A Dynamic Residual Learning Approach to Improve Physics-Constrained Neural Network Predictions in Unconventional Reservoirs

Predictive models that incorporate physical information or constraints are used for production prediction in subsurface systems. They come in many flavors; some include additional terms in the objective function, some directly embed physical functions and some use neural network layers to explicitly perform physical computations. In unconventional reservoirs that are characterized by tight fractured formations, a detailed and reliable description of the flow and transport processes is not yet available. Existing physics-based models use overly simplifying assumptions that may result in gross approximations. In physics-constrained neural network models, the network predictive performance can be degraded when the embedded physics does not represent the relationship within the observed data. We propose dynamic residual learning to improve the predictions from a physics-constrained neural network, whereby an auxiliary neural network component is introduced to compensate for the imperfect description of the constraining physics. When a dataset cannot be fully represented by a trained physics-constrained model, the predictions come with a large error or residual when compared to the ground truth. A deep neural network utilizing a masked loss function to enable learning from wells with varying production lengths is employed to learn the complex spatial and temporal correspondence between the well properties such as formation and completion parameters to the expected residuals. The new formulation allows for dynamic residual correction, avoids unintended bias due to less-than-ideal input data, and provides robust long-term predictions when partially-observed timesteps are present. The proposed method results in a final prediction that combines the prediction from the physics-constrained neural network with the predicted residual from the auxiliary neural network component. Several synthetic datasets with increasing complexity as well as a field dataset from Bakken are used for demonstration.