Physics-informed neural network with moving boundary constraints for modeling hydraulic fracturing

Hydraulic fracturing is an essential technique for hydrocarbon extraction. While mathematical models are commonly utilized to simulate hydraulic fracture propagation, they are computationally expensive due to the complexities of moving boundary conditions. Recent advances in data-driven models have reduced the computational burden; however, these approaches often fail to preserve the physical interpretability. To address this limitation, a physics-informed neural network (PINN) has emerged as a promising methodology that integrates governing physics-based equations into a loss function. However, conventional PINNs still face challenges in accurately modeling the moving boundary nature of fracture propagation, particularly due to the evolving domain of interest over time. In this study, we propose a PINN with a moving boundary constraint (MB-PINN) for hydraulic fracture propagation. This approach employs a dual-network architecture to model the spatiotemporal evolution of fractures and enforce constraints on moving boundaries. Additionally, this architecture captures the nonlinear effects across diverse scenarios by incorporating fracturing conditions as input variables. Our framework improves the accuracy of fracture propagation modeling by reducing prediction errors compared to conventional PINNs, while significantly enhancing the computational efficiency compared to complex high-fidelity models. These advancements make it a scalable and reliable tool for simulating complex fracture dynamics under diverse operational conditions in real-world applications.