The fundamental catalytic processes in the petrochemical and chemical industries are characterised by a multistage set of the specific chemical transformations with a significant number of the reactants participating therein. This has led in many practical situations to extremely complicated procedures for structural and parametric identification of the mathematical model for a catalytic reactor. These difficulties can be successfully overcome if the dimensionality of the model equations is sharply curtailed by the use of invariants of the physicochemical (reactor) systems which are derived a priori. The invariants proposed for reactor systems are represented by non-linear algebraic or integral algebraic equations, containing the macrokinetic parameters of the models. The invariants relationships differ substantially from one another when the boundary conditions for the differential equations or the structure of the models are changed. Using this fact, the authors propose a new method for the selection of the boundary conditions and the mathematical model for chemical reactors, based on the application of invariant relations. The practical use of this procedure opens new possibilities to researchers by substantially simplifying in many cases the analysis of catalytic processes in chemical reactors.