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Title: Identifying Backbones in Three-Dimensional Discrete Fracture Networks: A Bipartite Graph-Based Approach

Journal Article · · Multiscale Modeling & Simulation
DOI:https://doi.org/10.1137/18M1180207· OSTI ID:1489955

In this paper, we present a graph-based method to identify primary flow and transport sub-networks in three-dimensional discrete fracture networks (DFNs). The structure of a DFN lends itself to the use of graphs as a coarse-scale representation that retains the multiscale nature of flow and transport through fracture media. We develop a bipartite graph representation that integrates fracture network topology, fracture geometry, and hydraulic properties. We show that the two most common graph-representations of DFNs, vertices representing intersections and vertices representing fractures, are projections of this bipartite graph thereby providing a generalization of previous DFN-graph frameworks. The primary subnetworks in each DFN are identified by running a heuristic algorithm that determines the edge-disjoint shortest paths through the graph which correspond to the regions where the fastest transport occurs. The method does not have any user-defined parameters and terminates in a finite number of steps. The quality of the method is demonstrated by comparing transport simulations on the identified primary subnetwork and full network, which are in good agreement for early and middle times. In conclusion, these estimates of the first passage times can be achieved with close to an order of magnitude reduction of computational expense using the proposed method.

Research Organization:
Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
Sponsoring Organization:
USDOE Laboratory Directed Research and Development (LDRD) Program
Grant/Contract Number:
89233218CNA000001; AC52-06NA25396
OSTI ID:
1489955
Report Number(s):
LA-UR-18-23051
Journal Information:
Multiscale Modeling & Simulation, Vol. 16, Issue 4; ISSN 1540-3459
Publisher:
SIAMCopyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 27 works
Citation information provided by
Web of Science

References (66)

