Redlich-Kwong equation

Redlich-Kwong equation is an empirical real‑gas equation of state formulated in 1949 to improve the description of non‑ideal gas behavior by introducing temperature‑dependent attraction terms and a cubic form that corrects the ideal gas law at moderate pressures and temperatures. It has been influential in chemical engineering and physical chemistry for correlating vapor–liquid equilibria and compressibility factors, and it served as a bridge between simple two‑parameter models and more complex multi‑parameter approaches used in process simulation.

History

The development of the Redlich–Kwong equation involved researchers and institutions active in mid‑20th century physical chemistry, notably Otto Otto Redlich and Joseph Neng Shun Joseph Neng Shun Kwong, and built on a lineage of work that included contributions from Johannes Diderik van der Waals, Anders Jonas Ångström, Thomas Andrews, Ludwig Boltzmann, and experimental thermodynamic data compiled by laboratories such as the National Bureau of Standards and academic groups at University of Vienna and Caltech. Early antecedents include the two‑parameter law of corresponding states discussed by James Clerk Maxwell and refinement attempts by Pierre Louis Dulong and later investigators like Richard Tolman and Joseph E. Mayer. The 1949 publication emerged alongside contemporaneous efforts at Imperial College London and the Massachusetts Institute of Technology to produce usable, computationally tractable equations for industrial design, influencing engineers at firms such as DuPont and Royal Dutch Shell and researchers at the American Institute of Chemical Engineers.

Formulation

The Redlich–Kwong formulation modifies the ideal gas law by introducing an attraction term proportional to density and inversely proportional to the square root of absolute temperature, producing a cubic equation in molar volume similar in algebraic structure to the cubic developed by Johannes Diderik van der Waals. Its parameters are commonly expressed in terms of critical properties measured by investigators at facilities such as General Electric research labs and collated by organizations like International Union of Pure and Applied Chemistry; the reduced‑property form follows the corresponding states tradition advanced by E. A. Guggenheim. The mathematical structure was designed to reconcile empirical observations reported by experimentalists at institutions including University of Cambridge and Princeton University while remaining amenable to analytic manipulation used in textbooks from McGraw-Hill and lecture notes at Massachusetts Institute of Technology and Stanford University.

Thermodynamic Properties and Applications

Practitioners in process industries—engineers at BASF, ExxonMobil, and consulting groups descended from Arthur D. Little—use the equation to estimate compressibility factors, fugacities, and residual thermodynamic properties when designing equipment influenced by standards from American Petroleum Institute and methodologies promoted at conferences by AIChE. Academic applications include modeling vapor–liquid equilibria in research at ETH Zurich and petrochemical studies reported in journals affiliated with Royal Society of Chemistry and Elsevier. The Redlich–Kwong form yields expressions for isothermal compressibility and Joule–Thomson coefficients that have been compared with measurements from laboratories such as National Physical Laboratory and Argonne National Laboratory, and it was incorporated into early process simulators developed by teams at Shell Global Solutions and Fluor Corporation.

Comparison with Other Equations of State

Comparative assessments often involve equations developed by historical figures and organizations: the Johannes Diderik van der Waals equation, the Benedict–Webb–Rubin equation advanced in part by researchers at General Motors Research Laboratories, and cubic models such as the Soave modification and Peng–Robinson equation originating from work at ENI and Princeton University respectively. In many benchmark studies conducted at universities like University of Texas at Austin and national labs including Sandia National Laboratories, Redlich–Kwong performs better than van der Waals at moderate conditions but is supplanted by the Soave–Redlich–Kwong (a modification associated with G. Soave and industrial collaborators) and Peng–Robinson when accurate critical region behavior or liquid densities are required. Regulatory and standards bodies such as ISO and API have favored more flexible multi‑parameter formulations for custody transfer and safety analysis in applications overseen by companies including BP and Chevron.

Limitations and Modifications

Limitations identified by theoreticians at institutions such as Cambridge University and Harvard University include inaccurate liquid‑phase densities, poor critical‑region behavior, and deviations for associating fluids, prompting empirical and semi‑empirical modifications. Notable modifications include the Soave modification (temperature‑dependent alpha function introduced by G. Soave), the Pitzer acentric factor corrections developed by Kenneth Pitzer and collaborators, and further parameterizations by corporate research groups at TotalEnergies and academic consortia at Imperial College London. Advanced alternatives—multi‑parameter equations like Benedict–Webb–Rubin and modern Helmholtz energy formulations produced by researchers at NIST and GERG—address many of the original shortcomings, while hybrid strategies combine Redlich–Kwong structure with mixing rules informed by work from Michelsen and Huron and Vidal used in commercial simulators by AspenTech and Honeywell UOP.

Category:Equations of state