Incorporation of Physics into Machine Learning for Production Prediction from Unconventional Reservoirs: A Brief Review of the Gray-Box Approach

Abstract

Summary Prediction of well production from unconventional reservoirs is often a complex problem with an incomplete understanding of physics and a considerable amount of data. The most effective way for dealing with it is to use the gray-box approach that combines the strengths of physics-based models and machine learning (ML) used for dealing with certain components of the prediction where physical understanding is poor or difficult. However, the development of methodologies for the incorporation of physics into ML is still in its infancy, not only in the oil and gas industry, but also in other scientific and engineering communities, including the physics community. To set the stage for further advancing the use of combining physics-based models with ML for predicting well production, in this paper we present a brief review of the current developments in this area in the industry, including ML representation of numerical simulation results, determination of parameters for decline curve analysis (DCA) models with ML, physics-informed ML (PIML) that provides an efficient and gridless method for solving differential equations and for discovering governing equations from observations, and physics-constrained ML (PCML) that directly embeds a physics-based model into a neural network. The advantages and potential limitations of the methods are discussed. The future research directions in this area include, but are not limited to, further developing and refining methodologies, including algorithm development, to directly embed physics-based models into ML; exploring the usefulness of PIML for reservoir simulations; and adapting the new developments of how the physics and ML are incorporated in other communities to the well-production prediction. Finally, the methodologies we discuss in the paper can be generally applied to conventional reservoirs as well, although the focus here is on unconventional reservoirs.