Where Cj is the concentration of solute j ;\(\theta\) is the water content; q  is the Darcy velocity vector; D  is the hydrodynamic dispersion coefficient tensor; \(R_{j}\) is the reaction rate of solute j .
Multicomponent reactions involved in the model included aerobic respiration (AR), nitrification (NI) and denitrification (DN). The organic matter (DOC) was represented by the chemical formula ”CH2O”. All the reaction equations are as follows: