First order decay is a more complex method for analysing pollutant removal based on Exponential Decay. The method needs to act on the body of water in each stormwater control, rather than on the output. This method determines the percentage of pollutants removed depending on the amount of time taken for water to pass through the stormwater control.


First order decay – without background concentration 

The calculation for First order decay without background concentration uses the following formula:

Where: 

Cn+1 = the pollutant concentration at the end of the time interval

Cn = is the pollutant concentration at the beginning of the time interval

 = the time step of the interval

 = the decay constant, which can be specified in a number of ways:

Where

τ = the decay time constant or (mean) lifetime

T1/2 = the decay half-life

Generally τ is easier to estimate and more likely to be entered by the user. However, the calculator can be used to enter T1/2 or   if preferred.

First order decay – with background concentration

Realistically some pollutant concentrations are not reduced to zero. Users are able to specify a background (minimum) concentration (Cback) below which the pollutant concentration will not be reduced. 

The method is the same as for First order decay – without background concentration - other than the ability to enter Cback.