WellPINN: Accurate Well Representation for Transient Fluid Pressure Diffusion in Subsurface Reservoirs with Physics-Informed Neural Networks

Accurate representation of pumping wells is essential for reliable reservoir characterization and simulation of operational scenarios in subsurface flow models. Physics‐informed neural networks (PINNs) are emerging as a promising alternative to numerical models for reservoir modeling, offering seamless integration of monitoring data and governing physical equations. However, existing PINN‐based studies face major challenges in capturing fluid pressure near wells when using a source/sink term, particularly during the early stages after pumping begins. We address this problem by introducing WellPINN, a workflow in which an initially trained PINN infers fluid pressure across the entire reservoir domain using a large equivalent well radius. This initial PINN solution is then locally refined around the well by a set of subdomain PINNs that are trained for smaller equivalent well radii. Continuity across these subdomain interfaces as well as at the initial condition is ensured by hard‐constraining each PINN on its subdomain boundary. Our results demonstrate WellPINN as the first workflow of its kind to focus on accurate inference of fluid pressure from pumping rates throughout the entire injection period, significantly advancing the potential of PINNs for inverse modeling and operational scenario simulations. All data and code for this paper are openly available at https://doi.org/10.20350/DIGITALCSIC/17260.