The Optimum Monitoring Location of Pressure in Water Distribution System

Transcription

1 water Article The Optimum Monitoring Location Pressure in Water Distribution System Sanghyun Jun 1 Hyuk Jae Kwon 2, * 1 Infra division, POSCO E&C, 241 Incheon tower daero, Incheon 22009, Korea; clays@poscoenc.com 2 Department Civil Engineering, Cheongju University, Chungbuk 28503, Korea * Correspondence: hjkwon@cju.ac.kr; Tel.: Received: 17 January 2019; Accepted: 10 February 2019; Published: 12 February 2019 Abstract: This study proposes two methods for determination optimum monitoring locations changes in a water distribution system. A sensitivity analysis method is used to calculate change in a junction due to change in dem at or junctions. A analysis method is used to calculate summation a junction due to change in dem at anor junction. These methods are applied to a small sample pipe network, pilot plant, small distribution system for verification. Furrmore, unsteady analysis sample pipe network an experiment in pilot plant are conducted to verify availability accuracy proposed methods. To verify methods, leakage at J-55 was artificially produced at pilot plant. The change was measured at five different combination groups sensor locations. From results, it was found that top ed group sensor locations, J-116, J-140, J-22, J-68, had highest s sensitivity. The results newly developed methods for determination monitoring locations are in good agreement with results unsteady Finally, proposed methods are applied to a real distribution system a small city as a test bed. It is found that proposed methods for determining monitoring locations changes in water distribution system are useful effective. Keywords: monitoring location; water distribution system; change; ; sensitivity 1. Introduction Real-time monitoring is important to detect leakage abnormal changes for efficient management water distribution systems. Water in a distribution system should be cautiously monitored since it is a very important matter for maintenance. An optimal determination method for monitoring locations is necessary because it is impossible to install gauges at every place in a water distribution system. From results furr development, it will be possible to take good care junctions that are more sensitive more contributive than or junctions, as determination method can detect abnormal changes leakage. Pudar Liggett [1] presented basic research developments about leakage sensing. They proposed that leakage detection problem can be solved by back-tracing method using gauges or flow meters. Leakage can be detected by a comparison between measurement according to changes in flow rate in orifice changes due to real leakage measurement. A sensitivity matrix can be used for determination monitoring locations. The sensitivity matrix showed that leakage amount location could be sensitively related to data size accuracy measurement. Water 2019, 11, 307; doi: /w

2 Water 2019, 11, Liggett Chen [2] proposed a monitoring method using unsteady reverse analysis in water distribution system. They used method characteristics for unsteady analysis also used time-lagged calculations. Misiunas et al. [3] proposed a method for breakage or leakage detection using unsteady They showed that leakage location can be detected by back-tracing velocity an unsteady wave. The size leakage could be estimated by unsteady wave particular shape wave due to a sudden break. Vitkovsky et al. [4] suggested inverse transient analysis method to estimate leakage location amount by unsteady wave. The shape unsteady wave is important for successive application inverse transient They conducted leakage experiments in laboratory to verify method. The experimental results showed that leakage amount was successfully estimated leakage location was correctly determined. Jun et al. [5] developed an algorithm to determine monitoring location based on effective index matrix a water distribution system. The installation gauges can be restricted as initial investigation can be exceeded. The proposed method estimated location online gauges by conducting a column search on effective index matrix. Moreover, method was applied to Cherry Hill distribution system to verify its efficiency. Cheong et al. [6] suggested a method to determine optimum location gauges using entropy ory. In ir study, entropy ory was applied to overcome shortcomings previous methods. For example, previous methods were difficult to apply for a specific area, which does not have systematic management, as se methods need to verify calibrate measured data. Furrmore, most previous works focused on determination junctions that can minimize measurement cost. In this study, two optimum determination methods gauge locations are proposed, namely sensitivity analysis Experiments were conducted to verify methods by measuring changes due to leakage in a real-size pilot plant. The relatively more sensitive monitoring locations according to changes due to leakage were selected compared with selected junctions from results sensitivity analysis The sensitivity analysis analyses can be used as determination methods for monitoring locations to detect leakage or abnormal situation in a water distribution system. These methods can be used to determine wher or where specific facility should be installed in water distribution system. 2. Determination Monitoring Location Figure 1 shows a sample pipe network with 15 pipes, 11 junctions, 1 distributing reservoir. Tables 1 2 show properties pipes dem at junctions. L is length pipe, J is junction, D is pipe diameter, C is Hazen-Williams coefficient. Q is dem at junction. Table 1. Pipe properties sample pipe network. Pipe L (m) D (cm) C Table 2. Dem at junctions. Junction Q (m 3 /s)

