Residual-Enhanced Physics-Guided Machine Learning With Hard Constraints for Subsurface Flow in Reservoir Engineering.

Subsurface flow is the core of reservoir engineering. Research on subsurface flow problems can enhance our understanding of the development status of oilfields, thus enabling the prediction of the distribution of residual oil and the formulation of production plans. Machine learning-based methods have been widely studied in developing data-driven models to solve subsurface flow problem. However, a large amount of labeled data are required to build highly accurate models. It is applicable to embed domain-knowledge into data-driven machine learning methods to reduce data requirements. In this study, we propose a residual-enhanced physics-guided machine learning method with hard constraints (RHC-PGML) to predict reservoir pressure. Specifically, a physics-guided machine learning with hard constraints strategy is proposed, which makes the prediction results strictly satisfy the prior domain knowledge to improve the prediction accuracy of the model. In addition, we integrate residual learning in RHC-PGML model to compensate for systematic errors caused by the inability of the embedded physical mechanism to perfectly describe the complex seepage process and further improve the prediction accuracy. The proposed method is verified by a seepage problem in a heterogeneous reservoir model. The results show that the RHC-PGML method can obtain reliable prediction results in the case of sparse and limited data.