A comparative analysis between population balance method and interfacial area transfer equation approaches for modeling gas–liquid two-phase flow in a vertical circular pipe

This review explores the population balance method (PBM) and the interfacial area transport equation (IATE) for modeling gas–liquid two-phase flow in vertical pipes. While both methods capture bubble dynamics, they differ in theoretical formulation and computational demands. PBM excels in handling complex coalescence and breakup mechanisms, making it particularly suited for non-Newtonian fluids and high-pressure conditions (up to 2 MPa). However, its computational intensity limits its applicability to large-scale systems. IATE, in contrast, offers an efficient framework for predicting interfacial dynamics and flow regime transitions, making it advantageous for large-scale industrial simulations. However, its empirical correlations remain constrained to air–water systems and moderate pressures (up to 0.6 MPa), limiting its accuracy in complex fluid environments. This review synthesizes these methods’ principles, strengths, and limitations and discusses the implications of choosing one method over another depending on specific application requirements. The comparative analysis emphasizes the need to select appropriate modeling techniques based on targeted operational goals, contributing to more efficient and safer design in engineering practices.