NEWTON RAPHSON SOLUTIONS OF BIOCHEMICAL OXYGEN DEMAND (BOD) KINETICS
Keywords:
Wastewater, BOD kinetics, Newton- Raphson method, methods of determining BOD rate, total error, CD MSC, statistical reliabilityAbstract
As follow up on our previous studies, this paper evaluated Newton-Raphson method (NRM) solutions of Biochemical Oxygen Demand (BOD) kinetics with the aim of ascertain error free solutions. Non-linear regression, logarithms difference, NRM, least square, daily difference, Thomas, two points, ratio and Fujimoto methods were used to determine constants in BOD kinetics. Microsoft Excel Solver was applied to all the methods. Accuracies of all the methods were evaluated using relative error, Coefficient of Determination (CD), reliability and Model of Selection Criterion (MSC). The study revealed that the values of ultimate BOD and BOD removal rate were in the range of 859 to 1911 mg/l and - 0.140/d to - 0.449 /d respectively. Average total error for the methods were 23.85, 25.7, 74.72, 88.68, 1066.5, 1016.33, 149.12, 78.1 and (61.45 and 59.10) for non-liner regression, logarithms difference, least squares, Thomas, Fujimoto, Ratio, two points, daily difference and NRM ( matrix and graphical).
Accuracy, validity and good fitness of these methods were in order of non-linear regression (8.16) > Logarithm difference (7.72) > NRM (6.26) > least square (6.03) >daily difference (5.42)> Thomas (5.04)> two points (4.14) > ratio (0.63) and Fujimoto (0.51) on basis of their average MSC values. It was concluded that NRM could be used for BOD kinetics. NRM is among the best options because of their simplicity and flexibility as graphical and numerical solutions.
References
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Adrian D.D. and Sanders T.G.: Oxygen sag equation for half order BOD kinetics. Journal of Environmental Systems, Vol. 22, Number 4, 1993, , pp 341–351.
Akaike, H. An information criterion (AIC), Math. Sci. Vol. 14,1976 , pp 1-5.
APHA, Standard Method for the Examination of Water and Wastewater, 21st edn, America Water Works Association and Water Pollution Control Federation, Washington DC. 2012
Babatola, J.O; Oguntuase, A.M; Oke, I. A and Ogedengbe, M.O. (2008). An Evaluation of Frictional Factors in Pipe Network Analysis Using Statistical Methods. Environmental Engineering and Sciences, 25 (4) , 539-548
Barati, R 2013 Application of Excel Solver for Parameter Estimation of the Nonlinear Muskingum Models. KSCE Journal of Civil Engineering, 17(5):1139-1148
Borsuk M.E. and Stow C.A.: Byesian parameter estimation in a mixed-order of BOD decay. Water Research. Vol. 34, Number 6, 2000, pp1830–1836.
Fasanmi, F.O. Short-term Investigation of a one pond wastewater Stabilization system for Partial Treatment of a Domestic Wastewaters. Ife Journal of Technology, Vol. 4, Number 1, 1994, , pp 1-4.
Fujimoto Y. Graphical use of first stage BOD equation. Journal of Water Pollution Control Federation, Vol. 36, Number 1, 1964 , pp 69–71.
Gullemo, C.; Liliana, M. Carlos, E. V and Gonzales, J.F A short note on the determination of the kinetics parameters for the BOD test. Water SA, Vol. 25, Number 3, 1999, pp 377-380.
Hewitt J.P. and Hunter J.V.: A comparison of the methods used to calculate first order BOD equation constants. Water Research, Vol. 9, 1975, pp 683–687.
Hewitt J.P., Hunter J.V. and Lockwood D. A multiorder approach to BOD kinetics. Water Research, Vol. 13, 1979 , pp 325–329.
Hodgson, O. A. (2000) “Treatment of domestic sewage at Akuse (Ghana)â€, Water SA, 26 (3), 413-416 .
Hui, Z., Xue, Z., Luobin W., Kai, W. and Wendong, W. 2018 Development of a software tool for teaching realâ€time state simulation of water distribution networks, Computer Applications in Engineering Education, 26 (3), 577-588.
