multiphase processes are frequently assumed to evolve restricted by thermodynamic equilibrium relations. In this article, we study the possibility of multiphase systems to evolve far from thermodynamic equilibrium while contained in what we call a domain of physical feasibility. We show that processes evolving in the domain of feasibility have a positive definite internal entropy production rate. Being positive definite, the internal entropy production stands as a Lyapunov function candidate to characterize the stability of equilibrium for irreversible multiphase systems contained in the feasibility domain. In addition, the thermodynamic-based approach considered in our study provides phenomenological insight into the dynamic properties of multiphase systems. Counter-flow interface molar transport processes, for instance, are found to be thermodynamically stable provided that the transport is bounded by a function that depends on the deviation from thermodynamic equilibrium.

This article presents a modeling framework for a class of multiphase chemical systems based on non-equilibrium thermodynamics. Compartmental modeling is used to establish the dynamic properties of liquid-vapor systems operating far from thermodynamic equilibrium. In addition to the bulk-phase molar/energetic dynamics, interface transport processes yield to algebraic constraints in the model description. The irreversible system is thus written as a system of Differential-Algebraic Equations (DAEs). The non-equilibrium liquid-vapor DAE system is proven to be of index one. A local stability analysis for the model shows that the equilibrium state is unstable for non-isobaric operation regimes, whereas numerical evidence shows that isobaric operation regimes are stable. To extend the stability analysis, internal entropy production for the irreversible flash-drum is presented as a Lyapunov function candidate., Comment: Article sent to a journal for publication

In this note, we derive a dynamical model that tracks the evolution of the internal energy, the volume and the molar compositions of composite systems. The proposed modeling approach considers interface transport using a non-equilibrium thermodynamic perspective and predicts dynamical trajectories to thermodynamic equilibrium. Both closed and open systems are considered and, for both cases, it is shown that expected equilibrium properties are recovered. Numerical simulations based on the proposed model show the potential of the proposed non-equilibrium approach for open and closed multiphase systems.

For a class of continuous stirred tank bioreactors to produce ethanol at large scale, this work evaluates suitable control configurations in a model predictive control framework. The study makes several assumptions, including a non-square plant, a distinction between control and output variables, and the possible sets of available outputs. Since the outputs are obtained in a discrete form, also the effect of the sampling interval was evaluated. Operational-feasible configurations are discussed. Herein, it is highlighted that a conventional configuration of one input-one control variable driven by one output, is the best to maintain all the three states around their nominal values.