(352r) Derivative-Free Computation of High-Pressure Density, Isothermal Compressibility, Volume Expansivity of Pure Substances and Binary Systems By Van Der Waals Cubic Equation
AIChE Annual Meeting
2020
2020 Virtual AIChE Annual Meeting
Engineering Sciences and Fundamentals
Poster Session: Thermodynamics and Transport Properties (Area 1A)
Wednesday, November 18, 2020 - 8:00am to 9:00am
By definition, the computation of isothermal compressibility [-1/v (âv/âP)T] (because volume decreases with increasing pressure, the definition contain negative sign to make isothermal compressibilities positive) and volume expansivity [1/v (âv/âT)P] involves respective computation of first-order derivative of Volume with respect to Pressure (at fixed Temperature) and first-order derivative of Volume with respect to Temperature (at fixed Pressure) from the Van der Waals (VdW) theory of cubic equations of state. But, the direct computation of volume expansivity from the VdW cubic equations is very challenging because T (and P) are in the expansion of cubic equation in ν and consequently, a remedial action using cyclic triple product rule of partial differentiations is usually applied [1-10]. Even though the simplicity of the cyclic product rule relation can be observed as geometrical representation in the PâVâT diagram [4-5], the effects of the errors in the PvT relation are carried through to all thermodynamic property variations because they involve derivatives. Hence, major errors for the heat capacities (isochoric and isothermal specific heat), isothermal compressibility, and sound speed have been shown in 1996 by Gregorowycz, et al. [11]; and even if analytic VdW cubic equations are accurate for saturation volumes, they do not give reliable changes of volume upon compression and thus making the errors in the predicted isothermal compressibilities extremely large.
Consequently, this poster describes characteristics of the derivative properties for pure substances and binary systems by reforming the VdW 1873 equation as universal cubic equation of state typified by the Lawal-Lake-Silberberg (LLS) cubic equation. The results of the LLS cubic equation are compared with the results from several well-known cubic equation models. The extrema is achieved with the LLS cubic equation by the designed co-volume temperature-dependent parameter without requiring any density dependence in the attractive parameter of the LLS equation. The analysis of results show accurate description of the extrema is possible with such cubic model (the LLS cubic equation) without the co-volume parameter being any complex dependence on both temperature and density, as commonly done with some cubic models of the VdW theory of cubic equations of state.
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