Environmental Modeling Community of Practice

EPA On-line Tools for Site Assessment Calculation

Steady One-Dimensional Plume Length

Steady-State Transport in One Dimension
Plume Length Estimate
See bottom of page for equations solved.

Example Data Set
Example Description
Site Name
Date
Aquifer Type
Distance Unit
Time Unit
Porosity Bulk Density (ρ _b)

Hydraulic Conductivity (K)

Hydraulic Conductivity (K)

Gradient (i)

Seepage Velocity (q_s = v) Calculated result

Halflife T _1/2

Source Concentration C_o mg/L

Concentration for plume length defn. C

Case 3 Fixed Dispersivity

Plume Lengths (Iterative Solution)

Method Plume Length Dispersivity
Case 1) Dispersivity Regression

Case 2) One-tenth plume length

Case 3) Fixed Dispersivity

QA check (Direct Solution--Fixed Dispersivity)

Case 3) Fixed Dispersivity

The direct solution should match any of the iterative solution results with the same dispersivity. Enter a the fixed dispersivity of interest above to match cases 1, 2 or 3.

Plume Length for Steady One-Dimensional Transport

One-dimensional steady state transport equation

c = concentration [m/L ^-3 ]
t = time [T]
x = distance [L]
D = dispersion constant [L ² /T]
v = seepage velocity [L/T]
λ = first order decay constant [1/T]

with the initial and boundary conditions

Boundary conditions

Has the solution (rearranged for length, x):

Plume length solution

where the dispersion coeffeicient D, has been separated into a dispersivity, α and the seepage velocity v, and
c _L is the concentration that defines the plume length.
i.e., to find the distance (plume length) to the 0.02 mg/L contour, c _L is set to 0.02.

Allowing for the dispersivity to be a function of x, f(x):

Plume length solution, with dispersivity as a function of x

The calculator has three options for f(x):

Fixed Dispersivity
One-tenth the plume Length
Xu and Eckstien (1995) regression relation for plume length (L _p = x):

Dispersivity regression

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