Liquid holdup prediction in gas–liquid two-phase flow using RIME-optimized Gaussian process regression

Liquid holdup in gas–liquid two-phase flow is a fundamental parameter governing flow behavior in oil and gas production, chemical pipelines, reactors, and separation equipment, directly controlling mass and heat transfer efficiency. To overcome the restricted applicability of empirical correlations and the lack of uncertainty quantification, this study develops a liquid holdup prediction model by coupling Gaussian process regression (GPR) with the Rime-Ice Optimization Algorithm (RIME) optimization algorithm. Eight flow and fluid-property parameters, including pipe diameter, superficial liquid velocity, superficial gas velocity, inclination angle, gas density, liquid density, gas viscosity, and liquid viscosity, were selected as model inputs., trained on 1452 experimental data points from Mukherjee, Minami, Beggs, Abdul-Majeed, GA Payne, and other researchers. The RIME algorithm optimizes three GPR kernel hyperparameters by minimizing five-fold cross-validation root mean square error (RMSE), balancing global exploration via the soft-rime strategy and local exploitation via the hard-rime puncture mechanism. The RIME-GPR model achieves R2 of 0.9210 and 0.9126, RMSE of 0.0695 and 0.0732, and ratio of performance to deviation (RPD) of 3.5569 and 3.3819 on training and test sets, outperforming convolutional neural network (CNN), extreme learning machine (ELM), long short-term memory network (LSTM), support vector machine (SVM), radial basis function (RBF), and Transformer. External validation on 90 independent data points yields R2 = 0.90425, confirming strong cross-dataset generalizability.