EPA On-line Tools for Site Assessment Calculation

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.>

Inputs

Site Name

Date
Distance Unit ft m

Time Unit days years

Chemical mtbe benzene toluene ethylbenzene o-xylene p-xylene m-xylene total xylenes

Example Fuel 87 Octane gasoline (1) MTBE 89 Octane gasoline (3) MTBE 93 Octane gasoline (5) MTBE ----------------- 87 Octane gasoline (2) low MTBE 89 Octane gasoline (4) Low MTBE 93 Octane gasoline (6) Low MTBE ----------------- 87 Octane gasoline (1) Non-MTBE 87 Octane gasoline (2) Non-MTBE 89 Octane gasoline (3) Non-MTBE 89 Octane gasoline (4) Non-MTBE 93 Octane gasline (5) Non-MTBE 93 Octane gasline (6) Non-MTBE ----------------- Diesel 1 TPH Working Group Diesel 2 TPH Working Group Diesel fuel oil 1994 Diesel fuel oil (Alaska) ----------------- other

Solubility (S) mg/L

Optional Revised Solubility (S) mg/L

Porosity

Water Saturation Fraction of the pore space filled with water

NAPL Saturatio Fraction of the pore space filled with NAPL

Fraction Organic Carbon

Lens diameter

Smear zone thickness

Recharge rate in/yr mm/yr

Soil type sand clay

Hydraulic Conductivity (K) ft/day m/day ft/min cm/sec gal/day/ft2

Gradient (absolute value) (−i)

Distance (x)

Halflife T _1/2

Year Month Day

Beginning Date

Min. Concentration of Concern mg/L mg/l

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


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 _{o c} K _{o c}
f _{o c} = fraction organic carbon
K _{o c} = organic carbon/water partition coefficient

travel time t _{t r} = x R / q _s

t _{t r} = advective travel time^*
q _s = seepage velocity
R = retardation factor
x = distance
^* assuming one-dimensional, steady flow, constant gradient