Ian G. M. Robert I. M., and Daniel T. G A double exponential model for biochemical oxygen demand. Bioresource Technology Vol. 97 , 2006, , pp273–282.
Kalamkar, S. G., Rai, R. K., Shinde, S. M., Determination of Constants of BOD models- Proceedings of 3rd IRF International Conference, Goa, India, 10th May-2014.
Keshavan K., Weber W.J., and Carlson R.H. Discussion to “Second order equation for BOD†by Young J.C. and Clark J.W. Journal of the Sanitary Engineering Division ASCE, Vol. 91, Number SA3, 1965, pp. 136–140.
Liu J., Olsson G. and Mattiasson B. Short-term BOD (BODst) as a parameter for on-line monitoring of biological treatment process. Part I. A novel design of BOD biosensor for easy renewal of bio-receptor. Biosensors and Bioelectronics, Vol. 20, 2004, , pp 562–570.
Mahmood, T and Paice, M (2006). Aerated Stabilization Basin Design and Operating Practices in the Canadian Pulp and Paper Industry. Journal Environ. Sci. 5, 383-395.
Mara, D. D. Domestic Wastewater Treatment in Developing Countries. First Edition Earthscan, London. 2003.
Marske D.M., and Polkowsky L.B. Evaluation of methods for estimating biochemical oxygen demand parameters. Journal of Water Pollution Control Federation, Vol. 44, Number 10, 1972, pp 1987–2000.
Mason I.G., Mclachlan R.I., and Gerard D.T.: A double exponential model for biochemical oxygen demand. Bioresource Technology, Vol. 97, 2006 , pp 273–282.
Metcalf and Eddy Inc.( 1991). Wastewater Engineering Treatment , Disposal and Reuse, 3rd Edition, McGraw-Hill Book Company, New York,.
Moore E.W., Thomas H.A. and Snow W.B.: Simplified method for analysis of BOD data. Sewage and Industrial Wastes, Vol. October, 1950 , pp 1343–1355.
Navone R. A new method for calculating K and L for sewage. Water and Sewage Works, Vol. July, 1960 , pp 285–286.
Ogunfowokan, A.O. ; Okoh, E.K. ; Adenuga, A.A. and O.I. Asubiojo(2005.) . An Assessment of the Impact of Point Source Pollution from a University Sewage Treatment Oxidation Pond on a Receiving Stream-A Preliminary Study. Journal of Applied Sciences 5 (1): 36-43,
Oke, I. A; Olarinoye N.O.; Olajumoke, A.M and Oladepo, K.T.(2006c) A Novel Statistical Method For Determining Parameters In BOD Kinetic. Journal of Applied Sciences Research. 2(8), 503-509
Oke, I. A and Akindahunsi, A.A. (2005). A Statistical Evaluation of Methods of Determining BOD Rate. Journal of Applied Sciences Research, 1(2), 223-227
Oke, I. A and Otun, J.A. (2001 ) Mathematical Analysis of Economic Sizing Of Stabilization Pondsâ€. Nigerian Journal of Engineering, 9(1), 13-21,.
Oke, I. A. ; Ismail, A. ; Lukman, S. ; Fogji, P.U ; Adeosun, O. O. ; Amele, S.A. and Bolorunduro, A. K. An Improved Solution of First Order Kinetics for Biochemical Oxygen Demand. Ife Journal of Science Vol. 18, Number 3, 2016, pp 730- 739.
Oke, I. A.; Lukman , S; Amoko, J. S, and Fehintola E.. O (2018) An Evaluation of Solutions To Moment Method Of Biochemical Oxygen Demand Kinetics. NIJOTECH. 37(1), 1 – 12
Oke, I. A.; Lukman, S. and Ismail, A(2017). Development And Performance Evaluation Of A New Numerical Model For Groundwater Recharge Estimation. Nigeria Journal of Engineering , 23(2), 56 -65
Oke, I. A; Olarinoye N.O.; Olajumoke, A.M and Oladepo, K.T. A Novel Statistical Method For Determining Parameters In BOD Kinetic. Journal of Applied Sciences Research. Vol. 2, Number 8, 2006b , pp 503-509.
