Optimization of drinking water distribution networks: Computer-based methods and constructal design

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Abstract

A well-known application of water engineering is drinking water distribution through pipe networks in urban and rural areas. The present work addresses this issue with a specific focus on the network design. First, the paper presents a brief review of computer-based design methods and shows that a significant number of efforts have been pursued. Secondly, it proposes the approach of geometric analysis of the distribution networks as complementary points of the former optimization methods. Finally, an original illustrative application is proposed. The geometric and multi-scale optimization known as the constructal design is used to analytically optimize T-shaped network architectures subject to an operational water quality constraint. This illustrative application leads to the determination of an optimal geometry of the network that minimizes head losses (factor of pumping energy).

Highlights

► Computer-based design methods have been deeply used for drinking water networks. ► Geometric analysis is an excellent complementary point. ► The geometric optimization method called constructal design seems adapted. ► Constructal optimization of T-shaped networks is presented as illustration. ► Recommendations in direction of urban systems computer-based design methods.

Introduction

The optimal design and management of urban networks is an interdisciplinary challenge touching environment, water, electricity and urban planning as noticed in many works (Christodoulou et al., 2009, Ducrot et al., 2004, Kizito et al., 2009) and requires maximal computing skills (Akiba, 1982, Evatt, 1984, Ignizio, 1980, Keirstead and Shah, 2011, Miller et al., 2004, Moore and Kim, 1995). During last decades, numbers of researchers have put their interest on them in various aspects. This interest is understandable in many senses. First, these systems are huge economic infrastructures and their optimization is strongly needed in developing countries and even in western countries. Secondly, because of their very high importance, they require reliable design techniques for authorities to be assisted in investment decision making.

According to literature, many progresses have been made in the study of water distribution systems (WDSs) and today, they are capable of serving rural and urban communities reliably, efficiently, and safely, both now and in the future (Chase, Savic, & Walski, 2001). Though the complexity and the size of WDS vary dramatically (from African rural areas to overpopulated cities in western countries), they have the same basic function of delivering water from sources or treatment facilities to customers (Chase et al., 2001). Technologies and researches on these systems have considerably evolved over time and through civilizations (Babbitt and Doland, 1931, Haestad methods, 1999). Today water distribution networks (WDNs) are the most known, the most well-tried and the most used systems worldwide (Chase et al., 2001) in providing water to populations.

Being used for hot or cold water distribution, either for drinking water or agricultural irrigation, WDN as flow systems, are characterized by mechanical losses (head losses) that are factor pumping energy (Bejan and Lorente, 2007, Izquierdo et al., 2008, Tondeur and Luo, 2004), chemical and biochemical reactions that refer to water quality management questions (Kerneïs, Nakache, Deguin, & Feinberg, 1995).

To have a thorough understanding of these phenomena, in order to optimize and well manage WDN technically, economically and socially, an important amount of researches has been pursued during the last decades on the design (optimization and modeling). Various design methods have been developed, focusing on minimum cost objective (Alperovits and Shamir, 1977, Simpson et al., 1994), on reliability aspects (Bai et al., 2007, Chiplunkar et al., 1990, Fujiwara and Khang, 1990, Todini, 2000, Wechsatol et al., 2004), and on water quality (Bieupoude, 2011, Boulos et al., 1994) which is a critical environmental question (World Health Organization, 1996). Because of the complexity of the problem (Savic, Walter, Randall-Smith, & Atkinson, 2000) most of these methods are computer-based (Alperovits and Shamir, 1977, Bhave, 1988, Gessler, 1985, Pierro et al., 2009, Simpson et al., 1994) and based on complex iterative calculations. The aim of the design is to find trade-off between objectives and design constraints and to predict the future working conditions of the system.

The introduction of the latest technology which is modeling in 1980s was salutary in this field (Chase et al., 2001). Despite the last evolutions in modeling (due to the increase in computation skills), it remains a critical part of the design of water distribution systems. From gathering data, conception of the model itself (understanding, structuring and calibrating) to the implementation of the model, water researchers have provided sophisticated tools to reach the goals of rendering water systems reliable, efficient and safe (Augugliaro et al., 1998, Baños et al., 2010, Bolognesi et al., 2010, Chu et al., 2008, Eiben et al., 1994, Gupta et al., 1993, Gupta et al., 1999, Keedwell and Khu, 2005, Klempous et al., 1997, Mustonen et al., 2008, Savic and Walters, 1997).

