MODEL FOR DETERMINING THE COMPOSITION, AT EQUILIBRIUM, OF A REACTANT SYSTEM USING THE LAGRANGE MULTIPLIER METHOD

Description

Titi PARASCHIV, Dan POSTOLEA, Iustin PRIESCU, Octavian Constantin GRIGOROIU

The article addresses the method of applying the Lagrange Multiplier Method in determining the equilibrium composition for a reactive system. The study begins by presenting the general form of constrained optimization problems and describes the Lagrange multiplier method as an efficient tool for transforming these problems into unconstrained optimization formulations. The necessary and sufficient conditions for determining stationary values of unconstrained functions, fundamental for understanding the principles of the method, are outlined. The generalization of the problem for a function with multiple variables and constraints is developed by introducing the Lagrange function, and the application of the method is tailored to a reactive system. The study extends to the analysis of free enthalpy and Gibbs potential, presenting the assumptions and necessary conditions for determining the equilibrium composition in a chemical reactor. The study addresses a practical method of preprocessing obtained data, using the least squares method to transform functions into continuous functions.

https://doi.org/10.58679/UTM21284