Probabilistic Upscaling of Hydrodynamics in Geological Fractures Under Uncertainty

TL;DR

This paper introduces a scalable probabilistic workflow that combines Bayesian correction, deep learning, and flow upscaling to predict and quantify uncertainty in hydraulic properties of fractured geological media.

Contribution

It presents a novel hybrid approach integrating physics-informed and data-driven methods for uncertainty-aware flow predictions in complex fractures.

Findings

Probabilistic upscaling captures the impact of fracture heterogeneity on transmissivity.

The workflow yields uncertainty bounds consistent with physical behaviour.

It improves upon empirical aperture-permeability relations by accounting for bias and heterogeneity.

Abstract

Flow and transport in fractured geological media are strongly controlled by aperture heterogeneity and uncertainty in subsurface characterisation, yet most upscaling approaches rely on deterministic representations of fracture permeability. This study presents a scalable probabilistic workflow that bridges image-based fracture geometry and uncertainty-aware hydraulic predictions across scales. The approach integrates Bayesian correction of aperture-permeability model misspecification, a deep learning surrogate for predicting spatially distributed permeability statistics, and Darcy-scale flow upscaling to propagate uncertainty to effective transmissivity. The workflow is applied to natural shear fractures from core material in the Little Grand Wash Fault damage zone (Utah) and to simplified geometries derived from the same datasets. The Bayesian component quantifies uncertainty due to measurement errors and imperfect constitutive relations, while a Residual U-Net learns the effects of local heterogeneity and spatial correlation on predicted permeability uncertainty. Together, these components generate ensembles of permeability fields that are subsequently upscaled to probabilistic macroscopic flow responses. Results show that common empirical aperture-permeability relations are systematically biased for natural fractures, whereas the proposed probabilistic workflow yields uncertainty-aware permeability estimates consistent with physics-based behaviour. The method captures the impact of channelisation, connectivity, and complex 3D void geometries on transmissivity while quantifying the resulting uncertainty bounds. Computational efficiency arises from the proposed hybrid strategy for probabilistic upscaling, which combines physics-informed and data-driven approaches, preserves Stokes-flow consistency and supports uncertainty propagation without repeated high-fidelity simulations.