Numerical method and mathematical model for finding the equilibrium composition of the thermodynamic system of the T-Energy software package

Abstract

Objective. The aim of the study is to develop a mathematical model and numerical methods for finding the equilibrium composition of a thermodynamic system.Method. To find the equilibrium composition of the thermodynamic system, a combination of numerical methods was used: Lagrange, Newton–Raphson and Gauss.Result. The analysis of existing software systems and numerical methods used in them for the calculation of thermodynamic systems is carried out. Based on the analysis, practical implementation attempts, it was possible to develop a mathematical model consisting of numerical Lagrange methods (allows you to move from a conditional problem to an unconditional one); Newton–Raphson (an approximate method for solving a nonlinear system of equations); Gauss (solving a linear system of equations). For the convergence of the Newton–Raphson method, the required quantities were replaced by their squares, and ranges of variation were set for each quantity. The results of comparing the calculations of the equilibrium composition with the Terra program show satisfactory results.Conclusion. The T-Energy software package allows you to calculate the equilibrium composition for a thermodynamic system.

Keywords

• numerical method
• maximum search
• nonlinear equations
• thermodynamic system
• newton–raphson method