A physico-chemical method to calculate time-dependent reaction mixtures

A method is proposed to calculate multicomponent chemical reaction mixtures as a series of sequential, time-dependent thermochemical states. The procedure is based on the two general principles of physical chemistry, viz., decreasing Gibbs-energy for a natural process and the exponential Arrhenius rate law for the overall reaction kinetics. The calculation is performed in repeated sequences for a closed system element with known heat transfer to its surroundings. The temperature of each sequential reactor element is determined by a Gibbs-energy minimization routine (SOLGASMIX) connected to the closed system enthalpy balance iteration. The extent of overall reaction is limited by the Arrhenius kinetics, while the possible side reactions may reach equilibrium. The mass balance relations forming the subsidiary constraints of the Lagrange method are modified to facilitate the Gibbs-energy minimization for the intermediate “reactor states”. The well-known reaction of titanium (IV) chloride oxidation to titanium dioxide with such side reactions as chlorine dissociation and oxychloride formation is given as a calculational example.