The state of the cubic equations of state

The development of van der Waals cubic equations of state and their application to the correlation and prediction of phase equilibrium properties is presented and analyzed. The discussion starts with a brief account of the contributions to equation of state development during the years before van der Waals. Then, the original equation proposed in the celebrated thesis of van der Waals in 1873 and its tremendous importance in describing fluid behavior are analyzed. A chronological critical walk through the most important contributions during the first part of the 1900s is made, to arrive at the proposal that I consider to be the most outstanding since van der Waals: the equation proposed by Redlich and Kwong in 1949. The contributions after Redlich and Kwong to the modern development of equations of state and the most recent equations proposed in the literature are analyzed. The application of cubic equations of state to mixtures and the development of mixing rules is put in a proper perspective, and the main applications of cubic equations of state to binary and multicomponent mixtures, to high-pressure phase equilibria, to supercritical fluids, to reservoir fluids, and to polymer mixtures are summarized. Finally, recommendations on which equations of state and which mixing rules to use for given applications are presented.