Chemical reaction equilibria stoichiometric formulation

This model represents the most frequently used description of chemical reaction equilibrium and should be familiar to most chemical engineering students. However, for multicomponent mixtures in which multiple reactions may take place, this type of non-linear problems may be cumbersome to solve numerically. One important obstacle is that the non-linear equilibrium constant definitions may give rise to multiple solutions, hence we have to identify which of them are the physical solutions. The stoichiometric formulation might thus be inconvenient for mixtures containing just a few species for which only a few reactions are taking place. 

An important feature of the non-stoichiometric formulation is that no information about the reaction stoichiometry is required. However, the species that the mixture is composed of must be specified. Note also that this type of chemical reaction equilibrium calculations is sometimes referred to as a Gibbs reactor simulation. 

Here va and va are the stoichiometric coefficients for the reaction. The formulation is easily extended to treat a set of coupled chemical reactions. Reactive MPC dynamics again consists of free streaming and collisions, which take place at discrete times x. We partition the system into cells in order to carry out the reactive multiparticle collisions. The partition of the multicomponent system into collision cells is shown schematically in Fig. 7. In each cell, independently of the other cells, reactive and nonreactive collisions occur at times x. The nonreactive collisions can be carried out as described earlier for multi-component systems. The reactive collisions occur by birth-death stochastic rules. Such rules can be constructed to conserve mass, momentum, and energy. This is especially useful for coupling reactions to fluid flow. The reactive collision model can also be applied to far-from-equilibrium situations, where certain species are held fixed by constraints. In this case conservation laws... 

In 1879 Guldberg and Waage substituted the above formulation for the basic law of chemical reactions by its modem version in terms of the concept of mobile equilibrium. For the interaction between the initial substances A, B, C, taken in the stoichiometric ratio of a to to y, i.e. aA + / B + yC, the reaction rate, W, was expressed as... 

---