Mathematical modelling and numerical simulations for temporal and spatial biodegradation of oil-contaminated soil

The theory of enzymatic reaction-diffusion, represented by the Michaelis-Menten model, allows for some prediction of bioremediation of oil-contaminated soil. However, the prediction of temporal and three-dimensional spatial degradation and microbial behavior in contaminated soil have not yet been achieved. The current study proposes a novel mathematical model with feeding and chemotaxis function of microorganisms where the three-dimensional distribution of soil particles can be considered. Some numerical examples show that three-dimensional degradation patterns of oil-contaminated soils and microbial behavior with elapsed time can be quantitatively assessed using the proposed model.