Automatic History Matching of Aquifer Water-Drive Reservoirs Using Adaptive Moment Estimation with Decaying Regularization (AdamW)

Abstract This work builds on our previously published application of the Adam optimizer for automatic history matching. In this study, we extend that work by introducing a modified AdamW optimizer (Adaptive Moment Estimation with Decaying Regularization) to enhance the Adam-based approach. Originally developed for training large-scale deep learning models, AdamW offers a fast convergence rate with decay regularization, making it a promising method for integrating geostatistical realizations into history matching. Additionally, the high uncertainty in aquifer parameters often leads to inaccuracies in simulation model predictions. To address this, both aquifer and reservoir model parameters are adjusted during history matching, which expands the scope beyond traditional methods that focus primarily on reservoir parameters. This paper includes three primary components. First, a three-dimensional, three-phase black-oil simulator was developed based on a corner-point grid, with the Carter-Tracy water influx model integrated to simulate aquifer performance. Second, a discrete adjoint method was implemented to calculate gradients of the objective function with respect to model parameters, subject to the equality constraints imposed by the three-phase flow equations. These gradients are computed with respect to key parameters, including reservoir and aquifer permeability and porosity, as well as aquifer thickness and radius. Third, the modified AdamW algorithm was applied to perform automatic history matching, with a customized warm restart introduced to accelerate convergence and avoid local minima. The proposed method was validated using the PUNQ-S3 reservoir model, where the AdamW algorithm successfully achieved matching of water cut and GOR over a 16-year production period. Results from the case studies demonstrate that AdamW provides a robust convergence rate and effectively handles the challenges of matching long-term production data while simultaneously estimating both reservoir parameters and aquifer properties.