World Environmental and Water Resources Congress 2012: Crossing Boundaries © ASCE 2012
Reference Pressure for Extended Period Simulation of Pressure Deficient Water Distribution Systems Tiku T. Tanyimboh, PhD and Calvin Siew, PhD Department of Civil Engineering, University of Strathclyde Glasgow, John Anderson Building, 107 Rottenrow, Glasgow G4 0NG, UK; Tel. +44 (0)141 548 4366; Email:
[email protected],
[email protected]
ABSTRACT Regulatory authorities normally set minimum performance standards for water distribution systems (WDSs) in terms of the flow and pressure at a demand node. Based on the water supply regulations in the UK, the minimum residual pressure required is constant throughout the day and as such does not increase or decrease as the hourly demand increases or decreases. The minimum residual pressure required is the demand node residual pressure above which the demand is satisfied in full. Using head dependent modelling extended period simulation was carried out herein for a WDS. Results were obtained for a constant minimum residual pressure. The minimum residual pressure was also allowed to increase or decrease as the hourly demand increased or decreased. The results show that if the minimum residual pressure required is increased when the hourly demand increases, the WDS model will underestimate the amount of water supplied. Conversely if the minimum residual pressure required is decreased when the hourly demand deceases, the WDS model will overestimate the amount of water the WDS supplies. Keywords: Water distribution system; water supply; pressure driven analysis; demand driven analysis; extended period simulation; prescribed minimum residual pressure; water supply regulations
INTRODUCTION Computer models of water distribution systems (WDSs) are an indispensable element in the toolkit for design and operational management. Models of WDSs were used, originally, primarily for design purposes where the main objective was to ascertain there was adequate capacity in the distribution system to satisfy specified nodal demands and residual pressure heads. These models were thus formulated with an implied assumption that all nodal demands would always be satisfied in full. Thus the models are said to be demand driven. WDS models, however, are used increasingly for a multiplicity of functions other than design. Even if a WDS has sufficient capacity to satisfy the anticipated
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demands, abnormal operating conditions are often encountered due to factors such as large fire-fighting demands and pipe bursts that can reduce the pressure in the distribution system. If pressure-deficient WDSs are analysed with the traditional demand-driven analysis (DDA) models, inaccurate or infeasible results are obtained (Tanyimboh et al. 2003). To address this problem recent WDS models attempt to account for the relationship between the flow at a demand node and the pressure. Such models are thus said to be head driven. Significant progress on head-driven analysis (HDA) has been achieved in recent years. For example, Ackley et al. (2001) used a nonlinear optimization approach based on sequential quadratic programming the objective of which was to maximize the total flow delivered while satisfying all the relevant hydraulic constraints. Tanyimboh et al. (2003) used a robust, globally convergent Newton-Raphson method while Giustolisi et al. (2008) and Siew and Tanyimboh (2009) used the gradient method (Todini and Pilati 1988). A key parameter of HDA models is the prescribed minimum residual pressure (PMRP) at which the nodal demand should be delivered. In the UK, for example, the prescribed level of service (LOS) is a residual pressure head of 10m at the boundary stop tap with a flow of 9 liters per minute. This LOS is for operating conditions with normal demand for water. Alternative prescribed LOS are not mentioned – not even in connection with diurnal demand variations or peak demands. The clear implication is that there is only one prescribed LOS and it applies throughout the day and night despite the pronounced variations in demand. Indeed, in the UK, there is no prescribed LOS for fire-fighting purposes other than the duty on water utilities to maintain a constant supply of water at a sufficient pressure in the mains to reach the topmost storey of every building in the areas they serve. However, the fire-fighters can ask the water utility to assist by increasing flow and pressure where needed by reducing the flow in other areas. In the USA, the stipulated fire-fighting requirements often exceed the peaks in the domestic demand and, consequently, often govern the design of distribution mains. It can thus be deduced that fire-fighting or peak daily flows do not automatically lead to additional, more stringent prescribed LOS. In other words, for example, the required residual pressure (for the required flow of 9 liters per minute in the UK) at 08:00-09:00 (say) when the demand is highest is the same as at 02:00-03:00 (say) when the demand is lowest. Recently it has been suggested that the PMRP at demand nodes should vary throughout the day in order to track the daily demand pattern. The purpose of this paper is to illustrate the major anomalies that would result if PMRPs that track the daily demand pattern were to be used to carry out extended period simulation of pressure-deficient WDSs.
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METHODOLOGY The fraction of the demand that is satisfied, also known as the demand satisfaction ratio (DSR) (Ackley et al. 2001), under normal and pressure-deficient conditions can be obtained using the pressure-dependent nodal flow function proposed by Wagner et al. (1988), i.e. DSR j =
Qj Q req j
⎛ H j − H min j = ⎜ req ⎜ H − H min j ⎝ j
⎞ ⎟ ⎟ ⎠
1/ 2
;
Hjmin ≤ Hj < Hjreq
(1)
where, for node j, DSRj = demand satisfaction ratio; Qj = available or actual flow; Qjreq = demand; Hj = available or actual residual pressure head; Hjmin = residual pressure head below which flow is zero; and Hjreq = residual pressure head above which the demand is satisfied in full. Also, Qj = 0 for Hj < Hjmin and Qj = Qjreq for Hj ≥ Hjreq. It should be noted that other nodal head-flow functions than Eq. 1 exist and can be used instead, e.g. Tanyimboh and Templeman (2010). In the UK, Hjreq is taken as 10m at the boundary stop tap. However, as it is not practicable to measure the pressure at the boundary stop tap of every property, a surrogate standard is often used, i.e. a minimum residual pressure head of 15m in the distribution main supplying the property. Eq.1 can be re-written as shown in Eq. 2 by making Hjreq the subject of the equation.
