Environmental pollution with polycyclic aromatic hydrocarbons contained in sewage sludge – the mathematical model

Sewage sludge constitutes a type of waste generated during wastewater treatment in any treatment plant.The sludge that meets the quality conditions specified in the legal regulations, due to fertilising properties, can be used for natural purposes (in the recovery process on the surface of the earth or for the reclamation cover of landfills).However, sewage sludge contains various organic microcontaminants, such as, for example, Polycyclic aromatic hydrocarbons (PAHs) that are toxic to aquatic and soil organisms, and the legal regulations do not specify the acceptable concentrations of these compounds.However, the restrictions concerning PAHs in European legislation are proposed.The aim of the study was to use fractional order derivatives to develop a mathematical model describing changes in the concentration of PAHs in sewage sludge stored under natural conditions.The concentrations of selected PAHs were monitored for 3 months at fixed time intervals under the conditions reflecting the use of sludge for natural purposes.A qualitative and quantitative analysis of PAHs was carried out using the GC-MS system.For the mathematical description of changes in the concentration values of individual compounds, fractional order derivatives were used and approximation was carried out using the classical equation of the first order.The developed mathematical model allows for predicting changes in PAH concentrations regarding sludge as well as determining the time necessary to obtain the required concentration of these compounds.