Abstract

Since governments all over the world are paying more attention to water quality in water distribution systems (WDS), a method based on mass balance and first-order chlorine decay model was proposed to assess the efficiency of WDS involving water quality (represented by residual chlorine). The concepts of surplus chlorine factor (S) for nodes in individual pipes and comprehensive surplus chlorine factor (CS) for nodes in WDS were put forward to represent the water quality characteristic of nodes in WDS based on the assumption that the structure of the pipe network and quantity of chlorine dose are definite. The proposed method was applied to two examples of WDS and sensitivity analysis regarding chlorine decay coefficient (k0) was discussed. The results indicated that values of CS for nodes in WDS are affected by the inflow of nodes, which is determined by water demand and pipe length from water sources to nodes. In addition, the value of CS increases with k0 when the inflow of the node is larger than the optimized inflow. The results verified that the deduction of S for a single pipe can be generalized to WDS, and can measure the water quality characteristics for nodes in WDS easily.

NOMENCLATURE

     
  • WDS

    Water distribution system

  •  
  • DOM

    Dissolved organic matter

  •  
  • m

    Chlorine decay quantity

  •  
  • q

    Flow within the pipe

  •  
  • Qin

    Pipe inflow

  •  
  • Qout

    Pipe outflow

  •  
  • Cin

    Residual chlorine concentration at the inlet

  •  
  • Cout

    Residual chlorine concentration at the outlet

  •  
  • min

    Chlorine entering the pipe at the inlet

  •  
  • mout

    Chlorine leaving the pipe at the outlet

  •  
  • k0

    First-order kinetic decay coefficient

  •  
  • L

    Pipe length

  •  
  • D

    Pipe diameter

  •  
  • (Cout)max

    Maximum chlorine concentration at the outlet

  •  
  • k

    Chlorine transfer efficiency

  •  
  • (Qin)opt

    Optimized pipe inflow

  •  
  • S

    Surplus chlorine factor

  •  
  • CS

    Comprehensive surplus chlorine factor

INTRODUCTION

Water quality in water distribution systems (WDS) is currently of widespread concern, which is influenced by a number of factors including the water age, water storage facility, and disinfectant methods (Mau et al. 1996). Chlorine is the most widely used disinfectant for preventing finished water from regrowth of microbial pathogens (Kim et al. 2015). Most of the chlorine dosed is consumed in reactions with other substances remaining in the water after treatment, particularly dissolved organic matter (DOM) (Fisher et al. 2012). Therefore, the concentration of residual chlorine is required to be kept at a certain level, especially in the extremities of WDS (Li et al. 2013; Blokker et al. 2014). The most widely used chlorine decay model in WDS is the first-order decay model, expressed by Equation (1) as follows: 
formula
(1)
where C is the concentration of chlorine, t refers to time, and stands for the chlorine decay coefficient (Hallam et al. 2002; Al-Jasser 2007; Fisher et al. 2011; Kim et al. 2014). In this paper, water quality characteristics of nodes in WDS based on the first-order chlorine decay equation mentioned above were analyzed.

The hydraulic characteristic and mechanical reliability of WDS have been much studied in the literature (Vaabel et al. 2006; Tanyimboh & Templeman 2007; Wu et al. 2011; D'Ercole et al. 2018). Mechanical reliability was defined as the probability that a component (new or repaired) experiences no structural failures (Kansal & Kumar 1995). The hydraulic reliability refers to the probability that a water distribution pipe can meet a required water flow level at a required pressure at each nodal demand (Ostfeld 2001). In order to increase the hydraulic capacity of a network and overcome sudden failures in WDS, the concept of hydraulic power capacity with consideration of both flow and pressure was identified (Vaabel et al. 2006). The hydraulic characteristic of nodes represented by the concept of surplus power factor based on hydraulic power was defined and applied to measure network resilience (Wu et al. 2011). However, both flow and water quality are of equal importance for WDS. The capacity concerning water quality for WDS has not been researched sufficiently in past studies (Gupta et al. 2012). Models have been developed of the chlorine concentrations at nodes in WDS with consideration of chlorine decay (Boulos et al. 1995; Mau et al. 1996; Hallam et al. 2002). The fraction of delivered quality (FDQ) was expressed to influence the water quality reliability, which is the ratio of simulation runs of supplied concentration below the threshold concentration to all the simulation runs (Ostfeld et al. 2002). Similarly, the ratio of days that the residual chlorine fulfills the residual chlorine standards to simulated days was proposed to represent water quality reliability (Zhao et al. 2010). The concept of node chlorine availability was proposed to define the water quality reliability of WDS (Li et al. 2013). The optimal operations of booster stations were proposed with the objective of minimizing the chlorine injection quantity (Tryby et al. 2002; Ostfeld & Salomons 2006; Kang & Lansey 2010). However, from the aspect of water quality management, the chlorine injection to WDS often remains fixed with no relationship to water demand. Under such circumstances, the water quality characteristics of nodes are affected by many factors, such as distance from water source to nodes, diameters and flows of pipes connecting with nodes, water demand of nodes, and chlorine decay coefficient, etc. The contribution of this paper is to research the degree of effect of various factors on water quality characteristics of nodes in WDS.

