Model Development for Residual Chlorine

M. T. Bello *

Department of Civil Engineering, Usmanu Danfodiyo University, Sokoto, Nigeria.

M. H. Bichi

Department of Civil Engineering, Bayero University, Kano, Nigeria.

*Author to whom correspondence should be addressed.


The research is to develop a mathematical model for the decay of residual chlorine at the nodes and compare with results from Epanet 2.0. All the influencing parameters of initial chlorine Ccl(init(o)), bulk decay (Kb), wall decay (KW) and travel time (t), were well represented and the equation is developed applying the differential form of the first order chlorine decay model, describing reactions occurring in the bulk fluid and at the pipe wall, which was transformed in to chlorine concentration-based integral expression Ccl (t) =Ccl (o).e-kt ,  is the free chlorine (HOCL) concentration (mg/l) at time (t), which is also called the residual chlorine. is the chlorine concentration at time zero, which is the initial chlorine concentration in the entire water distribution systems. KW is the pipe wall decay coefficient of the particular water distribution pipe network directly affected by initial concentration. K is expressed in the study as the decay due to the quality of water, known as bulk decay coefficient (kb), per unit hour (t=1) at any particular node per hour. he developed mathematical model was a reflection of the reality in the study area Rcl (n)=Ccl (init). KW. е-Kb . The results of the model at nodes 31, 12, 13, 14, 18, 10, 17, 15, 20 and 21 are 0.18 mg/l, 0.19 mg/l, 0.19 mg/l, 0.19 mg/l, 0.19 mg/l, 0.19 mg/l, 0.20 mg/l, 0.19 mg/l, 0.20 mg/l, 0.19mg/l, respectively. Epanet 2.0 results for the same nodes were determine to be 0.17 mg/l, 0.21 mg/l, 0.22 mg/l, 0.20 mg/l, 0.21 mg/l, 0.21 mg/l, 0.25 mg/l, 0.24 mg/l, 0.20 mg/l, 0.20 mg/l, 0.18 mg/l. The correlation between the developed mathematical model residual chlorine results and Epanet 2.0 results gives moderate correlation of 0.561, signifying 60% pearson correlation and 0.01, 2-tailed significance level at 99%.

Keywords: Mathematical model, residual chlorine, epanet 2.0, bulk decay and wall decay coefficients

How to Cite

Bello, M. T., & Bichi , M. H. (2023). Model Development for Residual Chlorine. Journal of Engineering Research and Reports, 25(8), 40–47.


Download data is not yet available.


Yi Wu Z. Optimal calibration method for water distribution water quality model. Journal of Environmental Science and Health Part; 2006.

Boccelli DL, Tryby ME, Uber JG, Summers RS. A reactive species model for chlorine decay and THM formation under rechlorination conditions. Water research. 2003 Jun 1;37(11):2654-66.

Laura Monteiro, Rui MC, Viegas Didia IC, Covas, Jose Menaia. Modelling chlorine residual decay as influenced by temperature. Water and Environmental Journal; 2015.


Hua F, Westi JR, Barker RA, Forster CF. Modeling of chlorine decay in municipal water supplies. Water Res. 1999; 33(2): 2735.

Sokoto Town – Zone A – Sites and Services and Slum Upgrading Projects – Max Lock Group, Nigeria, Limited. Volume 4 – Final Report – November;1980.

Sokoto Water Supply Extensions – MRT Consulting Engineers (Nigeria) Limited – August, 1979

Rossman G, Rallis SF. Critical inquiry and use as action. The expanding scope of evaluation use. New Direction in Program Evaluation. 2000;88:55.

Ibrahim AQ, Onyenekwe PC, Nwaedozie IM. An efficiency assessment of Lower Usuma water treatment plant in Abuja Metropolis, Nigeria. IOSR Journal of Environmental Science, Toxicology and Food Technology. 2014;8(12):46- 53.

Clark RM, Rossman LA, Wymer LJ. Modeling distribution system water quality: Regulatory implications. J. Water Res. Pl. ASCE. 1994;121(6):423-428

Powell JC, Hallam NB, West JR, Forster CF, Simms J. Factors which control bulk chlorine decay rates. Water Res. 2000; 34(1):117-126.