INTERNATIONAL JOURNAL OF CIVIL AND STRUCTURAL ENGINEERING Volume 2, No 2, 2011

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1 INTERNATIONAL JOURNAL OF CIVIL AND STRUCTURAL ENGINEERING Volume 2, No 2, 2011 Copyright 2010 All rights reserved Integrated Publishing services Research article ISSN Balancing reservoir based approach for solution to pressure deficient water distribution networks Suribabu 1- Associate Professor 2- Associate Dean (Research) & L&T Chair Professor Centre for Advanced Research in Environment (CARE), School of Civil Engineering SASTRA University, Thanavur, Tamilnadu, India ABSTRACT ydraulic simulation models that simulate the behavior of water distribution systems under pressure deficient conditions is becog an important tool for reliability assessments and also for deriving the operational strategies during the failure of components. The conventional demand driven analysis (DDA) cannot directly simulate the network under pressure deficient conditions. In such cases, pressure dependent analysis (PDA) is superior to DDA. This paper introduces a new approach for solving pressure-deficient condition by connecting balancing reservoirs named as complementing reservoir at the nodes having deficiencies. The basis of this proposed approach is to complement flow from a complementary reservoir to the pressure deficient node; while the complementary reservoir is an imaginary balancing reservoir and the complement flow to a node is actually the shortfall at the node. The new approach called CRS (Complementary Reservoir Solution) approach is demonstrated through few cases. The results indicate that the proposed approach CRS approach is a promising method. Keywords: Water distribution systems, reliability, demand driven analysis, pressure dependent analysis 1. Introduction Analyzing water distribution systems under pressure-deficient conditions is a subect of great importance for water utilities around the world (Wu, 2007). Conventional approach of demand-driven analysis cannot accurately predict the behavior of water distribution network under pressure deficient conditions. Tremendous focus has been given for integrated development of pressure dependent function in conunction with governing euations for hydraulic flow network analysis to simulate the real behavior of network during abnormal operating scenarios. In order to overcome the weakness of demand-driven analysis, Bhave (1981, 1991) developed a method called Node Flow Analysis (NFA). Further, several models have been developed to incorporate pressure-driven demand analysis into hydraulic analysis, network reliability analysis and leakage analysis (Wagner et al 1988; Reddy and Elango 1989; Chandapillai 1991; Jowitt and Xu 1993; Gupta and Bhave 1996; Fuiwara and Li 1998; Tucciarelli et al 1999; Tanyimboh et al. 2001; Ozger and Mays 2004; Ang and Jowitt 2006; Giustolist et al a and b; Wu et al. 2009). Despite dferent pressure-demand formulation exists in the literature; the relation proposed by Wagner et al. (1988) is widely used in such analysis. This paper introduces a new simple approach in which balancing reservoir is connected to pressure deficient node for deteration of actual demand that can be given to consumer under the specied imum pressure. Received on September, 2011 Published on November

2 2. Literature Review Analyzing water distribution systems under pressure-deficient conditions is a subect of great importance for water utilities around the world (Wu, 2007). Conventional demand-driven analysis cannot accurately predict the hydraulic characteristic of water distribution network under pressure deficient condition. Bhave (1981) proposed a node flow analysis (NFA) that deteres the nodal outflow considering head-discharge relationship and is given by 0< = re < = 0( no ( adeuate re ( partial = 1 Where - flow available at node, re - flow reuired at node, - imum reuired head at node under normal working condition. - available head at, In NFA, the imum pressure and available nodal heads and also the reuired and available nodal flows are considered simultaneously. Later, Germanopoulos (1985) presented an empirical relationship to detere the nodal outflow as follows c [( ) /( des )] re = (1 10 ) 2 where C node constant. The actual outflow at the node is calculated iteratively and in which each level of iteration reuires one complete demand driven analysis. Reddy and Elango (1989) proposed a head dependent analysis for uncontrolled outlet with reference to residual heads available at the node. The relationship is given below ( ) 0. 5 = S 3 where S node constant. Use of this expression, reuires either calibrated or reasonable assumed node constant. Wagner et al (1988) proposed a generic formula which relates the head and flow as given below = = re re = 0( no ( adeuate re 1/ n ( partial < < re 4 where n exponent constant (its value often taken as either 1.85 or 2). If full outflow is expected at imum pressure, then above expression can be written as, 640

