EPA On-line Tools for Site Assessment Calculation

Transport from a Continuing or Pulse Concentration Source

One Dimensional Transport Equation

This calculator generates a breakthrough curve^* at a receptor and uses a one-dimensional model to determine the

First arrival time for a contaminant (above a specified threshold concentration),
Maximum Concentration, and
Duration of Contaminantion above the specified threshold

^*The breakthrough curve is the time history of concentration at a receptor located a specified distance from the contaminant source.

See bottom of page for equations solved.

Example Data Set
Example Description

Alternate access to example descriptions.

Inputs

Site Name
Date
Aquifer Type
Distance Unit
Time Unit
Time or Date Output

Chemical Data Source
Note:

Data revision date

Chemical

Porosity

Bulk Density (ρ _b )

Fraction
Organic Carbon

Hydraulic
Conductivity (K)

Gradient (i)

Distance (x)

Halflife T _1/2

Min.
Concentration
of Concern mg/L mg/l

Source
Concentration mg/L
C _o
Year Month Day
Beginning Date
Ending Date

Intermediate Results

K _oc

Estimated dispersivity α

Hydraulic Conductivity (K)

Seepage Velocity (q _s = v)

Retardation factor (R)

Source Duration Δt

Beginning Time of Breakthrough Curve

First Arrival

Breakthrough Curve Through Maximum Concentration

Mid Point

Additional Point

Maximum

Completion of Breakthrough Curve (for Pulse Sources)

Additional Point

Mid Point

Ending

Duration Above Threshold

Advective Travel Time

Advective Travel Time

First arrival time is earlier than the advective travel time

Ratio advective
to first arrival time

One Dimensional Transport From a Pulse Source

One-dimensional transport equation

R = retardation factor []
D = dispersion constant [L2/T]
v = seepage velocity [L/T]
μ = first order decay constant [1/T]

with the initial and boundary conditions

Boundary conditions

retardation factor

R = 1 + ρ _b k_d /θ

R = retardation factor
ρ _b = bulk density = ρ _s (1-θ)
ρ _s = solids density
θ = porosity
k _d = (soil) distribution coefficient = f _oc K _oc
f _oc = fraction organic carbon
K _oc = organic carbon/water partition coefficient

travel time t _tr = x R /v

t _tr = advective travel time ^*
v = seepage velocity
R = retardation factor
x = distance
^* assuming one-dimensional, steady flow, constant gradient

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Contact Jim Weaver to ask a technical question on this material.