In this paper, first, based on the concepts of surplus chlorine factor (S) for nodes in single pipes deduced from a mass balance and first-order chlorine decay model, the concept of comprehensive surplus chlorine factor (CS) for nodes in WDS is proposed to analyze water quality characteristic of nodes in WDS. Second, CS was applied to measure the water quality characteristics in two examples of WDS based on an EPANET hydraulic and water quality extended simulation, and a sensitivity analysis of k0 to CS is presented. Finally, values of CS of nodes in WDS were measured and compared, and the factors affecting CS are indicated and discussed.

METHODOLOGY

Surplus chlorine factor (S) for individual pipe

The ideal parameter for assessing water quality reliability should have clear physical meaning, be able to distinguish nodes in WDS, and be easy to calculate. Based on mass balance and the chlorine-decay model, we can obtain Equations (2) and (3) from the individual pipe shown in Figure 1. The quantity of decayed chlorine is termed m, and the flow within the pipe is termed q. 
formula
(2)
 
formula
(3)
where Qin is the inflow of the pipe (L/s), Qout is the outflow of the pipe (L/s), Cin is the concentration of residual chlorine at the inlet of the pipe (mg/L), Cout is the concentration of residual chlorine at the outlet of the pipe (mg/L), is the quantity of chlorine entering the pipe per second at the inlet (mg/s), and is the quantity of chlorine leaving the pipe per second at the outlet (mg/s). Suppose residual chlorine decay follows the first-order kinetic reaction equation, the concentration of residual chlorine at the outlet is expressed by Equation (4) as follows: 
formula
(4)
where is the first-order kinetic decay coefficient (s−1), and are the length (m) and diameter (m) of the single pipe, respectively.
Figure 1

Flows, concentration and chlorine loss for individual pipe.

Figure 1

Flows, concentration and chlorine loss for individual pipe.

Obviously, we can obtain Equations (5) and (6) for an individual pipe (shown in Figure 1), expressed as follows: 
formula
(5)
 
formula
(6)
In Equation (4), L, D, , and are usually known; however, varies depending on the event. Therefore, in Equation (4) can be expressed as a function of expressed by . The aim of this paper is to study the variation of , and try to find the variation pattern of with under the condition that the injection quantity of chlorine is definite. The optimized value of is to make the outlet chlorine concentration reach the maximum value so as to get the water quality at the best operational condition. Therefore, according to Equation (4), with the assumption that , we can deduce that gets its maximum value when can satisfy the condition expressed by Equation (7), as follows: 
formula
(7)
where is the optimized value of .
Accordingly, reaches the maximum value, which can be expressed by Equation (8) as follows: 
formula
(8)
where is the available maximum value of , corresponding to . From Equation (8) we can find out that has relationships with the pipe characteristics (length L and diameter D), chlorine decay constant k0, and the input chlorine quantity min. Therefore is a definite value for a given pipe. Usually the actual flow in a pipe is different from , thus the actual chlorine concentration at the outlet is often different from . Therefore, to assess the chlorine transfer efficiency, we can obtain Equation (9), expressed as follows: 
formula
(9)
where k refers to the chlorine transfer efficiency.
By combining Equations (4) and (7), the coefficient k can also be expressed by Equation (10) as follows: 
formula
(10)
In order to simplify Equation (10), parameter was defined by Equation (11) as follows: 
formula
(11)
In addition, can also be expressed by Equation (12) as follows: 
formula
(12)
Therefore, Equation (10) was transformed into Equation (13) as follows: 
formula
(13)

