Flexible design in water and wastewater engineering – Definitions, literature and decision guide

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Review Flexible design in water and wastewater engineering e Denitions, literature and decision guide Marc Spiller a, * , Jan H.G. Vreeburg a, b, 1 , Ingo Leusbrock a , Grietje Zeeman a a Department of Environmental Technology, Wageningen University, Bornse Weilanden 9, P.O. Box 17, 6700 AAWageningen, The Netherlands b KWR Watercycle Research Institute, PO Box 1072, 3430 BB Nieuwegein, The Netherlands article info Article history: Received 2 July 2014 Accepted 29 September 2014 Available online Keywords: Flexibility Robustness Adaptivity Design Uncertainty Planning Sustainability Waste water treatment/network abstract Urban water and wastewater systems face uncertain developments including technological progress, climate change and urban development. To ensure the sustainability of these systems under dynamic conditions it has been proposed that technologies and infrastructure should be exible, adaptive and robust. However, in literature it is often unclear what these technologies and infrastructure are. Furthermore, the terms exible, adaptive and robust are often used interchangeably, despite important differences. In this paper we will i) dene the terminology, ii) provide an overview of the status of exible infrastructure design alternatives for water and wastewater networks and treatment, and iii) develop guidelines for the selection of exible design alternatives. Results indicate that, with the exception of Net Present Valuation methods, there is little research available on the design and evalu- ation of technologies that can enable exibility. Flexible design alternatives reviewed include robust design, phased design, modular design, modular/component platform design and design for remanu- facturing. As developments in the water sector are driven by slow variables (climate change, urban development), rather than market forces, it is suggested that phased design or component platform designs are suitable for responding to change, while robust design is an option when operations face highly dynamic variability. © 2014 Elsevier Ltd. All rights reserved. 1. Introduction Currently, urban water and wastewater (hereafter called wa- ter) infrastructure and technologies have a lifetime of 25e100 years. Over this lifetime they have to function in systems that are increasingly subject to continuous and unpredictable changes (Gober, 2013; Milly et al., 2008). Water demand and wastewater discharge may change as a result of faster economic and urban development, water use habits, technological progress and accel- eration of climate change. As a result treatment and transport networks have to cope with unexpected changes in capacity affecting their operational efciency and effectiveness (Olsson and Newell, 1999; Panebianco and Pahl-Wostl, 2006). In addition, the introduction of sustainable urban water management sets new ambitions for water infrastructure and quality of treatment, including the recovery and reuse of water, nutrients and organics (Brown and Farrelly, 2009). This leads to changing requirements for collection and transport networks and treatment performance (Daigger, 2012; Olsson, 2013; Verstraete and Vlaeminck, 2011). To respond to these dynamics, scholars propose a transition towards exibility, adaptivity and robustness of future urban water systems (Daigger, 2012; Hering et al., 2013; Loucks, 1997; Vairavamoorthy, 2009; Wilderer and Schreff, 2000). Zandaryaa and Tejada-Guibert (2009) state that:urban water systems that can adapt to global changes are [ ] key, and urban water managers are urged to implement and design adaptive, exible, robust systems capable of responding to these changes rather than locking into standard, rigid solutions.Others specically demand adaptive water management to increase the potential or capability of the system to adjust, via changes in its characteristics or behaviour, so as to cope better with existing and future stresses(Pahl-Wostl, 2007; Pahl-Wostl et al., 2009). Yet others develop sustainability indicators and assessment frameworks of urban water systems that include exibility, robustness and adaptivity (Foxon and McIlkenny, 2002; Hellstrom et al., 2000; Sahely et al., 2005). Finally, there is a group of authors that focusses on tech- nology and infrastructure development that is exible and robust to cope with future change (Fane and Fane, 2005; Shannon et al., 2008). * Corresponding author. Tel.: þ31 (0) 317483344. E-mail address: [email protected] (M. Spiller). 1 Tel.: þ31 30 6069576. Contents lists available at ScienceDirect Journal of Environmental Management journal homepage: www.elsevier.com/locate/jenvman http://dx.doi.org/10.1016/j.jenvman.2014.09.031 0301-4797/© 2014 Elsevier Ltd. All rights reserved. Journal of Environmental Management 149 (2015) 271e281

Transcript of Flexible design in water and wastewater engineering – Definitions, literature and decision guide

Page 1: Flexible design in water and wastewater engineering – Definitions, literature and decision guide

lable at ScienceDirect

Journal of Environmental Management 149 (2015) 271e281

Contents lists avai

Journal of Environmental Management

journal homepage: www.elsevier .com/locate/ jenvman

Review

Flexible design in water and wastewater engineering e Definitions,literature and decision guide

Marc Spiller a, *, Jan H.G. Vreeburg a, b, 1, Ingo Leusbrock a, Grietje Zeeman a

a Department of Environmental Technology, Wageningen University, Bornse Weilanden 9, P.O. Box 17, 6700 AA Wageningen, The Netherlandsb KWR Watercycle Research Institute, PO Box 1072, 3430 BB Nieuwegein, The Netherlands

a r t i c l e i n f o

Article history:Received 2 July 2014Accepted 29 September 2014Available online

Keywords:FlexibilityRobustnessAdaptivityDesignUncertaintyPlanningSustainabilityWaste water treatment/network

* Corresponding author. Tel.: þ31 (0) 317483344.E-mail address: [email protected] (M. Spiller).

