GPS-X Technical Reference

209 Suspended Growth Models
MODELLING OF TEMPERATURE DEPENDENT KINETICS
In general, the relationship between the growth kinetics and the temperature may be expressed
using an asymmetrical bell shaped curve. The crest of the curve represents the maximum growth
rate at optimum temperature. The growth rate on either side of the crest decreases according to
some appropriate growth rate-temperature relationship.
There are a number of models which may be applied to model the temperature dependent kinetics
for biological reactions. Depending on the structure of the model, the model may require
estimation of model parameters which may be very different than the traditional temperature
coefficient approach used in the wastewater engineering. Generally, the Arrhenius equation is
used to model the temperature effect on kinetic parameters in the range of 5 o C-35 o C. This
equation requires one parameter of temperature coefficient. The values of temperature
coefficients are well researched. Therefore, using any other model which deviates from this
relationship will require recalculating of model parameters. To model such a curve the following
three parameter model was used.
1. Estimate the kinetic coefficient at the optimum temperature – The kinetic parameter
values in GPS-X are listed at 20°C; therefore, this value is translated to a value at the
optimum temperature using the following equations:
Equation 6.73
Equation 6.74
where:
k opt
k 20
T opt
θ 1
θ 2
= kinetic coefficient at T opt, unit
= kinetic coefficient at 20°C, unit
= optimum temperature at which the value of kinetic coefficients is
maximum, °C
= Arrhenius coefficient for low temperature
= Arrhenius coefficient for high temperature
GPS-X Technical Reference