# 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
$n = 1 - \frac{ρ_b}{ρ_s}* 100%$
Step 3: Calculate or enter the retardation factor
$R = 1 + \frac{ρ_bK_d}{n/100%}$
Step 4: Calculate first order rate constant
$ln(\frac{C}{C_o}) = -kt_\frac{1}{2}$

k = /year

Step 4: Enter the remaining data
Point calculation

Result:

Graph varying time
$C_{(x,t)} = \frac{C_0}{2}(e^{(\frac{x}{2α_x})(1-(1+\frac{4kRα_x}{v})^\frac{1}{2})} (erfc(\frac{x-(\frac{v}{R}t(1+\frac{4kRα_x}{v})^\frac{1}{2}}{2(α_x\frac{v}{R}t)^{\frac{1}{2}}}))$
Graph varying distance
$C_{(x,t)} = \frac{C_0}{2}(e^{(\frac{x}{2α_x})(1-(1+\frac{4kRα_x}{v})^\frac{1}{2})} (erfc(\frac{x-(\frac{v}{R}t(1+\frac{4kRα_x}{v})^\frac{1}{2}}{2(α_x\frac{v}{R}t)^{\frac{1}{2}}}))$