Data-driven methods have surged in popularity due to increased field development and data collection effort in the last two decades, and partly because flow physics in hydraulically fractured low-permeability formations is poorly understood. Such statistical tools have limited extrapolation ability and require sufficient training data, where training an under-determined neural network predictive model with limited data can result in overfitting and poor prediction performance. Unlike statistical models, physics-based models impose causal relations that can provide reliable predictions over a wide range of input. 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 enhance the extrapolation power of data-driven methods and constrain the output to adhere to the general production trends. We demonstrate two physics-constrained approaches (i.e., statistical approach and explicit approach) where physical flow functions are embedded into neural network models.
The performance of physics-constrained models is however dependent on the relevance of the embedded physics to the observed data. When the data cannot be fully represented by a physics-constrained model, the resulting prediction for any given input comes with a large residual error when compared to the ground- truth. We further employ residual learning and introduce an auxiliary neural network component to learn the complex relationship between the input parameters (such as formation and completion properties) and the expected residuals that represent the imperfect descriptions or uncaptured physical phenomena. In this paper, the integration of residual learning and physics-constrained models constitute the Physics- Guided Deep Learning (PGDL) model. The PGDL model augments the predictions from the residual learning model and the physics-constrained model resulting in final predictions that significantly reduce the amount of under and over estimations for a more robust production prediction. Several synthetic datasets with increasing complexity as well as a field dataset from Bakken are used to demonstrate the performance of the proposed PGDL model.