Oke, I. A; Otun, J.A and Adie, D.B (2009) An Assessment of Selected Methods in Environmental Pollution Control. Journal of Food, Agriculture and Environment, 7 (1), 186-191
Oke, I.A, Otun, J.A; Okuofu, C.A and Olarinoye (2006a). Efficacy of a Biological Treatment plant at Ahmadu Bello University, Zaria, Nigeria. Research Journal of Agricultural and Biological Sciences, 2(6), 452- 459.
Reynolds D.M. and Ahmad S.R. Rapid and direct determination of wastewater BOD values using a fluorescence technique. Water Research, Vol. 31, Number 8, 1997, pp 2012–2018.
Sheehy L.P. Rapid methods for solving first-order equations, Journal of Water Pollution Control Federation, Vol. 32, Number 6, 1960, pp 646–652.
Siwiec T., Kiedryńska L. Abramowicz, K., and Rewicka A. Analysis of chosen models describing the changes in BOD5 in sewages. Environment Protection Engineering, Vol. 38, Number 2, 2012, pp 61 - 76.
Siwiec T., Kiedryńska L. Abramowicz, K., Rewicka A. and Nowak, P BOD measuring and modelling methods – review. Land Reclamation. Vol. 43, Number 2, 2011 , pp 143–153.
Sohn M.J., Lee J.W., Chung C., Ihn G.S. and Hong D. Rapid estimation of biochemical oxygen demand using a microbial multi- staged bioreactor. Analytica Chimica Acta, Vol. 313, 1995, pp 221–227.
Srinivasa Rao, G.V.R.; Srinivasa, M. K and Nagendra B. D. Biokinetics of Removal of BOD and COD from Domestic Sewage Using Fluidized Bed Bio-Reactor. Research Inventy: International Journal of Engineering And Science. Vol. 5, Number 5, 2015 , pp 1-6.
Swamee P.K. and Ojha C.S.P. Modelling of BOD exertion curve. Water Research, Vol. 25, Number 7, 1991, pp 901–902.
Tay, K. G; Kek, S. L. and Rosmila A. K. 2014 . Solving Non-Linear Systems by Newton’s Method Using Spreadsheet Excel.
Thomas H.A. Graphical determination of BOD curve constants. Water and Sewage Works, Vol. March, 1950, pp 123–124.
van Loosdrecht, M.C.M., Nielsen, P.H.,Lopez-Vazquez, C.M., Brdjanovic, D., 2016 . Experimental Methods in Wastewater Treatment. 1st Edition, International Water Publishing Alliance House, London.
Viessman, W. (Jr). and Hammer, M. J. (1993). Water Supply and Pollution Control, 5th edn, Harper Collins College Publishers, New York.
Weber W.J. and Carlson R.H. Discussion to “Second order equation for BOD†by Young J.C. and Clark J.W. Journal of the Sanitary Engineering Division ASCE, Vol. 91, Number SA3, 1965, pp 140–147.
Young J.C. and Clark J.W. Second order equation for BOD. Journal Sanitary Engineering Division ASCE, Vol. 91, Number SA1, 1965, pp 43–57.
Adrian D.D. and Sanders T.G.: Oxygen sag equation for half order BOD kinetics. Journal of Environmental Systems, Vol. 22, Number 4, 1993, , pp 341–351.
Akaike, H. An information criterion (AIC), Math. Sci. Vol. 14,1976 , pp 1-5.
APHA, Standard Method for the Examination of Water and Wastewater, 21st edn, America Water Works Association and Water Pollution Control Federation, Washington DC. 2012
Babatola, J.O; Oguntuase, A.M; Oke, I. A and Ogedengbe, M.O. (2008). An Evaluation of Frictional Factors in Pipe Network Analysis Using Statistical Methods. Environmental Engineering and Sciences, 25 (4) , 539-548
Barati, R 2013 Application of Excel Solver for Parameter Estimation of the Nonlinear Muskingum Models. KSCE Journal of Civil Engineering, 17(5):1139-1148
Borsuk M.E. and Stow C.A.: Byesian parameter estimation in a mixed-order of BOD decay. Water Research. Vol. 34, Number 6, 2000, pp1830–1836.
Fasanmi, F.O. Short-term Investigation of a one pond wastewater Stabilization system for Partial Treatment of a Domestic Wastewaters. Ife Journal of Technology, Vol. 4, Number 1, 1994, , pp 1-4.
