Waterflooding Interwell Connectivity Characterization and Productivity Forecast with Physical Knowledge Fusion and Model Structure Transfer

Waterflooding reservoir interwell connectivity characterization is the fundamental work in oil development, aiming to inverse the vital connecting channels between injectors and producers. In this paper, we endow an artificial neural network (ANN) with strong interpretability through the ordinary differential equation (ODE) of the material balance equation, proposing a physical knowledge fusion neural network (PKFNN). In addition, the proposed model could inherit the knowledge learned from different injector–producer pairs, fully improving the training efficiency. In this way, PKFNN combines the merits of both physical and machine learning approaches. Firstly, based on the physical control law and the ODE of the material balance equation, we endow the model with highly transparent modular architectures in the framework of feedforward neural network. In this way, our work has both high interpretability and excellent approximation ability, combining the merits of the physical and machine learning approaches. The proposed model shows great performance on productivity forecast and interwell connectivity reflection in several reservoir experiments. PKFNN provides a novel way to enhance the interpretability and robustness of the data-driven-based interwell connectivity-analyzing models by integrating the physical knowledge of waterflooding reservoirs.