3 = = re re = 0( no ( adeuate 1/ n ( partial 0 0< < 5 Chandapillai (1991) proposed a relationship between the actual nodal outflows and heads in response to imum head as n = + K ( 6 ) Gupta and Bhave (1996) reviewed dferent methods used for predicting the performance of water distribution system under pressure deficient conditions. It was found that NFA approach based on Wagner (1988) predicted the behavior of serial network example better than the other two approaches, namely Bhave (1981) and Germanopoulos (1985). Tanyimboh et al (2001) has shown the derivation for the Wagner s head-flow relation by rearranging the euation (6) within the limitation of = for =. Furthermore, des Tanyimboh et al (2001) presented a modied relation for the same expression relating source head and outflow at demand node. Tucciarelli et al (1999) suggested pressure dependent leakage relation as follows = = re re, = 0( no sin 2, 0< 0 < 7 Ozger (2003) presented the semi-pressure driven analysis (SPDA) framework using EPANET toolkits for predicting the performance of a network under partially failed conditions and the same is used for reliability assessment of the network. Ozger (2003) was perhaps the first to use the articial reservoirs for analysis of pressure deficient networks. Subseuent Ozger and Mays (2004) used SPDA for reliability assessment in association with optimization model for optimal location of isolation valves considering reliability aspects. Recently, Ang and Jowitt (2006) presented a novel approach named PDNA for analyzing water distribution systems under pressure deficient conditions and illustrated the behavior of the system that can result. Rossman (2007) discussed the possibility of implementing the PDNA proposed by Ang and Jowitt (2006) in EPANET (Rossman, 2000) hydraulic solver using emitter feature. More recently, Wu et al (2009) proposed a pressure dependent demand (PDD) function as below and it is integrated with the global gradient algorithm. 641

4 where = 0, = = re re thr 0 1/ n thr, < 8 n thr 1/ thr, - threshold pressure above which the demand is independent of nodal pressure. While comparing the results of serial network presented by Gupta and Bhave (1996) and Ang and Jowitt (2006), PDD could not maximize the outflow to the nodes which are not pressure deficient under demand driven analysis. The solution to the serial network example states that the need of compromising the reference (design) demand at non-pressure deficient nodes in order to satisfy the demand at pressure deficient nodes either fully or partially. 3. Proposed Approach In the proposed approach complementing reservoirs are connected progressively to the nodes which are facing pressure deficit. By addition of complementing reservoir (act as external source) to the nodes, the demand at deficit node is getting satisfied with imum pressure. The following definitions are used in this paper. Minimum reuired pressure or imum pressure means the pressure at a node below which no-supply is possible from that node. A Critical Node (CN) is a node which faces pressure deficiency. If there are more than one CN, a node which has maximum deficiency is called the Most Critical Node (MCN). A Complementary Reservoir (CR) is a balancing or fictitious reservoir or imaginary reservoir which is generally added to a CN to complement the flow to the CN in order to satisfy the demand at that node. After simulating the network with CRS approach, a CR is to supply only to the attached node and the supply should be less than or eual to the demand and the flow from a CR to a CN is called complementing flow and is actually shortfall at that node as the CR is an imaginary one. While connecting a complementary reservoir (CR) to a node, a pipe, whose resistance is negligible, is used. The CR elevation is same as that of hydraulic gradient level (GL) reuired at that node. Since the resistance is negligible, flow can take place from CR to the CN. The CR can supply to the CN only the CN is not getting enough supply from the main source. If the network is not able to supply sufficient uantity to the CN, the CR can complement and demand at the CN will thus be satisfied. Knowing the supply from the CR to the CN, the water supplied by the network to the CN can be calculated as the demand us the supply from the CR. Thus this is the uantity that can be supplied by the network at the imum pressure. This can be easily veried by adopting this uantity as demand at the CN and simulating the system. The step-by-step procedure of applying the CRS approach with reasons is presented below. 1. Once a network system is known as a deficient one, add a complementing reservoir to MCN (Most Critical Node - the node which shows maximum pressure deficit). Set the elevation of the complementing reservoir same as imum hydraulic grade reuired at the node. 642

