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

Source Dissolved Sources

Primary Secondary Tanks Piping Spills Residual NAPL

Ground Water Flow Direction Pathways

Soil Vapors Ground Water Surface Water

Receptors

People Animals, Fish Ecosystems 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.

v

 

K dh n dx e C t



C e

0 ( 

kt

)

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 –Hydraulic conductivity –Gradient –Aquifer thickness –Aquitards/aquicludes

Source Plume Migration due to Advection Ground Water Flow Direction

v

 

K dh n dx e v



C



x

 

C



t

Ground Water Flow Rate Example Calculation

Ground Water Seepage Velocity (v ) = s hydraulic conductivity x gradient effective porosity

v s

 

Ki n e

   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.

v s



Ki n e

 10  4

cm

sec 0.011

ft ft

0.3

 ??

Travel Time  Distance ft Ground Water Flow Rate ft year 1,000 ft t = 1 X ft year  ??

years

1,000 ft t = 2 X ft year  ??

years

Input Parameters: Retardation

•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 Ground Water Flow Direction

K d



R = 1.8 For Benzene

f K oc oc R

R = 1.1 For MTBE R = 1 For Advective Front

K d

 

b

Retarded Ground Water Flow Rate Example Calculation

Travel Time = Ground Water Flow Rate ft year Distance ft 1,000 ft t = 1 3.45 ft year  264

years

1,000 ft t = 2 345 ft year  2.6

years

  R = 1.8 for benzene R = 1.1 for MTBE t 1, MTBE 1,000 ft =1.1

3.79 ft year  290

years

t 2, MTBE 1,000 ft =1.1

379 ft year  2.9

years

t 1, benz 1,000 ft =1.8

3.79 ft year  475

years

1,000 ft t 2, benz =1.8

379 ft year  4.7

years

Input Parameters: Dispersion

•Processes Simulated –Macroscopic spatial variability of hydraulic conductivity –Microscopic velocity variations •Input Parameters –Ground water seepage velocity –Dispersivity –Molecular diffusion coefficient

Source Ground Water Flow Direction

Fick's Law

Non-Dispersed Plume

D molecular dC dx

Dy Dz

D

Dispersed Plume

mechanical D total



D molecular



D mechanical

Dx

 

v

Input Parameters: Biodegradation and Decay

•Processes Simulated –Chemical transformation and decay –Biodegradation –Volatilization •Input Parameters –Initial concentrations –First order decay rate or half life

Source Decaying Front Dissolved Ground Water Flow Direction Retarded Front Advective/Dispersive Front (no decay or retardation)

C t



C e

0 (  

t

)

t

1/ 2  ln 2 

3-D Contaminant Fate and Transport in Ground Water

R



C



t

 

x



C



x



D x

 2

C



x

2 

D x

 2

C



y

2 

D x

 2

C



z

2   

C

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