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