A physics-constrained data-driven workflow for predicting bottom hole pressure using a hybrid model of artificial neural network and particle swarm optimization

Accurate and efficient prediction of bottom hole pressure (BHP) is important for managed pressure drilling (MPD), which is essential to ensure the safety of drilling in complex formations with a narrow pore/fracture pressure envelope. Without idealized assumptions and iterative solutions, the data-driven machine learning model has higher prediction accuracy and efficiency than the mechanistic hydraulics model. However, the machine learning models suffering from the significant impact of noise data and the strict restriction of the data field, often leads to anomalous deviations. Physical constraints are inherent mappings between output values and characteristic variables, which can be applied to model training to improve the robustness of the model. In this study, wellbore flow mechanism is considered as the physical constraint, and a physics-constrained data-driven workflow is proposed for stable prediction of BHP, which is more consistent with the hydraulic mechanism. Firstly, more than 400,000 groups of field pressure data are extracted as the training dataset by an automatic identification method of drilling state. And twelve characteristic parameters of BHP were optimized, including inlet flow rate, outlet density and wellhead pressure. Embedding physical constraints into the loss function of artificial neural network (ANN) as penalty terms can induce ANN model output results within the wellbore flow mechanism. Finally, particle swarm algorithm is introduced to solve the weight and bias of ANN globally without the derivative of the restructuring loss function. The proposed model is verified based on the field pressure data. It could be found that both experiential and knowledge-based constraints can improve the accuracy and stability of the ANN model, the prediction error is significantly reduced, MRE, RMSE and MAE were respectively reduced to 0.46%, 0.34 MPa and 0.27 MPa. RMSE decreased by 20.9%, MRE and MAE decreased by 19.3% and 18.1%, respectively. Meanwhile, the R2 of the model reached 0.9871. Sensitive parameters such as flow rate have a more significant effect on the prediction accuracy of BHP, while non-sensitive parameters such as mud density can eliminate the abnormal deviation of BHP more effectively, and the constraints of multiple parameters can be superimposed. Therefore, optimizing the constraint combination according to the fluctuation characteristics of BHP is crucial to improve the accuracy and stability of the ANN model. This is an innovative exploration of the physical constraints on the data-driven model of BHP, which can provide accurate and efficient references for managed pressure drilling.