Estimating the corrosion of compacted bentonite by a conceptual model based on microbial growth dynamics

The microbial corrosion of compacted bentonite by the dissolution of smectite is biophysically, chemically, and mathematically estimated using an energy conservation law established between Gibbs free energy of formation ΔG_f⁰ from the elements of smectite and the energy required for the growth and living maintenance requirement of microorganisms. The growth and decay dynamics of microorganisms are described with a universal Monod-type equation in which the specific growth rate and decay coefficient are given as a function of time considering the rapid development of a population of microorganisms at an initial stage and, in addition, by introducing the change of a density of colonies and the development of bio-films with time. The solution revealed that the corrosion depth of compacted bentonite depended primarily on the population density of microorganisms that had initially adhered onto the surface, the maximum thickness of bio-films, and a population of microorganisms at a stable living stage, although they depended on the specific growth and the specific decay rate, the ratio of energy required for maintenance to that required for the growth and the microbial consumption efficiency of energy to Gibbs free energy of smectite. In conclusion, a mean population of microorganisms came to the maximum value of an order of 10⁶ to 10⁷ cells/cm³ on the bentonite surface; the thickness of bio-films was 5-10 μm; and the microbial corrosion depth was estimated to be in the range of less than 0.2 to 2.0 mm per 10⁵ years in nature, provided the density of smectite was kept to be 1.6 Mg/m³ on the compacted bentonite.