3 facility should be installed in water distribution system. 2. Determination Monitoring Location Figure 1 shows a sample pipe network with 15 pipes, 11 junctions, 1 distributing reservoir. Tables 1 2 show properties pipes dem at junctions. L is length pipe, J is junction, D is pipe diameter, C is Hazen-Williams coefficient. Q is dem at junction. Water 2019, 11, Figure 1. Sample pipe network. Figure 1. Sample pipe network Sensitivity Analysis According to Change in Hazen Williams Coefficient Firstly, head at junctions flow rate at pipes are estimated without any change in dem. Sensitivity analysis according to change in Hazen Williams coefficient is conducted to determine monitoring location for leakage detection. For example, steady analysis is conducted by changing Hazen Williams coefficient pipe 1 from 100 to 120. At same time, Hazen Williams coefficients or pipes are maintained as 100 original coefficient. Sensitivity analysis is conducted using following equation: S j = k h j /k (1) h j=1 j where k is number pipes, j is junction number, h j is original, h j is change at each junction due to change in Hazen Williams coefficient. Therefore, change due to change in Hazen Williams coefficient is summed up averaged by number pipes. The priority for junctions is estimated by sensitivity. Table 3 shows results sensitivity Table 3. Results sensitivity analysis according to change in Hazen Williams coefficient Junction Pressure Contribution Analysis According to Change in Dem The change at a junction due to change in dem can cause a change at anor junction. Therefore, at each junction can be quantitatively measured. In this study, is estimated by averaged change. The steady-state network analysis is conducted by creating an additional dem at a junction. At this point, original at each junction will change. The difference between ith junction jth junction divided by original at ith junction is averaged compared with each or. As shown in Equation (2), one junction to anor can be quantitatively estimated compared with each or. [ k ( ) ] hi h j C i = /k (2) j=1 where k is number pipes, i,j is junction number, h i is original head at i junction h j is head at j junction due to change in dem at i junction. h i

4 Water 2019, 11, h is original head at Water where 2019, k 11, is 307 number pipes, i, j is junction number, i 4 11 i junction h j is head at j junction due to change in dem at This i junction. equation This isequation used to estimate is used to how estimate how change at achange junction at a due junction to dem due to can dem affect can affect at anor at junction. anor The junction. steady-state The steady-state analysis is conducted analysis is by conducted changingby changing dem at each dem junction. at each Atjunction. this time, At analysis this time, results analysis suchresults as such as at each junction at each should junction be changed should as be changed dem as at dem specific at junction specific is changed. junction is Therefore, changed. Therefore, change at change j junction at according j junction toaccording sudden to change sudden in dem change at in dem i junction at to i junction originalto original at i junction at can be i junction summed can up be summed averaged up by averaged number by junctions; number this junctions; is called this is called i junction. The i junction. change The can be change estimated can at be each estimated time when at each time dem when at a junction dem is at changed. a junction Therefore, is changed. Therefore, number total number junctions total should junctions be should size be size matrix. The amount matrix. The change amount due change to dem due to is 0.02 dem m 3 /s is in 0.02 m sample 3 /s in pipe sample network. pipe network. Figure 2 shows Figure 2 flowchart shows for flowchart determination for determination monitoring locations monitoring using locations using Table 4 shows results Table 4 shows estimation. results The results show estimation. that The results show that J-10 was highest in sample pipe network. J-10 was highest in sample pipe network. Leakage simulation: produce leak at node i Analysis pipe network in steady state Calculate : No Is I = k? Yes Sort C i Determine monitoring location Figure 2. Flowchart for determination monitoring location using Table Table Results Results Junction Junction