The relationship curve between k and is shown in Figure 2, where k is presented as a function of or . The scope of k is between 0 and 1.0. In effect, the water quality characteristics of WDS get better when the chlorine concentration at the outlet is higher. If , reaches the maximum value , which means that the pipe works at the best condition from the viewpoint of water quality corresponding to value of being 1.0 (also shown in Figure 2).

Figure 2

Relationship curves of surplus chlorine factor (S) and chlorine transfer coefficient (k) with .

Figure 2

Relationship curves of surplus chlorine factor (S) and chlorine transfer coefficient (k) with .

Since the coefficient k characterized the potentiality of chlorine concentration of the node, the concept of surplus chlorine factor (S) was proposed to represent the water quality characteristic of the node, expressed by Equation (14) as follows: 
formula
(14)
where S refers to surplus chlorine factor (S), which is applied to assess the characteristic of the node in view of water quality. The scope of S is between 0 and 1, which is similar to k. If S decreases, water quality reliability of WDS will be improved. When S decreases to 0, reaches , which means WDS work with maximum chlorine concentration at the outlet.
From Figure 2, we can also find that when decreases or increases from , always decreases. Combining Equations (13) and (14), we can also conclude that if or is fixed, k and S remain unchangeable. When varies in the range from 0 to 1.0, with the rise of , k increases and S decreases. On the contrary, when varies in the range from 1.0 to ∞, with the rise of , k decreases and S increases. The reason can be explained as follows. From Equation (14), we can deduce Equation (15), expressed as follows: 
formula
(15)

From Equation (15), we can find that when is bigger than 1.0, i.e. is in the scope of (0, 1.0), is greater than 0, which means that S decreases with the decrease of or the rise of . Similarly, when is smaller than 1.0, i.e. is in the scope of (1.0, ∞), is smaller than 0, which means that S increases with the decrease of or the rise of .

Relationship between surplus chlorine factor (S) and Qin under different chlorine decay constant k0

From Equations (10), (11), and (14), we can find parameters k and S vary with the decay coefficient k0 for the individual pipe. The chlorine decay coefficient k0 varies with flow velocity and temperature (Blokker et al. 2014). From Equation (8) we can draw the conclusion that always decreases with the increase of k0 when the other factors remain the same, which means that chlorine decay coefficient k0 affects the reachable maximum chlorine concentration negatively. In addition, with the increase of k0, the value of increases according to Equation (7), which means that water flow in the pipe will increase to meet the chlorine concentration of at the outlet. With the increased chlorine decay coefficient of k0, the chlorine concentration at the outlet decreases. Therefore, the variation of k and S with k0 depends on the relative increased degrees of and . The relationship curves between S and Qin under different values of k0 are shown in Figure 3. The values of k0 ranged from +20% to −20%.

Figure 3

Relationship curves between surplus chlorine factors (S) and Qin under different k0.

Figure 3

Relationship curves between surplus chlorine factors (S) and Qin under different k0.

With the increase of , S decreases from 1.0 to 0 initially, then increases with the rise of . When the value of S is 0, reaches the best value of . For a specific curve with certain k0, when is less than , S decreases with the rise of . On the contrary, if is greater than for certain k0, S increases with the rise of . The values of vary with k0. When k0 increases, also increases, which is in accordance with Equation (7). Among all the values of , is the smallest, corresponding to 0.8k0, and is the biggest, corresponding to 1.2k0. From Figure 3 we can also find that when is less than , the higher the chlorine decay coefficient k0 is, and the greater S is for the same . However, when is greater than , the higher the chlorine decay coefficient k0 is, and the smaller S is for the same . The reason can be explained by the fact that when is less than , is always bigger than 1.0. From Equation (15), we can obtain that is greater than 0. Therefore, if k0 increases, then increases correspondingly according to Equation (11), which leads to the rise of S that coincides with the curve in Figure 3. Moreover, when is greater than , then is always smaller than 1.0, which leads to being less than 0. Therefore, if k0 increases, then increases correspondingly according to Equation (11), which leads to the decline of S that also coincides with the curve in Figure 3.

