Modelling of Time-Dependent Interfacial Properties Due to Chemical Equilibrium Reactions in Demixed Fluid Systems

Modelling of time-dependent interfacial properties due to chemical equilibrium reactions in demixed fluid systems

Andreas Danzer, Sabine Enders

Karlsruhe Institute of Technology, Institute of Technical Thermodynamics and Refrigeration Engineering, Engler-Bunte-Ring 21, D-76131 Karlsruhe, Germany.

Email: andreas.danzer@kit.edu; sabine.enders@kit.edu

Key words: reactive extraction, impact of chemical reactions on interfacial properties, model calculations

Abstract:

Reactive extraction, the integration of reaction and extraction within one unit operation, is a promising process in a variety of applications. Compared with the conventional process of carrying out reaction and separation sequentially, the in-situ removal of products formed in the reaction zone can favorably influence conversion and selectivity, especially of equilibrium reactions. Together with a significantly reduced effort in the task of separation, this can result in major energy as well as capital cost savings. However, there are feasibility constraints resulting both from thermodynamics and chemistry. In addition, the process intensification leads to higher complexity and thus the need for research in terms of modelling productiveness. Because of that model calculations of hypothetically ternary liquid-liquid reactive extraction systems were performed in this work. The liquid-liquid phase equilibrium was calculated with the well-known, quite simple Margules activity model, the interfacial properties were modelled with the Margules equation in combination with the Density Gradient Theory [1-4] (DGT). It was assumed that the chemical reaction occurs in a A ⇋ B manner, whereas the solvent C does not participate in the chemical equilibrium reaction. Furthermore, the assumption was made that mass transfer occurs at speed of infinity, so the chemical reaction is rate determining, in contrast to the reach of phase equilibrium. The empirical constants of the Margules equation A_i,j, the so called influence parameter κ of the DGT as well as the chemical equilibrium constant K=k₁/k₂ were specified due to the need to serve as a model. For real systems, A_i,j must be fitted to experimental equilibrium data of the binary subsystems, the influence parameter κ has to be fitted at one experimental data point of the interfacial tension of each binary system with a miscibility gap and K is determined by the chemical reaction. It was found that the time, to reach chemical equilibrium in addition to the phase equilibrium, is strongly dependent on the shape of the miscibility gap as well as on the slope of the tie lines. Furthermore, the interfacial tension of the demixed system decreases over time, because of the fact that the product of the chemical equilibrium reaction act as a solubilizer. The slope of the interfacial tension over time strongly corresponds to the quotient of the reaction rate of forward and backward reaction. The new theoretical framework allows to the first time the calculation of time-dependent interfacial tensions and can further transferred to real systems.

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