A new temperature evolution equation that enforces thermodynamic vapour–liquid equilibrium in multiphase flows - application to CO2 modelling

Abstract

This work presents a novel framework for numerically simulating the depressurization of tanks and pipelines containing carbon dioxide ($\mathrm{CO}2$). The framework focuses on efficient solution strategies for the coupled system of fluid flow equations and thermodynamic constraints. A key contribution lies in proposing a new set of equations for phase equilibrium calculations which simplifies the traditional vapour–liquid equilibrium (VLE) calculations for two-phase $\mathrm{CO}2$ mixtures. The first major novelty resides in the reduction of the conventional four-equation VLE system to a single equation, enabling efficient solution using a non-linear solver. This significantly reduces computational cost compared to traditional methods. Furthermore, a second novelty is introduced by deriving an ordinary differential equation (ODE) directly from the UV-Flash equation. This ODE can be integrated alongside the governing fluid flow equations, offering a computationally efficient approach for simulating depressurization processes.