Though WDN are becoming well-known systems (Chase et al., 2001) in both modeling and optimization studies, there is still much to know about the precision of models and some design or optimization techniques to increase the performances of these systems.

Important reviews have been offered in literature. However these reviews included very little information on design methods based on geometric analysis of the networks architectures.

This paper offers a brief review on WDN design and optimization methods and highlights the need of geometric optimization approaches for urban systems. Then it introduces the geometric and multi-scale optimization known as the constructal design (Bejan & Lorente, 2008) through an illustrative application. In this application, T-shaped network architectures for drinking water distribution are analytically optimized subject to an operational water quality constraint.

Section snippets

Problem formulation

The optimization studies of urban systems are multi objective and complex (Duh and Brown, 2007, Neema and Ohgai, 2010, Poelmans and Rompaey, 2010) because they are space and time-dependent. In the particular case of drinking water distribution networks, except the time and space-dependence and water demand questions, the fundamental technical challenge relies on the management of head losses due to friction and local losses in the network (Carlier, 1972) and the degradation of water quality

Basis of the constructal approach

The idea of optimal design of flow structures has been put forward in engineering many years ago and the geometric scales have been evocated in a pioneering work of Hess (1914), later developed by Murray (1926) who explained the optimal diameters ratio of blood vessels.

The constructal theory was developed by Bejan, 2000, Bejan and Lorente, 2008. “First developed in the late 1990, constructal theory holds that flow architecture arises from the natural evolutionary tendency to generate greater

Remarks on the illustrative application

In Section 3.2, ΔH representing head losses due to mechanical irreversibilities of the system, are minimized subject to a water quality constraint by keeping in mind that minimizing flow resistances under an operational constraint could result in better geometries, as stated by the constructal approach (Bieupoude, 2011). As optimization result, an optimal geometry of T-shaped networks is found for two levels of construction (construct 1 and construct 2). A geometric characteristic and diameter

Acknowledgements

The International Institute for Water and Environmental Engineering 2iE, 01 BP 594 Ouagadougou 01, Burkina Faso (www.2ie-edu.org), and its financial partners are gratefully acknowledged for their supports that permitted to successfully achieve this work.

References (118)

  • A. Bejan et al.

    Constructal tree-shaped flow structures

    Applied Thermal Engineering

    (2007)
  • A. Bejan et al.

    The constructal law and the evolution of design in nature

    Physics of Life Reviews

    (2011)
  • A. Bejan et al.

    The constructal unification of biological and geophysical design

    Physics of Life Reviews

    (2009)
  • A. Bejan et al.

    Thermodynamic optimization of geometry: T- and Y-shaped constructs of fluid streams

    International Journal of Thermal Science

    (2000)
  • A. Bolognesi et al.

    Genetic heritage evolution by stochastic transmission in the optimal design of water distribution network

    Journal of Advances in Engineering Software

    (2010)
  • A.V. Chiplunkar et al.

    Analysis of looped water distribution networks

    Environmental Software

    (1990)
  • S. Christodoulou et al.

    Risk-based asset management of water piping networks using neurofuzzy systems

    Computers, Environment and Urban Systems

    (2009)
  • C. Chu et al.

    Application of immune algorithms on solving minimum-cost problem of water distribution network

    Journal of Mathematical and Computer Modeling

    (2008)
  • A.F. Colombo et al.

    A selective literature review of transient-based leak detection methods

    Journal of Hydro-Environment Research

    (2009)
  • R. Ducrot et al.

    Articulating land and water dynamics with urbanization: an attempt to model natural resources management at the urban edge

    Computers, Environment and Urban Systems

    (2004)
  • J. Duh et al.

    Knowledge-informed Pareto simulated annealing for multi-objective spatial allocation

    Computers, Environment and Urban Systems

    (2007)
  • A.R. Dzialowski et al.

