Solving the UVN-flash problem in TVN-space

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

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