Advection-Dispersion Equation (ADE) - PowerPoint PPT Presentation

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Advection-Dispersion Equation (ADE)

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Title: Advection-Dispersion Equation (ADE)


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 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)
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
ZB Fig. 3.25
3
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
ZB, 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
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)
stochastic hydraulic conductivity field
kriged 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
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
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Stochastic GWV
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