Prediction of Waterflooding Performance with a New Machine Learning Method by Combining Linear Dynamical Systems with Neural Networks

Jingjin Bai, Jiujie Cai, Jiazheng Liu, Bailu Teng

Machine learning methods have gained significant attention in forecasting waterflooding performance in recent years, but their accuracy often remains insufficient for practical field applications. This study proposes a hybrid framework that integrates a linear dynamical system (LDS) with a neural network (NN). The framework improves oil-rate prediction by decomposing the injection–production relationship into linear and nonlinear components. Specifically, the aggregate injection rate is approximately linearly related to total liquid production, which is effectively captured by the LDS model, based on reservoir material balance principles. In contrast, the oil fraction of the produced liquid, defined as the ratio of oil rate to liquid rate, is bounded between 0 and 1 and typically decreases over time. This nonlinear trend is accurately modeled using a neural network (NN). The parameters of the LDS–NN framework are learned from historical injection and production data via a supervised training process. Furthermore, key hyperparameters within the model can be adjusted to optimize the performance for different reservoir characteristics. The proposed hybrid method is evaluated using both simulated reservoir cases and real field data, and compared against the performance of LDS-only and NN-only models. The results demonstrate that the LDS–NN framework consistently provides more accurate oil-rate predictions than either standalone LDS or NN approaches, across both synthetic and real-world waterflooding scenarios.