When Cubic Law and Darcy Fail: Bayesian Correction of Model Misspecification in Fracture Conductivities

Abstract Structural uncertainties and unresolved features in fault zones hinder the assessment of leakage risks in subsurface storage. Understanding multi‐scale uncertainties in fracture network conductivity is crucial for mitigating risks and reliably modeling upscaled fault leakage rates. Conventional models, such as the Cubic Law, which is based on mechanical aperture measurements, often neglect fracture roughness, leading to model misspecifications and inaccurate conductivity estimates. Here, we develop a physics‐informed, AI‐driven correction of these model misspecifications by automatically integrating roughness effects and small‐scale structural uncertainties. Using Bayesian inference combined with data‐driven and geometric corrections, we reconstruct local hydraulic aperture fields that reliably estimate fracture conductivities. By leveraging interactions across scales, we improve upon traditional empirical corrections and provide a framework for propagating uncertainties from individual fractures to network scales. Our approach thereby supports robust calibration of conductivity ranges for fault leakage sensitivity analyses, offering a scalable solution for subsurface risk assessment.