Petroleum hydrocarbons remain major environmental contaminants, and understanding the mechanisms governing their biodegradation is essential for designing effective remediation plans. The strategy in this article is slightly different from other cases in the literature. Such literature models require, for their elaboration, a significant number of experiments; the number of experimental determinations is at least proportional to the square of the number of constants introduced in the mathematical expressions. For this reason, the strategy followed in this article is different—starting from a set of experiments carried out and presented in a coherent and published manner, a simple methodology for building specific and minimal models, which will allow solving specific problems, was effectively developed. This study develops a nonlinear mathematical structure, expressed as a system of coupled differential equations, that simultaneously describes the degradation of petroleum hydrocarbons and the dynamics of hydrocarbon-degrading bacteria and fungi in soil–sludge mixtures. The model was calibrated using experimental data obtained from biopiles prepared with different volumetric ratios of contaminated soil and sewage sludge. Approximate analytical solutions were derived and the distributed constants were evaluated. For a consistent discussion, the analytical solutions were assessed against numerical desk simulations performed with a classical fourth-order Runge–Kutta method, which accurately reproduced the nonlinear behavior of the specific system. This numerical approach was chosen in order to overcome the proper difficulties encountered in this strategy implementation. The results show that the soil–sludge ratio strongly influences biodegradation efficiency, while kinetic parameters determine whether microbial communities evolve toward a stationary regime or accelerated contaminant removal. The combined analytical–numerical framework provides a robust predictive tool for optimizing mixture composition and improving the design of bioremediation treatments for petroleum-contaminated soils.
Iorga et al. (Wed,) studied this question.