advection-dispersion equation (ade) assumptions 1.equivalent porous medium (epm) (i.e., a medium...
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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)
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
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
(MT3DMS manual,p. 2-14)
Sensitivity to themass transfer rate
Sensitivity to theporosity ratio
Z&B, Fig. 3.26
Dual domain model
Advection-dispersionmodel
Sensitivity to Dispersivity
Governing Equations – with linear sorption
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
Shapiro (2001)WRR
Tracer results in fracturedrock at Mirror Lake, NH
Injection Site
MADE-2 Tracer Test
Advection-dispersion model(One porosity value for entire model)
stochastic hydraulic conductivity fieldkriged hydraulic conductivity field
Observed
Dual domain model with akriged hydraulic conductivity field
Observed
Dual domain model with astochastic hydraulic conductivity field
Observed
Feehley & Zheng,2000, WRRResults with a stochastic K field
Feehley & Zheng (2000)WRR
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
Stochastic GWV
Stochastic GWV
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