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Dual Domain Models in Advection-Dispersion Equations for Heterogeneous Porous Media Analysis

Explore the application of dual domain models in advection-dispersion equations for fractured rock systems with different porosity domains. Analyze sensitivity to mass transfer rates, porosity ratios, and dispersivity effects. Consider parameters like mass transfer rate, fraction of sorption sites, and calibration techniques. Review tracer test results in fractured rock environments and ways to address unmodeled heterogeneity.

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Dual Domain Models in Advection-Dispersion Equations for Heterogeneous Porous Media Analysis

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  1. Advection-Dispersion Equation (ADE) Assumptions • Equivalent porous medium (epm) • (i.e., a medium with connected pore space • or a densely fractured medium with a single • network of connected fractures) • Miscible flow • (i.e., solutes dissolve in water; DNAPL’s and • LNAPL’s require a different governing equation. • See p. 472, note 15.5, in Zheng and Bennett.) 3. No density effects (density dependent flow requires a different governing equation, Z&B, Ch. 15)

  2. Dual Domain Models Fractured Rock Heterogeneous porous media Note the presence of “mobile” domains (fractures/high K units) and “immobile” domains (matrix/low K units) Each domain has a different porosity such that:  = m + im Z&B Fig. 3.25

  3. mass transfer rate between the 2 domains Governing Equations – no sorption Immobile domain Note: model allows for a different porosity for each domain  = m + im

  4. (MT3DMS manual, p. 2-14)

  5. Sensitivity to the mass transfer rate Sensitivity to the porosity ratio Z&B, Fig. 3.26

  6. Sensitivity to Dispersivity Dual domain model Advection-dispersion model

  7. Governing Equations – with linear sorption

  8. Dual Domain/Dual Porosity Models Summary Mass transfer rate Porosities “New” Parameters Porosities in each domain: m ; im ( = m + im) Mass transfer rate:  Fraction of sorption sites: f = m /  (hard-wired into MT3DMS) Treated as calibration parameters

  9. Shapiro (2001) WRR Tracer results in fractured rock at Mirror Lake, NH

  10. MADE-2 Tracer Test Injection Site

  11. Advection-dispersion model (One porosity value for entire model) kriged hydraulic conductivity field stochastic hydraulic conductivity field Observed

  12. Dual domain model with a kriged hydraulic conductivity field Observed

  13. Dual domain model with a stochastic hydraulic conductivity field Observed

  14. Feehley & Zheng, 2000, WRR Results with a stochastic K field

  15. Feehley & Zheng (2000) WRR

  16. Statistical model of geologic facies with dispersivity values representative of micro scale dispersion Ways to handle unmodeled heterogeneity • Large dispersivity values • Stochastic hydraulic conductivity field and “small” • macro dispersivity values • Stochastic hydraulic conductivity field with even • smaller macro dispersivity values & dual domain porosity • and mass exchange between domains Alternatively, you can model all the relevant heterogeneity

  17. Stochastic GWV

  18. Stochastic GWV

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