An improved Wilson equation for phase equilibrium K values estimation

Phase equilibrium K values are either estimated with empirical correlations or rigorously calculated based on fugacity values determined from an equation of state. There have been several empirical analytical equations such as Raoult’s Law, the Hoffman Equations (Hoffman A, Crump J, Hocott C. Equilibrium constants for a gas condensate system. J Petrol Technol 1953;5:1–10) and their modifications and the well-known Wilson Equation (Wilson G. A modified Redlich–Kwong equation of state applicable to general physical data calculations. In: AIChE National Meeting Paper15C, May 4–7, Cleveland, OH; 1969). along with several modifications. This work presents a new modification of the Wilson Equation for estimating phase equilibrium K values, predominantly for light hydrocarbon mixtures. The modification is based on correlating a subset of a database of K values, established from convergence pressure data. Results show the method to accurately correlate and predict the K value data, within 10% on average. Moreover, the predicted K factors provide remarkable results for such a simple model when used in a variety of phase equilibrium calculations. The results also show that the new model compares favorably with existing empirical analytical methods. Such a model would provide excellent initial estimates for rigorous thermodynamic calculations.

Chemical Equilibrium

Chemical Equilibrium reviews the principles of equilibrium in systems of gases and liquids, starting with the concepts of reversible and irreversible reactions and dynamic equilibrium. The equilibrium constant (K) and reaction quotient (Q) are described, and comparison of K and Q is used to determine the direction in which a reaction must proceed to reach equilibrium. Calculations involving K in terms of concentration and pressure are presented. The relationship between the magnitude of K, the equilibrium position and the concentrations of reactants and products is discussed for both homogeneous and heterogeneous equilibria. The chapter ends with a qualitative treatment of equilibrium based on Le Chatelier’s principle, as well as how changes in reaction conditions can disturb a chemical equilibrium and how the chemical reaction responds to those changes.

Additive Manufacturing of Compositionally-Graded AISI 316L to CoCrMo Structures by Directed Energy Deposition

In the present study, compositionally-graded structures of AISI 316L and CoCrMo alloy are manufactured by powder-based laser-beam directed energy deposition (DED-LB). Through a process-integrated adjustment of powder flow, in situ alloying of the two materials becomes feasible. Thus, a sharp and a smooth transition with a mixture of both alloys can be realized. In order to investigate the phase formation during in situ alloying, a simulation approach considering equilibrium calculations is employed. The findings reveal that a precise compositional as well as functional gradation of the two alloys is possible. Thereby, the chemical composition can be directly correlated with the specimen hardness. Moreover, phases, which are identified by equilibrium calculations, can also be observed experimentally using scanning electron microscopy (SEM) and energy-dispersive X-ray-spectroscopy (EDS). Electron backscatter diffraction (EBSD) reveals epitaxial grain growth across the sharp transition region with a pronounced <001>-texture, while the smooth transition acts as nucleus for the growth of new grains with <101>-orientation. In light of envisaged applications in the biomedical sector, the present investigation demonstrates the high potential of an AISI 316L/CoCrMo alloy material combination.