In this paper, we investigate the phase equilibrium problem for multicomponent mixtures under specified internal energy (U), volume (V), and mole numbers (N1,N2,…,Nn), commonly known as the UVN-flash problem. While conventional phase equilibrium calculations typically use pressure–temperature-mole number (PTN) specifications, the UVN formulation is essential for dynamic simulations of closed systems and energy balance computations. Existing approaches, including those based on iterative pressure–temperature updates and direct entropy maximization, can suffer from computational inefficiencies due to inner Newton iterations needed to solve for temperature T at specified internal energy U and volume V.

In this work, we present a reformulation of the UVN-flash problem that eliminates the need for the inner Newton iterations, addressing a computational bottleneck. We begin with stability analysis and discuss a strategy to generate the initial guess for the UVN-flash from the stability analysis results. We then reformulate the UVN-flash problem in TVN-space as constrained entropy maximization. We provide a detailed derivation of Michelsen's Q-function using the method of Lagrange multipliers, illustrating its direct application in solving the UVN-flash problem. Furthermore, we discuss the numerical methods used, including gradient and Hessian computations. The reformulation is validated against benchmark cases, demonstrating improved efficiency.

This work presents a novel framework for numerically simulating the depressurization of tanks and pipelines containing carbon dioxide (CO2). 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 CO2 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.