Comprehensive surplus chlorine factor (CS) for water distribution network

The consideration for the individual pipe can also be generalized for WDS. For a pipe net consisting of two pipes, shown in Figure 4, node n was connected with two single pipes.

Figure 4

Flows, concentration, and chlorine loss for a pipe net.

Figure 4

Flows, concentration, and chlorine loss for a pipe net.

From Figure 4, we can obtain Equations (16)–(18), expressed as follows: 
formula
(16)
 
formula
(17)
 
formula
(18)
where is the flow of node n, is the flow in pipe ① connecting with node n, is the flow in pipe ② connecting with node n.
The value of CS for node n is calculated by Equation (19) as follows: 
formula
(19)
where CS is the comprehensive surplus chlorine factor for node n, Si (i= 1, 2, …, K) is the surplus chlorine factor for node n through the ith pipe, Qi (i= 1, 2, …, K) is the flow of the ith pipe connecting with node n, and K is the number of pipes connected with node n.

For a given WDS that consists of multiple pipes, water sources and nodes, CS for nodes varies with the inflow to nodes, length of pipes from water sources to nodes, diameters of pipes connecting with nodes, water demand of nodes, and chlorine decay coefficient k0, etc. For a certain node in WDS, the length of pipes from water sources to nodes and the diameters of pipes connecting with nodes are determined beforehand. However, the inflow of a node is variable depending on water demand by users, including residents and industrial enterprises. The chlorine decay coefficient k0 varies with the water quality, water temperature, and the pipe material. Therefore, values of CS for nodes in a given WDS usually vary with water demand and chlorine decay coefficient k0. For nodes in a WDS, the length of pipes from water sources to nodes and the diameters of pipes connecting with nodes are different. The values of CS for nodes vary with the differences in pipe lengths and pipe diameters.

RESULTS AND DISCUSSION

Example 1

Base run

The proposed methodology was demonstrated for a small illustrative system shown in Figure 5 (Rossman 1994). The initial residual chlorine of the water works was supposed to be 0.5 mg/L. During the hydraulic simulation progress of EPANET2, the Hazen–Williams function was used as the hydraulic simulation model, and the roughness coefficient was assumed to be 100. During the water quality simulation progress, the chlorine decay coefficient k0 was set to be −1.55/day (Rossman 1994).

The system consists of 12 pipes, a water source, a pump, and an elevated storage tank. The system is subject to a 24-h representative demand pattern shown in Table 1.

Table 1

24-h demand pattern characteristics for example (Rossman 1994)

Time of day 1–2 3–4 5–6 7–8 9–10 11–12 13–14 15–16 17–18 19–20 21–22 23–24 
Multiplier of base demand 1.0 1.2 1.4 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.6 0.8 
Time of day 1–2 3–4 5–6 7–8 9–10 11–12 13–14 15–16 17–18 19–20 21–22 23–24 
Multiplier of base demand 1.0 1.2 1.4 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.6 0.8 

The pump is fed by a source that is at a constant water level of 243.8 m. The water is delivered to a storage elevated tank at node 2 (at a ground level of 259.1 m), and to eight consumers located at nodes 11, 12, 13, 21, 22, 23, 31, and 32. The pump has a shutoff head value of 101.3 m and a maximum flow rate of 189.3 L/s. The tank is cylindrical with a diameter of 15.4 m. Its minimum, initial, and maximum levels above ground are 30.5 m, 36.6 m, and 45.7 m, respectively. The results of the base run for the case study are shown in Figure 6 and Table 2.

