A simplified numerical algorithm for oxygen- and nitrate-based biodegradation of hydrocarbons using Monod expressions

Bioremediation has become an important remediation technology during the past few years. However, limited understanding of processes, data limitations and parameter uncertainty, and computationally intensive numerical solutions have reduced the interest to perform detailed field-scale modeling, especially with non-linear Monod expressions. In this paper, the focus was computational efficiency where a simplified numerical algorithm was developed to solve the non-linear reactions between the hydrocarbon, oxygen, nitrate, and a heterotrophic facultative microbial population. The numerical algorithm was presented using a commonly adapted conceptual model of reaction kinetics between different species with multi-term Monod expressions. The accuracy and efficiency of the algorithm were tested with an iterative solution using the Runge–Kutta method. Simulation results obtained from reaction only and one-dimensional advection–dispersion-reaction transport examples showed good accuracy while maintaining numerical stability. In general, the accuracy increased with contaminant concentrations relatively higher than the corresponding half-saturation constant. Also, the simplified algorithm is found to be much more computationally efficient than the iterative technique. The gain in computational efficiency was at least threefold and this gain increased with the increase of time step. Future work will explore the efficiency and accuracy of the proposed simplified algorithm with field-scale scenarios related to intrinsic and enhanced bioremediation.