Densities of hydrocarbons in their saturated vapor and liquid states

The Sum and differences of the saturated vapor and liquid densities of 23 hydrocarbons were used to develop the following reduced density relationships for these saturated states\documentclass{article}\pagestyle{empty}\begin{document}$$ \rho _{R_l } = 1 + \beta \left( {1 - T_R } \right) + \gamma \left( {1 - T_R } \right)^2 + \sigma \left( {1 - T_R } \right)^n ...\left( a \right) $$\end{document}\documentclass{article}\pagestyle{empty}\begin{document}$$ \rho _{R_v } = 1 + \beta \left( {1 - T_R } \right) + \gamma \left( {1 - T_R } \right)^2 + \delta \left( {1 - T_R } \right)^n ...\left( b \right) $$\end{document}The hydrocarbons considered included n‐parafins, olefins, diolefins, naphthenes, and aromatics. Constants β, γ, and δ, and exponent n were found to be dependent on,. Equation (a) can reproduce liquid densities with an overall average deviation of 1.1 % over the entire temperature range, while Equation (b) was found to apply only in the interval 0.900 ≤ T R ≤ 1.00 with an average deviation of 2.2%. For temperatures of T k < 0.90, the saturated vapor density was found to depend on temperature as follows\documentclass{article}\pagestyle{empty}\begin{document}$$ \rho _{R_v } = ke^{ - \frac{m}{T}} R\left( c \right) $$\end{document}where k and m were also found to be Z c dependent. Values calculated using Equation (c), when compared with 81 available experimental densities for 12 hydrocarbons, produced an average deviation of 3.0%.