5 Water 2019, 11, Pressure Sensitivity Analysis According to Change in Dem Pressure sensitivity analysis estimates change at a junction according to change in dem. The ratio change to original at each junction is summed up averaged by number junctions as sensitivity a junction. Therefore, number junctions should be size sensitivity matrix as steady-state analysis is conducted whenever dem conditions at each junction are changed. Pressure sensitivity, represented by Equation (3), is averaged differences ith junction due to change in dem. As shown in Equation (3), sensitivity each junction can be quantitatively estimated compared with each or. [ k ( ] hi h S i = i) /k (3) i=1 where k is number calculations, i is junction number, h i is original at i junction h i is changed at i junction according to change in dem at a specific junction. Table 5 shows results sensitivity analysis according to change in dem. Table 5. Results sensitivity analysis according to change in dem Junction h i Table 6 Equations (4) (5) can well explain sensitivity analysis The J-1 can be calculated by Equation (4) sensitivity J-1 is calculated by Equation (5). The number junctions is three number calculations is also three. [ ] (P1 A) + (P C 1 = 1 D) + (P 1 G) /3 (4) P 1 [ ] (P1 A) + (P S 1 = 1 B) + (P 1 C) /3 (5) P 1 Table 6. Examples at each junction according to simulation number. Simulation No. Pressure at J-1 Pressure at J-2 Pressure at J-3 0 P 1 P 2 P 3 1 A D G 2 B E H 3 C F I 3. Determination Monitoring Location Using Unsteady Analysis 3.1. Unsteady Analysis a Water Distribution System Unsteady analysis a pipe network shows flow rate at any location as a function time. Both continuity equation (Equation (6)) equation motion (Equation (7)) should be used in unsteady Although various methods were introduced to solve se two equations, results all methods were similar. The method characteristics [7 9] was selected for present study as it is numerically stable, accurate, convenient to use, has a short computation time. The equation motion continuity equation for method characteristics can be summarized as follows [9,10]: Q t + ga H x + f Q Q = 0 (6) 2DA

6 Water 2019, 11, c 2 Q ga x + H = 0 (7) t where Q represents flow rate, H is head, A is cross-sectional area pipe, c is speed wave, f is Darcy Weisbach friction coefficient. For present study, only friction loss is considered for head loss. Therefore, it is assumed that minor losses are negligible for present computations. Next, let us consider L 1 as equation motion L 2 as continuity equation. A linear combination equations, L = L 1 + λl 2 (where λ is Lagrangian multiplier) yields Equation (8). ( Q t ) ( Q H + λc2 + λga x t + 1 λ ) H + f Q Q = 0 (8) x 2DA It is noted that H = H(x, t) Q = Q(x, t). Thus, total derivatives may be written by chain rule as: dq dt = Q t + Q dx (9) x dt dh dt = H t + H dx x dt λ is defined by comparing Equation (8) with Equations (9) (10). In Equation (9), if dx dt is equal to λc 2, n first parensis Equation (8) is exactly same as Equation (9). In Equation (10), if dx dt is equal to λ 1, n second parensis Equation (8) is exactly same as Equation (10). Therefore, λ 1 = dx dt = λc2. λ = ± 1 c By using se equations, Equation (8) can be rewritten as: (10) (11) dq dt + ga c dh dt + f Q Q = 0 (12) 2DA dq dt ga c dh dt + f Q Q = 0 (13) 2DA Equation (12) is valid if dx dx dt = c. Furrmore, Equation (13) is valid if dt = c. The finite difference equations Equations (12) (13) can be written as follows: (Q n+1 i (Q n+1 i Q n i 1 ) + ga c (Hn+1 i Q n i+1 ) ga c (Hn+1 i H n i 1 ) + f t H n i+1 ) + f t 2DA Qn i 1 Qi 1 n 2DA Qn i+1 = 0 (14) Q n i+1 = 0 (15) where superscript n + 1 represents unknowns. The well-known stability convergence condition must be satisfied as: t x 1 (16) c In present study, c t/ x = 1 is used for stability condition for entire computation Results Unsteady Analysis Unsteady analysis was performed by method characteristics with assumption a sudden change in dem at each junction. It was assumed that an additional dem 0.02 m 3 /s occurred at each junction. At first calculation, it was assumed that a dem 0.02 m 3 /s suddenly occurred at J-1. Even though J-1 does not have dem, unsteady analysis was performed assuming that a dem abruptly occurred at J-1. At second calculation, unsteady analysis was performed assuming that an additional dem 0.02 m 3 /s occurred at J-2, which has a usual dem

