Anytown Water Distribution Network

The objective of the Anytown network problem is to determine the most economically effective design to reinforce the existing system to meet projected demands, taking into account pumping costs as well as capital expenditure. The town is formed around an old centre situated to the south east of pipe 34, where excavations are more difficult to undertake and consequently are more expensive. There is a surrounding residential area, with some existing industries near node 17 and a projected new industrial park to be developed to the north. Options include duplication (in a range of possible diameters) of any pipe in the system, addition of new pipes, selecting the operation schedule of pumping stations and provision of new reservoir storage at any location. Water is pumped into the system from a water treatment works by means of three identical pumps connected in parallel. The link and node data are available from input file . The US customary units have been used in this study.

The water in the treatment works is maintained at a fixed level of 10 ft. The average daily water use at each node for year 2005 as well as the elevation of the nodes and the bottoms of the tanks are given in input file . The variation in water use throughout the day are also summarized in input file.

The two existing tanks are operated with water levels between elevations 225 ft and 250 ft, giving an effective capacity of 156250 gal(US) for each tank. The volume of water below the level 225 ft and above 215 ft is retained for emergency needs, giving an emergency volume of 62500 gal(US) for each tank. A minimum pressure of at least 40 psi must be provided at all nodes at average day flow as well as instantaneous peak flow, which is 1.8 times the average day flow. All tanks should empty and fill over their operational ranges during the specified average demand day. The system is also subject to 3 fire flow conditions under which it must supply water at a minimum pressure of at least 20 psi. Details of 5different loading conditions are available from loading condition table. The fire flow duration is two hours with tanks starting at their low operating levels and one pump being out of service, and must be met while also supplying peak day flows, which are 1.3 times average day flow. It is assumed that during fire flow periods only the flow required for fires is supplied at the corresponding nodes.

Loading conditions

NodeIDElevation (ft)Average day demand
(gpm)
Instantaneous peak
(gpm)
Fire 1 (gpm)Fire 2 (gpm)Fire 3 (gpm)
1 20 500 900 650 650 650
2 50 200 360 260 260 260
3 50 200 360 260 260 260
4 50 600 1080 780 780 780
5 80 600 1080 780 1500 780
6 80 600 1080 780 1500 780
7 80 600 1080 780 1500 780
8 80 400 720 520 520 520
9 120 400 720 520 520 520
10 120 400 720 520 520 520
11 120 400 720 520 520 1000
12 50 500 900 650 650 650
13 50 500 900 650 650 650
14 50 500 900 650 650 650
15 50 500 900 650 650 650
16 120 400 720 520 520 520
17 120 1000 1800 1300 1300 1000
18 50 500 900 650 650 650
19 50 1000 1800 2500 1300 1300

35 existing pipes are considered for duplication or cleaning and lining. There are 6 additional new pipes. The range of each type of variable as well as the unit costs for pipe laying, cleaning and lining are given in the following Table. A pipe which has been cleaned and lined has a Hazen-Williams coefficient of C=125 and for new pipes C=130.

Pipe rehabilitation alternative costs

Pipe diameter (in)New pipes 
($/ft)
Duplicating existing pipes ($/ft)Clean and line existing pipes ($/ft)
CityResidentialCityResidential
6 12.8 26.2 14.2 17.0 12.0
8 17.8 27.8 19.8 17.0 12.0
10 22.5 34.1 25.1 17.0 12.0
12 29.2 41.4 32.4 17.0 13.0
14 36.2 50.2 40.2 18.2 14.2
16 43.6 58.5 48.5 19.8 15.5
18 51.5 66.2 57.2 21.6 17.1
20 60.1 76.8 66.8 23.5 20.2
24 77.0 109.2 85.5 30.1 -
30 105.5 142.5 116.1 41.3 -

Given a 24 hour operation cycle and 1 hour time step, the control variables for the three pumps give a further 24 design variable which is the number of pumps in operation during each hour. Following table gives five points on the characteristic curve for the pumps, together with the corresponding wire-to-water efficiencies. Pump station operating costs are based on a unit cost for energy, constant throughout the 24 hours, equal to $0.12/kWh. The present worth of energy costs are based on an interest rate of 12% and an amortization period of 20 years.