Fujimoto Y. Graphical use of first stage BOD equation. Journal of Water Pollution Control Federation, Vol. 36, Number 1, 1964 , pp 69–71.
Gullemo, C.; Liliana, M. Carlos, E. V and Gonzales, J.F A short note on the determination of the kinetics parameters for the BOD test. Water SA, Vol. 25, Number 3, 1999, pp 377-380.
Hewitt J.P. and Hunter J.V.: A comparison of the methods used to calculate first order BOD equation constants. Water Research, Vol. 9, 1975, pp 683–687.
Hewitt J.P., Hunter J.V. and Lockwood D. A multiorder approach to BOD kinetics. Water Research, Vol. 13, 1979 , pp 325–329.
Hodgson, O. A. (2000) “Treatment of domestic sewage at Akuse (Ghana)â€, Water SA, 26 (3), 413-416 .
Hui, Z., Xue, Z., Luobin W., Kai, W. and Wendong, W. 2018 Development of a software tool for teaching realâ€time state simulation of water distribution networks, Computer Applications in Engineering Education, 26 (3), 577-588.
Ian G. M. Robert I. M., and Daniel T. G A double exponential model for biochemical oxygen demand. Bioresource Technology Vol. 97 , 2006, , pp273–282.
Kalamkar, S. G., Rai, R. K., Shinde, S. M., Determination of Constants of BOD models- Proceedings of 3rd IRF International Conference, Goa, India, 10th May-2014.
Keshavan K., Weber W.J., and Carlson R.H. Discussion to “Second order equation for BOD†by Young J.C. and Clark J.W. Journal of the Sanitary Engineering Division ASCE, Vol. 91, Number SA3, 1965, pp. 136–140.
Liu J., Olsson G. and Mattiasson B. Short-term BOD (BODst) as a parameter for on-line monitoring of biological treatment process. Part I. A novel design of BOD biosensor for easy renewal of bio-receptor. Biosensors and Bioelectronics, Vol. 20, 2004, , pp 562–570.
Mahmood, T and Paice, M (2006). Aerated Stabilization Basin Design and Operating Practices in the Canadian Pulp and Paper Industry. Journal Environ. Sci. 5, 383-395.
Mara, D. D. Domestic Wastewater Treatment in Developing Countries. First Edition Earthscan, London. 2003.
Marske D.M., and Polkowsky L.B. Evaluation of methods for estimating biochemical oxygen demand parameters. Journal of Water Pollution Control Federation, Vol. 44, Number 10, 1972, pp 1987–2000.
Mason I.G., Mclachlan R.I., and Gerard D.T.: A double exponential model for biochemical oxygen demand. Bioresource Technology, Vol. 97, 2006 , pp 273–282.
Metcalf and Eddy Inc.( 1991). Wastewater Engineering Treatment , Disposal and Reuse, 3rd Edition, McGraw-Hill Book Company, New York,.
Moore E.W., Thomas H.A. and Snow W.B.: Simplified method for analysis of BOD data. Sewage and Industrial Wastes, Vol. October, 1950 , pp 1343–1355.
Navone R. A new method for calculating K and L for sewage. Water and Sewage Works, Vol. July, 1960 , pp 285–286.
Ogunfowokan, A.O. ; Okoh, E.K. ; Adenuga, A.A. and O.I. Asubiojo(2005.) . An Assessment of the Impact of Point Source Pollution from a University Sewage Treatment Oxidation Pond on a Receiving Stream-A Preliminary Study. Journal of Applied Sciences 5 (1): 36-43,
Oke, I. A; Olarinoye N.O.; Olajumoke, A.M and Oladepo, K.T.(2006c) A Novel Statistical Method For Determining Parameters In BOD Kinetic. Journal of Applied Sciences Research. 2(8), 503-509
Oke, I. A and Akindahunsi, A.A. (2005). A Statistical Evaluation of Methods of Determining BOD Rate. Journal of Applied Sciences Research, 1(2), 223-227
Oke, I. A and Otun, J.A. (2001 ) Mathematical Analysis of Economic Sizing Of Stabilization Pondsâ€. Nigerian Journal of Engineering, 9(1), 13-21,.
