An artificial neural network visible mathematical model for real-time prediction of multiphase flowing bottom-hole pressure in wellbores

Accurate prediction of multiphase flowing bottom-hole pressure (FBHP) in wellbores is an important factor required for optimal tubing design and production optimization. Existing empirical correlations and mechanistic models provide inaccurate FBHP predictions when applied to real-time field datasets because they were developed with laboratory-dependent parameters. Most machine learning (ML) models for FBHP prediction are developed with real-time field data but presented as black-box models. In addition, these ML models cannot be reproduced by other users because the dataset used for training the machine learning algorithm is not open source. These make using the ML models on new datasets difficult. This study presents an artificial neural network (ANN) visible mathematical model for real-time multiphase FBHP prediction in wellbores. A total of 1001 normalized real-time field data points were first used in developing an ANN black-box model. The data points were randomly divided into three different sets; 70% for training, 15% for validation, and the remaining 15% for testing. Statistical analysis showed that using the Levenberg-Marquardt training optimization algorithm (trainlm), hyperbolic tangent activation function (tansig), and three hidden layers with 20, 15 and 15 neurons in the first, second and third hidden layers respectively achieved the best performance. The trained ANN model was then translated into an ANN visible mathematical model by extracting the tuned weights and biases. Trend analysis shows that the new model produced the expected effects of physical attributes on FBHP. Furthermore, statistical and graphical error analysis results show that the new model outperformed existing empirical correlations, mechanistic models, and an ANN white-box model. Training of the ANN on a larger dataset containing new data points covering a wider range of each input parameter can broaden the applicability domain of the proposed ANN visible mathematical model.