A Line-Search-Based Algorithm for Multiphase Flash Calculations with CO 2 –Hydrocarbon System - Xu, Shijing; Wang, Guoqing; Gao, Bin; Tian, Jiaxin (ACS omega, 2024)
Multiphase flash calculations are pivotal in compositional simulation, necessitating a robust and efficient computational algorithm. In this work, we have developed a line-search-based algorithm framework for stability analysis and multiphase flash calculations. This algorithm is rooted in the modified Newton step and line-search method. The modified Newton step, derived from modified Cholesky factorization, ensures a descent direction, while the line search determines the degree of decrease. This combination facilitates convergence even in challenging regions for phase stability analysis and multiphase flash calculations, exhibiting superlinear convergence speed. Unlike traditional approaches that rely on successive substitution iteration and may resort to Newton iteration only if the Hessian matrix is positive definite, our algorithm incorporates modification via modified Cholesky factorization upon encountering a nonpositive definite Hessian matrix. We tested our algorithm with several classical fluids, demonstrating its efficiency and robustness. Furthermore, we assessed the algorithm's performance by computing the pressure-composition diagram for the CO -hydrocarbon system, where all calculations achieved rapid convergence without failure. This newly developed algorithm for phase stability analysis and multiphase flash calculations represents a significant advancement for compositional or chemical process simulations.