# Instantaneous Release into Groundwater

This section of Fate allows you to map the passage of a pollutant in groundwater. It models the migration of the pollutant through an aquifer over time or can determine how long it will take a pollutant to reach a given point, such as a river. In this situation, the pollutant may come from a spill or other one-time release such as a tanker truck accident.

Step 1 Manually convert input data to metric units: meters, kilograms, or curies.
Step 2: Calculate the retardation factor from the distribution coefficient $R = 1 + \frac{Ρ_bK_b}{n}$
Step 3: Correct for void volume of spill site $VV= A * n$
Step 4: Calculate the total mass of the pollutant spilled
$M_T = V * C$
Step 5: Calculate first order rate constant
$ln(\frac{C}{C_o}) = -kt_\frac{1}{2}$

k = /year

Step 6: Enter velocity and dispersion coefficient
Step 7: Verify data
Data Point Value Unit
Void volume (VV) m2
Retardation factor (R)
Mass of contaminent (MT)
First Order Rate Constant (k) /year
Point calculation

Result:

Graph varying time
$C_{(x,t)} = \frac{M}{A\sqrt{4\pi \frac{D}{R}t}}e^{-\frac{(x-\frac{v}{R}t)^2}{4\frac{D}{R}t}}$
Graph varying distance
$C_{(x,t)} = \frac{M}{A\sqrt{4\pi \frac{D}{R}t}}e^{-\frac{(x-\frac{v}{R}t)^2}{4\frac{D}{R}t}}$