5 2. Perform hydraulic analysis of the updated network and check the results. 3. Three cases are possible: (a) If there is another pressure-deficient node, the process needs to be continued. The CR connected to a critical node acts as another source reservoir at current state which may not supply to all critical nodes due to energy loss along the lines. ence, addition of CR is becog essential to other critical nodes. Go to step 1 and continue. (b) If there is no pressure-deficient node present; however, the complementing reservoir is supplying more than the demand at that associated critical node, it indicates that some more nodes have problem and needs further processing. A CR is to supply only to the attached node and the supply should be less than or eual to the demand. owever, in the process of hydraulic analyses, there are possibilities that a CR may supply to more than one node. The CN may generally be expected on an up-ground (where elevation is more than surroundings) or may be too far (energy loss is more for transport) from the source reservoir. If we add a CR for such a node, there is more possibility that apart from the critical node, the CR may supply water to other surrounding critical nodes too. As no CR should supply more than the reuired demand to the deficient nodes, addition of another CR is needed. Go to step 4 and continue. (c) If there is no pressure deficient-node present and the supply from the complementary reservoir is less than the demand of the associated node, then the process is over. Thus real supply possible to the node from the network is (demand complementary supply from CR). 4. Find the node at which the residual pressure is imum and add a complementary reservoir to that node setting the hydraulic gradient of the new CR is eual to that of old CR. It is to be noted that the CR at this state is added at the same hydraulic grade of the node to which it is attached, the supply from the previously added CR may flow to the new CR due to dference in hydraulic grade. ence the new CR should be at the same hydraulic grade of the first set CR. 5. Perform hydraulic analysis of the updated network and check the results. Check whether flow from node to CR is taking place. This can happen to a CR which is added in a previous step. As a newly added CR supplies some uantity to the system and the supply from the source reservoir is reduced; further re-routing of flow in the network also takes place. In this adustment, the node which was once deficit may now receive full supply from source reservoir with sufficient pressure. If flow is taking place from node to CR, remove that CR; add a CR to the node which is having next imum of the residual-pressures and go to step 5. Otherwise, go to step Demonstration with Single-loop Network The CRS approach is demonstrated with a simple, single-source, one-loop network presented in Fig.1. The network consists of a reservoir, four demand nodes and five links. The elevation of the reservoir is 20 m and all the demand nodes are at zero elevation. The diameters of the links are 400 mm, 350 mm, 300 mm, 250 mm and 250 mm respectively for links from 1 to 5. Each link is 1000 m long and azen-williams coefficient is 100 for all the links. The imum pressure head needed at each demand node is 15 m. The demands for nodes 2 to 5 are 20, 20, 25 and 35 l/s respectively under normal operating conditions. EPANET hydraulic network solver is used to simulate the water flow in distribution systems. Under normal operation, the node 5 gets imum pressure head of 15 m and all other demand-nodes are getting higher-pressure heads. Pressure-deficient conditions can be created in this network by breakage or isolation of the link 2 or 3 or 4 or 5. Table 1 shows the results obtained by demand-driven method (by EPANET) for normal operation and pressure- 643

