Unsteady- and steady-state kinetic models

A laboratory catalytic reactor that is a closed system, is said to be a static system. The kinetic model for complex reactions taking place in the reactor is of the form 

Here c is the vector column of substance concentrations, T is the transposed stoichiometric matrix, and w(c) is the vector column of reaction rates determined from eqns. (6) (8). It is an unsteady-state kinetic model. 

Let us write such a model for the catalytic reaction of methane with steam on a nickel catalyst. Its detailed mechanism has been given above. 

After multiplying matrix T by the vector column of the reaction rates, w, we obtain an unsteady-state kinetic model 

For a closed system the laws of mass conservation for various atoms must be met 

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