Pump characteristics

 

Discharge 
(gpm)
Pump head 
(ft)
Efficiency (%) 
(wire to water)
0 300 0
2000 292 50
4000 270 65
6000 230 55
8000 181 40

All nodes are considered as potential sites for new tanks, except those which are already connected directly to the existing tanks. Tanks are connected to a node by a short pipe, known as a riser, of known length (101 ft) but of variable diameter. Tank costs are considered as a function of volume and are given in the following table. Intermediate tank sizes are considered in the proposed methods and the corresponding costs are determined linearly according to the standard sizes and costs.

Tank costs

 

Tank volume 
(gal)
Cost 
($)
50000 115000
100000 145000
250000 325000
500000 425000
1000000 600000

References

  1. Walski, T. M., Brill, E. D., Gessler, J., Goulter, I. C., Jeppson, R. M., Lansey, K., Han-Lin Lee, Liebman, J. C., Mays, L., Morgan, D. R., and Ormsbee, L. (1987). Battle of the network models:epilogue. Journal of Water Resources Planning and Management, ASCE, 113(2), 191-203.
  2. Walters, G. A., Halhal, D., Savic, D., and Ouazar, D. (1999). Improved design of Anytown distribution network using structured messy genetic algorithms. Urban Water, 1, 23-38.
  3. Murphy, L. J., Dandy, G. C., and Simpson, A. R. (1994). Optimum design and operation of pumped water distribution systems. Proceedings of the Conference on Hydraulics in Civil Engineering, Brisbane, Australia:Institution of Engineers, Australia, 149-155.
  4. Farmani R., Walters G.A. and Savic D.A. (2005) Trade-off between total cost and reliability for Anytown water distribution network, ASCE journal of water resources planning and management, Vol. 131, No.3, pp.161-171.
  5. Farmani R., Walters G.A. and Savic D.A. (2006) Evolutionary multi-objective optimization of the design and operation of water distribution network:total cost vs. reliability vs. water quality, Journal of Hydroinformatics (in press)
  6. Farmani R., Savic D.A. and Walters G.A. (2005) Fuzzy rules for hydraulic reliability-based design and operation of water distribution systems. ASCE conference, EWRI 2005, Anchorage, Alaska, on CD-Rom.
  7. Farmani R., Walters G.A. and Savic D.A. (2004) The Simultaneous Optimization of Anytown Pipe Rehabilitation, Tank Sizing, Tank Siting and Pump Operation Schedules. ASCE conference. USA, On CD-Rom
  8. Farmani R., Walters G.A. and Savic D.A. (2004) Multi-objective optimization of cost, reliability and water quality of Anytown system in relation to dual objective optimization, Modelling and Control for Participatory Planning and Managing Water Systems Conference, Italy, on CD-Rom.
  9. Vamvakeridou-Lyroudia, L.S., Walters, G.A. and Savic D.A., (2005). “Fuzzy multiobjective design optimisation of water distribution networks”, Jour. Wat. Res, Plan. Man., ASCE, 131(6), pp. 467-476.
  10. Vamvakeridou-Lyroudia, L.S., Savic D.A. and Walters, G.A. (2006). “Fuzzy hierarchical decision support system for water distribution network optimisation”, Civil Eng. and Env. Systems, (accepted for publication).
  11. Vamvakeridou-Lyroudia, L.S., Walters, G.A. and Savic D.A. (2004). “Fuzzy multiobjective design optimisation of water distribution networks”, Report No.2004/01, Centre for Water Systems, School of Engineering, Computer Science and Mathematics, University of Exeter, Exeter, U.K., 98p.

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