Prediction of thermodynamic derivative properties of fluids by Monte Carlo simulation

Abstract

We compute second order derivatives of the Gibbs energy by Monte Carlo simulation in the isobaric–isothermal ensemble for fluids made of rigid and flexible molecules and test the accuracy of the simple interactions potential. The thermal expansivity and the isothermal compressibility can be calculated directly during a simulation run. The total heat capacity is obtained as the sum of the residual heat capacity computed using the fluctuation method and the ideal heat capacity, which cannot be determined by Monte Carlo simulation and must be taken from experimental data. The Joule–Thomson coefficient is obtained by the combined use of thermal expansivity and total heat capacity. The fluctuation method proves to converge very well, with limitation at low pressure for the Joule–Thomson coefficient. The fluctuation method has been extensively tested on pure light hydrocarbons (methane, ethane and butane) in the vapour and liquid states. In the case of methane, we used a united atom Lennard-Jones potential (D. Möller, J. Oprzynski, A. Müller and J. Fischer, Mol. Phys., 1992, 75, 363). Detailed comparison with experimental heat capacities, volumetric properties and Joule–Thomson coefficients at pressures up to 100 MPa showed excellent agreement. The inversion of the Joule–Thomson effect is predicted with an excellent accuracy. In the case of ethane and n-butane, we used an anisotropic united atoms potential (P. Ungerer, C. Beauvais, J. Delhommelle, A. Boutin, B. Rousseau and A. H. Fuchs, J. Chem. Phys., 2000, 112, 5499). Comparison with experimental data available up to 10 MPa shows that ethane properties are well predicted. For n-butane, derivative properties have been determined in the gas and in the liquid state with good agreement in both phases. Finally, tests made on a methane–ethane system at pressures up to 100 MPa show that the fluctuation method can be extended to mixtures without any further complication.