  To enable fast uncertainty quantification of fluid flow in a discrete
fracture network (DFN), we present two approaches to quickly compute fluid flow
in DFNs using combinatorial optimization algorithms. Specifically, the
presented Hanan Shortest Path Maxflow (HSPM) and Intersection Shortest Path
Maxflow (ISPM) methods translate DFN geometries and properties to a graph on
which a max flow algorithm computes a combinatorial flow, from which an overall
fluid flow rate is estimated using a shortest path decomposition of this flow.
The two approaches are assessed by comparing their predictions with results
from explicit numerical simulations of simple test cases as well as stochastic
DFN realizations covering a range of fracture densities. Both methods have a
high accuracy and very low computational cost, which can facilitate much-needed
in-depth analyses of the propagation of uncertainty in fracture and
fracture-network properties to fluid flow rates.
