Representative configurations from Mayer-sampling Monte Carlo simulations. On the bottom is shown a configuration from the calculation of for (butane), and on the top is a configuration from calculation of for . Molecules are colored differently only to make them more distinguishable in the figure.
Virial coefficients computed in this study, excluding the contributions from molecular flexibility. Temperature is scaled by literature values (Ref. 7) (or best estimate) of the critical temperature for the model, and virial coefficients are scaled by the chain length as indicated, and are plotted on an arcsinh scale. Curves proceed in sequence from to the largest computed, as indicated on each plot. Confidence limits are smaller than the line thickness, except where shown.
Compressibility factor, as a function of density, for butane at (a) 350 K and (b) 550 K, comparing the virial equation truncated at various orders as indicated to an accurate empirical correlation (Ref. 20).
Schematic illustration of the behavior of the second-derivative critical criterion following temperature-density lines for which the spinodal condition is satisfied (zero first derivative).
Critical properties as given by the VEOS to various orders as a function of -alkane carbon number. Results are compared to values obtained by Monte Carlo simulation applied to evaluate the critical points for the same model (Ref. 7) and to the experimental data for real alkanes (Ref. 19). Error bars are indicated only when larger than the symbol size. Lines join points as a guide to the eyes.
Lines showing for four model alkanes approximate upper limits of applicability of the ideal-gas (IG) model and the virial equation to various orders . Dash-dotted lines: methane (Ref. 13); solid lines: ethane; dashed lines: butane; and dotted lines: octane. Thick black lines ending at the critical point are spinodals for from VEOS6 (right-most curve) and from VEOS4 (left-most curve). Temperatures and densities are reduced by critical values for the same model (Ref. 7).
Critical properties as given by for the model alkanes examined in this study.
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