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

Working With Simple Models to Predict Contaminant Migration

Matt SmallU.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 DirectionGround Water Flow Direction

Dissolved

Source

Sources ReceptorsPathwaysPrimaryTanksPipingSpills

SecondaryResidual NAPL

SoilVaporsGround WaterSurface Water

PeopleAnimals, FishEcosystemsResources

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 ( )0

kttC C e

e

K dhv

n 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

Plume Migration due to Advection

Source

Input Parameters: Ground Water Flow

C Cvx t

Ground Water Flow DirectionGround Water Flow Direction

e

K dhv

n dx

•Processes Simulated–Ground Water Flow Rate, Seepage Velocity, or Advection

•Input Parameters–Hydraulic conductivity

–Gradient

–Aquifer thickness

–Aquitards/aquicludes

Ground Water Flow Rate Example Calculation

s

hydraulic conductivity x gradientGround Water Seepage Velocity (v ) =

effective porosity se

Kiv

n

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.

410 0.011sec

??0.3s

e

cm ft

Ki ftv

n

Distance ftTravel Time

ftGround Water Flow Rate year

1 2

1,000 ft 1,000 ftt = ?? t = ??

ft ftX X year year

years years

Input Parameters: Retardation

Ground Water Flow DirectionGround Water Flow Direction

R = 1.8 For BenzeneR = 1.8 For Benzene R = 1.1 For MTBER = 1.1 For MTBE

R = 1 For Advective FrontR = 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

1 d bd oc oc

KK f K R

Source

Retarded Ground Water Flow Rate Example Calculation

ftGround Water Flow Rate yearTravel Time =

Distance ft

1 2

1,000 ft 1,000 ftt = 264 t = 2.6

ft ft3.45 345 year year

years years

R = 1.8 for benzene R = 1.1 for MTBE

1, benz 2, benz

1,000 ft 1,000 ftt =1.8 475 t =1.8 4.7

ft ft3.79 379 year year

years years

1, MTBE 2, MTBE

1,000 ft 1,000 ftt =1.1 290 t =1.1 2.9

ft ft3.79 379 year year

years years

Input Parameters: Dispersion

mechanicalD v

total molecular mechanicalD D D

Ground Water Flow DirectionGround Water Flow Direction

Dispersed Plume

Dx

Dz

Dy

Non-Dispersed Plume

Source

Fick's Law molecular

dCF D

dx

•Processes Simulated–Macroscopic spatial variability of hydraulic conductivity

–Microscopic velocity variations

•Input Parameters–Ground water seepage velocity

–Dispersivity

–Molecular diffusion coefficient

Input Parameters:Biodegradation and Decay

Ground Water Flow DirectionGround Water Flow DirectionAdvective/Dispersive Front Advective/Dispersive Front (no decay or retardation)(no decay or retardation)

Retarded FrontRetarded Front

Dissolved

Decaying FrontDecaying Front

Source

( )0

1/ 2

ln 2

ttC C e

t

•Processes Simulated–Chemical transformation and decay

–Biodegradation

–Volatilization

•Input Parameters–Initial concentrations

–First order decay rate or half life

3-D Contaminant Fate and Transport in Ground Water

2 2 2

2 2 2x x x x

C C C C CR D D D Ct 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