A SEMI-PRESSURE-DRIVEN APPROACH TO RELIABILITY ASSESSMENT OF WATER DISTRIBUTION NETWORKS S. S. OZGER PhD Student, Dept. of Civil and Envir. Engrg., Arizona State Univ., 85287, Tempe, AZ, US Phone: +1-480-965-3589 Fax: +1-480-965-0557 E-mail: sozger@asu.edu L. W. MAYS, Ph.D., P.E., P.H. Prof., Dept. of Civil and Envir. Engrg., Arizona State Univ., 85287, Tempe, AZ, US Phone: +1-480-965-3589 Fax: +1-480-965-0557 E-mail: mays@asu.edu ABSTRACT: Hydraulics of water distribution networks can be approached from two different perspectives. In demand-driven analysis, primacy is given fully to nodal demands regardless of actual pressures. Pressure-dependent approach, on the other hand, recognizes a relationship between nodal heads and nodal flows. While the demand-driven approach works well under normal operating conditions, recent research has shown that the pressure-driven approach produces much more realistic results under partially failed conditions of a network and should be used primarily for reliability assessment of water distribution networks. Practical difficulties of using pressure-driven analysis, including field data assembly and calibration of the models and the absence of robust methods for their computational solutions, have made it very desirable that techniques based on existing demand-driven techniques be developed for predicting deficient network performances and reliability assessments of water distribution networks. This paper describes the development and application of a semi-pressure-driven approach, DD-ADF method, around one of the most commonly used network hydraulic models, namely EPANET. Example applications demonstrate that unrealistic results from an initial demand-driven analysis in the form of pressure deficiencies could be transformed into partial fulfillment of nodal demands without losing computational efficiency. Keywords: water distribution networks, reliability, pressure-driven, demand-driven INTRODUCTION Early work in the optimal design and operation of water distribution systems considered cost as the main obective to be minimized subect to meeting consumer demands under a range of desired pressures. In the last decade or so, however, the water industry and researchers have began considering water quality and reliability as two additional maor concerns in design and operation of water distribution systems. Reliability assessment of water distribution networks requires prediction of deficient network performance under a range of partially failed conditions including but not limited to simulation of fire-flow demands, pipe breaks, valve breaks, pump failures, high demand loadings etc. Hydraulics of a water distribution network can be approached from two different perspectives. The difference between them comes from the level of primacy given to nodal demands vs. nodal pressures. The first approach assumes that consumer demands are always satisfied regardless of the pressures throughout the system and formulates the constitutive equations accordingly to solve for the unknown nodal heads. This approach is called demand-driven analysis and is used by almost all the traditional network hydraulic solvers, such as EPANET by Rossman (1994) and KYPIPE by Wood (1980). 1
The maor drawback of the demand-driven approach is that it fails to measure a partially failed network performance that may result from abnormalities in physical and non-physical system components (e.g., pipe breaks, fire-fighting demands etc.). In such cases, if demand-driven analysis is used, it may produce very unrealistic results. For example, it would not be surprising to see such warning messages as Negative pressures at 6:00 hrs. from the EPANET model while nodal demands are presumed fully satisfied during the same time period. In reality, the volume of water delivered to a node begins to shortfall of the required demand as the pressure at that node falls below some threshold value. Almost all demand-driven models possess a partial recognition of this weakness with similar warning messages when negative pressures are calculated from a network hydraulic analysis. The second approach to network hydraulic analysis is called head-driven (also called pressuredriven or pressure-dependent) analysis. Here, the primacy is given to pressures. A node is supplied its demand fully only if a minimum required supply pressure is satisfied at that node. If the minimum pressure requirement cannot be met, then only a fraction of the nodal demand can be satisfied. That fraction is determined by recognition of a relationship between nodal head and nodal outflow. However, there is a high amount of effort needed to be able to use pressuredependent analysis since it