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Hybrid analytical and finite element numerical modeling of mass and heat transport in fractured rocks with matrix diffusion

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Abstract

Quantification of mass and heat transport in fractured porous rocks is important to areas such as contaminant transport, storage and release in fractured rock aquifers, the migration and sorption of radioactive nuclides from waste depositories, and the characterization of engineered heat exchangers in the context of enhanced geothermal systems. The large difference between flow and transport characteristics in fractures and in the surrounding matrix rock means models of such systems are forced to make a number of simplifications. Analytical approaches assume a homogeneous system, numerical approaches address the scale at which a process is operating, but may lose individual important processes due to averaging considerations. Numerical stability criteria limit the contrasts possible in defining material properties. Here, a hybrid analytical–numerical method for transport modeling in fractured media is presented. This method combines a numerical model for flow and transport in a heterogeneous fracture and an analytical solution for matrix diffusion. By linking the two types of model, the advantages of both methods can be combined. The methodology as well as the mathematical background are developed, verified for simple geometries, and applied to fractures representing experimental field conditions in the Grimsel rock laboratory.

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Authors and Affiliations

  1. Edinburgh Collaborative of Subsurface Science and Engineering (ECOSSE), School of Geoscience, University of Edinburgh, West Mains Road, Edinburgh, EH9 3JW, Scotland

    Christopher I. McDermott

  2. INTERA Engineering, Ltd., 1 Raymond Street, Ottawa, ON, K1R 1A2, Canada

    Robert Walsh

  3. Institute of Geology, University of Bern, Berne, Switzerland

    Ralph Mettier

  4. Paul Scherrer Institut, Villigen PSI, Villigen, Switzerland

    Georg Kosakowski

  5. Helmholtz Center for Environmental Research, Leipzig, Germany

    Olaf Kolditz

Authors
  1. Christopher I. McDermott
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  2. Robert Walsh
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  3. Ralph Mettier
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  4. Georg Kosakowski
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  5. Olaf Kolditz
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Correspondence to Christopher I. McDermott.

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McDermott, C.I., Walsh, R., Mettier, R. et al. Hybrid analytical and finite element numerical modeling of mass and heat transport in fractured rocks with matrix diffusion. Comput Geosci 13, 349–361 (2009). https://doi.org/10.1007/s10596-008-9123-9

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  • DOI: https://doi.org/10.1007/s10596-008-9123-9

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