(352u) Reformulating and Restructuring the Van Der Waals 1873 Cubic Equation of State: State-of-the-Art Review in Engineering Literature for Progress and Further Applications
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
While myriad cubic equations in the literature may seems alarming, Van der Waals objective clearly stated in the 1910 Nobel Lecture, â... to determine the relation between p, v and T for a substance,â expected those many cubic equations to come from a universal (or generic) cubic polynomial equation. Consequently, this broad literature review of the philosophy to reform cubic equations reported in the Engineering Research Journals since 1873 to the present shows the optimal way to reformulate the Van der Waals 1873 cubic theory is to reconcile the disagreement between the 1873 PVT equation and the 1880 reduced equation (known universally as the Law of Corresponding States) wherein the 1873 PVT equation is specified by two molecular parameters (a, b) while the reduced equation (which is the 1873 PVT equation scaled by substance critical properties: Pc, Vc, Tc) is unequivocally prescribed by the four Van der Waals molecular parameters (Zc, â¦w, â¦a, â¦b) that molecular theory has revealed as essentially capturing the size, shape, structure and intermolecular attractive force of the individual pure substances.
Applications of the reformed 1873 equation are demonstrated for volumetric properties (compressibility factor, isothermal compressibility, volume expansivity, second- and third virial coefficients), coexistence gas-liquid densities and high pressure phase equilibria as well as critical properties of binary and ternary systems. The prospect of applying the Van der Waals theory of cubic equations in diversity applications is illustrated for derivative properties (enthalpy, entropy, internal energy, isothermal and isochoric heat capacities, Joule-Thomson coefficient, speed of sound), transport properties (dynamic viscosity, kinematic viscosity, thermal conductivity, thermal diffusivity, Prandtl number, Eucken number, diffusivity (or diffusion coefficient), interfacial (or surface) tension, dielectric constant) and hydrodynamic regime-phase transition of estimating pressure-drop in multiphase fluid flow in pipes and irregular conduits.
This comprehensive review on reformulation of cubic equations of state is a fitting documentary honoring the eightieth birthday of the Sixth Editor of AIChE J., the 1977 Founder and Co-Chair of the Asilomar, Pacific Grove, California Conference of the triennial PPEPPD Conference (which as a preferred reference (for my graduate thermo-class) has been affectionately nickname SS-60 for Storvick-Sandler ACS Symposium Series 60), the 1980 Editor and Co-Chair of the Second PPEPPD Conference in Berlin (West Germany), the Sectional Chair of Phase Equilibria & Properties at the 1995 Annual Meeting of AIChE at Miami Beach, Florida, the overall Program Chairman of the 1998 Annual Meeting of AIChE at Miami Beach, Florida, the Teacher and the Author of Textbooks on Applied Molecular Thermodynamics, Professor Emeritus Stanley (Stan) Sandler of the Chemical and Biomolecular Engineering Department at the University of Delaware. Happy birthday Stan!
[1] Robert Reid (Fluid Phase Equil. (1983), 13, 1-14)
[2] Deiters-de Reuck (Fluid Phase Equil. (1999), 161, 206-219)
[3] J. J. Martin (Ind. Eng. Chem. Fund. 1979, 18(2), 81)