Advection-Dispersion Equation (ADE)

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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 DNAPLs and
• LNAPLs 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, ZB,
Ch. 15)
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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
ZB Fig. 3.25
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Governing Equations no sorption
Immobile domain
Note model allows for a different porosity for
each domain ? ?m ?im
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(MT3DMS manual, p. 2-14)
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Sensitivity to the mass transfer rate
Sensitivity to the porosity ratio
ZB, Fig. 3.26
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Sensitivity to Dispersivity
Dual domain model
Advection-dispersion model
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Governing Equations with linear sorption
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Dual Domain/Dual Porosity Models Summary
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
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Shapiro (2001) WRR
Tracer results in fractured rock at Mirror Lake,
NH
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MADE-2 Tracer Test
Injection Site
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Advection-dispersion model (One porosity value
for entire model)
stochastic hydraulic conductivity field
kriged hydraulic conductivity field
Observed
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Dual domain model with a kriged hydraulic
conductivity field
Observed
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Dual domain model with a stochastic hydraulic
conductivity field
Observed
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Feehley Zheng, 2000, WRR
Results 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
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Stochastic GWV
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Stochastic GWV
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