Building on earlier phases of the project that statistically analysed static fracture networks and investigated irregular fracture geometries, the goal of the present phase is to study the combined effects of heterogeneity, network topology, and geometric irregularity on subsurface processes. In particular, we focus on pressure diffusion, the required level of model complexity to represent effective behaviour, and the transport of mass in fractured porous media. All relevant factors are treated in a stochastic manner, including heterogeneous hydraulic and mechanical properties, random fracture networks, and irregular fracture geometries. The overarching objective is to improve the understanding of processes relevant to applications such as the testing and operation of geothermal reservoirs in fractured formations.
Pressure stimulation in randomly fractured and heterogeneous media is investigated using coupled hydro-mechanical models and Monte Carlo simulations. These simulations allow us to identify characteristic phenomena such as multiple pressure-diffusion time scales, preferential pressure-propagation pathways, and competitive interactions between fractures. The effective macroscopic pressure response is analysed across ensembles of realizations, and global sensitivity analyses are performed to relate observed behaviour to governing parameters describing heterogeneity, fracture geometry, and network structure.
Based on these results, simplified proxy models are developed to capture the effective pressure response without explicitly resolving the full stochastic and geometric complexity of the system. These proxies are formulated as reduced, lower-dimensional pressure-diffusion models with physically constrained and flexible parameterizations that incorporate the dominant effects identified in the detailed simulations. By systematically varying both the functional form of these parameterizations and the geometric complexity of the proxy models, we derive minimal yet expressive representations that provide accurate and interpretable descriptions of the effective behaviour.
Finally, the implications of irregular fracture geometries and random networks for advective–diffusive transport are examined. Dispersion models are derived for individual fractures and extended to fracture networks using stochastic descriptions of particle arrival times. This approach enables efficient prediction of breakthrough-curve statistics and provides insight into mixing, non-Fickian transport, and asymptotic dispersion behaviour in complex fractured systems.
