1. Working With Simple Models to Predict Contaminant Migration Matt Small U.S. EPA, Region 9, Underground Storage Tanks Program Office

2. 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.”

3. Modeling Process Determine modeling objectives Review site conceptual model Compare mathematical model capabilities with conceptual model Model calibration Model application

4. Site Conceptual Model Ground Water Flow Direction Dissolved Source SourcesReceptorsPathways Primary Tanks Piping Spills Secondary Residual NAPL Soil Vapors Ground Water Surface Water People Animals, Fish Ecosystems Resources

5. 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. 2+2=4

6. 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)

7. Model Selection Select the simplest model that will fit the available data

8. 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.

9. 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

10. Plume Migration due to Advection Source Input Parameters: Ground Water Flow Ground Water Flow Direction Processes Simulated –Ground Water Flow Rate, Seepage Velocity, or Advection Input Parameters –Hydraulic conductivity –Gradient –Aquifer thickness –Aquitards/aquicludes

11. Ground Water Flow Rate Example Calculation 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.

12. Input Parameters: Retardation Ground Water Flow Direction R = 1.8 For Benzene R = 1.1 For MTBE R = 1 For Advective Front Processes Simulated –Retarded contaminant transport –Adsorption and desorption processes –Interactions between contaminants, soil, and water Input Parameters –Fraction of organic carbon –Organic carbon partitioning coefficient –Soil bulk density –Porosity Source

13. Retarded Ground Water Flow Rate Example Calculation R = 1.8 for benzene R = 1.1 for MTBE

14. Input Parameters: Dispersion Ground Water Flow Direction Dispersed Plume Dx Dz Dy Non-Dispersed Plume Source Processes Simulated –Macroscopic spatial variability of hydraulic conductivity –Microscopic velocity variations Input Parameters –Ground water seepage velocity –Dispersivity –Molecular diffusion coefficient

15. Input Parameters: Biodegradation and Decay Ground Water Flow Direction Advective/Dispersive Front (no decay or retardation) Retarded Front Dissolved Decaying Front Source Processes Simulated –Chemical transformation and decay –Biodegradation –Volatilization Input Parameters –Initial concentrations –First order decay rate or half life

16. 3-D Contaminant Fate and Transport in Ground Water

17. Numerical Model Example

18. Model Output

19. 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.

20. 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