H
req j
=H
min j
(
+ Hj −H
min j
⎛ Q req ⎜ j ⎜ Qj ⎝
)
2
⎞ ⎟ ; Hj ≥ Hjmin ⎟ ⎠
(2)
In Eq. 2, for the purposes of extended period simulation (EPS), Qjreq/Qj represents the demand factor DFj if Qjreq is taken as the time-varying demand; Qj the prescribed minimum flow (9 liters per minute in the UK); and (Hj – Hjmin) the prescribed minimum residual pressure head (denoted as MH) (MH = 10m at the boundary stop tap in the UK). The demand factor represents the variation in water demand throughout the day. For example, a demand factor value of, say, 1.3 for the 9th and 10th hours means that the water consumption during both of these hours is 1.3 times the base demand. In other words the demand factor provides the value of the demand at any given instant relative to the base demand. Accordingly, for EPS purposes it is convenient to re-write Eq. 2 as H req = H min + MH × DF j2 j j
(3)
On the basis of Eq. 3, Giustolisi et al. (2008) and Wu et al. (2009) discussed Hjreq values that depend on the demand factor DFj. In other words Hjreq increases when
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DFj increases and, conversely, Hjreq decreases when DFj decreases. Giustolisi et al. (2008) also assessed the hydraulic performance of WDSs over 24 hours using HDA with values of Hjreq that varied with DFj according to Eq. 3. However, at least in the UK, the prescribed LOS does not support the idea that Hjreq depends on the demand factor (OFWAT 2004). HDA results were generated herein with two sets of Hjreq values. The first set consisted of a fixed value of 15m throughout the day while values for the second set were calculated based on the demand factor using Eq. 3. The hydraulic simulations were carried out using a computer program developed by Siew and Tanyimboh (2009) that is based on the gradient method (Todini and Pilati 1988). DDA (EPANET 2) results were also included for cross-checking purposes and to further emphasise the differences between the two HDA approaches based on fixed and variable Hjreq values.
RESULTS AND DISCUSSION A simple network whose details are available in Ang and Jowitt (2006) was used (Fig. 1). The reservoir water levels are: 100m (Reservoir 1) and 98m (Reservoir 2). The nodal elevations are: 90m (Nodes 1 -- 3); 88m (nodes 4 -- 6); and 85m (Nodes 7 -- 9). The base demand (i.e. the demand for which DFj = 1.0) at all nodes was taken as 25 L/s. Hjmin = 0 and Hjreq =15m for all demand nodes. All pipes are 1000m long, with a Hazen–Williams coefficient of 130. The pipe diameters are: 300mm (Pipes 1 – 7); 250mm (Pipes 8 – 12); and 200mm (Pipes 13 and 14). The two approaches based on fixed and fluctuating Hjreq values lead to significantly different results (Figs. 2--4) as discussed below.
Figure 1. Layout of the demonstration network
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Fig. 2 shows the variation of the demand factor and the network DSR (i.e. the ratio of the flow delivered to the flow required) for both approaches over 24 hours. The demand variations can be divided into three different categories, i.e. DF < 1.0, DF > 1.0 and DF = 1.0. Based on Eq. 3, a DF value that is less than 1.0 reduces Hjreq. For example, at 02:00 a.m. when the demand factor is 0.7, the resulting Hjreq from Eq. 3 is 7.35m, which is 51% less than the reference value of 15m. Self-evidently this Hjreq of 7.35m is less stringent than an Hjreq of 15m and seemingly enables the WDS to satisfy all the demands in full, albeit at a lower residual pressure.
Figure 2. Extended period simulation results
This is illustrated in Fig. 3 where the approach based on Eq. 3 yields identical results to DDA (this implies all the nodal residual pressures are satisfactory). Unfortunately this creates the misleading impression that all nodal demands are fully satisfied (i.e. network DSR = 1). In reality, however, the network DSR, based on the UK statutory reference residual pressure head of 15m is only 0.88, which is the DSR value at 02:00 a.m. in Fig. 2. The performance of the network is thus overestimated by a significant margin if Eq. 3 is used to determine the value of Hjreq during periods of low demand. On the other hand, based on Eq. 3, a demand factor greater than 1.0 increases Hjreq. For example, at 10:00 when the demand factor is 1.3, Hjreq from Eq. 3 is 25.35m which is 69% higher than the UK statutory requirement of 15m. Accordingly, a much higher residual pressure head than 15m is seemingly required if the demands are to be satisfied in full. This can be seen in Fig. 4 where the nodal heads for the varying Hjreq are higher than those for the fixed Hjreq of 15m.
