Calculation of the transport properties of dense fluids using modified Enskog theory and an appropriate equation of state

Abstract

In this work, a new method based on the modified Enskog theory (MET) is presented for calculation of transport properties at high densities ( ρ > ρ c). The main limitation of using the MET is lack of experimental data for co-volume, b 0. We have substituted b 0 from hard sphere (HS) theory and zero density transport properties from the kinetic theory of gases for HS in the MET expression, because of the fact that dense fluids behave more and less like a HS fluid. As a result, a simple linear expression for the self diffusion ( D) and quadratic expressions for viscosity ( η) and thermal conductivity ( λ) coefficients have been obtained in terms of Y at high densities ( ρ > ρ c), where Y = ( T ( ∂ p / ∂ T ) ρ ) / ρ R T − 1 . To evaluate the obtained expressions, we have used experimental values of densities and the transport properties and calculated Y from the reported accurate equation of state (EOS) for argon and xenon. We have noticed that the quadratic fits for viscosity and thermal conductivity and the linear fit (when T < T c) for self diffusion hold quiet well with the correlation coefficient, R 2 ≥ 0.9994, when ρ > ρ c. Also, we have found that the curves for different isotherms of a fluid fall onto a common curve at high densities over entire temperature range for which experimental data exist, but the curves depend on the nature of fluid. So, by using experimental data of transport properties for one isotherm and an accurate EOS for calculation of Y for a dense fluid, we may calculate the corresponding property of that fluid for any other isotherm. In this work, we have used this approach to predict the viscosity coefficient of n-alkanes from propane to n-octane and cyclohexane at different densities ( ρ > ρ c) and temperatures. To do such predictions, we need an accurate EOS for each compound which is not generally available. For this reason, we have made use of the modified linear isotherm regularity (MLIR). Therefore, using the calculated values of density and thermal pressure coefficient from the MLIR and the coefficients of the viscosity expression for each of these fluids, their viscosities have been predicted with the average percentage error less than 1.6%. To make the approach more general, we have used the principle of corresponding states to present viscosity expression independent of fluid in terms of the reduced variables. Therefore, one may use experimental data for one isotherm of an arbitrary fluid to find the coefficients of the reduced viscosity expression. Then, these coefficients may be used for other fluids at the same reduced temperature, T r, to calculate the reduced viscosity. Here, we have selected n-butane as a reference compound because of abundance of experimental data. We have used the coefficients of the expression for n-butane and density and Y have been calculated from the MLIR, this approach gives viscosity of hydrocarbons with the average percentage error less than 1.7%. Similar approach has been used to calculate the self diffusion coefficient and thermal conductivity of dense fluids.