A physics-constrained long-term production prediction method for multiple fractured wells using deep learning

Abstract

Production prediction of hydraulic fractured wells is often complicated due to the incomplete understanding of production mechanisms and insufficient amount of available data. As a prevalent approach, machine learning can capture nonlinear patterns of production variation but often yields physically inconsistent predictions due to the lack of involvement of physical laws, especially for out-of-sample scenarios. In this work, we propose a novel physics-constrained deep learning framework for long-term production prediction of multiple fractured wells based on a Bidirectional gated recurrent unit (BiGRU) and Deep hybrid neural network (DHNN) combined neural network (BiGRU-DHNN). The proposed approach can take full advantage of the complementary strengths of physics knowledge and machine learning to better acquire the dynamics of time-series production. Static and dynamic, temporal and spatial data of fractured wells are treated as additional variables to enforce physical constraints on the long-term production forecasting with a multi-step-ahead prediction strategy. Two multi-well field cases are conducted to compare the prediction performance of the proposed physics-constrained BiGRU-DHNN method with some conventional time-series machine learning models, including Recurrent neural network (RNN), Long short-term memory (LSTM), Gated recurrent unit (GRU) and BiGRU, by ignoring physical constraints. The results demonstrate that the proposed method outperforms conventional machine learning methods under the constraints of geological properties, logging curves, well information, fracturing parameters and field operations. By considering the physics-based dependencies between constraints and production, the BiGRU-DHNN model significantly improves the accuracy, robustness and generalization of the long-term production prediction of fractured wells in a gridless and efficient manner. Furthermore, the contribution mechanisms of these constraints to the model prediction performance are also investigated to improve its interpretability, which provides guidance to field personnel on which kind of constraints should be prioritized and addressed if uncertainties exist in the practical application. The findings are expected to provide insight into the integration of physics into machine learning for accurate production prediction and to be employed as a potential tool to support fracturing design optimization.