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.

A High Order Accurate Finite Difference Method for the Drinfel’d–Sokolov–Wilson Equation

We analyse numerically the periodic problem and the initial boundary value problem of the Korteweg-de Vries equation and the Drindfeld–Sokolov–Wilson equation using the summation-by-parts simultaneous-approximation-term method. Two sets of boundary conditions are derived for each equation of which stability is shown using the energy method. Numerical analysis is done when the solution interacts with the boundaries. Results show the benefit of higher order SBP operators.

Influence of Cr, Mn, Co and Ni Addition on Crystallization Behavior of Al13Fe4 Phase in Al-5Fe Alloys Based on ThermoDynamic Calculations

Alloying is an effective method to refine coarse grains of an Al13Fe4 phase and strengthen Al-Fe alloys. However, the grain refinement mechanism remains unclear in terms of the thermodynamics. Herein, the influence of M-element, i.e., Cr, Mn, Co and Ni, addition on the activity of Al and Fe atoms, Gibbs free energy of the Al13Fe4 nucleus in Al-Fe melt and the formation enthalpy of an Al13Fe4 phase in Al-Fe alloys is systematically investigated using the extended Miedema model, Wilson equation, and first-principle calculations, respectively. The results reveal that the addition of different M elements increases the activity of Fe atoms and reduces the Gibbs free energy of the Al13Fe4 nucleus in Al-Fe melt, where the incorporation of Ni renders the most obvious effect, followed by Mn, Co, and Cr. Additionally, the formation enthalpy decreases in the following order: Al78(Fe23Cr) > Al78(Fe23Mn) > Al13Fe4 > Al78(Fe23Ni) > Al78(Fe23Co), where the formation enthalpy of Al78(Fe23Ni) is close to Al78(Fe23Co). Moreover, the presence of Ni promotes the nucleation of the Al13Fe4 phase in Al-Fe alloys, which reveals the mechanism of grain refinement from a thermodynamics viewpoint.

Liquid-vapor equilibrium and evaporation rate of Cd-Zn liquid alloy

In this study, LVE (liquid-vapor equilibrium) data of cadmium-zinc system were determined at pressure of 7.5 Pa. We compare the use of the Redlich-Kister polynomials with the Wilson equation in fitting activities. The LVE for Cd-Zn system in vacuum distillation was modeled using the two models. The results of the two models are reliable, the Redlich-Kister polynomialsis better than the Wilson equation. The LVE phase diagram is reliable for predicting the process of vacuum distillation for Cd-Zn system. Evaporation rates of elements in Cd-Zn alloy were experimental measured and calculated by the Langmuir equation. Experimental data on the evaporation of pure metals Cd and Zn are included. The evaporation coefficients of zinc and cadmium under vacuum conditions were calculated. The deviations were discussed. Comparing calculations with experimental results, it can be found that the trend is consistent. The activation energies of Cd and Zn in the Cd-Zn alloy under experimental conditions were also calculated.

Isobaric vapor-liquid equilibria of ternary lead-tin-antimony alloy system at 2 Pa

In this study, experimental vapor-liquid equilibria data of the ternary Pb-Sn-Sb alloy system are determined using a new experimental method. The experimental VLE data passed the thermodynamic consistency test(Van Ness test), suggesting that the experimental results are reliable. The activities of the components of Pb-Sn-Sb ternary alloy and those of the corresponding three constituent binaries were calculated using the Wilson equation. The predicted values are in good agreement with the data determined from experiments, and the average relative deviation and average standard deviation were smaller than ? 4.00%and ? 0.03for all constituent binaries, respectively, which indicates that the Wilson equation is reliable for calculating the activity of the components of the Pb-Sn-Sb ternary alloy. The VLE data of the Pb-Sn and Sb-Sn binary alloys and Pb-Sn-Sb ternary alloy were calculated based on the VLE theory and Wilson equation. The calculated VLE data were in good agreement with the data determined from experiments, indicating that this method is reliable for calculating the VLE of alloy systems. The proposed study offers a valid method for analyzing the composition of products that are dependent on the distillation temperature and system pressure during vacuum distillation, which is of great significance to the experimental design of this process.