1 Tel.: þ31 30 6069576.

http://dx.doi.org/10.1016/j.jenvman.2014.09.0310301-4797/© 2014 Elsevier Ltd. All rights reserved.

a b s t r a c t

Urban water and wastewater systems face uncertain developments including technological progress,climate change and urban development. To ensure the sustainability of these systems under dynamicconditions it has been proposed that technologies and infrastructure should be flexible, adaptive androbust. However, in literature it is often unclear what these technologies and infrastructure are.Furthermore, the terms flexible, adaptive and robust are often used interchangeably, despite importantdifferences. In this paper we will i) define the terminology, ii) provide an overview of the status offlexible infrastructure design alternatives for water and wastewater networks and treatment, and iii)develop guidelines for the selection of flexible design alternatives. Results indicate that, with theexception of Net Present Valuation methods, there is little research available on the design and evalu-ation of technologies that can enable flexibility. Flexible design alternatives reviewed include robustdesign, phased design, modular design, modular/component platform design and design for remanu-facturing. As developments in the water sector are driven by slow variables (climate change, urbandevelopment), rather than market forces, it is suggested that phased design or component platformdesigns are suitable for responding to change, while robust design is an option when operations facehighly dynamic variability.

© 2014 Elsevier Ltd. All rights reserved.

1. Introduction

Currently, urban water and wastewater (hereafter called “wa-ter”) infrastructure and technologies have a lifetime of 25e100years. Over this lifetime they have to function in systems that areincreasingly subject to continuous and unpredictable changes(Gober, 2013; Milly et al., 2008). Water demand and wastewaterdischarge may change as a result of faster economic and urbandevelopment, water use habits, technological progress and accel-eration of climate change. As a result treatment and transportnetworks have to cope with unexpected changes in capacityaffecting their operational efficiency and effectiveness (Olsson andNewell, 1999; Panebianco and Pahl-Wostl, 2006). In addition, theintroduction of sustainable urban water management sets newambitions for water infrastructure and quality of treatment,including the recovery and reuse of water, nutrients and organics(Brown and Farrelly, 2009). This leads to changing requirements for

collection and transport networks and treatment performance(Daigger, 2012; Olsson, 2013; Verstraete and Vlaeminck, 2011).

To respond to these dynamics, scholars propose a transitiontowards flexibility, adaptivity and robustness of future urban watersystems (Daigger, 2012; Hering et al., 2013; Loucks, 1997;Vairavamoorthy, 2009; Wilderer and Schreff, 2000). Zandaryaaand Tejada-Guibert (2009) state that:” … urban water systemsthat can adapt to global changes are [ … ] key, and urban watermanagers are urged to implement and design adaptive, flexible,robust systems capable of responding to these changes rather thanlocking into standard, rigid solutions.” Others specifically demandadaptive water management to increase “the potential or capabilityof the system to adjust, via changes in its characteristics orbehaviour, so as to cope better with existing and future stresses”(Pahl-Wostl, 2007; Pahl-Wostl et al., 2009). Yet others developsustainability indicators and assessment frameworks of urbanwater systems that include flexibility, robustness and adaptivity(Foxon and McIlkenny, 2002; Hellstr€om et al., 2000; Sahely et al.,2005). Finally, there is a group of authors that focusses on tech-nology and infrastructure development that is flexible and robustto cope with future change (Fane and Fane, 2005; Shannon et al.,2008).

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Fig. 2. Conceptual representation of changes in capacity or load of an urban watersystem over 30 years as a result of seven growth or shrinkage assumption. The bracketon the right shows how a robust design would cope with the variability. The dashedlines indicate how a flexible or adaptive design would respond to variability.

M. Spiller et al. / Journal of Environmental Management 149 (2015) 271e281272

Jeffrey et al. (1997) were the first to argue for flexible technologyin water and wastewater management: “if [water and wastewater]technologies are to make a genuine contribution to the achieve-ment of sustainable communities and a sustainable world, then thepertinent focus of attention should be on the design, operation, andmanagement of adaptive technologies and technological systems.”The argument of Jeffrey et al. (1997) is that adaptive managementand the design of adaptive, flexible and robust urbanwater systemsrequires technologies that can incorporate innovation and canrespond to change. More recently, Maurer (2013) concluded thatone open issue for research is the identification and quantificationof flexibility to adapt to future events such as innovative technicaldevelopment.

A common feature across the literature reviewed above is thatthe concepts of “robustness”, “flexibility” or “adaptivity” are usedinterchangeably and there is no collective view of what a “flexible”,“robust” or “adaptive” water or wastewater infrastructure consti-tutes. However, it is imperative to define a common terminologyand understand design alternatives that can facilitate flexibility,robustness or adaptivity, because early planning and design de-cisions have a significant impact on the performance and costs oftechnologies, products and infrastructure (Maurer, 2009; Ramaniet al., 2010). The purpose of this review is firstly to define theterms “robust”, “adaptive” and “flexible”, secondly to provide anoverview of the status of flexible infrastructure design alternativesin water and wastewater networks and treatment and thirdly toprovide guidelines for decision makers about when and where toapply design alternatives. Finally future research directions will beindicated.