Table 2

Average comprehensive surplus chlorine factors (CS) in 24 h for nodes in Figure 5

Nodes 11 12 13 21 22 23 31 32 
Average values of CS 0.55 0.71 0.49 0.68 0.55 0.25 0.59 0.47 
Nodes 11 12 13 21 22 23 31 32 
Average values of CS 0.55 0.71 0.49 0.68 0.55 0.25 0.59 0.47 
Figure 6

Variation curves of time multiplier and comprehensive surplus chlorine factor (CS).

Figure 6

Variation curves of time multiplier and comprehensive surplus chlorine factor (CS).

The variation curves of the time multiplier and comprehensive surplus chlorine factors (CS) for all nodes in 24 h calculated by Equation (19) are shown in Figure 6. We can also find that for almost all nodes besides node 13, values of CS were the smallest at the 19th–20th hour when water demand is also the least, which means that values of CS for nodes vary with characteristics of the demand pattern for these nodes. It can be explained that when water demand decreases, the flow decreases accordingly, which leads to direct increase of under the condition that chlorine injection is fixed. The outlet concentration increases with , which leads to the increase of k and decrease of S. The condition is consistent with the case for a single pipe, shown in Figure 3, when is greater than .

For comparing water quality characteristics of nodes in WDS, the average values of CS for nodes in 24 h are shown in Table 2.

From Table 2, we can find that the average value of CS for node 23 is significantly less than other nodes. The reason for this is that values of for all nodes are greater than obtained by Equation (7), and is always less than 1.0, but for node 23 is closer to , since node 23 is the terminal node of the pipe network. Therefore, for node 23 is closer to 1.0 than other nodes according to Equation (11), which leads to a smaller value of CS. The conclusion is in accordance with the case shown in Figure 3 for a single pipe; that is, the closer the node inflow is to , the smaller CS is for the node.

Sensitivity analysis

Since chlorine decay coefficient k0 is of significant importance in WDS, the sensitivity analysis of k0 to CS is performed. The decay coefficient k0 is set to vary from −20% to +20% compared with k0 in the base run keeping other data the same as that in the base run. The results of average values of CS for all nodes are shown in Table 3. We can observe that values of CS for nodes 11, 13, 22, 23, 31, and 32 decrease with the increase of k0. Although node 12 and node 21 do not comply with the conclusion completely, the variation trends of CS with k0 are the same as other nodes. Based on Figure 3, the relationship between S and k0 depends on Qin for individual pipes. According to the analysis above, that values of for all nodes are greater than , S decreases with the rise of k0. Although a water distribution network is more complex than an individual pipe, the calculations of CS are on the basis of S of individual pipes. Therefore, the variation trend of average values of CS for all nodes with chlorine decay coefficient k0 can be explained by the conclusions resulting from individual pipes.

Table 3

Average comprehensive surplus chlorine factor (CS) for all nodes in Example 1 (k0 varies from −20% to +20%)

Nodes Chlorine decay coefficient
 
0.8k0 0.9k0 k0 1.1k0 1.2k0 
11 0.64 0.61 0.55 0.54 0.51 
12 0.79 0.76 0.71 0.72 0.70 
13 0.59 0.55 0.49 0.48 0.45 
21 0.79 0.77 0.71 0.72 0.70 
22 0.63 0.60 0.55 0.55 0.52 
23 0.34 0.30 0.25 0.23 0.20 
31 0.68 0.64 0.59 0.58 0.55 
32 0.57 0.53 0.47 0.46 0.43 
Nodes Chlorine decay coefficient
 
0.8k0 0.9k0 k0 1.1k0 1.2k0 
11 0.64 0.61 0.55 0.54 0.51 
12 0.79 0.76 0.71 0.72 0.70 
13 0.59 0.55 0.49 0.48 0.45 
21 0.79 0.77 0.71 0.72 0.70 
22 0.63 0.60 0.55 0.55 0.52 
23 0.34 0.30 0.25 0.23 0.20 
31 0.68 0.64 0.59 0.58 0.55 
32 0.57 0.53 0.47 0.46 0.43 

In addition, the hourly variations of CS for node 21 and node 23 are shown in Figures 7(a) and 7(b).

Figure 7

Variation of comprehensive surplus chlorine factor (CS) for (a) node 21 under various k0 and (b) node 23 under various k0.

