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.

Effective management of gas influx is crucial in oil and gas drilling operations to prevent uncontrolled gas release and blowout hazards. When gas influxes enter a wellbore or marine riser within non-Newtonian drilling fluids, the processes associated with gas dispersion and suspension can significantly alter the behavior of gas migration. This consideration becomes crucial in non-circulating wells where it is essential to monitor and accurately predict changes in pressure. This study investigates gas influx behavior and interfacial area concentration (IAC) transport through detailed full-scale experiments and numerical simulations. Helium gas was injected into a 5160-foot wellbore filled with synthetic oil-based mud (SBM). High-resolution distributed fiber-optic sensing (DFOS) system was used to monitor the gas migration process, analyzing gas slip velocities, slug lengths, and suspension concentrations. A numerical simulator using the two-fluid model (TFM) and interfacial area transport equation (IATE) simulated gas influx behaviors, with results compared to experimental data. The IATE-based modeling framework accurately captured bubble breakdown, coalescence, and suspension processes, achieving good agreement with experimental data, including gauge measurements, distributed temperature sensing (DTS), and distributed acoustic sensing (DAS). This approach showed improved accuracy over traditional models like the drift-flux model, particularly in gas suspension interpretation. Sensitivity analysis highlighted the impact of gas influx size, gas bubble dispersion, and suspension processes on surface pressure build-up due to changes in system compressibility. In addition, the presented case study was translated into field predictions (the migration of methane influx in water-based mud (WBM)) based on the proposed and validated models. The obtained results provided valuable references for field applications. The experimental data using helium and SBM is beneficial in decoupling the complex physical processes involved during gas migration. This is also a novel practice for implementing the IATE in well-scale multiphase flow simulations, which has proved to be an effective tool for predicting the dynamics of gas influx distributions.