2. Flexibility, adaptivity and robustness e definition

To characterise the concepts of robustness, adaptivity and flex-ibility we will use literature from product design, civil engineering,aerospace and car manufacturing where these designs and con-cepts are used frequently. Saleh et al. (2003) propose to distinguishwhether a design can respond to known or unknown environ-mental changes and whether the operating objectives of thetechnology are likely to change during the lifetime of the tech-nology (Fig. 1).

According to Ryan et al. (2013), who conducted a literature re-view on robustness, adaptivity and flexibility terminology inmanufacturing engineering, robustness describes a way ofdesigning technologies or technical systems in such a way thatfunctionality and performance across a bandwidth of known butchanging operating conditions is ensured (De Neufville andScholtes, 2011; Holling and Gunderson, 2002; Ross et al., 2008).Zang et al. (2005) emphasise the relationship of the technologywith its surrounding environment: “a product or process is said tobe robust when it is insensitive to the effects of sources of vari-ability, even though the sources themselves have not been elimi-nated”. Fig. 2 conceptualises these properties of robustness.

Fig. 1. Changeability design options as a function of the technical system's objectivesand change in the environment (adapted from Saleh et al., 2003).

Following a method adapted from Maurer (2009), it estimates ofpossible operating ranges of water or wastewater assets forpossible load/capacity growth rates (�7,�5,�2, 0, 2, 5, 7%) over a30-year period. To reflect uncertainty around this general growthtrend an annual random variability of ± 50% of growth is imple-mented (equations (1)e(3) in appendix).

The load/capacity in year 30 ranges from 0.08 to 7 (a factor of>80), so technology applying a robust design philosophy wouldhave to cover this operating range. The emphasis here is on copingor resisting to environmental change without any change to theinfrastructure (Ryan et al., 2013). The operational objectives are setbefore implementation and, as a consequence of this robust design,are less likely to be able to respond to unexpected operational re-quirements that lie beyond the initial planning assumptions (Salehet al., 2003). De Neufville and Scholtes (2011) call this a “bunkermentality”, referring to the fact that robust design in civil engi-neering entails the construction of over-sized structures to guardagainst uncertain developments.

Unlike robustness, flexibility entails changes in structure, scale,functionality and operating objectives after the technology hasbeen implemented (Fricke and Schulz, 2005; Ross et al., 2008; Salehet al., 2003). In other words, the technology or infrastructure isdesigned to keep the options open to cope with new operationalrequirements as they occur. In Fig. 2 this is visualised using thedashed lines. As demand increases the infrastructure or technologycan bemodified to supply the increasing or decreasing capacity. It isproposed that every time such as change is made there is an op-portunity to implement technological advances (Fricke and Schulz,2005). A short comparison will make this distinction clearer.

� Robust - A wastewater treatment system that will maintainfunctionality for 25 years under conditions of changing waterdemand and discharge, changing wastewater composition,higher effluent water quality standards and wear and tear.

� Flexible - A wastewater treatment system that allows integra-tion of unpredicted advances in treatment technology, changesin capacity and resource recovery options after implementation.

The key difference between adaptivity and flexibility is that thelatter implies change as a result of external intervention by achange agent (i.e. human action) (Fricke and Schulz, 2005; Rosset al., 2008). Contrary to this, adaptivity is the property of adesign to deliver functionality by changing itself. No changes areimplemented by an external change agent, but internal attenuatorsin combination with sensors create a feedback that ensures adap-tation to changing circumstance (Campisano et al., 2013). Despite

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advances in system control in general and in water and wastewaterdesign in particular, currently no technological systems are capableof autonomously altering their operation objectives beyond whatwas pre-conceived. Hence, the term adaptive is more suitable forsocio-technical or natural systems where the change agent (thehuman or natural selection) are included in the system boundaries(Walker et al., 2006).

3. Design alternatives for flexibility

3.1. Robustness of design

Robustness is an essential part of flexible systems and tech-nology. Studies of natural systems provide evidence for a balancebetween stability (or resistance to change) and ability to change(Folke, 2006; Gunderson, 2000; Holling and Gunderson, 2002;Holling, 1973). These studies demonstrate that systems are ableto cope within a range of conditions, without changing structure orfunctionality. However, when an environmental change exceeds athreshold the system transform, altering its structure and operatingconditions. Indeed, the ability to be robust e coping with externalchange - while also being able to change is suggested by Gundersonand Holling (2002) as an essential property of any sustainablesystem, whether natural or socio-technical.

Robustness of design can be achieved through either robustcontrol or robust parameter design (Saleh et al., 2003). Robustparameter design is a method pioneered by Taguchi (1986). A re-view of application developments of this method is provided byRobinson et al. (2004). The goal of robust parameter design is tooptimise a defined quality characteristic of a design by choosing theright combination of control variables, such as materials, whileminimising the variation imposed on the process by the noisevariables, i.e. external changes. More simply put the choice ofmaterials, capacities, durability, etc. is optimised to ensure a pre-defined performance target over the lifetime of a product for ex-pected environmental variations. The result of the robust param-eter design is “passive robustness”, that is, a product that will bedurable or lasting (Walker et al., 2013). Similarly, robust controlleads to lasting performance over a known range of operationalrequirement by means of “active robustness”. In this approachnegative feedbacks are implemented through attenuators (pressurevalves, aerators) and mathematical tools (models and algorithms)in combination with sensors to enable technical systems to main-tain performance by adjusting to variation in their environment(Olsson and Newell, 1999). While this is similar to adaptive designas defined above, active robustness does not enable the change ofoperating objectives, it is simply a control mechanism.

