An artificial neural network visible mathematical model for predicting slug liquid holdup in low to high viscosity multiphase flow for horizontal to vertical pipes

Slug liquid holdup (SLH) is a critical requirement for accurate pressure drop prediction during multiphase pipe flows and by extension optimal gas lift design and production optimization in wellbores. Existing empirical correlations provide inaccurate predictions because they were developed with regression analysis and data measured for limited ranges of flow conditions. Existing SLH machine learning models provide accurate predictions but are published without any equations making their use by other researchers difficult. The only existing ML model published with actual equations cannot be considered optimum because it was selected by considering artificial neural network (ANN) structures with only one hidden layer. In this study, an ANN-based model for SLH prediction with actual equations is presented. A total of 2699 data points randomly divided into 70%, 15%, and 15% for training, validation, and testing was used in constructing 71 different network structures with 1, 2, and 3 hidden layers respectively. Sensitivity analysis revealed that the optimum network structure has 3 hidden layers with 20, 5, and 15 neurons in the first, second, and third hidden layers, respectively. The optimum network structure was translated into actual equations with the aid of the weights, biases, and activation functions. Trend analysis revealed that this study’s model reproduced the expected effects of inputs on SLH. Test against measured data revealed that this study’s model is in agreement with measured data with coefficient of determinations of 0.9791, 0.9727, 0.9756, and 0.9776 for training, testing, validation, and entire datasets, respectively. Comparative study revealed that this study’s model outperformed existing models with a relative performance factor of 0.002. The present model is presented with visible mathematical equations making its implementation by any user easy and without the need for any ML framework. Unlike existing ANN-based models developed with one hidden layered ANN structures, the present model was developed by considering ANN structures with one, two, and three hidden layers, respectively.