Development of robust and efficient methods for the computation of multi-phase systems has long been a challenge in both chemical and petroleum engineering as well as in materials science. Several techniques have been developed, particularly those which apply the Gibbs free energy minimization. In addition to calculation of global equilibrium problems, practical simulation of multi-phase chemical reactors would benefit from such multiphase algorithms, where reaction rates are taken into account. In the present work, the method of Lagrange multipliers has been used to incorporate such additional constraints to the minimization problem, which then allow reaction rate models to be included in the Gibbsian multi-component calculation /1, 2/. The extension of the conservation matrix brings about the possibility to include reaction kinetic restrictions to control the extents of chemical reactions in terms of their affinity. A generic algorithm which combines the Gibbs energy of the control volume system with the salient heat and mass transfer and reaction rates has been developed.

The method has been used for several scale-up studies of complex chemical reactors with simultaneous chemical reactions and phase changes. The model has been validated with both thermodynamically consistent data and with practical plant measurements. An industrial case example of a titanium(IV)chloride burner used in titanium dioxide pigment manufacturing will be described in detail.

/1/Koukkari, P.; Pajarre, R.: Introducing Mechanistic Kinetics to the Lagrangian Gibbs Energy Calculation, Computers and Chemical Engineering, Vol 30 (2006), 1189-1196.

/2/Koukkari, P., Gani, R. and Pajarre, R.: Calculation of Thermochemical Properties and Processes with the Constrained Free Energy Method, to be published.