Sewage discharge and water self-decay: Streeter and Phelps model application


Due to the high waste deposition in superficial water, studies are necessary to emphasize the importance to monitor and apply tools, such as mathematical modelling. In this study, we used the classic Streeter and Phelps model to simulate the travel time necessary to depurate organic matter in the Tatu stream, at Limeira, São Paulo, Brazil, and to simulate the point-to-point depuration of organic matter in comparison to point-to-point empirical analysis. According to the simulations, organic matter would be established to 10 mg/L \(\hbox {O}_2\) in few hours of time course of water without discharges in the stream, having the watercourse self-decay capacity. In addition, the analysis indicates that possible launches are being carried out along the stream, because, at the collection points, the obtained results presented higher biochemical oxygen demand than the expected for organic matter depuration, which denote discharges occurrences. Thus, this study emphasizes the relevance of monitoring actions and puts the model as a suitable tool to identify discharge sources in water.

This is a preview of subscription content, access via your institution.

Fig. 1

Source: Adapted from Google \(\hbox {Earth}^{{\textregistered }}\)

Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9


  1. Ali I, Asim M, Khan T (2012) Low cost adsorbents for the removal of organic pollutants from wastewater. J Environ Manag 170–183

  2. Apha (2012) Standard methods for the examination of water and wastewater. Apha, Washington

  3. Brazil (2005) CONAMA \(\text{n}^o 357\), Ministry of the Environment, Resolution of March 17, 2005. Accessed 14 Dec 2016

  4. Churchill MA, Elmore HL, Buckingham RA (1962) The prediction of stream reaeration rates. Am Soc Civ Eng J 88:1–46

    Google Scholar 

  5. Duncan JS, Savage N, Street A (2014) Competition for water. In: Nanotechnology applications for clear water, 2nd edn. Solutions for improving water quality, vol 35. Elsevier, pp 529–555

  6. Fan FM, Fleischmann AS, Collischonn W, Ames DP, Rigo D (2015) Large-scale analytical water quality model coupled with GIS for simulation of point sourced pollutant discharges. Environ Model Softw 64:58–71

    Article  Google Scholar 

  7. Gray NF (1992) Biology of wastewater treatment. Oxford University Press, New York

    Google Scholar 

  8. Jiang T (2017) Characteristics of dissolved organic matter (DOM) and relationship with dissolved mercury in Xiaoqing River-Laizhou Bay estuary, Bohai Sea, China. Environ Pollut.

  9. MMA-Ministério do Meio Ambiente (2014) Conjuntura dos Recursos Hídricos, Encarte especial sobre a crise hídrica, Agência Nacional das Águas, Brasil. Accessed 13 Nov 2016

  10. Munster U, De Haan H (1998) The role of microbial extracellular enzymes in the transformation of dissolved organic matter in humic waters. Aquat Humic Subst Ecol Stud 133:199–257

    Article  Google Scholar 

  11. Odebrecht (2015) Processos de tratamento de esgoto de Limeira. Accessed 10 Oct 2016

  12. Owen DM, Amy GL, Chowdhury ZK, Paode R, McCoy G, Viscosil K (1995) NOM characterization and treatability. J Am Water Works Assoc 87(1):4663

    Article  Google Scholar 

  13. Owens M, Edwards RW, Gibbs JW (1964) Some reaeration studies in streams. Int J Air Water Pollut 8:469–486

    Google Scholar 

  14. Regattieri SMCB (2007) Geoquímica de águas e sedimentos da bacia do ribeirão Tatu, Limeira-SP, dissertation, Geo Sciences Institute, State University of Campinas-UNICAMP, Brazil

  15. Scheili A, Delpla I, Sadiq R, Rodriguez MJ (2016) Impact of raw water quality and climate factors on the variability of drinking water quality in small systems. Water Resour Manag 30:2703–2718

    Article  Google Scholar 

  16. Sibil R, Berkun M, Bekiroglu S (2014) The comparison of different mathematical methods to determine the BOD parameters, a new developed method and impacts of these parameters variations on the design of WWTPs. Appl Math Model 38:641–658

    Article  Google Scholar 

  17. Snis (2017) National Sanitation Information System, Ministry of cities, Brazil. Accessed 30 Jan 2017

  18. Streeter HW, Phelps EB (1925) A study of the pollution and natural purification of the Ohio river, United States Public Health Service. Public Health Bull 1:146

    Google Scholar 

  19. Teixeira MR, Rosa SM, Souza V (2011) Natural organic matter and disinfection by-products formation potential in water treatment. Water Resour Manag 25:3005–3015

    Article  Google Scholar 

  20. Tundisi JG, Tundisi-Matsumura T (2008) Limnologia. Oficina de Textos, São Paulo

    Google Scholar 

  21. Von Sperling M (2008) Estudos e modelagem da qualidade da água de rios, DESA, Ed. UFGM, Minas Gerais, cap. 1, 2, 6, 7 e 8

  22. Von Sperling M (2009) Introdução à qualidade das águas e ao tratamento de esgoto, Princípios do tratamento biológico de águas residuárias. Ed. UFMG, Minas Gerais, pp 19–49, cap. 1.3–1.7

  23. Wang Q, Li S, Jia P, Qi C, Ding F (2013) A review of surface water quality models, review article. Sci World J 2013:7

    Google Scholar 

  24. Wetzel RG, Likens GE (1991) Limnological analyses. Springer, New York

    Book  Google Scholar 

  25. Yang YS, Wang L (2010) A review of modelling tools for implementation of the eu water framework directive in handling diffuse water pollution. Water Resour Manag 24:1819–1843

    Article  Google Scholar 

Download references


Funding was provided by Capes.

Author information



Corresponding author

Correspondence to Amanda de Cássia da Cunha.

Additional information

Communicated by Jose Alberto Cuminato.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

de Cássia da Cunha, A., Coneglian, C.M.R. & Poletti, E.C.C. Sewage discharge and water self-decay: Streeter and Phelps model application. Comp. Appl. Math. 37, 3514–3524 (2018).

Download citation


  • Superficial water quality
  • Dissolved oxygen (DO)
  • Water management
  • Water reoxygenation
  • Water deoxygenation

Mathematics Subject Classification

  • 34-00
  • 92B05