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Title: Robust system size reduction of discrete fracture networks: a multi-fidelity method that preserves transport characteristics

Abstract

In this paper, we propose a multi-fidelity system reduction technique that uses weighted graphs paired with three-dimensional discrete fracture network (DFN) modelling for efficient simulation of subsurface flow and transport in fractured media. DFN models are used to simulate flow and transport in subsurface fractured rock with low-permeability. One method to alleviate the heavy computational overhead associated with these simulations is to reduce the size of the DFN using a graph representation of it to identify the primary flow sub-network and only simulate flow and transport thereon. The first of these methods used unweighted graphs constructed solely on DFN topology and could be used for accurate predictions of first-passage times. However, these techniques perform poorly when predicting later stages of the mass breakthrough. We utilize a weighted-graph representation of the DFN where edge weights are based on hydrological parameters in the DFN that allows us to exploit the kinematic quantities derivable a posteriori from the flow solution obtained on the graph representation of the DFN to perform system reduction and predict the later stages of the breakthrough curve with high fidelity. We also propose and demonstrate the use of an adaptive pruning algorithm with error control that produces a prunedmore » DFN sub-network whose predicted mass breakthrough agrees with the original DFN within a user-specified tolerance. Lastly, the method allows for the level of accuracy to be a user-controlled parameter.« less

Authors:
ORCiD logo [1]; ORCiD logo [1]; ORCiD logo [1]; ORCiD logo [1]; ORCiD logo [1]; ORCiD logo [1]
  1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22); USDOE Laboratory Directed Research and Development (LDRD) Program
OSTI Identifier:
1477661
Report Number(s):
LA-UR-18-23489
Journal ID: ISSN 1420-0597
Grant/Contract Number:  
AC52-06NA25396
Resource Type:
Accepted Manuscript
Journal Name:
Computational Geosciences
Additional Journal Information:
Journal Volume: 22; Journal Issue: 6; Journal ID: ISSN 1420-0597
Publisher:
Springer
Country of Publication:
United States
Language:
English
Subject:
58 GEOSCIENCES; 97 MATHEMATICS AND COMPUTING; Earth Sciences; discrete fracture networks; fractured porous media; subsurface flow and transport; graph theory; multi-fidelity

Citation Formats

Srinivasan, Shriram, Hyman, Jeffrey De'Haven, Karra, Satish, O'Malley, Daniel, Viswanathan, Hari S., and Srinivasan, Gowri. Robust system size reduction of discrete fracture networks: a multi-fidelity method that preserves transport characteristics. United States: N. p., 2018. Web. doi:10.1007/s10596-018-9770-4.
Srinivasan, Shriram, Hyman, Jeffrey De'Haven, Karra, Satish, O'Malley, Daniel, Viswanathan, Hari S., & Srinivasan, Gowri. Robust system size reduction of discrete fracture networks: a multi-fidelity method that preserves transport characteristics. United States. doi:10.1007/s10596-018-9770-4.
Srinivasan, Shriram, Hyman, Jeffrey De'Haven, Karra, Satish, O'Malley, Daniel, Viswanathan, Hari S., and Srinivasan, Gowri. Mon . "Robust system size reduction of discrete fracture networks: a multi-fidelity method that preserves transport characteristics". United States. doi:10.1007/s10596-018-9770-4. https://www.osti.gov/servlets/purl/1477661.
@article{osti_1477661,
title = {Robust system size reduction of discrete fracture networks: a multi-fidelity method that preserves transport characteristics},
author = {Srinivasan, Shriram and Hyman, Jeffrey De'Haven and Karra, Satish and O'Malley, Daniel and Viswanathan, Hari S. and Srinivasan, Gowri},
abstractNote = {In this paper, we propose a multi-fidelity system reduction technique that uses weighted graphs paired with three-dimensional discrete fracture network (DFN) modelling for efficient simulation of subsurface flow and transport in fractured media. DFN models are used to simulate flow and transport in subsurface fractured rock with low-permeability. One method to alleviate the heavy computational overhead associated with these simulations is to reduce the size of the DFN using a graph representation of it to identify the primary flow sub-network and only simulate flow and transport thereon. The first of these methods used unweighted graphs constructed solely on DFN topology and could be used for accurate predictions of first-passage times. However, these techniques perform poorly when predicting later stages of the mass breakthrough. We utilize a weighted-graph representation of the DFN where edge weights are based on hydrological parameters in the DFN that allows us to exploit the kinematic quantities derivable a posteriori from the flow solution obtained on the graph representation of the DFN to perform system reduction and predict the later stages of the breakthrough curve with high fidelity. We also propose and demonstrate the use of an adaptive pruning algorithm with error control that produces a pruned DFN sub-network whose predicted mass breakthrough agrees with the original DFN within a user-specified tolerance. Lastly, the method allows for the level of accuracy to be a user-controlled parameter.},
doi = {10.1007/s10596-018-9770-4},
journal = {Computational Geosciences},
number = 6,
volume = 22,
place = {United States},
year = {2018},
month = {9}
}

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Figures / Tables:

Fig. 1 Fig. 1: (A) A discrete fracture network made up of 10 fracture meshed with 17988 nodes and 36512 triangular elements. (B) The graph representation (vertices are red spheres and edges are black lines). The graph is made up of 11 vertices and 17 edges.

