## Determination of phase equilibria for long-chain linear hydrocarbons by Monte Carlo simulation.

##### Abstract

The focus of this study was to determine the coexistence phase equilibria for three groups of long-chain linear hydrocarbons (n-alkanes, 1-alkenes and 1-alcohols) using Monte Carlo simulation. Three common transferable united-atom force fields were used in the simulations: OPLS-UA (Jorgensen et al., 1984), TraPPE-UA (Martin and Siepmann, 1998) and NERD (Nath, Escobedo, de Pablo and Patramai, 1998). Isothermal phase equilibria was calculated over a temperature range from approximately the normal boiling point up to just below the critical temperature. The liquid and vapour densities and vapour pressures were determined from the simulations. The density results were then fitted using least-squares regression to the scaling law and the law of rectilinear diameters in order to estimate the critical properties. The vapour pressure data were fitted using least-squares to the Clausius-Clapeyron equation to estimate the normal boiling points. The NVT-Gibbs ensemble method was used to simulate the pure-component coexistence of the vapour and liquid phases. The NPT-Gibbs ensemble was used to simulate the n-alkane binary mixtures. Two forms of configurational-bias Monte Carlo (standard CBMC and coupled-decoupled CBMC) were used to increase the number of swap moves accepted during the simulations. Dual-cutoff CBMC was implemented with a second cut-off of sA in order to speed up the CBMC calculations. Minimum image and a spherical potential truncation after 14A were implemented with standard tail corrections. BICMAC and TOWHEE were the two Fortran-77 codes used to simulate the hydrocarbon compounds. BICMAC was used in the simulations of non-polar molecules and TOWHEE was used in the simulations of polar molecules. System sizes ranged from 300 (for the CB'S) down to 100 molecules (for the Czo's). The simulations were typically equilibrated for at least 30000 cycles and production runs ranged from 50000 to 120000 cycles for the different hydrocarbon groups. Standard deviations of the calculated thermophysical properties were between 1-3% for the liquid densities and 10-20% for the vapour densities and vapour pressures. It was found that the coexistence density curves were generally in good agreement with experiment for all the hydrocarbon groups investigated (the OPL5-UA force field being the exception). The chain-length appeared to have littl e effect on the quality of the calculated thermophysical properties. The chain-length did however increase the time required to perform the simulations substantially. The va pour pressures were consistently over-predicted by NERD and TraPPE-UA. The normal boiling pOints were typically under-predicted by 2-5%. The critical tempe ratures and densities were predicted to within 1-5% of experimental values. The n-alkane mixtures were satisfactorily predicted using the NPT-Gibbs ensemble. While both the NERD and TraPPE-UA force fields were shown to be substantially more accurate compared to the OPLS-UA force field, there was little difference between their predictions. Thus, it is likely that the added complexity of using the bond-stretching potential (used by NERD) is unnecessary. The results of this study show that Monte Carlo simulation may be used to predict vapour-liquid coexistence properties of long-chain hydrocarbons and to approximate critical properties. However, current force fields require more refinement in ord er to accurately predict the hydrocarbon thermophysical properties. Plus, faster computing speeds are required before Monte Carlo simulation becomes an industrially viable method.