Use of Finite Difference Method to Study a Model System of Nitrification at Low substrate Concentrations

A mathematical model of nitrification in a column is developed in which time (t) and distance are considered independently, using a finite difference approach incorporating the following equations for removal of substrate (S) and growth of biomass (m):

where μ is the maximum specific growth rate, K s the saturation constant for growth, k a growth limiting factor and D the dilution rate. This model gives new qualitative and quantitative predictions and in particular predicts overshoots and undershoots in conversion product concentrations following decreases and increases in dilution rate. The model was tested using an experimental system consisting of a column of glass beads, inoculated with Nitrobacter, through which was passed a constant flow of medium containing 1 p.p.m. N as NO2 −; effluent was analysed for nitrite and nitrate.

Short undershoots, lasting several hours, were due to reactivation of bacteria following nutrient starvation. Expected overshoots and undershoots lasting several days were also observed. However, these were not asymmetrical, as predicted, since washout of cells as a limiting growth factor and delay of adjustment to growth rate to different substrate concentrations were not considered.