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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

  1. First arrival time for a contaminant (above a specified threshold concentration),
  2. Maximum Concentration, and
  3. 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.




Alternate access to example descriptions.

Inputs




 













b )











mg/L mg/l

mg/L
C o



Intermediate Results












Beginning Time of Breakthrough Curve
Breakthrough Curve Through Maximum Concentration





Completion of Breakthrough Curve (for Pulse Sources)







Advective Travel Time


earlier than the advective travel 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 kd

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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