Figure 7

Variation of comprehensive surplus chlorine factor (CS) for (a) node 21 under various k0 and (b) node 23 under various k0.

We can find from Figure 7(a) that although node 21 does not comply with the conclusion that average values of CS decrease with the increase of k0, the hourly variation of CS corresponding to k0 is the same as other nodes; that is, CS decreases with the increase of k0, which is in accordance with the case shown in Figure 3 when is greater than .

We can also find from Figure 7(b) that although average values of CS for node 23 follow the conclusion that average values of CS decrease with the increase of k0, the hourly variation of CS does not follow the same conclusion for the valley hour of 18 h–19 h. The reason is that the inflow of node 23 is smaller than other nodes, and when the water demand is lower, the inflow of node 23 becomes lower than , which leads to the increase of CS with k0. The conclusion is also is in accordance with the case shown in Figure 3, when is less than; that is, the higher the chlorine decay coefficient k0, the bigger the water quality characteristic CS for the node.

Comparing results in Figures 7(a) and 7(b), hourly values of CS for node 21 are greater than hourly values of CS for node 23. The reason is that at node 23 is smaller than at node 21, and is closer to , which leads to the values of CS for node 23 being less than the values of CS for node 21, which means that the water quality characteristic of node 23 is better than node 21.

The variations of CS for all nodes under various k0 corresponding to peak hour (8th hour) and valley hour (19th hour) were analyzed and are shown in Figures 8(a) and 8(b).

Figure 8

Variation of comprehensive surplus chlorine factor (CS) at (a) peak hour (8th hour) for all nodes under various k0 and (b) valley hour (19th hour) for all nodes under various k0.

Figure 8

Variation of comprehensive surplus chlorine factor (CS) at (a) peak hour (8th hour) for all nodes under various k0 and (b) valley hour (19th hour) for all nodes under various k0.

From Figure 8(a), we can conclude that at peak hour (8th hour), values of CS for all nodes decrease with the increase of k0, which is in accordance with the results above. Moreover, under various k0, values of CS decrease in the order of node 21 > node 12 > node 31> node 11 > node 13> node 22 > node 32> node 23, which means that at peak hour the water quality characteristic is best at node 23, and worst at node 21. However, from Figure 8(b) at the valley hour (19th hour), we can find that the variation trend of CS for almost all nodes decreases with the rise of k0 except for node 23, which is similar to the peak hour (8th hour). For node 23 at the valley hour (19th hour), the values of CS increased with the rise of k0, which means that the water quality characteristic of node 23 became worse with the increase of k0. The values of CS decreased in the order of node 21 > node 12> node 22 > node 31 > node 11 > node 32> node 13 > node 23.

Comparing results in Figures 8(a) and 8(b), values of CS at the peak hour (8th hour) are greater than at the valley hour (19th hour), which is in accordance with results obtained from Figure 6. When water demands at the valley hour are lower than water demands at the peak hour, the water quality characteristics of nodes are improved.

Example 2

In this case, the concept of CS for the node was applied to a real-life network shown in Figure 9 (Example 3 of EPANET software (Rossman 1994)). The system consists of two sources, one elevated tank, 117 pipes, 97 demand nodes, and two pumps (the complete data used were exactly as that of Example 3, in Rossman (1994), and thus are not repeated here). The coefficient of chlorine decay was set to be −1.55/day.

Figure 9

Example 2.

Figure 9

Example 2.

The results of CS for typical nodes in Example 2 are shown in Table 4.