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Works referenced in this record:

Extracting Hydrocarbon From Shale: An Investigation of the Factors That Influence the Decline and the Tail of the Production Curve
journal, May 2018

  • Lovell, A. E.; Srinivasan, S.; Karra, S.
  • Water Resources Research, Vol. 54, Issue 5
  • DOI: 10.1029/2017WR022180

Multi-scale finite-volume method for elliptic problems in subsurface flow simulation
journal, May 2003


Multiscale direction-splitting algorithms for parabolic equations with highly heterogeneous coefficients
journal, September 2016

  • Srinivasan, Shriram; Lazarov, Raytcho; Minev, Peter
  • Computers & Mathematics with Applications, Vol. 72, Issue 6
  • DOI: 10.1016/j.camwa.2016.07.032

Dispersion and Mixing in Three‐Dimensional Discrete Fracture Networks: Nonlinear Interplay Between Structural and Hydraulic Heterogeneity
journal, May 2018

  • Hyman, J. D.; Jiménez‐Martínez, J.
  • Water Resources Research, Vol. 54, Issue 5
  • DOI: 10.1029/2018WR022585

A Parallel Solver for Large Scale DFN Flow Simulations
journal, January 2015

  • Berrone, Stefano; Pieraccini, Sandra; Scialò, Stefano
  • SIAM Journal on Scientific Computing, Vol. 37, Issue 3
  • DOI: 10.1137/140984014

A particle tracking transport method for the simulation of resident and flux-averaged concentration of solute plumes in groundwater models
journal, May 2010

  • Robinson, Bruce A.; Dash, Zora V.; Srinivasan, Gowri
  • Computational Geosciences, Vol. 14, Issue 4
  • DOI: 10.1007/s10596-010-9190-6

Topology of fracture networks
journal, January 2013

  • Andresen, Christian André; Hansen, Alex; Le Goc, Romain
  • Frontiers in Physics, Vol. 1
  • DOI: 10.3389/fphy.2013.00007

Machine learning for graph-based representations of three-dimensional discrete fracture networks
journal, January 2018

  • Valera, Manuel; Guo, Zhengyang; Kelly, Priscilla
  • Computational Geosciences, Vol. 22, Issue 3
  • DOI: 10.1007/s10596-018-9720-1

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

  • Hyman, J. D.; Painter, S. L.; Viswanathan, H.
  • Water Resources Research, Vol. 51, Issue 9
  • DOI: 10.1002/2015WR017151

The Origin, Prediction and Impact of Oil Viscosity Heterogeneity on the Production Characteristics of Tar Sand and Heavy Oil Reservoirs
journal, January 2008

  • Larter, S.; Adams, J.; Gates, I. D.
  • Journal of Canadian Petroleum Technology, Vol. 47, Issue 01
  • DOI: 10.2118/08-01-52

A mixed hybrid Mortar method for solving flow in discrete fracture networks
journal, October 2010


A PDE-Constrained Optimization Formulation for Discrete Fracture Network Flows
journal, January 2013

  • Berrone, Stefano; Pieraccini, Sandra; Scialò, Stefano
  • SIAM Journal on Scientific Computing, Vol. 35, Issue 2
  • DOI: 10.1137/120865884

A Multiscale Finite Element Method for Elliptic Problems in Composite Materials and Porous Media
journal, June 1997

  • Hou, Thomas Y.; Wu, Xiao-Hui
  • Journal of Computational Physics, Vol. 134, Issue 1
  • DOI: 10.1006/jcph.1997.5682

A quasi steady state method for solving transient Darcy flow in complex 3D fractured networks
journal, January 2012


Upscaling discrete fracture network simulations: An alternative to continuum transport models: UPSCALING FRACTURE NETWORK SIMULATIONS
journal, February 2005


Advancing Graph-Based Algorithms for Predicting Flow and Transport in Fractured Rock
journal, September 2018

  • Viswanathan, H. S.; Hyman, J. D.; Karra, S.
  • Water Resources Research, Vol. 54, Issue 9
  • DOI: 10.1029/2017WR022368

Particle tracking approach for transport in three-dimensional discrete fracture networks: Particle tracking in 3-D DFNs
journal, September 2015

  • Makedonska, Nataliia; Painter, Scott L.; Bui, Quan M.
  • Computational Geosciences, Vol. 19, Issue 5
  • DOI: 10.1007/s10596-015-9525-4