7 Water 2019, 11, m 3 /s. The sensor location can be determined by sensitivity analysis for real leakage because a sudden additional dem can be considered as leakage at a specific junction. Table 7 shows change at each junction after unsteady A total 11 unsteady analyses were performed as shown in Table 7, as J-14 is considered as a reservoir neglected for calculation. Figure 3 shows oscillations at (a) J-7 (b) J-10. The analysis conditions t = s, x = 10 m, c = 1250 m/s (Courant Number = 1.0), Darcy Weisbach coefficient = were applied. As shown in figures, at J-10 responds more sensitively for change in dem. A change is defined as difference between maximum minimum due to a sudden change in dem. In Table 7, first row shows each junction next rows show change due to a sudden change in dem at each junction. The first column shows original piezometric head obtained from steady-state Piezometric Head (m) Table 7. Pressure change at each junction due to a sudden change in dem. No. J-2 (m) J-3 (m) J-4 (m) J-5 (m) J-6 (m) J-7 (m) J-8 (m) J-9 (m) J-10 (m) J-11 (m) J-12 (m) Water , 11, (a) (b) Figure 3. Pressure oscillations at (a) J-7 (b) J Determination Monitoring Location Using Using Results Unsteady Analysis Unsteady flow flow was was produced by by changing boundary condition by by introducing a sudden change in in dem. A sudden change in in dem can can cause a change that that can can be be observed at at any any place in in piping system. The The results unsteady analysis can can be be used for for determination monitoring locations. locations. Firstly, Firstly, height height due to due a sudden to a sudden change in change dem in should dem be should estimated. be The estimated. ratio The ratio height to height original to original at each junction at each is summed junction upis summed averaged up by averaged number by junctions number to compute junctions to compute sensitivity. In sensitivity. this study, sensitivity In this study, wassensitivity prescribedwas shown prescribed in Equation as shown (2) in Equation estimated. (2) Table estimated. 8 shows Table results 8 shows estimation results suggesting estimation top suggesting top sensor location. The first sensor location is determined as J-5, second is J-9, third is J-10. Table 9 shows results analysis using results unsteady As shown in Table 9, first sensor location is determined as J-9, second is J-5, third is J-12.

8 In this study, changes due to artificial leakage were measured at four arbitrary places. Water 2019, 11, sensor location. The first sensor location is determined as J-5, second is J-9, third is J-10. Table 9 shows results analysis using results unsteady As shown in Table 9, first sensor location is determined as J-9, second is J-5, third is J-12. Table 8. Results sensitivity analysis using results unsteady Junction Table 9. Results analysis using results unsteady Junction Applications to Pilot Plant Test Bed 4.1. Pilot Plant Figure 4 shows front view pilot plant. The pilot plant is constructed with one pump, 144 junctions, 179 cast iron pipes, which have same diameter 0.1 m. The length long side Water is 2019, approximately 11, m Figure 4. Front view pilot plant. Figure 4. Front view pilot plant. The proposed methods for determination monitoring locations were confirmed by unsteady The proposed It was proved methods that for methods determination are outsting monitoring because locations ir short were calculation confirmed time by unsteady simplicity. In this It was study, proved monitoring that methods location are in outsting pilot plant because was determined ir short by calculation time simplicity. analysis In this sensitivity study, analysis monitoring as shown location in Table in 10. The pilot first, plant second, was determined third ed by monitoring locations are analysis J-143, J-142, sensitivity J-141, analysis respectively. as shown However, in Table J-143, 10. The J-142, first, second, J-141 are third very ed last monitoring down streams locations are plant. J-143, Therefore, J-142, J-116 J-141, should respectively. be determined However, as J-143, top J-142, ed monitoring J-141 are location very last in down this pilot streams plant. plant. Therefore, J-116 should be determined as top ed monitoring location in this pilot plant. Table 10. monitoring location for pilot plant. Method Pressure Pressure sensitivity 1st 2nd 3rd 4th 5th 6th 7th 8th th

