Balances independent, reactive system

This result will be employed in conjunction with the thermal energy balance for reactive systems. If there is only one chemical reaction, then subscript j is not required and dFi/vi is independent of component i ... 

It is easy to demonstrate that in the reactive system with an arbitrary set of monomolecular (or reduced to monomolecular) reactions, the station ary state with respect to the intermediate concentration corresponds to the minimum in the value of functional (3.6) even under conditions that are far from equilibrium of the system. In other words, the functional 0( Ao( ) is, by definition, the Lyapunov function of this system. In fact, for a system that consists of monomolecular reactions in its stationary state, in respect to linearly independent (i.e., not related via mass balance with other intermediates) intermediate A , the following expression is valid ... 

To carry out degree-of-freedom analyses of reactive systems you must first understand the concepts of independent equations, independent species, and independent chemical reactions. We explain these concepts in the next section, following which we outline and illustrate the three approaches to reactive system balance calculations. 

Finally, when you are using either molecular species balances or extents of reaction to analyze a reactive system, the degree-of-freedom analysis must account for the number of independent chemical reactions among the species entering and leaving the system. Chemical reactions are independent if the stoichiometric equation of any one of them cannot be obtained by adding and subtracting multiples of the stoichiometric equations of the others. 

The design of a complete set of governing equations for the description of reactive flows requires that the combined fluxes are treated in a convenient way. In principle, several combined flux definitions are available. However, since the mass fluxes with respect to the mass average velocity are preferred when the equation of motion is included in the problem formulation, we apply the species mass balance equations to a (/-component gas system with q — independent mass fractions Wg and an equal number of independent diffusion fluxes js. However, any of the formulations derived for the multicomponent mass diffusion flux can be substituted into the species mass balance (1.39), hence a closure selection optimization is required considering the specified restrictions for each constitutive model and the computational efforts needed to solve the resulting set of model equations for the particular problem in question. 

These definitions present convenient and simplifying properties ( ) the dimensions of the system are reduced, simplifying the depiction of equilibrium (figure 3.3) (Frey and Stichlmair, 19996 Barbosa and Doherty, 1987a) (ii) they have the same numerical values before and after reaction (m) they sum up to unity (iv) they clearly indicate the presence of reactive azeotropes when Xi =Yf, (v) the nonreactive hmits are well defined (vi) the number of linear independent transformed composition variables coincides with the number of independent variables that describe the chemical equihbrium problem and vii) the lever rule is valid as the chemical reaction no longer impacts the material balance. 

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