A Large-Scale Flow and Tracer Experiment in Granite: 2. Results and Interpretation journal December 1991
Control-volume distributed multi-point flux approximation coupled with a lower-dimensional fracture model journal March 2015
Analysis and Visualization of Discrete Fracture Networks Using a Flow Topology Graph journal August 2017
Topology of fracture networks journal January 2013
Mimetic finite difference approximation of flows in fractured porous media journal May 2016
Theory of anomalous chemical transport in random fracture networks journal May 1998
A PDE-Constrained Optimization Formulation for Discrete Fracture Network Flows journal January 2013
A Parallel Solver for Large Scale DFN Flow Simulations journal January 2015
Effective permeability of fractured porous media with power-law distribution of fracture sizes journal September 2007
Scaling of fracture systems in geological media journal August 2001
Connectivity of random fault networks following a power law fault length distribution journal July 1997
Influence of spatial correlation of fracture centers on the permeability of two-dimensional fracture networks following a power law length distribution: FRACTURE CORRELATION AND PERMEABILITY journal January 2004
Hydraulic properties of two-dimensional random fracture networks following a power law length distribution: 2. Permeability of networks based on lognormal distribution of apertures journal August 2001
Hydraulic properties of two-dimensional random fracture networks following power law distributions of length and aperture: PERMEABILITY OF HETEROGENEOUS FRACTURE NETWORKS journal December 2002
Influence of fracture scale heterogeneity on the flow properties of three-dimensional discrete fracture networks (DFN): 3D FRACTURE NETWORK PERMEABILITY journal November 2012
Derivation of equivalent pipe network analogues for three-dimensional discrete fracture networks by the boundary element method journal September 1999
Flow Simulation in Three-Dimensional Discrete Fracture Networks journal January 2009
Inference of field-scale fracture transmissivities in crystalline rock using flow log measurements: TRANSMISSIVITY INFERENCE FROM FLOW LOGS journal November 2010
Numerical and analytical modeling of advective travel times in realistic three-dimensional fracture networks: MODELING OF ADVECTIVE TRAVEL TIMES journal February 2011
Channeling and Fickian Dispersion in fractal simulated porous media journal December 1993
Topological impact of constrained fracture growth journal September 2015
Dispersion in three-dimensional fracture networks journal March 2001
Understanding hydraulic fracturing: a multi-scale problem
  • Hyman, J. D.; Jiménez-Martínez, J.; Viswanathan, H. S.
  • Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 374, Issue 2078 https://doi.org/10.1098/rsta.2015.0426
journal October 2016
Fracture size and transmissivity correlations: Implications for transport simulations in sparse three-dimensional discrete fracture networks following a truncated power law distribution of fracture size: FRACTURE SIZE AND TRANSMISSIVITY CORRELATIONS journal August 2016
Conforming Delaunay Triangulation of Stochastically Generated Three Dimensional Discrete Fracture Networks: A Feature Rejection Algorithm for Meshing Strategy journal January 2014
Predictions of first passage times in sparse discrete fracture networks using graph-based reductions journal July 2017
Dispersion and Mixing in Three‐Dimensional Discrete Fracture Networks: Nonlinear Interplay Between Structural and Hydraulic Heterogeneity journal May 2018
dfnWorks: A discrete fracture network framework for modeling subsurface flow and transport journal November 2015
Influence of injection mode on transport properties in kilometer-scale three-dimensional discrete fracture networks: INFLUENCE OF INJECTION MODE IN 3-D DFNs journal September 2015
The state of the art in monitoring and verification—Ten years on journal September 2015
Multi-scale groundwater flow modeling during temperate climate conditions for the safety assessment of the proposed high-level nuclear waste repository site at Forsmark, Sweden journal July 2014
Emergence of anomalous transport in stressed rough fractures journal November 2016
Anomalous transport on regular fracture networks: Impact of conductivity heterogeneity and mixing at fracture intersections journal August 2015
A general gridding, discretization, and coarsening methodology for modeling flow in porous formations with discrete geological features journal October 2016
Effect of advective flow in fractures and matrix diffusion on natural gas production journal October 2015
Modeling flow and transport in fracture networks using graphs journal March 2018
On the physical meaning of the dispersion equation and its solutions for different initial and boundary conditions journal January 1978
The Behavior of Dense, Nonaqueous Phase Liquids in Fractured Clay and Rock journal September 1991
Connectivity, permeability, and channeling in randomly distributed and kinematically defined discrete fracture network models: PERMEABILITY OF DISCRETE FRACTURE NETWORK journal November 2016
Evaluating the effect of internal aperture variability on transport in kilometer scale discrete fracture networks journal August 2016
Particle tracking approach for transport in three-dimensional discrete fracture networks: Particle tracking in 3-D DFNs journal September 2015
Modeling and simulation of pore-scale multiphase fluid flow and reactive transport in fractured and porous media journal January 2009
Zur allgemeinen Kurventheorie journal January 1927
Shale gas and non-aqueous fracturing fluids: Opportunities and challenges for supercritical CO2 journal June 2015
Trends, prospects and challenges in quantifying flow and transport through fractured rocks journal February 2005
A quasi steady state method for solving transient Darcy flow in complex 3D fractured networks journal January 2012
Efficient Monte Carlo With Graph‐Based Subsurface Flow and Transport Models journal May 2018
Pathline tracing on fully unstructured control-volume grids journal July 2012
Transport behavior in three-dimensional fracture intersections: TRANSPORT IN THREE-DIMENSIONAL FRACTURE INTERSECTIONS journal August 2003
A mixed hybrid Mortar method for solving flow in discrete fracture networks journal October 2010
A Generalized Mixed Hybrid Mortar Method for Solving Flow in Stochastic Discrete Fracture Networks journal January 2012
Radionuclide Transport in Fast Channels in Crystalline Rock journal August 1986
Minimum Hydraulic Resistance and Least Resistance Path in Heterogeneous Porous Media: MINIMUM HYDRAULIC RESISTANCE journal October 2017
Transverse dispersion of contaminants in fractured permeable formations journal March 1996
Inclusion of Topological Measurements into Analytic Estimates of Effective Permeability in Fractured Media: FRACTURE PERMEABILITY FROM TOPOLOGY journal November 2017
Representative hydraulic conductivities in saturated groundwater flow journal January 2006
A methodology for the characterization of flow conductivity through the identification of communities in samples of fractured rocks journal February 2014
A descriptive study of fracture networks in rocks using complex network metrics journal March 2016
On the Reconstruction of Darcy Velocity in Finite-Volume Methods journal November 2012
Disjoint paths in a network journal January 1974
A quick method for finding shortest pairs of disjoint paths journal July 1984
Connectivity metrics based on the path of smallest resistance journal February 2016
Machine learning for graph-based representations of three-dimensional discrete fracture networks journal January 2018
Dissolution of non-aqueous-phase liquids and aqueous-phase contaminant transport in discretely-fractured porous media journal June 1996
Effects of simplifying fracture network representation on inert chemical migration in fracture-controlled aquifers: EFFECTS OF FRACTURE NETWORK SIMPLIFICATION journal January 2009
Modeling of flow and mixing in 3D rough-walled rock fracture intersections journal September 2017

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Robust system size reduction of discrete fracture networks: a multi-fidelity method that preserves transport characteristics journal September 2018
Characterizing the Impact of Fractured Caprock Heterogeneity on Supercritical CO$$_2$$ Injection journal November 2019
Minimum Hydraulic Resistance Uncertainty and the Development of a Connectivity‐Based Iterative Sampling Strategy journal July 2019
Model reduction for fractured porous media: a machine learning approach for identifying main flow pathways journal March 2019