Research Project B04

In the first funding phase, we represented fracture networks as elevated hydraulic conductivity values with channel-like structures in (randomly) heterogeneous porous media. Following this approach, we developed efficient Markov Chain Monte Carlo (MCMC) methods for Bayesian inversion of such fields. We also developed a novel statistical analysis and random generation of fracture images via the Radon transform (see Figure 1). The extended-and-randomized Radon transform can generate randomized fracture images that match the statistics of fracture length, aperture (including roughness), density, angles and connectivity, as provided by an example image.

In the current (second) funding phase, we investigate the effects of (random) material heterogeneity on the initiation and propagation of fractures. This involves a fundamentally new approach to stochastic modeling of fracture propagation: we incorporate a random series of directional decisions during fracture propagation, resulting in irregular fracture patterns, as seen in Figure 2. We implement this inside the time stepping of a phase field model from Project B01.

We also collaborate with Project B02 on the use of spatial random fields of mechanical (Lamé) parameters. These advances provided insights into the scaling behavior between mechanical heterogeneity and irregular fracture geometries (Figure 3). We are further collaborating with Project D03, Project B03, and Project INF on the stochastic validation of transport models with irregular and uncertain fracture geometries.

Our goal for the third funding period will be to understand the effects of heterogeneity and irregularities on processes such as pressure diffusion during hydraulic stimulation and the transfer of heat and mass. Figure 4 exemplifies such a complex domain. Specific goals will include: previously unexplored phenomena during responses of fracture networks to oscillatory hydraulic stimulation, developing simplified proxy models for the effective behavior of pressure diffusion, and investigating consequences on heat/mass transport. We will build on a pressure diffusion simulation framework composed in FEniCS and preCICE from project D02, collaborate on realistic statistics of fracture networks and mechanically heterogeneous materials with projects B02 and B05, and perform benchmarking our proxy models jointly with D03.

Contributing to the “salt vision” of the overall CRC, we will also investigate the effect of clogging in fracture networks on the aforementioned processes, where we discuss the formulation of fracture clogging as a random growth problem with C04.