3.2. Modular design

In engineering, modules are defined as components or groups ofcomponents which can be added or removed from the productnon-destructively as a unit and which provide only one basicfunction necessary for the product to operate as desired(Gershenson et al., 2003; Ulrich and Eppinger, 2008). A guidingdesign rule is that interactionwithinmodules should bemaximisedand interdependencies between modules minimised (Gershensonet al., 2004; Gu and Sosale, 1999). As a result of these designrules, modules are independent from the system and changingthem has a minimal systemic impact, which allows the incrementalintroduction of new technologies (Fricke and Schulz, 2005). Toachieve the “plug in plug out” characteristics of modular designs,interfaces should be highly standardised. This characteristic allowsrapid mixing and matching of elements to come up with combi-nations that suit new operational requirements (Baldwin and Clark,

2002; De Neufville and Scholtes, 2011). Flexibility in functionalityand operating objectives can be achieved by reconfigurations ofexisting modules or addition of new modules.

Gershenson et al. (2003) reviewed the benefits of modulardesign. According to them, life-cycle costs are reduced througheconomies of scale, as larger quantities of modules for differentapplications can be produced. Furthermore, modular design facili-tates parallel development processes; teams canwork onproducingindividual components in different locations and integrate theminto a final product. Serviceability and maintenance benefit fromgrouping components into easily removable units. When a failureoccurs the module can be identified and temporarily replaced,while the faulty module is repaired. Finally, modular design is usedfor life cycle design to enable assembly and recovery of materialsproducts (Gu and Sosale, 1999). The disadvantages of modular de-signs are the high initial development cost, since the design effort islikely to be comparatively long and complex. Modular designs arealso likely to have a lower performance as they are not customisedtowards specific circumstances (Fricke and Schulz, 2005).

3.3. Platform design

Platform designs employ a base or components that are sharedacross technologies or infrastructure (Gu et al., 2004; Simpsonet al., 2001). By sharing components, platform designs offer flexi-bility in product differentiation and increased responsiveness tonew customer demands (Robertson and Ulrich, 1998). Gu et al.(2004) distinguished component platform and modular plat-forms. Component platforms are design solutions that use onecommon basic element to develop a range of products. This is acommon approach in car manufacturing where a range of models isbuilt on the same wheel base. However, once a design has beenimplemented components are non-removable and therefore limitthe flexibility of the response. On the contrary modular platforms,as the name suggests, serve as a basis for modules that can beattached and removed from the platform. Hence, these types ofmodules allow previous implementation decisions to be reversed.

In general, platforms need to be autonomous, that is, the func-tionality of the platform should not be affected by the modules orelements attached to it. Platform designs also feature elements ofrobustness and oversizing. Pipes in water infrastructure or struc-tural components are designedwith redundant capacity to cater forlater expansion, which increases development costs.

3.4. Phased design

In phased design, construction or implementation of infra-structure progresses step by step, by first satisfying current de-mands for capacity and functionality and then expanding or addingas demand grows (De Neufville and Scholtes, 2011). Flexibility isthus achieved by keeping future options open, enabling exploita-tion of new information and technological advances as theybecome available. As with component platforms, phased designsrequire an initial commitment into oversized elements to cater forlater expansion. Furthermore, additional phases once build cannotbe removed non-destructively.

A key attribute of phased design is the preconception of a laterdevelopment at the design stage. Depending on the specific infra-structure or technology there are a variety of options to implementphased design including the provision of expansion areas, con-struction of extra capacity for load bearing (e.g. houses, bridges)orconstruction of appropriate interfaces for later expansion (DeNeufville and Scholtes, 2011). For all these designs the guidingprinciples is that the first phase must be able to function inde-pendently from potential later additions.

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2 Depending on soil type, depth of excavation, surface type. Not including cost asa result of traffic interruptions.

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One disadvantage of phased design is that by initially buildingsmall, economies of scalemay bemissed (De Neufville and Scholtes,2011). Furthermore, phased designs may require large upfront in-vestments into redundant capacity (expansion area, larger pipediameters, structural components) and interfaces for later expan-sion. However, these are often off-set by the lower cost of imple-menting change as illustrated by De Neufville et al. (2006).

3.5. Design for remanufacturing

Design for disassembly and reuse or “design for remanufactur-ing” is a design approach that enables the continuous reuse ofmaterials in an “as new” condition (Hatcher et al., 2011). Anotherarticulation of this is the Cradle to Cradle design, which hasdeveloped into a certified design approach (Cradle to CradleProducts Innovation Institute, 2011). Here products are designedto have “the potential to remain safely in a closed-loop system ofmanufacture, recovery and reuse, maintaining the highest valuethrough many product life cycles” (Braungart et al., 2007;McDonough and Braungart, 2002). According to Braungart et al.(2007) this enables short product lifetimes and thus frequentrenewal and incorporation of innovation. In this design alternative,flexibility is achieved through continuous, but environmentallysound and economically viable renewal. Practical applications arefound in the automobile industry and consumer electronics(Hatcher et al., 2011; Kumar and Putnam, 2008).

