Mathematical modelling and simulation of microbial carbonate precipitation: the urea hydrolysis reaction

Microbial carbonate precipitation is expected to play a major role in next-generation soil improvement technologies. To date, research into this method has relied on experimental and/or observational approaches. However, in order to understand the long-term effects of microbial carbonate precipitation and apply these to real environments, it is necessary to employ a predictive approach to determine the future state of the soil when using this soil improvement method. In this work, a mathematical model and numerical simulations based on the reaction–diffusion system for the microbial urea hydrolysis reaction are proposed. These techniques may be used to provide the spatiotemporal precipitation patterns of carbonates between soil particles and the particle surfaces. The simulation results revealed that the characteristic precipitation patterns depend on the diffusion of carbonates caused by the microbial urea hydrolysis reaction, and there was a significant shift in the amount of carbonate from a dissipated state into an equilibrium state.