Solving the UVN-flash problem in TVN-space

Abstract

In this paper, we investigate the phase equilibrium problem for multicomponent mixtures under specified internal energy ($U$), volume ($V$), and mole numbers ($N_1,N_2,\dots ,N_n$), 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.