Flow channeling in heterogeneous fractured rocks
journal, May 1998

  • Tsang, Chin-Fu; Neretnieks, Ivars
  • Reviews of Geophysics, Vol. 36, Issue 2
  • DOI: 10.1029/97RG03319

Predictions of first passage times in sparse discrete fracture networks using graph-based reductions
journal, July 2017


Effect of advective flow in fractures and matrix diffusion on natural gas production
journal, October 2015

  • Karra, Satish; Makedonska, Nataliia; Viswanathan, Hari S.
  • Water Resources Research, Vol. 51, Issue 10
  • DOI: 10.1002/2014WR016829

dfnWorks: A discrete fracture network framework for modeling subsurface flow and transport
journal, November 2015


A Large-Scale Flow and Tracer Experiment in Granite: 2. Results and Interpretation
journal, December 1991

  • Abelin, Harald; Birgersson, Lars; Moreno, Luis
  • Water Resources Research, Vol. 27, Issue 12
  • DOI: 10.1029/91WR01404

Derivation of equivalent pipe network analogues for three-dimensional discrete fracture networks by the boundary element method
journal, September 1999

  • Dershowitz, W. S.; Fidelibus, C.
  • Water Resources Research, Vol. 35, Issue 9
  • DOI: 10.1029/1999WR900118

A Generalized Mixed Hybrid Mortar Method for Solving Flow in Stochastic Discrete Fracture Networks
journal, January 2012

  • Pichot, G.; Erhel, J.; de Dreuzy, J. -R.
  • SIAM Journal on Scientific Computing, Vol. 34, Issue 1
  • DOI: 10.1137/100804383

A New Approach to Simulating Flow in Discrete Fracture Networks with an Optimized Mesh
journal, January 2007

  • Mustapha, Hussein; Mustapha, Kassem
  • SIAM Journal on Scientific Computing, Vol. 29, Issue 4
  • DOI: 10.1137/060653482

A methodology for the characterization of flow conductivity through the identification of communities in samples of fractured rocks
journal, February 2014

  • Santiago, Elizabeth; Velasco-Hernández, Jorge X.; Romero-Salcedo, Manuel
  • Expert Systems with Applications, Vol. 41, Issue 3
  • DOI: 10.1016/j.eswa.2013.08.011

Understanding hydraulic fracturing: a multi-scale problem
journal, October 2016

  • 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
  • DOI: 10.1098/rsta.2015.0426

Conforming Delaunay Triangulation of Stochastically Generated Three Dimensional Discrete Fracture Networks: A Feature Rejection Algorithm for Meshing Strategy
journal, January 2014

  • Hyman, Jeffrey D.; Gable, Carl W.; Painter, Scott L.
  • SIAM Journal on Scientific Computing, Vol. 36, Issue 4
  • DOI: 10.1137/130942541

Power-law velocity distributions in fracture networks: Numerical evidence and implications for tracer transport: POWER-LAW VELOCITY DISTRIBUTIONS IN FRACTURE NETWORKS
journal, July 2002

  • Painter, Scott; Cvetkovic, Vladimir; Selroos, Jan-Olof
  • Geophysical Research Letters, Vol. 29, Issue 14
  • DOI: 10.1029/2002GL014960

Scaling of fracture systems in geological media
journal, August 2001

  • Bonnet, E.; Bour, O.; Odling, N. E.
  • Reviews of Geophysics, Vol. 39, Issue 3
  • DOI: 10.1029/1999RG000074

Flux formulation of parabolic equations with highly heterogeneous coefficients
journal, October 2018

  • Minev, Peter; Srinivasan, Shriram; Vabishchevich, Petr N.
  • Journal of Computational and Applied Mathematics, Vol. 340
  • DOI: 10.1016/j.cam.2017.12.003

On the physical meaning of the dispersion equation and its solutions for different initial and boundary conditions
journal, January 1978


A thermodynamic basis for the derivation of the Darcy, Forchheimer and Brinkman models for flows through porous media and their generalizations
journal, January 2014


Pathline tracing on fully unstructured control-volume grids
journal, July 2012


Flow Simulation in Three-Dimensional Discrete Fracture Networks
journal, January 2009

  • Erhel, Jocelyne; de Dreuzy, Jean-Raynald; Poirriez, Baptiste
  • SIAM Journal on Scientific Computing, Vol. 31, Issue 4
  • DOI: 10.1137/080729244

Modeling flow and transport in fracture networks using graphs
journal, March 2018


Quantifying Topological Uncertainty in Fractured Systems using Graph Theory and Machine Learning
journal, August 2018


Identifying Backbones in Three-Dimensional Discrete Fracture Networks: A Bipartite Graph-Based Approach
journal, January 2018

  • Hyman, Jeffrey D.; Hagberg, Aric; Osthus, Dave
  • Multiscale Modeling & Simulation, Vol. 16, Issue 4
  • DOI: 10.1137/18M1180207