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Advection-Dispersion Equation (ADE)

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

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Advection-Dispersion Equation (ADE)

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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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