Modelling the flowing bottom hole pressure of oil and gas wells using multivariate adaptive regression splines

One crucial factor that aids the evaluation of oil and gas well productivity is the flowing bottom-hole pressure (FBHP). However, accurately determining the FBHP has been challenging for the oil and gas industry. Traditional methods, such as using downhole gauges or relying on empirical and mechanistic models, have limitations, prompting the exploration of alternative approaches such as machine learning (ML). However, most ML models operate as black box models, lacking transparency and interpretability. In this study, the multivariate adaptive regression splines algorithm was used to develop a FBHP estimation model. The model includes eight input variables and was built using 1001 data points from literature. The results show that the model achieved a coefficient of correlation, root mean square error and average absolute percentage error values of 0.94, 130 and 4.2% respectively. Compared to existing models, the developed model exhibited improved predictive accuracy. Sensitivity analysis indicates that water flow rate and depth had the largest effect on FBHP estimation, each contributing 17.5%, while oil API gravity had the least effect with a contribution of 3.5%. This study showcases a novel model that is explicitly presented, interpretable and physically validated, making the model suitable for integration into software applications. These attributes are lacking in many existing FBHP estimation models. By utilizing this model, the costs associated with downhole gauges can be saved, and real-time estimations can be obtained in the field. The model would be useful to oil industry players producing from unconventional wells where downhole gauges are rarely installed.