We develop a new coupled hydro-mechanical-chemical (HMC) model to investigate the stress-controlled evolution of dissolution cavities along a hectometer-scale heterogeneous fracture. The fracture is conceptualized to consist of numerous patches associated with spatially-variable, stress and dissolution-dependent local stiffnesses and apertures. We consider the complete coupling relationships among mechanical deformation, fluid flow, and chemical dissolution within the fracture. More specifically, our model captures non-linear fracture deformational responses and their consequences on localized flow pattern and dissolutional aperture growth, as well as the feedback of dissolution to mechanical weakening and stress redistribution. We elucidate how geomechanical processes affect the aperture and flow patterns and the formation of small to large dissolution cavities. Our simulation results show that stress retards the permeability increase with the extent of retardation positively related to a dimensionless penetration length lp′. Stress induces the splitting of the dissolution front, promoting localized flow and branched dissolution. At low lp′ (wormhole dissolution regime), stress also promotes the sustained growth of dissolution branches. Hence, there is no apparent increase in global flow heterogeneity. At high lp′, stress transitions the system from uniform dissolution into wormhole formation. Wormholes initiate from remote stiffer regions and converge toward the inlet. Our results have important implications for understanding various dissolution phenomena in subsurface fractured rocks, ranging from karstification to reservoir acidization.

Fracture distribution plays a significant role in the behavior of subsurface environments, affecting such activities as geothermal production, exploitation and management of groundwater resources, and long-term storage of nuclear waste and carbon dioxide. A key challenge in these and other applications is to estimate the fracture network properties from sparse and noisy observations. We evaluate the utility of cross-borehole thermal experiments for this task, using both physics-based particle-tracking (PBPT) heat-transfer approach and its deep neural network (DNN) surrogates. Synthetic data are provided by the PBPT simulations and used to train and test the DNN surrogates over a full range of the fracture network properties. We propose regionalized and step-by-step training techniques to reduce the computational cost of expensive PBPT forward solves over large ranges of the (to-be-estimated) parameters. Our numerical experiments suggest the feasibility of training a regionalized DNN surrogate over parameter ranges for which the PBPT solves are fast and extrapolating its predictions to parameter ranges with few additional data. We analyze the balance between computational cost and model accuracy, and provide both PBPT and DNN models for applications to others kinds of data.

A two-dimensional particle-based heat transfer model is used to train a deep neural network. The latter provides a highly efficient surrogate that can be used in standard inversion methods, such as grid search algorithms. The resulting inversion strategy is utilized to infer statistical properties of fracture networks (fracture density and fractal dimension) from synthetic thermal experimental data. The (to-be-estimated) fracture density is well constrained by this method, whereas the fractal dimension is harder to determine and requires adding prior information on the fracture network connectivity. The method is tested on several fracture networks and hydraulic conditions.