requires calibration of models upon extensive field data collection and assembly to determine the relationship between nodal heads and nodal flows. The second maor drawback of head-driven analysis is that it lacks robust methods for the computational solution of the constitutive equations. Almost all the traditional network hydraulic models are built upon demand-driven approach. Therefore, it is very desirable that reliability analysis techniques based on interpretations or transformations of demand-driven results from a pressuredriven perspective be developed (Tanyimboh, Tabesh, and Burrows 2001). The aim of this paper is to describe a semi-pressure-driven framework developed around demand-driven analysis. The technique called the Demand-Driven-Available-Demand-Fraction (DD-ADF) method can be used for more realistic reliability assessment of water distribution networks compared to pure demand-driven analysis. ALTERNATIVE METHODS An essential part of any network reliability model is the phase of predicting deficient-network performance under partially failed conditions. In the usual demand-driven analysis, it is presumed that a nodal demand is always satisfied regardless of validity of calculated pressures. What happens in reality is that as pressures fall below some threshold value, there begins a shortfall in the volume of water actually delivered to consumers. The threshold value for a unction depends on the type of service connection as well as the type of development in the area served by that unction. For example, the pressure required at the street level for excellent flow to a 3-story building is about 290 kpa (42 psi). The Office of Water Services in England specifies a minimum acceptable static pressure of 7 m (~ 68.5 kpa or 10 psi) below which customers may be entitled to compensation for less than satisfactory service. In general, nodal heads of 15 to 25 m will guarantee satisfactory service at all related stop taps in a distribution system (Tanyimboh et al. 1999). Reliability models based on demand-driven simulation use pressures deficiencies to evaluate system performance. Cullinane et al. (1992) proposed a fuzzy continuous relationship to 2
transform pressure deficiency at each node into a nodal availability index between 0 and 1. The maor weakness of this approach, other than the use of a fuzzy relationship, is the validity of calculated pressure deficiencies. As demonstrated by pressure-dependent analysis in many cases, pressure deficiencies in a demand-driven analysis occur at the expense of fulfillment of nodal demands, one of the maor presumptions of demand-driven approach. Considering the above weaknesses of the demand-driven simulation, it has been recognized that nodal flows and heads be considered simultaneously for better prediction of a deficient network performance. Gupta and Bhave (1996) provide a detailed comparison of various flow-head relationships proposed by researchers. Typically the relationship is expressed H = H + K Q min n where H is the head at node when the demand at that node is Q, K is a flow resistance coefficient and n is an exponent. H min is the threshold pressure head below which outflow at the node is unsatisfactory or zero. This value is usually the minimum of outlet elevations in the locality served by unction. In the absence of such data, it can be taken as the elevation of the unction itself. (1) Unfortunately, reliability models predicting deficient network performance based on flow-head relationships similar to (2) are limited to relatively simple applications. Gupta and Bhave (1996) used an approach termed node flow analysis (NFA) to predict deficient performance of serial networks only. Tanyimboh et al. (2001) improved NFA to assess reliability of looped networks. The technique called the Source Head Method is used to approximate outflow only at the nodes with a shortfall in head that are identified using results from demand-driven analysis. The reliability in their approach is defined as the time-averaged value of the ratio of the flow supplied to the flow demanded. However, the Source Head Method is only applicable to single-source networks. PROPOSED APPROACH Failure of a water distribution network implies a deficiency in the level of service that is usually of limited aerial extent such as in the vicinity of a failed component or around a fire-fighting demand point (Tanyimboh et al. 2001). Deficiency usually appears as either pressure and/or flow falling below some specified values at one or more nodes within the network. Demand-driven analysis under partially failed conditions of a network recognizes only pressure deficiencies at the expense of fulfilling consumer demands. From a