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A Brief Introduction to Ground Water Flow and Contaminant porosity


									 Working With Simple Models to
 Predict Contaminant Migration

             Matt Small
U.S. EPA, Region 9, Underground Storage
         Tanks Program Office
      What is a Model?
• A systematic method for analyzing real-
  world data and translating it into a
  meaningful simulation that can be used
  for system analysis and future prediction.
• A model should not be a “black box.”
         Modeling Process
• Determine modeling objectives
• Review site conceptual model
• Compare mathematical model capabilities
  with conceptual model
• Model calibration
• Model application
            Site Conceptual Model



                          Ground Water Flow Direction

    Sources                          Pathways           Receptors
Primary   Secondary                    Soil             People
Tanks     Residual NAPL                Vapors           Animals, Fish
Piping                                 Ground Water     Ecosystems
Spills                                 Surface Water    Resources
        Mathematical Model
• A mathematical Model is a highly idealized
  approximation of the real-world system
  involving many simplifying assumptions
  based on knowledge of the system,
  experience and professional judgment.

                                    (  kt )
                        Ct  C0 e
                 K dh
                 ne dx
            Model Assumptions
• Common simplifying assumptions
  –   2-Dimensional flow field (no flux in z direction)
  –   Uniform flow field (1-D flow)
  –   Uniform properties (homogenous conductivity)
  –   Steady state flow (no change in storage)
            Model Selection
• Select the simplest model that will fit the
  available data
            Input Parameters
• Model input parameter values can be either
  variable, uncertain, or both.
  – Variable parameters are those for which a value can
    be determined, but the value varies spatially or
    temporally over the model domain.
  – Uncertain parameters are those for which a value
    cannot be accurately determined with available data.
• To evaluate variability and uncertainty we can
  use several possible values to describe a given
  input parameter and bound the model result.
    Lumped Input parameters
• To simplify the mathematics, and quantify
  poorly understood (complex) natural
  phenomena, subsurface processes are
  typically described by five parameters:
  – source
  – velocity
  – retardation
  – dispersion
  – decay
  Input Parameters:
  Ground Water Flow
•Processes Simulated
   –Ground Water Flow
   Rate, Seepage Velocity,
   or Advection
•Input Parameters            Source    Plume Migration
                                       due to Advection
   –Hydraulic conductivity
   –Aquifer thickness
   –Aquitards/aquicludes         Ground Water Flow Direction

                                            K dh                 C C
                                      v                      v   
                                            ne dx                x t
       Ground Water Flow Rate
         Example Calculation
                                            hydraulic conductivity x gradient            Ki
Ground Water Seepage Velocity (vs ) =                                           vs  
                                                   effective porosity                    ne

 Hydraulic conductivity (K) estimated to be between 10-2 and 10-4 cm/sec.
 Ground water gradient measured from ground water contour map 0.011 ft/ft.
 Effective Porosity estimated to be 30% or 0.3.
                                                cm        ft
                                         104       0.011
                                  Ki            sec       ft
                           vs                               ??
                                  ne              0.3

                                                Distance ft
                 Travel Time 
                                  Ground Water Flow Rate ft

                 1,000 ft                               1,000 ft
          t1 =              ?? years            t2 =              ?? years
                 X ft                                   X ft
                      year                                   year
  Input Parameters: Retardation
•Processes Simulated
   contaminant transport
   –Adsorption and                     R = 1.8 For Benzene        R = 1.1 For MTBE
   desorption processes
   –Interactions between      Source

   contaminants, soil, and
•Input Parameters                                            R = 1 For Advective Front

   –Fraction of organic           Ground Water Flow Direction
   –Organic carbon
   partitioning coefficient                                            K d b
   –Soil bulk density            K d  f oc Koc          R  1
Retarded Ground Water Flow
 Rate Example Calculation
                               Ground Water Flow Rate ft
            Travel Time =
                                            Distance ft

                   1,000 ft                             1,000 ft
          t1 =                 264 years       t2 =                2.6 years
                 3.45 ft                               345 ft
                         year                                 year

                            R = 1.8 for benzene
                            R = 1.1 for MTBE

                    1,000 ft                                       1,000 ft
 t1, MTBE =1.1                  290 years       t 2, MTBE =1.1                2.9 years
                  3.79 ft                                         379 ft
                          year                                           year

                   1,000 ft                                      1,000 ft
 t1, benz =1.8                 475 years      t 2, benz =1.8                4.7 years
                 3.79 ft                                        379 ft
                         year                                          year
 Input Parameters: Dispersion
•Processes Simulated
   –Macroscopic spatial
   variability of hydraulic
   conductivity                                                  Dy

   –Microscopic velocity           Source    Non-Dispersed               Dispersed   Dx
   variations                                Plume                       Plume
•Input Parameters
   –Ground water                                                 Dz
   seepage velocity
                                     Ground Water Flow Direction
   –Molecular diffusion
   coefficient                Fick's Law  F  Dmolecular
                                                                      Dmechanical   v

                                            Dtotal  Dmolecular  Dmechanical
  Input Parameters:
  Biodegradation and Decay
•Processes Simulated
   transformation and
                                        Decaying Front         Retarded Front
   –Volatilization             Source

•Input Parameters
   –Initial concentrations
                                                                 Advective/Dispersive Front
   –First order decay rate   Ground Water Flow Direction         (no decay or retardation)
   or half life
                                                                     (  t )
                                                     Ct  C0e
                                                               ln 2
                                                     t1/ 2 
    3-D Contaminant Fate and
    Transport in Ground Water

  C      C     2C    2C     2C
R     x     Dx 2  Dx 2  Dx 2   C
  t      x     x     y     z
Numerical Model Example
Model Output
  Making Regulatory Decisions
• What models can do:
  – Predict trends and directions of changes
  – Improve understanding of the system and
    phenomena of interest
  – Improve design of monitoring networks
  – Estimate a range of possible outcomes or
    system behavior in the future.
 Making Regulatory Decisions
• What models CANNOT do:
  – Replace site data
  – Substitute for site-specific understanding of
    ground water flow
  – Simulate phenomena the model wasn’t
    designed for.
  – Represent natural phenomena exactly
  – Predict unpredictable future events
  – Eliminate uncertainty

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