A mathematical model for the determination of the parameters of a gas in an open thermodynamic system in contact with the environment

Leaks in gaseous storage and supply systems impose security and economic threats that are influenced by the heat exchange. A methodology is proposed to assess thermodynamic changes in a leaky system utilizing a mathematical model for the "pipe-hole" scenario based on the Poiseuille equation for laminar gas leakage with a capillary diameter below 0.1 m. Differential equations are derived to analyze the time-dependent thermodynamic variations of compressed air in the “pipe-hole” system via the energy balance equation. A mathematical model was developed for general case studies of open thermodynamic variable-mass gas systems. The FORTRAN software tool was used to solve the system of differential equations using the Runge-Kutta method, with four orders of accuracy. A specific examination was conducted on a thermodynamic system that lacks a constant gas supply and stationary convective heat exchange in a single-layer gas container with the environment. The ranges of the control parameter variation were considered as follows: air pressure p 0 from 150 kPa to 300 kPa and temperature T a from 15 °C to 25 °C. This study reveals how the density, pressure, and temperature of compressed air vary over time owing to leakage and heat fluxes. It was determined that as initial air pressure decreases from р 0 = 150 kPa, the impact of heat flow rates markedly surpasses that of air leakage rates. A potential application of this research could be the software for monitoring devices for high-pressure systems designed for the storage and distribution of gaseous energy carriers.