A Comprehensive Review of Liquid Holdup Forecasting in Gas–Liquid Two-Phase Pipe Flows

Liquid holdup (H_L) prediction in gas–liquid two-phase flows (TPF) has been studied extensively for decades. However, existing reviews and empirical correlations have largely treated key controlling parameters, particularly liquid viscosity and pipe inclination, as independent or secondary factors. This review is based on prior studies by providing a systematic synthesis of the coupled effect of high viscosity (200–800 mPa·s) and pipe inclination (0° to 90°) on both general liquid holdup (H_L) and slug liquid holdup (H_Ls). These effects are regime-dependent: negligible in low-viscosity flows but dominant in high-viscosity, large-diameter, and undulating pipelines. The review identifies two critical limitations of current models: their systematic underprediction for high-viscosity fluids and their failure to account for inclination-driven H_L variations, which can be as high as 10–30%. Consequently, this review advocates a paradigm shift toward data-driven intelligent models (e.g., Artificial Neural Networks (ANNs) and Convolutional Neural Networks (CNNs)) trained on comprehensive, well-curated datasets that explicitly capture the viscosity–inclination coupling. These hybrid models, which combine data-driven learning with physical constraints, provide the most viable path to overcome the fundamental limitations of current correlations and achieve accurate H_L and H_Ls prediction for the design and operation of real-world, undulating pipeline systems handling viscous fluids.