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Izquierdo, Joaquín; Campbell, Enrique; Montalvo, Idel; Pérez-García, Rafael; Ayala-Cabrera, David

Error analysis of some demand simplifications in hydraulic models of water supply networks. (English) Zbl 1302.90113

Abstr. Appl. Anal. 2013, Article ID 169670, 13 p. (2013).
Summary: Mathematical modeling of water distribution networks makes use of simplifications aimed to optimize the development and use of the mathematical models involved. Simplified models are used systematically by water utilities, frequently with no awareness of the implications of the assumptions used. Some simplifications are derived from the various levels of granularity at which a network can be considered. This is the case of some demand simplifications, specifically, when consumptions associated with a line are equally allocated to the ends of the line. In this paper, we present examples of situations where this kind of simplification produces models that are very unrealistic. We also identify the main variables responsible for the errors. By performing some error analysis, we assess to what extent such a simplification is valid. Using this information, guidelines are provided that enable the user to establish if a given simplification is acceptable or, on the contrary, supplies information that differs substantially from reality. We also develop easy to implement formulae that enable the allocation of inner line demand to the line ends with minimal error; finally, we assess the errors associated with the simplification and locate the points of a line where maximum discrepancies occur.

MSC:

90B90 Case-oriented studies in operations research
90B10 Deterministic network models in operations research
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[1] Izquierdo, J.; Pérez, R.; Iglesias, P. L., Mathematical models and methods in the water industry, Mathematical and Computer Modelling, 39, 11-12, 1353-1374 (2004) · Zbl 1093.91051 · doi:10.1016/j.mcm.2004.06.012
[2] Izquierdo, J.; Montalvo, I.; Pérez-García, R.; Matías, A., On the complexities of the design of water distribution networks, Mathematical Problems in Engineering, 2012 (2012) · Zbl 1264.90028 · doi:10.1155/2012/947961
[3] Savić, D. A.; Banyard, J. K., Water Distribution Systems (2011), London, UK: ICE Publishing, London, UK
[4] Montalvo, I., Optimal design of water distribution systems by particle swarm optimization [doctoral dissertation] (2011), Valencia, Spain: Universidad Politécnica de Valencia, Valencia, Spain
[5] EPA (Environmental Protection Agency), EPANET
[6] Jung, B. S.; Boulos, P. F.; Wood, D. J., Pitfalls of water distribution model skeletonization for surge analysis, Journal of the American Water Works Association, 99, 12, 87-98 (2007)
[7] Izquierdo, J.; Montalvo, I.; Pérez-García, R.; Izquierdo, F. J., Son válidas ciertas simplificaciones en el estudio de los transitorios hidráulicos, X Seminario Iberoamericano de Planificación, Proyecto y Operación de Sistemas de Abastecimiento de Agua (SEREA ’11)
[8] Anderson, E. J.; Al-Jamal, K. H., Hydraulic-network simplification, Journal of Water Resources Planning and Management, 121, 3, 235-244 (1995) · doi:10.1061/(ASCE)0733-9496(1995)121:3(235)
[9] Ulanicki, B.; Zehnpfund, A.; Martínez, F., Simplification of water distribution network models, Proceedings of the 2nd International Conference on Hydroinformatics, International Water Association
[10] Grayman, W. M.; Rhee, H.; Hotchkiss, R. H.; Glade, M., Assessment of skeletonization in network models, Proceedings of the Joint Conference on Water Resource Engineering and Water Resources Planning and Management, ASCE · doi:10.1061/40517(2000)196
[11] Walski, T. M.; Chase, D. V.; Savic, D. A.; Grayman, W.; Beckwith, S.; Koelle, E., Advanced Water Distribution Modeling and Management (2003), Waterbury, Conn, USA: Haestad Methods, Waterbury, Conn, USA
[12] Perelman, L.; Ostfeld, A., Water distribution system aggregation for water quality analysis, Journal of Water Resources Planning and Management, 134, 3, 303-309 (2008) · doi:10.1061/(ASCE)0733-9496(2008)134:3(303)
[13] Deuerlein, J. W., Decomposition model of a general water supply network graph, Journal of Hydraulic Engineering, 134, 6, 822-832 (2008) · doi:10.1061/(ASCE)0733-9429(2008)134:6(822)
[14] Grayman, W. M.; Murray, R.; Savic, D. A.; Starrett, S., Effects of redesign of water systems for security and water quality factors, Proceedings of the World Environmental and Water Resources Congress, ASCE · doi:10.1061/41036(342)49
[15] Perelman, L.; Ostfeld, A., Water-distribution systems simplifications through clustering, Journal of Water Resources Planning and Management, 138, 3, 218-229 (2012) · doi:10.1061/(ASCE)WR.1943-5452.0000173
[16] Herrera, M.; Izquierdo, J.; Pérez-García, R.; Ayala-Cabrera, D., Water supply clusters by multi-agent based approach, Proceedings of the 12th Annual International Conference on Water Distribution Systems Analysis (WDSA ’10), ASCE · doi:10.1061/41203(425)79
[17] Herrera, M.; Izquierdo, J.; Pérez-García, R.; Montalvo, I., Multi-agent adaptive boosting on semi-supervised water supply clusters, Advances in Engineering Software, 50, 131-136 (2012) · doi:10.1016/j.advengsoft.2012.02.005
[18] Di Nardo, A.; Di Natale, M., A heuristic design support methodology based on graph theory for district metering of water supply networks, Engineering Optimization, 43, 2, 193-211 (2011) · doi:10.1080/03052151003789858
[19] Giustolisi, O.; Laucelli, D.; Berardi, L.; Savić, D. A., Computationally efficient modeling method for large water network analysis, Journal of Hydraulic Engineering, 138, 4, 313-326 (2012) · doi:10.1061/(ASCE)HY.1943-7900.0000517
[20] Todini, E.; Pilati, S.; Coulbeck, B.; Orr, C. H., A gradient algorithm for the analysis of pipe networks, Computer Applications in Water Supply, 1, 1-20 (1988), Taunton, UK: Research Studies Press, Taunton, UK
[21] Rudin, W., Principles of Mathematical Analysis. Principles of Mathematical Analysis, International Series in Pure and Applied Mathematics (1976), New York, NY, USA: McGraw-Hill, New York, NY, USA · Zbl 0346.26002
[22] Bartle, R. G.; Sherbert, D. R., Introduction to Real Analysis (2000), Ontario, Canada: John Wiley & Sons, Ontario, Canada · Zbl 0494.26002
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