Reduced-Order Models of Discrete Fracture Networks Through Flow-Physics on Graph Representations

ABSTRACT: We present an algorithm for system-reduction of DFNs using graph representations that inherit hydrological parameters like permeability and make sensible the notion of flow and transport on the graph. The graph is pruned based on edge fluxes obtained from solving the flow equations on the graph and the algorithm has a single parameter that can be modified to directly control the size of the sub-graph. Mapping the sub-graph back to its pre-image yields a pruned DFN on which simulation of flow and transport is much faster due to decreased system size. Earlier methods that were based on topological mapping of DFNs to graphs yielded accurate times for first breakthrough, but the methods presented here are capable of also predicting the later mass breakthrough with great fidelity. This is important in applications such as contaminant remediation and hydrocarbon extraction where the time scale of interest is longer and late-arriving mass is significant, thus requiring an accurate representation of the later stages of the breakthrough curve.