What question did this study set out to answer?

The aim is to develop a predictive model for liquid holdup in a two-phase gas-liquid vertical flow using artificial neural networks.

April 19, 2026Journal of Engineering and Applied Science0 citationsOpen Access

Predicting slug liquid holdup in a two-phase gas–liquid vertical flow

NONicholas N. OmehFederal University of Technology Owerri UDUgochukwu I. DuruFederal University of Technology Owerri ANAngela N. NwachukwuFederal University of Technology Owerri

Key Points

The aim is to develop a predictive model for liquid holdup in a two-phase gas-liquid vertical flow using artificial neural networks.
Conducted feature selection using machine learning algorithms to identify key parameters.
Developed feed-forward ANN models with varying hidden layers.
Applied regularization and k-fold cross-validation to ensure model robustness.
Evaluated performance using metrics like R² and RMSE.
The single-hidden-layer ANN with 15 neurons achieved an R² of approximately 0.994 and RMSE of approximately 0.051.
Validation performance was stable across different folds.
Sensitivity analysis showed that lower superficial gas velocity decreases liquid holdup, while higher superficial liquid velocity increases it.

Abstract

Abstract The accuracy of existing liquid holdup models is limited to the range of data used in their development. In this study, a dynamic model for predicting liquid holdup in a two-phase gas liquid vertical flow is developed using artificial neural networks and a wider range of actual and synthetic data obtained from Literature. Prior to the model’s development, feature selection was conducted using Matlab’s machine learning algorithms (MRMR, ANOVA, CHI2, Kruskal wallis and ReliefF), to identify the most influential parameters affecting liquid holdup. Although all eight parameters were used in developing the liquid holdup model, the feature-selection results were used to determine the relative importance of each parameter influencing liquid holdup. Feed‑forward ANN models (1–3 hidden layers) were then trained with Levenberg–Marquardt on stratified splits (70/15/15). Regularization (L2) and k‑fold cross‑validation (k = 5) were applied to mitigate overfitting, and performance was evaluated using R 2, RMSE, average relative error (ARE), and the standard deviation of relative error (SDRE). Results from the analysis reveal that single‑hidden‑layer ANN with 15 neurons was more effective than the two and three hidden layer neural architecture, with overall R 2 ≈ 0. 994 and RMSE ≈ 0. 051. Across folds, validation performance remained stable. Sensitivity analysis indicates lower superficial gas velocity (Vsg) decreases liquid holdup (HL) and higher superficial liquid velocity (Vsl) increases liquid hold-up (HL) within the tested ranges; while pipe diameter and liquid viscosity show positive associations with HL, consistent with slug hydrodynamics. This study offers a transparent ANN approach for vertical slug holdup within 50–100 mm pipes, spanning Vₒ₆=0. 11 – 13. 15 m/s and Vₒ₋=0. 02 – 2. 35 m/s ranges, eliminating the need for complex and time-consuming calculations.

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