DeepONet-embedded physics-informed neural network for production prediction of multiscale shale matrix–fracture system

As a rising method for reservoir-scale production analysis, machine learning (ML) models possess high computational efficiency with robust capability of nonlinear mapping. However, their accuracy and interpretability are commonly limited owing to the absence of intrinsic physical mechanisms, solely by the data fitting. This work proposes a novel DeepONet-embedded physics-informed neural network (DE-PINN), which comprises a forward network to connect the matrix/fracture characteristics and production performance, and a sampling network to acquire the location of sampling points within shale reservoirs. DeepONets are constructed by the selected layers of these networks to output the field variables in governing equations that include mass/momentum conservation equations coupled with multiscale transport mechanisms. Through the automatic differentiation method, these equations are solved by the obtained field variables, and the residuals generated during the solution are integrated into the loss function as physical constraints. Compared with traditional data-driven machine learning models, the DE-PINN exhibits better performance in forecasting the production rate and cumulative production, achieving the mean absolute percentage error (MAPE) of approximately 3% and adjusted R2 values in the test set exceeding 0.98. This model demonstrates the advantage by realizing superior predictive precision with fewer production data samples under complex geological conditions of the shale reservoirs.