pressure-driven point of view, on the other hand, the problem that needs to be addressed is to find a way determining the available flows subect to minimum pressure requirements at the minority of pressure-deficient nodes, which can be identified from demand-driven analysis. The method proposed herein can do this. Demand-driven available-demand-fraction (DD-ADF) method starts with the usual demanddriven analysis. Next, nodes at which pressures are insufficient to fully supply their demands are identified. A nodal pressure is insufficient if it is less than the pressure threshold, below which the volume of water actually delivered begins to short fall of the demand. The threshold value for each node can be approximated by the expected maximum outlet level in the locality served by that node. Note that this definition is significantly different from the H min in (1) that is usually taken as the minimum of outlet elevations served by node. 3
Once pressure-deficient unctions are identified from an initial demand-driven analysis, the problem that needs to be addressed is to determine the available flows at those nodes, presumably knowing that the remaining nodes are fully satisfactory in terms of both pressure and demand. For this purpose, the following modifications are made at each pressure-deficient node (1) {New node elevation} = {Original node elevation} + {Threshold pressure head} (2) Set demand to zero (3) Connect an artificial reservoir to the node by an infinitesimally short CV pipe that allows flow only from the node to the reservoir (4) {Artificial tank elevation} = {New node elevation} With these modifications, demand at each pressure-deficient unction in DD-ADF algorithm is treated as an unknown while a pressure threshold is imposed. Figure 1 shows a flowchart of the DD-ADF algorithm. Note that the algorithm proceeds in an iterative manner. That is, if one or more artificial reservoirs receive more water than their nodes demand, those artificial reservoirs are removed from the network and the original elevations and demands at the corresponding nodes are restored. For network reliability assessment, a performance index can be defined at each node as avl Q ADF = (2) D avl where ADF is the available demand fraction at node, Q is the available flow to node, D is the total consumer demand allocated to node. Network-wide-available-demand fraction is then given by Q all nodes avl ADF net = (3) D all nodes It can be shown, mathematically, that the systemwide ADF is equivalent to the demand weighted average of nodal ADFs. Thus, unlike conventional reliability models based on pressure deficiencies, there is a deterministic relationship between nodal reliabilities and the system reliability in this approach. APPLICATION OF PROPOSED METHODOLOGY To provide a more effective description of the proposed semi-pressure-driven approach, an analysis was conducted on the distribution network presented in Fig. 3. Pipe and node characteristics of the given network are listed in Tables 3 and 4. First, a fully functional network (i.e., no pipe failures) is analyzed. Then, assuming no simultaneous pipe failures can occur, all single pipe failure scenarios are simulated. The threshold pressure head, below which there begins a shortfall in fulfillment of nodal demand, is taken as 15 m for all unctions of the application network. 4
Run hydraulics using EPANET Record network nodes at which pressures are below the minimum acceptable Modify pressure-deficient node properties Assign an artificial tank to each pressure deficient node Run hydraulics using EPANET Remove those artificial tanks from the system. Restore corresponding nodal properties Do any of artificial tanks receive more water than needed? Yes No Calculate Nodal and Network ADFs STOP FIG. 1. Flowchart of DD-ADF Algorithm Table 3 shows a comparison of results between a pure demand-driven analysis and DD-ADF algorithm when Pipe 3 in the application network fails. Note that there are nine demand nodes at which the minimum pressure threshold of 15 m can not be satisfied to fully supply their demands. Table 4 summarizes the results from all single pipe failure scenarios that are simulated using the proposed semi-pressure-driven approach, DD-ADF algorithm. Note that the total network demand is 3146.4 m 3 /hr and Eq. (3) is used to calculate network ADFs. 5