6 deficient conditions with isolation of links 2, 3, 4 and 5, one at a time. According to the problem specication, the imum reuired pressure head at all demand nodes is 15 m. ence, we cannot draw water with pressure less than 15 m. owever, the demand-driven model assumes all the demands are met and provides pressure heads less than the imum reuired. For example, when link 3 is isolated, pressure at node 4 shows 2.36 m. The out flow at that node is possible only flow is drawn at an elevation less than or eual to 2.36 m. This states that no water can be drawn above 2.36m. If reduced demand is set at those pressure deficient nodes, there is possibility of meeting such a demand with imum reuired pressure of 15 m. Now the uestion is how to evaluate the reduced outflow at pressure deficient nodes that is satisfied against the imum nodal pressure. The CRS approach is demonstrated to estimate the reduced demand in the next paragraph. As per the CRS approach, the CR is connected at a demand node where the pressure deficiency is maximum. The first CR is set at an elevation eual to the imum G expected at the node where the CR is connected. The CR is connected to the demand node by a link with negligible resistance. In this study, a 300 mm diameter, 0.1 m length link with azen-williams coefficient of 100 is used for connection. When link 2 is isolated, the maximum pressure deficiency is at node 3. ence a CR is connected at node 3. Setting the CR s elevation as 15 m, the network is analyzed again. The flow from the CR takes place towards connected node in order to satisfy the designated demand at that node. Now analysis shows no pressure deficit at that node and flow is drawn from CR. owever, node 5 still suffers from pressure deficiency (14.47 m < 15 m). ence another CR is connected with node 5 at the same elevation of first CR and hydraulic analysis is carried out once again. Now none of the nodes suffer from pressure deficiency. Figure 1 shows the diagrammatic representation of CR data associated while link 2 is isolated. The CR at node 3 complements a supply of l/s, which indicates that source reservoir cannot supply this uantity of flow. The demand at node 3 is 20 l/s and the source reservoir supplies only ( =) 0.09 l/s. Similarly at node 5, CR complements a supply of l/s while the source reservoir supplies ( =) l/s. To check the results, hydraulic simulation may be performed again by setting these demands at nodal points and removing the complementary reservoirs. Table 2 provides the outflow and pressure head at nodes when dferent pipe fails. Status Table 1: Pressure head for single source one-loop network Pressure head (m) at Node 2 Node 3 Node 4 Node 5 Normal operation Link 2 isolated * 10.52* 2.13* Link 3 isolated * 2.36* 4.31* Link 4 isolated * 9.74* Link 5 isolated * * Denote pressure deficient node, ie pressure head less than 15 m. 644

7 20 m m m 2 (Isolated) 2 3 CR 15 m l/s 20 l/s 20 l/s 3 25 l/s 35 l/s m m CR 15 m l/s Figure 1: Flow and pressure head at nodes when link 2 is isolated Table 2: Outflows and pressure head for one-loop network under single link failure Status Outflows (l/s) and pressure head (m) Node 2 Node 3 Node 4 Node 5 Total outflow Link 2 isolated 20 (18.83) 0.09 (15.00) 25 (16.37) (15.00) Link 3 isolated 20 (18.73) 20 (17.45) 0.07 (15.00) (15.00) Link 4 isolated 20 (17.92) 20 (16.83) 25 (17.12) (15.00) Link 5 isolated 20 (18.19) 20 (17.94) 25 (16.03) (15.00) Demonstration with Other Networks A single-source two-loop network presented by Ang and Jowitt (2006) is considered for further illustration of the methodology. CRS approach and PDNA provide same results for all isolations except link 2 and link 3. It is found that PDNA could not provide realistic results for cases when link 2 or link 3 is isolated. PDNA ends in negative residual pressure heads as we get in demand-driven analysis. When link 2 is isolated, PDNA ends with negative residual pressure head (-2 m) at node 3. When link 3 is isolated, PDNA ends with negative residual pressure head (-0.76 m) at node 4. owever, for the above cases, the CRS approach provides partial outflow with imum pressure. While using PDNA, in order to bring the pressure to imum value at the critical nodes, the demand at that node should be reduced. owever, it is not possible in these cases since outflow is zero at the critical nodes. This limitation of PDNA is due to the reason that it supplies water from network to articial reservoir. owever, the CRS approach uses a reverse approach that the CR supplies to the network and hence does not face this limitation. The applicability of CRS algorithm is also tested using multiple source network presented by Ang and Jowitt (2006). The CRS approach provides the same results produced using the PDNA approach. The complete analysis and results of these two examples are available in Neelakantan and Suribabu (2010). 4. Conclusion An alternative method for the solution of pressure-deficit water distribution has been presented. The solution methodology is demonstrated through the networks used by Ang and Jowitt (2006). The approach developed in this paper provides a reliable, efficient means of explicitly detering the extent of shortfall in outflow that a network experiences under 645

