Physics- Guided Deep Learning for Improved Production Forecasting in Unconventional Reservoirs

The complexity of physics based modeling of fluid flow in hydraulically fractured unconventional reservoirs, together with the abundant data from repeated factory style drilling and completion of these resources, has prompted the development and application of data-driven statistical models for predicting hydrocarbon production performance. More recently, machine learning algorithms have been widely studied in developing data-driven prediction models for unconventional reservoirs. These models often require a large amount of high quality training data with sufficient range to avoid excessive extrapolation and produce reliable predictions. Unlike statistical models, physics based models represent causal relations between input and output variables to provide predictions beyond available data. While a detailed physics based description of fluid flow in unconventional reservoirs is not yet available, approximate physical flow functions have been proposed to capture the general production behavior of unconventional wells. These physical functions can be augmented with the available data to improve data-driven methods by constraining the models to adhere to the general production trends. In this paper, we develop a physics-constrained data-driven model by embedding physical flow functions into neural network models. Since the performance of the physics-constrained model depends on the relevance of the embedded physics, a sizeable residual prediction error is expected if the collected data do not sufficiently match the embedded model. The residual model typically represents errors in the description of inputs or any missing physical phenomenon. We compensate for such errors through residual learning, where an auxiliary neural network is designed to learn the complex relationship between the input parameters (such as formation and completion properties) and the expected prediction residuals. The new physics-guided deep learning (PGDL) model augments any physics-constrained prediction model with residual learning to increase its prediction accuracy. Several synthetic and actual field data sets, from the Bakken play, are used to demonstrate the performance of the PGDL model.