    Development of predictive models for geosmin-related taste and odor in Kansas, USA, drinking water reservoirs

    Water Research

    (2009)
  • B. Dziegielewski et al.

    Predicting future demands for water

    Treatise on Water Science, chap. 1.10

    (2011)
  • M. Eslami et al.

    Thermal resistance in conductive constructal designs of arbitrary configuration: A new general approach

    Energy Conversion and Management

    (2012)
  • B.S. Evatt

    New computer graphic tools for transportation planners

    Computers, Environment and Urban Systems

    (1984)
  • L. Ghodoossi

    Conceptual study on constructal theory

    Energy Conversion and Management

    (2004)
  • I. Gupta et al.

    Optimization of water distribution systems

    Environmental Software

    (1993)
  • I. Gupta et al.

    Genetic algorithm for optimization of water distribution systems

    Environnemental Modelling and Software

    (1999)
  • J.P. Ignizio

    An introduction to goal programming with applications in urban systems

    Computers, Environment and Urban Systems

    (1980)
  • J. Izquierdo et al.

    Sensitivity analysis to assess the relative importance of pipes in water distribution networks

    Mathematical and Computer Modelling

    (2008)
  • E. Keedwell et al.

    A hybrid algorithm for the design of water distribution networks

    Engineering Applications of Artificial Intelligence

    (2005)
  • J. Keirstead et al.

    Calculating minimum energy urban layouts with mathematical programming and Monte Carlo analysis techniques

    Computers, Environment and Urban Systems

    (2011)
  • A. Kerneïs et al.

    The effects of water residence time on the biological quality in a distribution network

    Water Research

    (1995)
  • F. Kizito et al.

    Development of decision support tools for decentralised urban water supply management in Uganda: An action research approach

    Computers, Environment and Urban Systems

    (2009)
  • L. Kuddusi et al.

    A critical review of constructal theory

    Energy Conversion and Management

    (2008)
  • Lage

    Professor Adrian Bejan on his 60th birthday

    International Journal of Heat and Mass Transfer

    (2008)
  • H. Liao et al.

    Interactive water quality modeling within a GIS environment

    Computers, Environment and Urban Systems

    (1994)
  • S. Lorente et al.

    Svelteness, freedom to morph, and constructal multi-scale flow structures

    International Journal of Thermal Sciences

    (2005)
  • S. Lorente et al.

    Constructal design of distributed energy systems: Solar power and water desalination

    International Journal of Heat and Mass Transfer

    (2012)
  • S. Lorente et al.

    Fundamentals of tree-shaped networks of insulated pipes for hot water and exergy

    Exergy, An International Journal

    (2002)
  • G. Lorenzini et al.

    Constructal design applied to the optimization of complex geometries: T-Y-shaped cavities with two additional lateral intrusions cooled by convection

    International Journal of Heat and Mass Transfer

    (2012)
  • L. Luo et al.

    Optimal distribution of viscous dissipation in a multi-scale branched fluid distributor

    International journal of thermal sciences

    (2005)
  • R. Marti et al.

    Principles of scatter search

    European Journal of Operational Research

    (2006)
  • M. Mehrgoo et al.

    Constructal design of humidification-dehumidification desalination unit architecture

    Desalinaion

    (2011)
  • A.F. Miguel

    Constructal design of solar energy-based systems for buildings

    Energy and Buildings

    (2008)
  • A.F. Miguel

    Dendridic structures for fluid flow: Laminar, Turbulent and constructal design

    Journal of Fluids and Structures

    (2010)
  • E.J. Miller et al.

    Microsimulating urban systems

    Computers, Environment and Urban Systems

    (2004)
  • J.E. Moore et al.

    Mills’ urban system models: Perspective and template for LUTE (Land Use/Transport/Environment) applications

    Computers, Environment and Urban Systems

    (1995)
  • S.M. Mustonen et al.

    Evaluating online data of water quality changes in a pilot drinking water distribution system with multivariate data exploration methods

    Water Research

    (2008)
  • M.N. Neema et al.

    Multi-objective location modeling of urban parks and open spaces: Continuous optimization

    Computers, Environment and Urban Systems

    (2010)
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