The choice of materials that can be recovered and remanufac-tured is of key concern in design for reuse and disassembly. Com-posite materials are to be avoided as this does impair recovery(McDonough and Braungart, 2002). Modularisation methods areapplied to attain better reusability and disassembly by groupingmaterials with similar lifetimes and recovery properties (Desai andMital, 2003; Gu and Sosale, 1999; Hatcher et al., 2011; Ishii, 1998;Kimura et al., 2001).

Whether design for remanufacturing does indeed lead togreater flexibility must be confirmed empirically. In the context ofincreasing resource shortages and higher customer awareness,design for remanufacturing systems is lucrative and economical(Hatcher et al., 2011). However, the advanced reverse logistics inparticular are a challenge for the economic and environmentalperformance of design for remanufacturing.

4. Flexible design alternatives for water and wastewaterinfrastructure

4.1. Water and wastewater networks

4.1.1. Design for robustnessThe most common response to uncertainty about future de-

velopments in drinking water networks is to optimise the designfor predicted future circumstance. Like in the robust parameterdesign (Taguchi, 1986), the methods applied in water and waste-water network engineering have led to passive robustness throughdimensioning the pipe network for rare discharge or demand sit-uations (Huang et al., 2010; Tsegaye, 2013). For example, in theNetherlands the drinking water network is designed for firefightingwater demand between 30 and 240 m3/h, while in the remotesections of the network maximum flow will rarely exceed 15 m3/h(Vreeburg et al., 2009). Similarly, combined sewers are designed forpeak rainfall events, while separate sewers are dimensioned tomeet expected future wastewater discharge scenarios. Whether forwater or wastewater networks, the negative consequences of over-dimensioning are a flow below the self-cleaning velocity (for waternetworks typically 0.35 m/s) and a build-up of sediments and gases(Vreeburg et al., 2009). Under specific circumstances, this can lead

to a situation where regular additional flushing of the network isrequired, consequently increasing cost as shown in a case study byPanebianco and Pahl-Wostl (2006).

4.1.2. Phased designTraditional centralised networks can be expanded spatially as

necessary, i.e. their design permits phasing. The challenge is ratherto dimension the capacity of the network appropriately. The choicelies between accepting over- or under-capacity or constructing anew network when necessary. Tsegaye (2013) used a Net PresentValuation (NPV)method to compare a traditional robust designwitha phased design option that can be developed into a decentralisedsystem by disconnecting it from the main grid. He proposes toachieve this flexibility through the introduction of parallel pipingand a high density of valves for later disconnection. His results showthat a flexible design is 14%e72% cheaper than a design with idlenetwork capacity. This corroborates the findings of Huang et al.(2010) who used a genetic algorithm to demonstrate that it can bemore cost efficient to build a small network first and then increasecapacity when demand occurs. Similarly, Vreeburg et al. (2009)proposed the design of a velocity-based drinking water networkwhich is 20% cheaper than traditional layout. The savings are ach-ieved by diminishing the amount of pipe material and trenching asthese networks are not looped and have a smaller pipe diameter. Inpractice this has led water companies “… not to build redundantcapacity but to extend networks when the expansion is needed”(Vreeburg et al., 2009). Similarly, for rainwater drainage systems,Deng et al. (2013) used a scenario-based NPV evaluation to showthat phased construction is more cost-efficient than non-phasedalternatives.

An alternative to the expansion of centralised networks is thestepwise development of autonomous decentralised networks incombinationwith treatment systems. By designing in these smaller,discreet units the uncertainty over future developments can bereduced. Autonomous decentralised units are designed near theactual required capacity (Fane and Fane, 2005; Tchobanoglous andHarold Leverenz, 2013; Wilderer and Schreff, 2000). However,decentralised networks are likely to experience relatively highdiurnal and seasonal fluctuations in demand. Thus, Olsson (2013)argues that the ability to respond to and to cope with changes isalso important for the operation of decentralised systems.

4.1.3. Modular designPrimary and secondary water and sewerage pipes commonly

have a modular design. Modularity is implemented through the useof push-fit-joints that are not bolted, screwed or glued (Marques,2013), which makes them easy to install and fit. However, thispush-fit jointing is unlikely to increase the flexibility of networks ashigh costs for labour and trenching (50e75%2 of overall costs(Langdon, 2009)) constrain its economic viability for the imple-mentation of change.

4.1.4. PlatformsAn option to reduce the installation costs of network infra-

structure are (Multi) Utility Tunnels (MUTs) (or utility corridors,utilidor), defined as: ‘‘any system of underground structure con-taining one or more utility service which permits the placement,renewal, maintenance, repair or revision of the service without thenecessity of making excavations…” (APWA,1997). These structuresare examples of platform design, as MUTs are structures that serveas hosts for network components.

