Law of Mass Action Based Kinetic Approach for the Modelling of Parallel Mass Transfer Limited Reactions: Application to Metallurgical Systems

The objective of this paper was to present a new law of mass action based rate expression for mass transfer limited reversible reactions. A simple reaction model was derived for parallel oxidation of silicon, chromium and carbon under conditions relevant to the argon-oxygen decarburization (AOD) process. Our hypothesis is that when the forward rate coefficients approach infinite values, the composition at the reaction surface approaches a constrained equilibrium. In numerical analysis, however, only finite numbers are allowed and therefore only finite values are accepted for rate coefficients. In order to circumvent this problem, additional residual affinity constraints were introduced. This assures that the affinities of all the reactions at the reaction front reach a pre-defined non-zero residual affinity and the rate coefficients remain finite. The calculated equilibrium composition is essentially the same as that obtained with the equilibrium coefficient method. In the case of effective gas side mass transfer, the component having the highest mole fraction or the highest mass transfer rate on the liquid side consumes most of the oxygen. When the gas side mass transfer rate is decreased, the mass transfer rate of oxygen begins to limit the overall rate and the partial pressure of oxygen at the reaction interface decreases. Then, the role of interfacial equilibrium becomes important as the species start to compete for the oxygen. The proposed method provides a transparent and direct solution of the mass transfer limited reaction rates and is thus suitable for process simulators and CFD software.