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Figure 3. Nodal heads at 02:00
In reality, however, the higher nodal heads – this could be misconstrued as indicative of superior performance -- actually correspond to a much smaller DSR value of only 0.43 for the network as a whole. The network DSR value of 0.43 is the DSR value at 10:00 a.m. for the varying Hjreq in Fig. 2. It may be noted that the DDA with an implied DSR of 1.0 gave the smallest nodal heads at 10:00 (Fig. 4). Of course, as expected, the nodal heads computed for both fixed and fluctuating Hjreq values are identical when the demand factor is 1.0. It is worth observing, also, that in general daily peaks in demand result not from increases in the per capita consumption but, rather, are caused by the synchronisation of the normal demands of multiple properties. Therefore, provided the prescribed LOS is met, there should be enough flow and pressure to satisfy the requirements of the individual properties. The synchronization of demands implies that the flow through the WDS is greater during the daily peaks with corresponding increases in the head losses through the WDS. WDSs normally cope with the peak demands by a variety of means including service reservoirs. Therefore, if the PMRP is achieved, then, assuming that the per capita consumption remains at the expected level, there would appear to be no absolute need for the water utilities to increase further the residual pressure head at the point of delivery. This interpretation is in fact consistent with the requirement in the UK that if two properties share a service pipe then the prescribed minimum residual pressure head remains unchanged, i.e. 10m at the boundary stop tap, while the flow rate is doubled to 18 liters per minute.
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Figure 4. Nodal heads at 10:00
SUMMARY AND CONCLUSIONS It was suggested recently that the prescribed minimum residual pressure at a demand node should vary throughout the day in order to track the daily demand pattern. The purpose of this paper is to illustrate the major anomalies that would result if PMRPs that track the daily demand pattern were to be used to carry out extended period simulation of pressure-deficient WDSs. EPS results based on HDA were compared herein for fixed and varying values of the PMRP. The results show conclusively that, for pressure-deficient WDSs, PMRPs that track the daily demand pattern lead to underestimation of the available flow when demands are above average and, conversely, overestimation of the available flow when demands are below average. The modelling errors that would be introduced in this way could be large enough to cause serious errors in the operational management decisions for WDSs. They could potentially also lead to overdesign of WDSs. By contrast, the regulatory requirements in the UK appear to suggest that the reference pressure is constant throughout the day variations in demand notwithstanding.
ACKNOWLEGMENT This paper is based on research funded in part by the UK Engineering and Physical Sciences Research Council (EPSRC Grant Number EP/G055564/1). The authors are
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grateful to the British Government (Overseas Research Students’ Award Scheme) and the University of Strathclyde Glasgow for funding the second author’s PhD programme.
REFERENCES Ackley, J. R. L., Tanyimboh, T. T., Tahar, B., and Templeman, A. B. (2001). “Headdriven analysis of water distribution systems.” Water Software Systems: Theory and Applications, Ulanicki, B., Coulbeck, B. and Rance, J., eds., Research Studies Press, England, ISBN 0863802745, Vol. 1, Chapter 3:183-192. Ang, W. H., and Jowitt, P. W. (2006). “Solution for water distribution systems under pressure-deficient conditions.” J. Water Resour. Plan. Mngt, 132(3), 175-182. Giustolisi, O., Kapelan, Z., and Savic, D. A. (2008). “Extended period simulation analysis considering valve shutdowns.” Journal Water Resources, Planning and Management, 134(6), 527-537. OFWAT (2004). “Levels of Service for the Water Industry in England and Wales. 2002-2003 Report.” Ofwat Centre, 7 Hill Street, Birmingham B5 4UA, UK. Siew, C. Y. M., and Tanyimboh, T. T. (2009). “Augmented gradient method for head dependent modeling of water distribution networks.” Proceedings, 11th Annual Water Distribution Systems Analysis Symposium, May 17-21, 2009, Kansas City. Tanyimboh, T. T., Tahar, B., and Templeman, A. B. (2003). “Pressure-driven modelling of water distribution systems.” Water Science and Technology – Water Supply, 3(1-2), 255-262. Tanyimboh, T. T, and Templeman, A. B. (2010). “Seamless pressure-deficient water distribution system model”, J. Water Management, ICE, 163(8), 389-396. Twort, A. C., Ratnayaka, D. D., and Brandt, M. J. (2000). Water Supply. Arnold, London. Todini, E., and Pilati, S. (1988). “A gradient algorithm for the analysis of pipe networks.” Computer Applications in Water Supply, Volume 1, Coulbeck, B., and Orr, C-H, eds., Research Studies Press, England. Wagner, J. M., Shamir, U., and Marks, D. H. (1988). “Water distribution reliability: simulation methods.” J. Water Resources Planning and Mngt, 114(3), 276-294. Wu, Z. Y., Wang, R.H., Walski, T. M., Yang, S. Y., Bowdler, D., and Baggett, C. C. (2009). “Extended global-gradient algorithm for pressure-dependent water distribution analysis.” J. Water Resour. Plan. Mngt, 135(1), 13–22.
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