9 Water 2019, 11, Method 1st Table 10. monitoring location for pilot plant. 2nd 3rd 4th 5th 6th 7th 8th Pressure Pressure sensitivity th In this study, changes due to artificial leakage were measured at four arbitrary places. At first, monitoring location was determined by two methods. Pressure changes due to leakage were measured to confirm results monitoring location. Therefore, analysis sensitivity analysis were performed using measured change. From results analysis, first monitoring location was J-116, second, third, fourth were J-140, J-22, J-68, respectively. Therefore, first combination monitoring location is J-116, J-140, J-22, J-68. The leakage was produced at J-55 was measured at J-116, J-140, J-22, J-68. Five different combinations monitoring locations were used to measure at four different places. Figure 5 shows Combination 1 monitoring locations in pilot plant. The leakage point was fixed as J-55. Leakage amount was controlled by a valve at J-55 from m 3 /s to m 3 /s. Combination 1 is group top ed junctions such as J-116, J-140, J-22, J-68. The line upstream was maintained as 9 m (88,200 N/m 2 ). After fixing leakage location at J-55, five combinations four gauges measured changes according to artificial leakage. The nearest junctions to leakage location are J-68, J-27, J-70. Therefore, combinations are equally combined to avoid combination nearest junctions. Table 11 shows change in different combinations due to leakage at J-55. It is observed that Water 2019, 11, Combination 1 shows highest number for both sensitivity. Figure 5. Plan view pilot plant. Figure 5. Plan view pilot plant. Table 11. Results sensitivity measurement. Therefore, combinations are equally combined to avoid combination nearest junctions. Sensor Location for Pressure for Pressure Table Combination 11 shows Number (Junction change Number) in different combinations Sensitivity Analysis due to leakage Contribution at J-55. It is Analysis observed that Combination 1 shows highest number for both 1 22, 68, 116, sensitivity. 2 27, 70, 74, , 74, 114, Table 11. Results 27, 70, 114, 119 sensitivity 2 measurement. 3 5 Combination Number 68, 113, 134, 140 Sensor Location (Junction Number) 5 for Pressure Sensitivity Analysis 4 for Pressure Contribution Analysis 1 22, 68, 116, , 70, 74, , 74, 114, , 70, 114, , 113, 134,

10 Water 2019, 11, Therefore, combinations are equally combined to avoid combination nearest junctions. Table 11 shows change in different combinations due to leakage at J-55. It is observed that Combination 1 shows highest number for both sensitivity Test Bed A small block H city was selected for test bed as shown in Figure 6. In this area, 5000 people use this piping system, which contains 889 hydrants, 148 junctions, 162 pipes, 1 distributing reservoir. The house is a one- or two-story private house that has a rotop water tank. One distributing reservoir is only 15 m high in elevation supplies 802 m 3 /day ( m 3 /s) water. This pipe network consisted a 15-year old Polyvinyl Chloride (PVC) or Polyethylene (PE) pipe with a pipe diameter m. The length longest pipe is 298 m. Pressure analysis was conducted for test bed. Twenty-five junctions out 148 junctions were selected analyzed by changing dem at 25 junctions, as shown in Figure 6. The original dem at each 25th junction was changed by an additional dem m 3 /s. From results, it was found that top ed Water 2019, junction 11, 307 is J-138. As shown in Table 12, J-139, J-148, J-110, 11 J are second, third, fourth, fifth ed junctions, respectively. Figure 6. Small block pipe network test bed. Table 12. Figure Results 6. Small block pipe network analysis test for bed. test bed. Table 112. Results analysis 7 for 8 test 9bed. 10 Junction Junction Pressure analysis was conducted with same conditions analysis for test bed. From Pressure results, it was found analysis that was topconducted ed junction with same conditions analysis ratio isfor J-148. As test shown bed. From in Table 13, results, J-138, it J-139, was found J-110, that J-21 are top ed second, junction third, fourth, fifth ed junctions, ratio is J- respectively As shown Fromin Table results, 13, J-138, it was J-139, found J-110, that results J-21 are second, sensitivity third, analysis fourth, are similar fifth ed to results junctions, respectively. From results, it was found that results sensitivity analysis are similar to results Table 13. Results sensitivity analysis for test bed. Table 13. Results sensitivity analysis for test bed Junction Junction Conclusion In present study, two determination methods monitoring locations in a water distribution system were developed applied to a pilot plant a real test bed. The proposed methods were analysis sensitivity analysis, which were applied to pilot plant compared with experiments for verification. From results, it was found that top ed monitoring location was concentrated to downstream pilot plant piping system. Therefore,

