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Modified Fractional-Order Activated Sludge Model (MFASM) for Aerobic Microbial Growth in Wastewater

Mostafa M El-Seddik

This paper presents a modified fractional-order activated sludge model (MFASM) for substrate degradation and nutrient removal. The modified model is based on Activated Sludge Model 1 (ASM1) for bacterial growth incorporated with the hereditary growth of microorganisms in a couple of pH value acclimatizing proton translocation theory for substrate dissociation. A novel modification is accomplished in the ASM to obtain the extra degree of freedom for biomass concentration through fractional order derivatives based on Grünwauld-Letinkov numerical technique. A significant decline in Chemical Oxygen Demand (COD) and NH4-N removal efficiency from 85% to 60% can be obtained as the biomass fractional order fluctuates between 0.9 and 0.1. Also, the specific growth rate of bacteria can be simulated over long time periods to reveal the history of accumulated biomass in activated sludge process. Moreover, the integer order model of ASM can be indicated at fractional order of 1. In this regard, the MFASM is strictly investigated to reveal the influence of both pH value and heterotrophic biomass deterioration on effluent COD. Furthermore, the simulated results are examined for the long term interaction of autotrophs in nitrification process.