(624e) 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.

Literature:

[1] J.W. Cahn, J.E. Hilliard, J. Chem. Phys. 28 (1958) 258.

[2] C.I. Poser, I.C. Sanchez, Macromolecules 14 (1981) 361.

[3]
T. Grunert, H. Rudolph, S. Enders, Zeitschrift für Physikalische Chemie 227
(2013) 1.

[4]
T. Grunert, S. Enders, Fluid Phase Equilibria 381 (2014)
46.