Transient flow modeling in fractured media using graphs.

We describe a method to simulate transient fluid flows in fractured media using an approach based on graph theory. Our approach builds on past work where the graph-based approach was successfully used to simulate steady-state fluid flows in fractured media. We find a mean computational speedup of the order of 1400 from an ensemble of a 100 discrete fracture networks in contrast to the O(10^{4}) speedup that was obtained for steady-state flows earlier.

Characterizing the impact of particle behavior at fracture intersections in three-dimensional discrete fracture networks.

We characterize the influence of different intersection mixing rules for particle tracking simulations on transport properties through three-dimensional discrete fracture networks. It is too computationally burdensome to explicitly resolve all fluid dynamics within a large three-dimensional fracture network. In discrete fracture network (DFN) models, mass transport at fracture intersections is modeled as a subgrid scale process based on a local Péclet number.

Branching of hydraulic cracks enabling permeability of gas or oil shale with closed natural fractures.

While hydraulic fracturing technology, aka fracking (or fraccing, frac), has become highly developed and astonishingly successful, a consistent formulation of the associated fracture mechanics that would not conflict with some observations is still unavailable. It is attempted here. Classical fracture mechanics, as well as current commercial software, predict vertical cracks to propagate without branching from the perforations of the horizontal well casing, which are typically spaced at 10 m or more.

Quantifying Topological Uncertainty in Fractured Systems using Graph Theory and Machine Learning.

Fractured systems are ubiquitous in natural and engineered applications as diverse as hydraulic fracturing, underground nuclear test detection, corrosive damage in materials and brittle failure of metals and ceramics. Microstructural information (fracture size, orientation, etc.) plays a key role in governing the dominant physics for these systems but can only be known statistically.

Predictions of first passage times in sparse discrete fracture networks using graph-based reductions.

We present a graph-based methodology to reduce the computational cost of obtaining first passage times through sparse fracture networks. We derive graph representations of generic three-dimensional discrete fracture networks (DFNs) using the DFN topology and flow boundary conditions. Subgraphs corresponding to the union of the k shortest paths between the inflow and outflow boundaries are identified and transport on their equivalent subnetworks is compared to transport through the full network.