Estimating Flow Rates through Fracture Networks using Combinatorial Optimization

TL;DR

This paper introduces two combinatorial optimization methods, HSPM and ISPM, for rapid and accurate estimation of fluid flow rates in discrete fracture networks, significantly reducing computational costs.

Contribution

The paper presents novel graph-based algorithms, HSPM and ISPM, for fast fluid flow estimation in DFNs, enabling efficient uncertainty quantification.

Findings

High accuracy in flow rate predictions

Very low computational cost

Effective across various fracture densities

Abstract

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.