Step Release into Groundwater

This section of Fate will aid you in the conceptual understanding of how a constant source of pollution will flow in an isotropic or homogeneous aquifer. Inn addition, this model allows for the first order degradation of a pollutant. A leaky landfill is an excellent example of the concept demonstrated by this module.

Step 1 Manually convert input data to metric units: meters, kilograms, or curies.

Step 2: Calculate or enter the porosity of the aquifer

Bulk Density
ρ_b = g/cm³ Solids Density
ρ_s = g/cm³ \[ n = 1 - \frac{ρ_b}{ρ_s}* 100% \] Porosity
n = %

Porosity
n = %

Step 3: Calculate or enter the retardation factor

Distribution Coefficient
K_d = cm³/g Bulk Density
ρ_b = g/cm³ Porosity
n = % \[ R = 1 + \frac{ρ_bK_d}{n/100%}\] Retardation factor
R = (unitless)

Retardation factor
R = (unitless)

Step 4: Calculate first order rate constant

Half-Life

\[ln(\frac{C}{C_o}) = -kt_\frac{1}{2} \]

k = /year

Step 4: Enter the remaining data Initial concentration
C₀ = Longitudinal dispersivity
α_x = m Linear water velocity
v = m/year First order rate constant
k = /year Retardation factor
R =

Point calculation Distance
Meters Time
Years

Result:

Graph varying time Distance (fixed)
meters

\[C_{(x,t)} = \frac{C_0}{2}(e^{(\frac{x}{2α_x})(1-(1+\frac{4kRα_x}{v})^\frac{1}{2})} (erfc(\frac{x-(\frac{v}{R}t(1+\frac{4kRα_x}{v})^\frac{1}{2}}{2(α_x\frac{v}{R}t)^{\frac{1}{2}}}))\]

Graph varying distance Time
Hours

\[C_{(x,t)} = \frac{C_0}{2}(e^{(\frac{x}{2α_x})(1-(1+\frac{4kRα_x}{v})^\frac{1}{2})} (erfc(\frac{x-(\frac{v}{R}t(1+\frac{4kRα_x}{v})^\frac{1}{2}}{2(α_x\frac{v}{R}t)^{\frac{1}{2}}}))\]