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 (r_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 C_o	mg/L
	Year Month Day
Beginning Date
Ending Date

Intermediate Results


K_oc
Estimated dispersivity a
Hydraulic Conductivity (K)
Seepage Velocity (q_s = v)
Retardation factor (R)
Source Duration Dt

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 Threashold

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]
m = first order decay constant [1/T]

with the initial and boundary conditions

retardation factor R = 1 + r_bk_d /q

R = retardation factor
r_b = bulk density = r_s(1-q)
r_s = solids density
q = 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

Page author: Jim Weaver, of U.S. EPA, Office of Research and Development, Athens Georgia who last modified this content on: June 5, 2003

EPA On-line Tools for Site Assessment Calculation

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