Fourier Neural Operator-Accelerated Physics-Informed Framework for Ultra-Long-Term Fracture Conductivity Prediction in Shale Reservoirs

Abstract Accurate and efficient prediction of hydraulic fracture conductivity in shale reservoirs over ultra-long-term (>5 years) production lifecycles is critical for optimizing well performance and development strategies. While comprehensive, traditional physics-based coupled models face prohibitive computational costs when simulating the complex interplay of mechanics, fluid flow, and irreversible damage (e.g., creep, plasticity) within Supported Grain-Porous Media Fracture Systems (SG-PMFS), severely limiting large-scale sensitivity analyses and design optimization. This study proposes a physics-informed data-driven framework centered on the Fourier Neural Operator (FNO) to achieve rapid, ultra-long-term prediction of hydraulic fracture conductivity. A high-fidelity numerical model, incorporating multi-physics mechanisms such as shale creep, proppant embedment and crushing, and fluid-solid coupling, was used to generate the training dataset. A key finding is an intrinsic trade-off revealed in recursive prediction using FNO models trained on different timesteps (1-month, 3-month, and 12-month): the short-timestep model excels in initial accuracy but suffers from significant error accumulation in long-term forecasts, whereas long-timestep models exhibit superior long-term stability and accuracy at the expense of initial precision. To address this challenge, a novel Hierarchical Temporal Aggregation (HTA) strategy is introduced. This strategy dynamically switches between the optimal models based on the prediction horizon, leveraging the high precision of the short-timestep model for the initial phase and the stability of long-timestep models for later stages. Results demonstrate that the HTA strategy effectively mitigates the accumulation of recursive errors, maintaining the Mean Absolute Percentage Error (MAPE) consistently below 2% throughout the medium-to ultra-long-term forecast. Compared to the high-fidelity physics-based simulations, this framework achieves a computational speed-up exceeding three orders of magnitude (>1440x). This methodology provides a decision-support tool for fracture design and production strategy optimization in unconventional reservoirs, significantly enhancing the feasibility of ‘what-if’ scenario analyses.