A robust and efficient solution for COSMO-based activity coefficient models

• A robust and efficient solution procedure for COSMO-based activity coefficient models has been developed. • This solution procedure enables integrating COSMO-based models into second-order convergent phase equilibrium calculation algorithms. • The self-consistency equation in COSMO-based models can be obtained by minimizing the system energy from pairwise segment interactions. • The relationship between COSMO-based models and SAFT models has been elucidated. COSMO-based activity coefficient models, such as COSMO-RS and COSMO-SAC, offer a powerful tool that bridges quantum chemical calculations with macroscopic phase equilibrium calculations. These models utilize a group contribution methodology similar to UNIFAC but require an expensive numerical solution of the self-consistency equation for interactions among all surface segments, representing a primary bottleneck in their application to analyses that involve extensive phase equilibrium calculations. This work demonstrates that the self-consistency equation can be derived by minimizing the system energy from all pairwise segment interactions. The derivation leads to an optimization-based second-order solution procedure that ensures convergence and enhances efficiency. We demonstrate the robustness and efficiency of the proposed solution using various examples, including a comparison with the classical successive substitution method, and illustrate that COSMO-based models can be coupled with modern second-order convergent algorithms for phase equilibrium calculations. Furthermore, this work reveals the similarity between COSMO-based models and the SAFT method.