Energy landscape analysis for two-phase multi-component NVT flash systems by using ETD type high-index saddle dynamics

With the increasingly accurate modeling and simulation demands and techniques, obtaining the knowledge of the multi-component phase equilibrium states holds the bottleneck challenge in the study of multi-phase fluid flow. In order to resolve the shortages in computational efficiency and stability in the conventional iterative flash calculation, a new phase equilibrium prediction method is proposed by solving the saddle point of the multi-phase system. In this paper, the HiSD (High-index saddle point dynamics) algorithm is used for the first time to calculate the saddle points on the energy landscape of the two-phase two-component NVT flash model based on the Peng-Robinson equation of state, and the up-down search algorithm of HiSD is applied to generate the solution landscape of the flash system. The Rosenbrock-Euler ETD (exponential time differencing) format is involved to reduce the interference of system rigidity to the calculation. It can be referred from the numerical analysis that there are at most the 1st-order saddle points in the energy landscape of the two-component two-phase NVT flash system, and all these saddle points are located on one straight line of the hyperplane, where the energy is equal everywhere. All these 1st-order saddle points can converge to the same or equivalent local minima, which indicates that the two-component two-phase flash system is a system with only one single solution with physical meanings. In addition, the saddle points also obey a linear relationship and the energy remains the same at different temperatures. Therefore, using the method proposed in this paper, the conventional two-step efforts of phase stability test and phase separation calculation can be simplified. The 1st-order saddle points of the system can be directly calculated, reducing the need for an initial guess. The local minima can be directly searched through the downward direction of the saddle point, which greatly reduces the calculation amount of phase equilibrium calculations. Furthermore, the minimum states at different temperatures can be calculated in batch by using one certain initial value, which significantly improves the adaptability and reliability for complex engineering problems with drastic temperature changes.