A Fast and Robust Reformulation of the UVN-Flash Problem via Direct Entropy Maximization

TL;DR

This paper introduces a new, efficient method for solving the UVN-flash problem by reformulating it as a direct entropy maximization task, eliminating nested iterations and improving computational robustness.

Contribution

The authors develop a novel reformulation of the UVN-flash problem as a direct entropy maximization approach, enhancing computational efficiency and robustness over existing methods.

Findings

Demonstrates improved computational efficiency over traditional methods.

Eliminates nested iterations and inner Newton solvers.

Validated against benchmark cases showing robustness.

Abstract

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, suffer from computational inefficiencies due to nested iterations and reliance on inner Newton solvers. In this work, we present a novel reformulation of the UVN-flash problem as a direct entropy maximization problem that eliminates the need for inner Newton iterations, addressing key computational bottlenecks. We derive two new novel formulations: 1) a formulation based on entropy and internal energy and (2) an alternative formulation based on Helmholtz free energy. We begin with a stability analysis framework, followed by a reformulation of the UVN flash problem in natural variables. We then introduce our novel approach and discuss the numerical methods used, including gradient and Hessian computations. The proposed method is validated against benchmark cases, demonstrating improved efficiency and robustness.