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Correlation and Prediction of Transport Properties in near-Critical and Supercritical Fluids Using the Speadmd Model

J. Richard Elliott1, Zeynep N. Gerek2, and Neil H. Gray2. (1) Chemical and Biomolecular Engineering, University of Akron, Akron, OH 44325-3906, (2) The University of Akron, Dept. of Chemical Engineering, Akron, OH 44325

The Step Potential Equilibria And Discontinuous Molecular Dynamics (SPEADMD) model provides a basis for molecular modeling of thermodynamic and transport properties. It is based on Discontinuous Molecular Dynamics (DMD) and second order Thermodynamic Perturbation Theory (TPT). DMD simulation is applied to the repulsive part of the potential, complete with molecular details like interpenetration of the interaction sites, 110° bond angles, branching, and rings.1,2 The thermodynamic effects of disperse attractions and hydrogen bonding are treated by TPT. This approach accelerates the molecular simulations in general and the parameterization of the transferable potentials in particular. Transferable potentials have been developed and tested for over 200 components comprising 22 families.

Unfortunately, there is no theory comparable to TPT when treating transport properties.3 Most theories of transport properties rely on empirical variations of correlations for spherical reference fluids. Furthermore, existing correlations are typically specific to a given range of conditions: gas, dense gas, or liquid, for example. Near-critical and supercritical fluids are generally between these liquid and dense gas regimes, and solutes may be significantly non-spherical. In the present work, we develop an entirely general framework for estimating transport properties of molecules and mixtures that may be spherical or polymeric over any desired range of conditions. We isolate the effects of disperse attractions by independently simulating transport properties for the reference potential over a range of densities. These simulations are applied to n-alkanes from C2-C16 with packing fractions ranging from 0.1-0.6 and temperatures ranging from 300-500K. Diffusivity, shear viscosity, and thermal conductivity were simulated by equilibrium molecular dynamics using the Einstein relations. The effects of attractive forces were treated with a perturbation expansion in reciprocal temperature to represent the added frictional contribution, fA. The coefficients of the fA expansions for each property were determined by correlating experimental data for C2-C16.

Comparing to experimental data is complicated by the influence of the softness of the potential. Softness necessitates a small correction for the effective density before comparison with experiment is feasible. With these adaptations, we obtained ~9% AAD for diffusivity, ~6% AAD for viscosity, and ~4 %AAD for thermal conductivity of alkanes from methane through n-hexadecane. These compare to ~39 %AAD for diffusivity by the method of Liu et al.,4 and ~26 %AAD for viscosity, and ~11 %AAD for thermal conductivity by the TRAPP method.5 On a preliminary basis, the methodology has been extended to non-alkanes by relating the transport displacements of the reference fluids to equivalent n-alkane reference fluids. This relation is established purely through simulations of the given molecular structure and requires no added empirical parameter. A single, compound-specific parameter is introduced to characterize the effective strength of the attractive energy relative to the reference n-alkane (e eff). Alternative methods require the introduction of two compound-specific parameters. With these adaptations, we obtained ~19% AAD for diffusivity, ~14% AAD for viscosity, and ~26 %AAD for thermal conductivity of 35 non-alkanes. These compare to ~66 %AAD for diffusivity by the method of Liu et al., and ~15 %AAD for viscosity, and ~37 %AAD for thermal conductivity by the TRAPP method.

Keywords: Physical properties, molecular dynamics simulation, vapor pressure, density, phase equilibria, thermodynamic perturbation theory, intramolecular correlations, diffusivity, shear viscosity, and thermal conductivity.

(1) Cui, J.; Elliott Jr., J. R. Phase Diagrams for Multi-Step Potential Models of n-Alkanes by Discontinuous Molecular Dynamics/Thermodynamic Perturbation Theory.J. Chem. Phys. 2002, 116, 8625.

(2) Unlu, O.; Gray, N. H.; Gerek, Z. N.; Elliott, J. R. Transferable Step Potentials for the Straight Chain Alkanes, Alkenes, Alkynes, Ethers, and Alcohols.Ind. Eng. Chem. Res. 2004, 43, 1788-1793.

(3) Alder, B. J.; Alley, W. E.; Rigby, M. Correction to the Van Der Waals Model for Mixtures and for the Diffusion Coefficient.Physica 1974, 73, 143-155.

(4) Liu, H.; Silva, C. M.; Macedo, E. A. Unified approach to the self-diffusion coefficients of dense fluids over wide ranges of temperature and pressure: hard-sphere, square-well, Lennard-Jones and real substances.Chem. Eng. Sci. 1998, 53, 2403.

(5) Huber, M. L.; Hanley, H. J. M. In Transport properties of fluids: their correlation, prediction, and estimation; Millat, J., Dymond, J. H., Nieto de Castro, C. A., Eds.; Cambridge University Press: New York, 1996.