Table 4

Average comprehensive surplus chlorine factor (CS) for nodes in Example 2

Nodes Water demand of nodes (L/sInflow of nodes (L/sOutflow of nodes (L/sDiameters of pipes connected with nodes (mm) Average comprehensive surplus chlorine factor (CS
11 11.245 11.245 0.000 400, 400 0.848 
15 11.983 34.687 22.704 300, 300, 300, 300 0.964 
19 14.869 470.546 455.677 750, 750, 300, 300 0.969 
27 0.497 8.890 8.393 200, 200 0.873 
30 2.332 6.953 4.621 300, 300 0.662 
35 4.372 384.523 380.151 750, 750 0.957 
38 0.795 359.491 358.696 750, 750, 350 0.990 
40 0.219 0.219 0.000 350 0.211 
44 0.000 75.843 75.843 750, 600 0.998 
49 0.000 5.069 5.069 200, 300 0.998 
64 0.000 45.475 45.475 300, 300 0.996 
70 3.488 3.488 0.000 350 0.698 
73 1.391 1.391 0.000 300 0.520 
86 0.000 36.040 36.040 300, 200, 300 0.976 
91 0.000 31.084 31.084 300, 200, 300 0.972 
92 0.000 30.837 30.837 300, 200, 300 0.996 
Nodes Water demand of nodes (L/sInflow of nodes (L/sOutflow of nodes (L/sDiameters of pipes connected with nodes (mm) Average comprehensive surplus chlorine factor (CS
11 11.245 11.245 0.000 400, 400 0.848 
15 11.983 34.687 22.704 300, 300, 300, 300 0.964 
19 14.869 470.546 455.677 750, 750, 300, 300 0.969 
27 0.497 8.890 8.393 200, 200 0.873 
30 2.332 6.953 4.621 300, 300 0.662 
35 4.372 384.523 380.151 750, 750 0.957 
38 0.795 359.491 358.696 750, 750, 350 0.990 
40 0.219 0.219 0.000 350 0.211 
44 0.000 75.843 75.843 750, 600 0.998 
49 0.000 5.069 5.069 200, 300 0.998 
64 0.000 45.475 45.475 300, 300 0.996 
70 3.488 3.488 0.000 350 0.698 
73 1.391 1.391 0.000 300 0.520 
86 0.000 36.040 36.040 300, 200, 300 0.976 
91 0.000 31.084 31.084 300, 200, 300 0.972 
92 0.000 30.837 30.837 300, 200, 300 0.996 

For nodes at the extremities of the WDS in Example 2, the average values of CS were lower than other nodes, which are 0.662, 0.221, 0.698, and 0.52 for node 30, 40, 70, and 73, respectively. The reason is that the inflows of nodes 30, 40, 70, and 73 are 6.953, 0.219, 3.488, and 1.391 L/s, respectively, lower than other nodes, which leads to the decrease of CS, and improvement of the water quality characteristic of nodes. Moreover, the smaller inflow of nodes leads to a lower value of CS. For example, the inflows of the four nodes increase in the order of node 40 < node 73 < node 30 < node 70. Accordingly, the values of CS for the four nodes increase in the same order. Although the inflow of node 27 is less than node 11, the pipe diameter connecting to node 27 is smaller than node 11, which leads to the value of CS at node 27 being larger than the value of CS at node 11. The reason for this is that is affected by pipe diameter, pipe length from water sources to node, and inflow of nodes together, which is shown in Equation (11). The value of determines the water quality characteristic of nodes expressed by CS.

CONCLUSION

In this paper, the concept of surplus chlorine factor (S) for a node in a single pipe based on the mass balance and first-order chlorine decay model was deduced. The relationship between S and , and the variation under different k0 for a single pipe were revealed. In addition, comprehensive surplus chlorine factor (CS) for nodes in WDS based on S was put forward, and applied to two examples of WDS during 24 h in a day (shown in Figures 5 and 9). The results indicated that the value of CS decreases with the decrease of inflow at the node, which is caused by lower water demand and longer pipe length from water sources to node. In addition, average values of CS decrease with the increase of chlorine decay coefficient k0. The conclusions are in accordance with the results obtained from a single pipe when is greater than. When the inflow at the node which is further from water sources becomes lower than at the valley hour, the value of CS increases with the increase of chlorine decay coefficient k0. In addition, the diameters of pipes connecting with nodes also affect the water quality characteristics of nodes; that is, the larger the pipe diameter, the better the water quality characteristics of nodes. The proposed method was proved to be efficient and easy to use for analyzing the water quality characteristic of nodes in WDS.

ACKNOWLEDGEMENTS

This work was funded by the Special S & T Project on Treatment and Control of Water Pollution from Bureau of Housing and Urban-rural Development of Jiangsu Province numbered as 2014ZX07405002.

REFERENCES

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