Improvement of augmented free-water flash algorithm based on HV mixing rule and simulated annealing optimization algorithm

The calculation of three-phase equilibrium in CO₂-hydrocarbon-water mixtures holds significant importance within numerical simulations, particularly in applications such as CO₂-enhanced oil recovery and carbon dioxide sequestration. However, due to the non-ideality of CO₂ and the polarity of water, three-phase equilibrium calculations often encounter convergence challenges. The augmented free-water flash algorithm [6], specifically focusing on CO₂ dissolution in the aqueous phase, addresses the convergence challenges encountered by traditional three-phase flash algorithms. Despite its accuracy diminishes under conditions of high pressure and high CO₂ concentrations, limiting its capability to accurately describe CO₂ dissolution in oil-gas-water multiphase systems. The G^E (excess Gibbs free energy) type mixing rule can be effectively integrated with equations of state, including PR and SRK, by utilizing activity models like NRTL and UNIFAC, which can be applied to the calculation of thermodynamic parameters for both nonpolar and polar systems and high-pressure complex systems. In this study, based on the augmented free-water assumption, we have developed a new augmented free-water three-phase flash algorithm for CO₂/hydrocarbon/water mixtures. This algorithm integrates the PR equation of state with the NRTL activity model, employing the HV mixing rule for CO₂-water interactions and the Van der Waals rule for other non-polar components. Furthermore, to enhance computational efficiency, the algorithm incorporates the simulated annealing global optimization algorithm, replacing Newton iteration to more effectively identify the global minima of the complex objective function. The example calculations show that the improved augmented free-water flash algorithm has higher accuracy and efficiency than the traditional augmented free-water flash algorithm. The augmented free-water three-phase flash algorithm proposed in this paper offers a precise model for phase equilibrium calculations essential for numerical simulations in CO₂-enhanced oil recovery and carbon dioxide sequestration.