Effect of Dividing the Water Transmission Pipe Line in Modeling Residual Chlorine, Case Study: Isfahan Water Transmission Line

In assessing the quality of drinking water in transmission and distribution lines, the 14 study on chlorine reactions is of particular importance. Chlorine decay happens in bulk 15 and wall and it is mainly affected by the water age which depends on the transmission 16 line length. Residual chlorine concentration in Isfahan water transmission line (IWTL) 17 is simulated through three decay models, namely the first order, parallel first order and 18 second order single reactant (SR model) which incorporated in EPANET and EPANET 19 MSX, respectively. The results of the models are compared through two approaches, 20 one is the one-part approach (OPA) whereby chlorine decay simulation is performed 21 taking into account the whole line as one section and the second is multi-part approach 22 (MPA) whereby the line is divided into two sections and decay coefficients of chlorine 23 for each section are separately determined. Results show that in the OPA, the SR model 24 in summer and the parallel model in winter are the best kinetic models. While in the 25 MPA, the results of first order model has the same order of accuracy as the more 26 complex models of parallel and SR models. EPANET MSX s/w. The average RMSE volumes are reduced from 0.078 in OPA to 30 0.029 in MPA in summer and from 0.059 to 0.015 in winter, indicating that the dividing 31 the line in simulation procedure and considering the individual decay coefficient for 32 each part, considerably improves the results, more effectively than the application of 33 advanced decay models. 34

where ccl is the concentrations of chlorine (mg L -1 ), kb is bulk decay coefficient 66 (time -1 ), n is order of reaction, ccl * is the limited concentration of chlorine (mg L -1 ), kb1 67 and kb2 are bulk decay rate coefficients for fast and slow reactions, respectively (time -68 1 ), x is a fraction of the initial concentration, [React] is the concentration of the species 69 that react with chlorine, cf and cs are the concentrations of fast and slow reducing agents 70 respectively, and kbf and kbs are bulk decay rate coefficients for fast and slow reactions 71 respectively (L mg -1 time -1 ). x i,t is the concentration of the i th aqueous species at time t 72 that reacts with chlorine with rate constant ki [15]. Parallel and second-order 2R models 6 are developed, because some compounds in drinking water e.g. iron are fast reactive, 74 whereas some e.g. manganese are slow reactive [3,10,13]. The required time for fast 75 reactions is about 3 to 4 h [7]. Several studies are performed to investigate on the most 76 suitable bulk decay coefficients [3][4][5]10,16]. The SR model is simulated by combined 77 concentration of chlorine and other substances in the kinetic equations of decay. Eqs. 78 (8) to (10) formulated by Boccelli et al to simulate SR model [1]. 79 where CA is the concentration of chlorine, CB is the concentration of reactive 80 component, kA is decay rate coefficient for the chlorine, kB is decay rate coefficient for 81 the reactive component, and a and b are stoichiometry coefficients [1,17]. 82 The first order model is generally applied for the reaction of chlorine wall decay, as 83 Eq. (11): 84 = 4 ( + ) (11) where kf is the mass transfer coefficient (length divided by time), kw is the wall 85 reaction rate coefficient (length divided by time) and D is the pipe's diameter 7 [5,16,18,19]. The wall decay coefficient depends on characteristics of the distribution 87 pipes such as diameter, age, roughness, pipe material and the volume of biofilm formed 88 on the pipe surfaces [7,9,11]. 89 In order to simulate chlorine decay reactions, the bulk decay coefficient (kb) and the 90 wall decay coefficient (kw) need to be specified. In this study, the effect of dividing the water transmission pipe line in modeling 129 procedure, on improving residual chlorine prediction is of concern. For this purpose,  Table 1. 11  and 18°C as an average water temperature in winter and summer, respectively.

13
Determination of bulk decay coefficients based on water age were derived for OPA and 176 MPA at 6°C and 18°C, where the water age in the OPA is 0-82 h, while in the MPA it 177 is 0-18h in the first part and 18-82h in the second part at T= 18°C. 178 The result of the measurement of chlorine concentration at 18ºC is shown in Figure  179

185
The estimation of kb1 (the coefficient of fast reaction) and kb2 (the coefficient of 186 slow reaction) is necessary to apply the parallel first order model. Therefore, the kb 187 coefficients for kinetic models at 18° and 6° are calculated as shown in Figure 2. The 188 results are summarized in Table 2. 189   The correlation coefficients (R 2 ) between the results of the model and measurement are 216 0.958 and 0.978 for summer and winter, respectively, indicating that the hydraulic simulation is in acceptable level of accuracy. 218 The schematics of transmission line and the hydraulic simulation results for summer 219 flow condition is shown in Figure 3. The node colors in Figure 3 represent the water 220 age and the numbers adjacent to the lines show the maximum flow rate (L sec -1 .). Water 221 age is important in this analysis because when it is increased, the residual concentration 222 of disinfectant decreases and microorganisms' growth increases [2]. 223  The procedure of hydraulics and chlorine residual concentration for OPA and MPA 257 in EPANET is summarized in Figure 4. 258  According to Table 4, in the OPA simulation for T=18ºC, the SR and parallel models 274 with respectively RSME of 0.0425 and 0.0600, estimate chlorine consumption more 275 accurate than the first order model with RMSE equal to 0.0954. For T=6ºC in the OPA, 276 the parallel model performs better than SR and first order models. 277 Applying MPA with different bulk decay coefficients for each part, results in a 278 significant improve in the results, as indicated in Table 4. Therefore, a similar level of 279 accuracy achieved the three simulated kinetic models in MPA and applying first order 280 kinetic model in MPA is more effective than applying more complex kinetic models in 281 OPA. According to Table 4, the SR model in 18ºC and parallel model in 6ºC in both 282 approaches have minimum RMSE and are selected for wall decay coefficient 283 determination. 284

5.2.
Chlorine wall decay simulation 285 After selecting the best bulk decay models, the wall decay coefficient volume, kw 286 is estimated for the models. For this purpose, the model is run for a range of kw to obtain 287 the least RSME. In summer for example, the best wall decay coefficient of 0.04 m d -1 288 provides the least RMSE of 0.0668 mg L -1 for OPA, as shown in Figure 7. In MPA, the 289 wall decay coefficient is obtained for each part separately to reach to the least RMSE.   In the MPA, no significant advantages found between the kinetic models. In the 336 former approach, RMSE of the first order and the best kinetics models are 0.0290 and 337 each part (MPA) is more effective than applying most sophisticated kinetics models. 339 In the MPA, the bulk decay coefficient for the first and second parts is 0.204 and IWTL route Note: The designations employed and the presentation of the material on this map do not imply the expression of any opinion whatsoever on the part of Research Square concerning the legal status of any country, territory, city or area or of its authorities, or concerning the delimitation of its frontiers or boundaries. This map has been provided by the authors.

Figure 2
Bulk decay coe cient at 18 ° C with OPA and MPA using the bottle test   Comparison between observed and predicted chlorine concentration (mg L-1) in a) T=18°C and b) T=6°C