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M. Spiller et al. / Journal of Environmental Management 149 (2015) 271e281 275

MUTs have been implemented for electricity, telecom, districtheating, water and wastewater in many cities including Barcelona,Helsinki, London, Madrid, Valencia, Oslo, Paris, Rouen, and Lyon(Cano-Hurtado and Canto-Perello, 1999; Legrand et al., 2004). Theycome in two forms (Cano-Hurtado and Canto-Perello, 1999):

I. searchable e allowing for selective access usually throughremovable lids

II. visitable e allowing for man entry along the entire length of theMUT.

Hunt et al. (2014) further classified them into flush-fitting de-signs located at ground level under the pavement and tunnelconstructions that are shallow (0.5e2 m) or deep (2e80 m). MUTshave been found to facilitate flexibility through lower costs ofrenewal, decommissioning (or even re-use for a purpose other thanoriginally intended) and upgrading when compared to trenching(Table 1). In urban areas with a high number of underground util-ities and the need for frequent access to the utility network, MUTsare particularly cost effective (Hunt et al., 2014). Therefore MUTsappear to be an option to implement new network infrastructuresuch as non-potable water pipes, grey and black water seweragepipes, vacuum pipes and storm water drainage when necessary(Hunt et al., 2014). Indeed, there is evidence that the MUTs built inthe 19th century facilitated the development of undergroundelectricity networks (Cano-Hurtado and Canto-Perello, 1999).However, concerns were raised about the location of differentutilities in a confined space such as fire risk, explosion, high risk forall utilities from dramatic failure of one utility and cross contami-nation between sewer and water networks (Table 1).

4.1.5. Design for remanufacturingIn recent years polyvinylchloride (PVC) and polyethylene (PE)

has been used more frequently as drinking water pipe material due

Table 1Advantages and disadvantages of MUTs (#Cano-Hurtado and Canto-Perello,1999; þHunt et al., 2014;*2005; ^Rogers and Hunt, 2006).

Advantages Disadvantages

No need for further excavationover the lifetime (60e100 years) þ

High initial investment outlay andassociated long-term maintenanceresponsibility, which is highlyunlikely to come from any singleutility company ^

Reduced and shorter disturbanceof above ground activities(footpaths, roads) due to smallerequipment and no excavation þ

Construction method is reportedlynot well known*

Repeated damage to third partyinfrastructure, roads, trees isavoided þ

Congestion below ground can beso extreme that only deep MUTsare possible if continuity of serviceprovision is to be provided whilethe new system is commissioned. þ

Protection from tree roots andground movement þ,*

Safety issues e.g.: explosion - housinggas and electricity together;contamination of drinking waterfrom sewerage#,*

Improved accessibility andassessment þ,*,#

Difficult and costly for largegravity flow sewers#,*

Facilitate renewal anddecommissioning (or even re-usefor a purpose other than intended)and upgrading

Preventing unwanted access*

Faults and breakdowns are reducedby approximately 80e95% andasset life is extended byapproximately 15e30% þ

MUTs are also argued to beinflexible because they are difficultand expensive to move*

Require a smaller combined areathan the equivalent utilitiesinstalled via open-cut#

its ease of installation and handling (light weight). Other drinkingwater pipe materials include cast iron, concrete and steel. The mostwidely used material for wastewater pipes is concrete, but PVC orhigh density polyethylene are also used.

The authors are not aware of any studies that focus on design forremanufacturing of water or wastewater pipes, nor are therestudies about the end of life management of pipes. In practice,Dennison et al. (1999) report that plastic pipe collection systemsexist in the UK. From the Netherlands it is reported that 20% of theinner and outer pipe surfaces are made from recovered pipes, while60% of core material is made from old pipes (Bureauleiding, 2014).

Generally, ferrous metals and plastics are more suitable forreuse than concrete. Scrap steel can be repeatedly recycled at nearly100% efficiency. In the Netherlands about 80% of the ferrousmetal isrecycled and 100% of the steel reinforcements are recycled fromscrap (Tam and Tam, 2006). If collected separately, plastic (PVC, PE)can be reusedwith an efficiency of 70%e90%, in high value products(street furniture, construction panels). For pipe material it is sug-gested that it can be recycled into new pipes seven times(Bureauleiding, 2014). On the contrary, about 90% of the wasteconcrete is used as low value filling material (Li, 2008; Tam andTam, 2006). Thus, while the dominant use of PE and PVC in thedrinking water networks allows reuse and remanufacturing, theabundant use of concrete for sewer networks is not conducive toreuse. In addition, sewerage pipe reuse is limited because theycorrode severely (Nielsen et al., 2008) and because of potentialhealth and environmental impacts from heavy metals, pathogensandmicro pollutants. Studies on the environmental impact of waterpipes show that PVC and PE pipes have a better environmentalperformance than ductile iron and glass fibre reinforced polymer(Sanjuan-Delm�as et al., 2013).

4.2. Water and wastewater treatment plants

4.2.1. Design for robustnessWater and wastewater treatment plants are commonly

designed to be robust against changing input parameters resultingfrom precipitation, temperature difference and population change(Rivas et al., 2008). In treatment plants, passive and active robust-ness are implemented.

4.2.1.1. Passive robustness. The planning horizon of sewage treat-ment plants is typically about 30 years and the uncertaintiesinvolved in these predictions are usually large (Sin et al., 2009).Engineers therefore increasingly use methods including MonteCarlo simulations and optimisation models to design treatmentplants optimised for multiple parameters (e.g. solid retention time,energy demand, quality requirements, etc.) (Al-Redhwan et al.,2005; Belia et al., 2009; Rivas et al., 2008). Despite these efforts,the resulting designs still incorporates idle capacity e robustness-to cope with future variability in operating conditions. Maurer(2009) shows that as uncertainty and urban growth increase, theidle capacity and costs of traditionally designed wastewater treat-ment plants will increase. He further argues that engineers areincentivised to build large, and therefore robust treatment plants,because they seek to harness economies of scale. There is evidencethat such economies of scale do exist, but that they are off-set byphased design (Maurer, 2009).

