Abstract
The kinetic gas theory, in particular the equations of Chapman and Enskog, proved to be good and widely applicable approximations for modeling transport properties like diffusion coefficients, viscosities and thermal conductivities. However, these equations rely on at least the Lennard-Jones parameters and for polar gases also the dipole moment. In the scientific literature, the Lennard-Jones parameters are fitted to only one experimentally determined transport coefficient. This approach leads to good agreement between the Chapman Enskog equations employing the so obtained parameters with the experimental data for this specific transport property. However, utilizing the same parameters for modeling different transport properties oftentimes leads to distinct deviations. In this work, it is shown that the subset of Lennard-Jones parameters with which the Chapman Enskog equations can predict the experimental results with deviations comparable to the experimental uncertainty are not identical for each transport property. Hence, fitting towards one property doesn’t necessarily yield parameters that are suited to describe the other transport properties. In this publication, the Lennard-Jones parameters and a temperature dependent Eucken correction factor, leading to a significantly higher accuracy than the classical Eucken correction and also its modification by Hirschfelder, are therefore fitted towards all three transport properties simultaneously for seven exemplary gases. This approach leads to a significantly better agreement with experimental data for the three transport properties than the classical approach that relies on fitting to one single transport property and can be utilized to determine accurate sets of Lennard-Jones parameters and Eucken correction factors for any gas species. It provides a computationally inexpensive and practical method for the precise calculation of transport properties over a wide range of temperatures relevant for processes in the chemical industry.
Highlights
Introduction and theoryThe accurate determination of diffusion coefficients, thermal conductivities and viscosities of gases has a decisive impact on the precision of computational models in chemical engineering
These subsets can be determined for each different transport property and since the diffusion coefficient is based on a collision integral with a different order than the thermal conductivity and the viscosity (please see Eqs. (1), (2), and (3)), these subsets can differ markedly
If the LJ parameters were fitted to viscosity data alone, as it is oftentimes done in the literature, there is a chance that the obtained parameters are not suited for describing the thermal conductivity or the binary diffusion coefficient
Summary
Introduction and theoryThe accurate determination of diffusion coefficients, thermal conductivities and viscosities of gases has a decisive impact on the precision of computational models in chemical engineering. The development of potential energy surfaces (PES) for interactions between two gas molecules using quantum mechanical ab initio calculations was employed extensively for calculating properties like the second virial coefficient, diffusion coefficients, thermal conductivities and viscosities of gases based on the kinetic theory for polyatomic gases [1, 2]. This approach is fully predictive and showed good precision for a variety of gases [3, 4]. Due to its simplicity, the here proposed approach can be carried out by non-experts in the field for any desired gas species for which experimental data is available
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