8 pressure-deficient conditions. The basis of the method is to supplement nodal flow from complementary reservoir, therein maintaining the imum or reuired pressure. The uantity that is supplied by the complementary reservoir is the short fall in meeting designated demand at the node. The CRS approach is simple compared to PDNA as it involves lesser number of additions and removal of imaginary reservoirs; however further research may be reuired to identy the limitations, any. The solution algorithm presented here can easily be embedded with existing hydraulic network simulators such as EPANET to assess the behavior of network not only under pressure deficient condition but also helps to detere the actual outflow for defined pressure for a node under normal operating conditions. Acknowledgements The authors acknowledge the financial support of Department of Science and Technology, Government of India through their research grants SR/S3/MCE/07/2002-SERC-Engg and DST/TSG/WP/2007/07. The authors thank SASTRA University for providing facilities for this research. 5. References 1. Ang, W.K., and Jowitt, P.W., (2006), Solution for water distribution systems under pressure-deficient conditions, Journal of Water Resources Planning and Management, 132(3), pp Bhave, P.R. (1991), Analysis of flow in water distribution networks, Technomic Publishing Co., Lancaster, Pa. 3. Bhave, P.R., (1981), Node flow analysis of water distribution systems, Journal of Transportation Engineering, 107(4), pp Chandapillai, J., (1991), Realistic simulation of water distribution system, Journal of Transportation Engineering, 117(2), pp Fuiwara, O., and Li, J., (1998), Reliability analysis of water distribution networks in consideration of euity, redistribution, and pressure-dependent demand. Water Resources Research, 34(7), pp Germanopoulos, G., (1985,) A technical note on the inclusion of pressure-dependent demand and leakage terms in water supply network models, Civil Engineering Systems, 2(3), pp Giustolisi, O., Savic, D., and Kapelan, Z., (2008), Pressure-driven demand and leakage simulation for water distribution networks, Journal of ydraulic Engineering, 124(9), pp Gupta, R., and Bhave, P.R., (1996), Comparison of methods for predicting deficientnetwork performance. Journal of Water Resources Planning and Management, 122(3), pp Jowitt, P.W. and Xu. C., (1993), Predicting the failure effects in water distribution networks. Journal of Water Resources Planning and Management, 119(1), pp

9 10. Neelakantan, T.R. and Suribabu, C.R., (2010), Optimal rehabilitation and expansion of water distribution network, Research proect report, Department of Science and Technology, New Delhi. 11. Ostfeld, A., Kogan, D., and Shamir, U., (2002), Reliability simulation of water distribution systems single and multiuality, Urban Water, 4, pp Ozger, S., (2003). A semi-pressure-driven approach to reliability assessment of water distribution networks. Ph.D. Dissertation, Department of Civil and Environmental Engineering, Arizona State University, Tempe, Ariz. 13. Ozger, S.S., and Mays, L.W., (2004), Optimal location of isolation valves in water distribution systems: A reliability/optimization approach, ( wmays/ch07_mays_ pdf). 14. Reddy, L.S., and Elango, K., (1989), Analysis of water distribution networks with head dependant outlets, Civil Engineering Systems, 6(3), pp Rossman, L.A. (2000), EPANET programmer s Toolkit Manual, Water Supply and Water Resources Division, National Risk Management Research Laboratory, U.S. Environmental Protection Agency, Cincinnati. 16. Rossman, L.A., (2007), Discussion of Solution of water distribution systems under pressure-deficient conditions by W.K. Ang and P.W. Jowitt, Journal of Water Resources Planning and Management, 133(6), pp Suribabu, C.R. (2006). Optimal design of water distribution networks, PhD dissertation, SASTRA University, Thanavur, India. 18. Tanyimboh, T.T., Tabesh, M., and Burrows, R., (2001), Appraisal of source head methods for calculating reliability of water distribution networks, Journal of Water Resources Planning and Management, 127(4), pp Tucciarelli, T., Criisi, A., and Teri, D., (1999), Leak analysis in pipeline systems by means of optimal valve regulation, Journal of ydraulic Engineering, 125(3), pp Wagner, J.M., Shamir, U., and Marks, D.., (1988), Water distribution reliability: Simulation methods, Journal of Water Resources Planning and Management, 114(3), pp Wu, Z.Y., (2007), Discussion of Solution of water distribution systems under pressuredeficient conditions by W.K. Ang and P.W. Jowitt, Journal of Water Resources Planning and Management, 133(6), pp Wu, Z.Y., Wang, R.., Walski, T.M., Yang, S.Y., Bowdler, D., and Baggett, C.C., (2009), Extended global-gradient algorithm for pressure-dependent water distribution analysis, Journal of Water Resources Planning and Management, 135(1), pp