11 Water 2019, 11, Conclusion In present study, two determination methods monitoring locations in a water distribution system were developed applied to a pilot plant a real test bed. The proposed methods were analysis sensitivity analysis, which were applied to pilot plant compared with experiments for verification. From results, it was found that top ed monitoring location was concentrated to downstream pilot plant piping system. Therefore, fourth, fifth, sixth, seventh ed monitoring locations, namely J-116, J-140, J-22, J-68, were chosen for monitoring location. To verify methods, leakage at J-55 was artificially produced at pilot plant. The change was measured at five different combination groups sensor locations. From results, it was found that top ed group sensor locations, J-116, J-140, J-22, J-68, had highest sensitivity. The analysis sensitivity analysis were applied to a small sample piping system. To verify two methods, unsteady analysis was conducted. The results proposed method were similar to results unsteady Finally, two methods were applied to a real distribution system a small city as a test bed. It was verified that newly developed methods monitoring locations were useful effective. These two methods can be applied to determine monitoring location to determine where a hydraulic device can be installed in a distribution system for operation management water supply system. For future study, two methods for monitoring location in a water distribution system will be tested by installing sensors in real water distribution system. Author Contributions: Conceptualization, H.J.K. S.J.; Methodology, H.J.K.; Investigation, H.J.K.; Writing Original Draft Preparation, H.J.K. S.J. Funding: This research received no external funding. Conflicts Interest: The authors declare no conflict interest. References 1. Pudar, P.S.; Liggett, J.A. Leaks in pipe networks. J. Hydraul. Eng. 1991, 118, [CrossRef] 2. Liggett, J.A.; Chen, L. Inverse transient analysis in pipe networks. J. Hydraul. Eng. 1994, 120, [CrossRef] 3. Misiunas, D.; Vitkovsky, J.; Olsson, G.; Simpson, A.; Lambert, M. Pipeline break detection using transient monitoring. J. Water Resour. Plan. Manag. 2005, 131, [CrossRef] 4. Vitkovsky, J.P.; Lambert, M.F.; Simpson, A.R.; Liggett, J.A. Experimental observation analysis inverse transients for pipeline leak detection. J. Water Resour. Plan. Manag. 2007, 133, [CrossRef] 5. Jun, H.D.; Cho, M.S.; Back, C.W.; Yoo, D.G.; Kim, J.H. A methodology to determine realtime monitoring locations for water distribution systems based on effect index matrix. In Proceedings KWAR Annual Conference, 22 May 2008; Korea Water Resources Association: Kyungju, Korea, 2008; pp Chung, G.H.; Chang, D.I.; Yoo, D.G.; Jun, H.D.; Kim, J.H. Determination Optimal Pressure Monitoring Locations for Water Distribution. J. Korea Water Resour. Assoc. 2009, 42, [CrossRef] 7. Chaudhry, H.M. Applied Hydraulic Transients; Springer: New York, NY, USA, Watters, G.W. Analysis Control Unsteady Flow in Pipe lines; Butterworths: Boston, MA, USA, Wylie, B.E.; Streeter, V.L. Fluid Transients in Systems; FEB Press: Ann Arbor, MI, USA, McInnis, D.; Karney, B.W. Transients in distribution networks: Field tests dem models. J. Hydraul. Eng. ASCE 1995, 121, [CrossRef] 2019 by authors. Licensee MDPI, Basel, Switzerl. This article is an open access article distributed under terms conditions Creative Commons Attribution (CC BY) license (