Advection-Dispersion Equation (ADE)
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Advection-Dispersion Equation (ADE)
Assumptions
1. Equivalent porous medium (epm) (i.e., a medium with connected pore space or a densely fractured medium with a single network of connected fractures)
2. 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)
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Dual Domain Models
Z&B Fig. 3.25
Note the presence of“mobile” domains (fractures/high K units) and“immobile” domains (matrix/low K units)
Fractured Rock Heterogeneous porous media
Each domain has a different porosity such that: = m + im
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Immobile domain
Governing Equations – no sorption
Note: model allows for a different porosity for each domain = m + im
mass transfer rate between the 2 domains
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(MT3DMS manual,p. 2-14)
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Sensitivity to themass transfer rate
Sensitivity to theporosity ratio
Z&B, Fig. 3.26
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Dual domain model
Advection-dispersionmodel
Sensitivity to Dispersivity
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Governing Equations – with linear sorption
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Dual Domain/Dual Porosity ModelsSummary
“New” ParametersPorosities in each domain: m ; im ( = m + im)
Mass transfer rate:
Fraction of sorption sites: f = m / (hard-wired into MT3DMS)
Porosities Mass transfer rate
Treated as calibration parameters
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Shapiro (2001)WRR
Tracer results in fracturedrock at Mirror Lake, NH
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Injection Site
MADE-2 Tracer Test
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Advection-dispersion model(One porosity value for entire model)
stochastic hydraulic conductivity fieldkriged hydraulic conductivity field
Observed
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Dual domain model with akriged hydraulic conductivity field
Observed
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Dual domain model with astochastic hydraulic conductivity field
Observed
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Feehley & Zheng,2000, WRRResults with a stochastic K field
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Feehley & Zheng (2000)WRR
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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
Statistical model of geologic facies with dispersivityvalues representative of micro scale dispersion
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Stochastic GWV
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Stochastic GWV
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