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Optimal design of single and multiple stage activated sludge processes

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The present paper describes a rational approach to minimum cost design of an integrated activated sludge process which includes activated sludge reactor, secondary clarifier and sludge recycle. The cost of anaerobic digestion of excess sludge produced is also considered. Procedures for optimal design of both single and multiple stage activated sludge processes, considering construction and operational costs are developed. Biomass concentration in aeration tank and return sludge are utilized as the primary independent design variables to which system performance is related for single stage process. In the multiple stage process, additional design variables (flow and volume fractions for each stage) are included in design vector. Liquid-biomass separation is based on the batch solids flux theory. The optimization problem is framed as minimization of capital and operating cost subject to the constraints determined by effluent quality criteria and process variables affecting the performance. The interior penalty function method is used. Results definitely favor the application of multiple stage process over single stage. The major factor which appears to be contributing to reduction in cost is the biological solids retention time and hence the aeration tank volume.

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A sc :

area of the secondary clarifier,M 0 L 2 T o, m2


biochemical oxygen demand,ML −3 T o, mg L−1


biological solids retention time,M 0 L 0 T, day

C o :

solids concentration in the effluent from the aeration tank,ML −3 T o, mg L−1

C 1 :

capital cost of aeration tank, $ yr−1


capital cost of return sludge pumps, $ yr−1

C 2,2 :

cost of electrical power consumed in sludge pumping, $ yr− 1

C 3 :

capital cost of secondary clarifier, $ yr−1

C 4 :

capital cost of anaerobic digester, $ yr-−1

C 5,1 :

capital cost of blower installation for diffused air system, $ yr−1

C 5,2 :

capital cost of diffusers, $ yr−1

C 5,3 :

cost of electrical power consumed in aeration, $ yr−1

F :

objective function


fixed suspended solids in the raw wastewater,ML −3 T 0, mg L−1

g :

empirical constant related to settling characteristics,M O LT −1, m s−1

g j :


h :

empirical constant related to settling characteristics

HP t :

total horse power requirement,ML 2 T −3, HP

k :

maximum specific substrate utilization rate,M o L o T −1, day−1

K :

substrate utilization rate constant,M −1 L 3 T −1, L mg−1 day−1

K d :

microbial decay coefficient,M O L 0 T −1, day−1

K s :

saturation constant,ML −3 T 0, mg L−1

m :

number of constraints


mixed liquor suspended solids,ML −3T0, mg L−1


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Aggarwal, A., Tare, V. Optimal design of single and multiple stage activated sludge processes. Water Air Soil Pollut 42, 67–85 (1988). https://doi.org/10.1007/BF00282392

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  • Sludge
  • Activate Sludge
  • Anaerobic Digestion
  • Aeration Tank
  • Solid Retention Time