A physics-guided eXtreme gradient boosting model for predicting the initial productivity of oil wells

Abstract

The initial productivity of oil wells is an important index in oilfield development. Due to the nonlinear relationship among the numerous affecting factors of productivity, productivity prediction methods based on seepage theory are difficult to characterize this nonlinear relationship. The machine learning method provides a novel theory to solve this problem. However, the data-driven machine learning method neglects the physical-based seepage theory. For balancing the advantage of the seepage model and the data-driven model, the productivity formula was used to guide the machine learning algorithm for achieving nonlinear regression in this study. Therefore, an innovative physics-guided eXtreme Gradient Boosting (XGBoost) trees algorithm was proposed to predict the initial productivity. The productivity formula was employed as the physical constraint and combined with the mean-square error (MSE) loss function of the XGBoost algorithm. A hyperparameter was introduced to balance the productivity formula and the MSE formula for constructing this adaptive physics-guided loss function. Moreover, the random subsampling cross-validation approach was adopted to train the XGBoost model. The grid search approach was introduced to optimize the hyperparameters of the model. The results show that based on the numerical simulator data, the initial productivity prediction accuracy of physics-guided XGBoost was verified as 94.67%, which was higher than the completely data-driven model. Moreover, the robustness of the novel adaptive physics-guided loss function for improving forecasting accuracy had been validated with sample sizes between 50 and 20000. By introducing the physics-guided sampling process and loss function, the applicability of the XGBoost algorithm has been extended to small sample conditions. Furthermore, the practical accuracy of physics-guided XGBoost was verified as 84.74% by 162 oil wells in the Penglai oilfield. Therefore, the application value of combining the physical knowledge with the XGBoost model has been confirmed in oilfield situations.