Oke, I. A. ; Ismail, A. ; Lukman, S. ; Fogji, P.U ; Adeosun, O. O. ; Amele, S.A. and Bolorunduro, A. K. An Improved Solution of First Order Kinetics for Biochemical Oxygen Demand. Ife Journal of Science Vol. 18, Number 3, 2016, pp 730- 739.
Oke, I. A.; Lukman , S; Amoko, J. S, and Fehintola E.. O (2018) An Evaluation of Solutions To Moment Method Of Biochemical Oxygen Demand Kinetics. NIJOTECH. 37(1), 1 – 12
Oke, I. A.; Lukman, S. and Ismail, A(2017). Development And Performance Evaluation Of A New Numerical Model For Groundwater Recharge Estimation. Nigeria Journal of Engineering , 23(2), 56 -65
Oke, I. A; Olarinoye N.O.; Olajumoke, A.M and Oladepo, K.T. A Novel Statistical Method For Determining Parameters In BOD Kinetic. Journal of Applied Sciences Research. Vol. 2, Number 8, 2006b , pp 503-509.
Oke, I. A; Otun, J.A and Adie, D.B (2009) An Assessment of Selected Methods in Environmental Pollution Control. Journal of Food, Agriculture and Environment, 7 (1), 186-191
Oke, I.A, Otun, J.A; Okuofu, C.A and Olarinoye (2006a). Efficacy of a Biological Treatment plant at Ahmadu Bello University, Zaria, Nigeria. Research Journal of Agricultural and Biological Sciences, 2(6), 452- 459.
Reynolds D.M. and Ahmad S.R. Rapid and direct determination of wastewater BOD values using a fluorescence technique. Water Research, Vol. 31, Number 8, 1997, pp 2012–2018.
Sheehy L.P. Rapid methods for solving first-order equations, Journal of Water Pollution Control Federation, Vol. 32, Number 6, 1960, pp 646–652.
Siwiec T., Kiedryńska L. Abramowicz, K., and Rewicka A. Analysis of chosen models describing the changes in BOD5 in sewages. Environment Protection Engineering, Vol. 38, Number 2, 2012, pp 61 - 76.
Siwiec T., Kiedryńska L. Abramowicz, K., Rewicka A. and Nowak, P BOD measuring and modelling methods – review. Land Reclamation. Vol. 43, Number 2, 2011 , pp 143–153.
Sohn M.J., Lee J.W., Chung C., Ihn G.S. and Hong D. Rapid estimation of biochemical oxygen demand using a microbial multi- staged bioreactor. Analytica Chimica Acta, Vol. 313, 1995, pp 221–227.
Srinivasa Rao, G.V.R.; Srinivasa, M. K and Nagendra B. D. Biokinetics of Removal of BOD and COD from Domestic Sewage Using Fluidized Bed Bio-Reactor. Research Inventy: International Journal of Engineering And Science. Vol. 5, Number 5, 2015 , pp 1-6.
Swamee P.K. and Ojha C.S.P. Modelling of BOD exertion curve. Water Research, Vol. 25, Number 7, 1991, pp 901–902.
Tay, K. G; Kek, S. L. and Rosmila A. K. 2014 . Solving Non-Linear Systems by Newton’s Method Using Spreadsheet Excel.
Thomas H.A. Graphical determination of BOD curve constants. Water and Sewage Works, Vol. March, 1950, pp 123–124.
van Loosdrecht, M.C.M., Nielsen, P.H.,Lopez-Vazquez, C.M., Brdjanovic, D., 2016 . Experimental Methods in Wastewater Treatment. 1st Edition, International Water Publishing Alliance House, London.
Viessman, W. (Jr). and Hammer, M. J. (1993). Water Supply and Pollution Control, 5th edn, Harper Collins College Publishers, New York.
Weber W.J. and Carlson R.H. Discussion to “Second order equation for BOD†by Young J.C. and Clark J.W. Journal of the Sanitary Engineering Division ASCE, Vol. 91, Number SA3, 1965, pp 140–147.
Young J.C. and Clark J.W. Second order equation for BOD. Journal Sanitary Engineering Division ASCE, Vol. 91, Number SA1, 1965, pp 43–57.
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