4.2.1.2. Active robustness. Increasingly, water treatment processesare automated using real time control systems to improve effi-ciency and plant performance (Campisano et al., 2013; Schützeet al., 2004). Real time control systems make a treatment plantmore robust, by automatically responding to changing conditionsin the treatment train as a result of changing influent conditions

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Table 2Selected modular water and wastewater treatment system suppliers. Results basedon a Google search with the terms module, container, water and treatment (refer-ences supplied in separate list).

Ref. No Firm name Application Treatment process

1 TIMBR™ High strengthorganic sewage(industrial)

Membrane Bio Reactor

2 Culligan Water/sewage(Industrial, business)

Reverse Osmosis,deionisation, UV

3 Envirochemie Water/sewage(Industry)

Precipitation-flocculation,dissolved air floatation,reverse osmosis,Membrane Bio Reactor

4 HeadworksBIO™ Sewage (Domestic,construction,military)

Moving bed reactor

5 SIMEM Water andwastewater

Activated sludge type,moving bed reactor,pre-chlorination, slowsand filtration, activatedcarbon

6 BoilerEquipment Plant

Water (Domestic) Membrane filtration,water disinfection

7 Hydrasyst Sewage (Mining Membrane Bio Reactor

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(external disturbance e flow rate, nutrient loading and tempera-ture can vary by a factor between 2 and 10) or treatment plantinternal disturbances such as poor pumping operation or air flow(Olsson and Newell, 1999). Thus, better controls can extend theoperational range of treatment plants.

4.2.2. ModulesModularity for flexibility is proposed as an important charac-

teristic of water technology in the 21st century (Hering et al., 2013;Olsson, 2013; Shannon et al., 2008; Wilderer and Schreff, 2000).Daigger (2012) claims that “… the modular nature of 21st centuryinfrastructure is an important feature so that it can easily be addedand expanded in response to demand …”. However, only a limitedamount of literature on modularity and evaluation of its flexibilitycould be found. Two types of modular design can be distinguishedin water and wastewater treatment:

I. True modules i.e. components that are part of a treatment trainII. Mobile, small footprint, containerised technologies e either a

full treatment or major parts (e.g. pre-, main-, tertiary-treatment).

and construction)8 Waterskrubr Water/sewage Reverse osmosis, ultra

filtration, MembraneBio Reactor

9 VeoliaSouth Africa

Water (domestic) Sand filtration, carbonfiltration, reverse osmosis,ion exchange

4.2.2.1. True modules. The most frequent application of modulardesign in water and wastewater treatment is for membrane tech-nologies (Shannon et al., 2008). Membranes need regular replace-ment, because they are subject to fouling. Modular design enablesthe simple scaling of treatment plants from household to districtsize and the cost efficient maintenance through “plug in plug out”functionality (Fane and Fane, 2005). It also allows the quickimplementation of novel higher performance membranes. World-wide, membranes are used for drinking water treatment, desali-nation and clean water industrial purposes. By the end of the 20thcentury the membrane bioreactor process, where a cross flow flatsheet membrane is submerged into activated sludge, was morewidely adopted, leading to an increase in the application ofmodularmembranes also for wastewater treatment (Fane and Fane,2005; Rachwal and Judd, 2006; van Voorthuizen et al., 2008).

The application of modular design to other processes is lesscommon. The “modular sustainable wastewater treatment” devel-oped by the water board of the Province of Limburg (Netherlands)is an example where modules have been implemented at differentpoints in a wastewater treatment plant (Pelzer et al., 2012). Thepre-treatment sand traps and screens are designed using “plug inplug out” functionality. They can be isolated hydraulically and canbe easily disconnected and replaced by modules of three differentsizes. The design is simplified as all elements are above ground,which enables easy maintenance and exchange of modules. Tanksare constructed from ring segments or U-shaped concrete frames tomake the design scalable. Insofar as possible, each tank fulfils onlyone function. Commonly, nitrogen removal through nitrificationand denitrification takes place in different sections of one reactor.To achieve independence of the processes, each process step takesplace in a separate tank or settler. For rate limiting processes suchas denitrification this offers the opportunity to implement newprocesses at a later stage. For example, the common denitrificationprocess can be replaced by higher efficiency and smaller footprintANAMMOX processes that uses ammonium as electron donor(Dongen, 2001; Hendrickx et al., 2014).

4.2.2.2. Modulation via small scale e containerised technologies.The second type of modular design is small scale containerisedtreatment systems. Due to a lack of academic literature, a review ofcommercial suppliers has been conducted (Table 2). Results showthat containerisedmembrane bioreactors units are themost widely

applied modular technology in wastewater treatment. Othermethods applied are moving bed reactors or in a few cases acti-vated sludge plants. In drinking water treatment, reverse osmosis,ultra filtration and ion exchange dominate. Mobility and their ca-pacity for pre-fabrication are the flexibility characteristics of thesetechnologies. Due to these properties they are applied in emer-gency situations, such refugee camps, as a temporary solution(Fenner et al., 2007).