RES1 1 1 2 3 3 4 2 4 RES2 9 8 7 5 6 15 7 10 6 11 5 14 13 12 10 16 9 20 8 21 13 17 19 11 18 12 FIG. 2. Application Network Pipe ID Length (m) D (mm) C (H-W) 1 609.60 762 130 2 243.80 762 128 3 1524.00 609 126 4 1127.76 609 124 5 1188.72 406 122 6 640.08 406 120 7 762.00 254 118 8 944.88 254 116 9 1676.40 381 114 10 883.92 305 112 11 883.92 305 110 12 1371.60 381 108 13 762.00 254 106 14 822.96 254 104 15 944.88 305 102 16 579.00 305 100 17 487.68 203 98 18 457.20 152 96 19 502.92 203 94 20 883.92 203 92 21 944.88 305 90 Table 1. Pipe Characteristics Node ID Elevation (m) Demand (CMH) 1 27.43 0.0 2 33.53 212.4 3 28.96 212.4 4 32.00 640.8 5 30.48 212.4 6 31.39 684.0 7 29.56 640.8 8 31.39 327.6 9 32.61 0.0 10 34.14 0.0 11 35.05 108.0 12 36.58 108.0 13 33.53 0.0 RES1 60.96 N/A RES2 60.96 N/A Table 2. Node Characteristics 6
Demand-driven Semi-pressure-driven Node ID Demand (cmh) Pressure (m) Available Demand (cmh) Pressure (m) ADF Junc 1 0.00 32.96 0.00 33.16 - Junc 2 212.40 26.62 212.40 26.91 1.000 Junc 3 212.40 5.77 212.40 17.91 1.000 Junc 4 640.80 2.76 165.77 15.00 0.259 Junc 5 212.40 11.83 212.40 19.97 1.000 Junc 6 684.00 3.40 497.97 15.00 0.728 Junc 7 640.80 6.67 640.80 17.01 1.000 Junc 8 327.60 4.77 274.74 15.00 0.839 Junc 9 0.00 16.39 0.00 20.94 - Junc 10 0.00 17.34 0.00 20.87 - Junc 11 108.00 11.40 108.00 16.48 1.000 Junc 12 108.00 9.35 66.25 15.00 0.613 Junc 13 0.00 5.32 0.00 14.83 - RES 1-1480.75 0.00-1168.45 0.00 - RES 2-1665.65 0.00-1222.28 0.00 - Table 3. Comparison Between Demand-driven and Semi-pressure-driven Analyses Broken Pipe ID Number of iterations Total Available Supply (CMH) Network ADF 2 3 1233.81 0.3921 1 3 1233.81 0.3921 6 3 1309.00 0.4160 3 3 2390.72 0.7598 4 3 2825.85 0.8981 9 3 2846.44 0.9047 15 3 2930.40 0.9314 21 3 3015.84 0.9585 17 2 3027.60 0.9622 16 3 3038.40 0.9657 12 3 3039.12 0.9659 19 3 3046.67 0.9683 11 3 3062.98 0.9735 14 3 3092.60 0.9829 8 3 3095.90 0.9839 7 3 3097.30 0.9844 5 3 3102.57 0.9861 No breaks 3 3102.64 0.9861 13 3 3103.00 0.9862 10 3 3103.72 0.9864 18 3 3108.48 0.9879 20 2 3145.15 0.9996 Table 4. Network ADFs Resulting From Singe Pipe Breaks 7
DISCUSSION OF RESULTS When Pipe 3 failure is simulated using usual demand-driven analysis, there are nine nodes that appear to be pressure deficient (i.e., pressure < 15 m). This indicates that demands at those nodes can not be fully satisfied. The shortfalls in nodal supplies are later found using DD-ADF algorithm. Note that although nodes 3, 5, 7, and 11 are found to be pressure-deficient from the demand-driven analysis, semi-pressure-driven analysis reveals that those nodes are deficient in terms of neither pressure nor supply. Tanyimboh and Tabesh (1997) have also found that when a network with locally insufficient heads is simulated using demand driven approach, the deficiency appears to be far more serious and widespread than it is in reality. In fact, DD-ADF algorithm proceeds in an iterative manner for the same reason. Network available demand fractions for single pipe breaks are shown in increasing order in Table 4. Note that the network can not fully satisfy the given demand loading even when there are no pipe breaks. An even more interesting result is that there are four pipe break scenarios in which the system performance is better than that of the fully functional network. CONCLUSIONS A semi-pressure-driven approach, DD-ADF algorithm, is presented in this paper for more realistic reliability assessment of water distribution networks. The proposed methodology uses demand-driven results as a starting point and proceeds in an iterative manner using one of the most commonly used demand-driven software, namely EPANET (Rossman 1994). Reliability, in the present paper, is defined as the ratio of the flow supplied to the flow required and thus, has a physical interpretation unlike the reliability models based on pressure deficiencies. Other merits of the semi-pressure-driven approach proposed include a high computational efficiency and simplicity. It has been shown that with the demand-driven analysis, system deficiency is far more serious and widespread than it is in reality. Another interesting conclusion is that more piping in a network does not always improve system performance. REFERENCES Cullinane, M., Lansey, K., and Mays, L. (1992). Optimization-availability based design of water-distribution networks. Journal of Hydraulic. Engineering, ASCE 118(3), 420-441. Gupta, R., and Bhave, P. R. (1996). Comparison of methods for predicting deficient network performance, Journal of Water Resources Planning and Management, ASCE, 122(3), 214-217. Tanyimboh, T. T., and Tabesh, M. (1997) Discussion of Comparison of methods for predicting deficient network performance, Journal of Water Resources Planning and Management, ASCE, 123(6), 369-370. Tanyimboh, T. T., Burd, R.., Burrows, R., and Tabesh, M. (1999). Modelling and Reliability Analysis of Water Distribution Systems, Water Science Tech., Elsevier Science Ltd, 39(4), 249-255. 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, ASCE, 127(4), 206-213. 8