Physics Informed Machine Learning for Production Forecast

Understanding the reservoir behavior is vital knowledge required for various aspects of the reservoir management cycle such as production optimization and establishment of the field development strategy. Reservoir simulation is the most accurate tool for production forecast, but often it is very expensive from aspects of computational time and investment in the model building process. In this work, the machine learning methods for accurate production forecast that honor the material balance constraints are presented. The presented hybrid model approach consists of several main components. The material balance constraints are necessary during the training process to avoid unphysical solutions and to honor conservation laws. For this reason, the Capacitance Resistance Model (CRM) was chosen due to its intuitive form and flexibility in describing reservoirs of various complexities. Another part of the solution is represented by powerful machine learning methods such as Generalized Additive Models (GAM), Gradient Boosting, and Convolutional and Recurrent Neural Networks. Neural Networks and Gradient Boosting methods are very popular machine learning techniques. However, in this work, it is demonstrated that GAM can also produce results comparable to the former methods while holding additional attractive properties. The basis functions of GAM are the splines, which are smooth functions with continuous derivatives. Such properties are very useful for optimization tasks. GAM is an extension of standard Generalized Linear Models (GLM), which provides rich tools for model explainability. It is hence also advantageous for the understanding how the reservoir behaves through such models. The implemented approach was applied to the publicly available data with an existing history matched reservoir model for the offshore field with several injectors and producers. This allowed us to compare results and build machine learning models that describe communication between wells and can be further analyzed though the simulation model. Machine learning methods are constantly improving at solving difficult problems, while it often suffers from nonphysical solutions and unexplainable models. The presented method holds the properties of explainable regression models while providing powerful predictability capabilities within material balance constraints. By no means does it try to replace the reservoir simulation but offers a complementary solution, which is reliable and necessary in cases where there is no full reservoir model available.