What challenges arise when using equations of state near the critical point?

Near-critical challenges: large property fluctuations and long correlation lengths not captured by classical EOS, density differences between phases vanish creating convergence difficulties, classical EOS has wrong critical exponents (mean-field behavior), liquid and vapor roots of cubic EOS merge making phase identification difficult, and numerical instabilities in flash calculations. Mitigation: use specialized near-critical formulations (crossover models), implement robust phase stability analysis (tangent plane criterion), use continuation methods for flash calculations, apply regularization techniques, and avoid operating in near-critical region if possible. Some advanced EOS (PC-SAFT with crossover) handle critical region better.