4.2.3. Platform designWith the exception of the modular system from Limburg dis-

cussed above, there is no literature on platform design inwater andwastewater engineering (Pelzer et al., 2012). The system in Limburguses standardisation of the spatial and interface layout of pipes,gutters and treatment steps and the modules can be “plugged” intothis platform. Furthermore, all treatment steps are hydrologicallyindependent as they branch directly off the central gutter, whichfacilitates easy decoupling of the technologies. The standard layoutis shared by all future water treatment works in the province ofLimburg, thus ensuring compatibility across plants and simplifyingmaintenance.

4.2.4. Phased designMaurer (2009) and more recently Wang (2014) suggest staged

development of wastewater treatment plants as a means to achievehigher cost efficiency and conclude that phasing improves overallplant utilisation. Using the specific NPV, defined as the net presentvalue per unit of service, they also demonstrate that the higherinitial investments in the phased development can be off-set byreducing idle capacity. Maurer (2009) further shows that at aprojected urban growth rate of population equivalent < 2%/year, amaximum of 20% additional capital expenditure should not beexceeded, while this can be up to 100% for growth rates of popu-lation equivalent > 8%/year. Maurer (2009) does not show howphased designs can be implemented. A common approach used for

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Fig. 3. Phased development option in water treatment works Kralingen Rotterdam.Expansion area in solid line, existing treatment works in dashed line. Water treatmentworks at Kralingen were built in 1977 at a time when it was perceived as likely thatwater demand would increase further and more capacity would be required in thefuture, as a consequence an expansion area of the same size was purchased.

M. Spiller et al. / Journal of Environmental Management 149 (2015) 271e281 277

treatment plants is to provide an expansion area that allowsexpansion when needed (Fig. 3).

Phasing through decentralisation of treatment is an alternativeapproach. Fane and Fane (2005) indicate that a sequence ofdecentralized units can be installed at a lower present value costthan a large centralized systemwith the equivalent Life Cycle Costsper unit of wastewater treated. Maurer (2013) gives a morecautious conclusion and suggests that a good entry market fordecentralised treatment is in areas with high demand growth andlarge forecast uncertainty, because they can respond to demandchanges flexibly. Wang (2014) confirmed the findings of Maurer(2013), arguing that under most circumstances investment intodecentralised treatment systems can be viable as a result of costsaving on idle capacity. In addition, when recovery and reuse ofnutrients and energy are considered, decentralised systems arelikely to deliver further economic and environmental benefits (Faneet al., 2002; Gikas and Tchobanoglous, 2009; Tervahauta et al.,2013).

4.2.5. Design for remanufacturingThe authors were unable to find evidence of the design of water

or wastewater treatment plants for remanufacturing. Environ-mental legislation and concern about resource shortage maystimulate research in this area (Kumar and Putnam, 2008). A firstindication for this is the assessment of embodied greenhouse gasemissions of assets by the UKwater sector in response to regulation(Keil et al., 2013).

5. Discussion

5.1. State of the art in water engineering

Flexible design has not widely been addressed in the water andwastewater engineering literature, despite a number of scholarswho refer to it as an important characteristic of future infrastruc-ture (Daigger, 2012; Jeffrey et al., 1997; Maurer, 2013). Exceptions tothis are theoretical comparisons of robust designs, phased expan-sion and decentralisation using NPV evaluations techniques forwater networks (Deng et al., 2013; Huang et al., 2010; Tsegaye,2013) and wastewater treatment plants (Maurer, 2013, 2009;Wang, 2014).

For network infrastructure, the works of Cano-Hurtado andCanto-Perello (1999) and Hunt et al. (2014) on MUTs provide a

research direction that should be explored further. They hint at thepotential for flexibility of MUTs from a historical and theoreticalperspective. An empirical analysis of existingMUTs and their role infacilitating changes in networks would be of value. More academicanalysis of the remanufacturing of pipes is necessary as well as acritical evaluation of whether this can facilitate flexibility. Due tothe high labour costs of pipe installation, remanufacturing is un-likely to be a good strategy to support flexibility, but it could bestrategy to improve resource use efficiency.

For treatment plants, it is surprising to find that modular sys-tems and their ability to facilitate flexibility are rarely mentioned inthe academic literature, particularly as this has been proposed byscholars as a key area of innovation in the 21st century (Daigger,2012; Shannon et al., 2008). Modules are mainly investigated inrelation to easy servicing and maintenance of membrane filtrationprocesses. Containerised treatment solutions are offered by anumber of manufacturers, but the flexibility of these technologieshas not been addressed in depth. The application of modules torespond to change in the operational environment is limited topractical reports (Pelzer et al., 2012) and has not been discussed inthe academic literature. A similar picture emerges for platformdesign and design for remanufacturing. Here, industry reports therecycling and remanufacturing of pipes from the Netherlands andEngland (Bureauleiding, 2014; Dennison et al., 1999).

To further the development of flexible technologies for urbanwater systems, the applicability of methods from other sectors towater and wastewater engineering should be explored. Methodsmay include Design for Variety to develop modular platforms(Martin and Ishii, 2002), the use of interaction matrices (Gu andSosale, 1999), the flexible platform design process introduced bySuh et al. (2007) or the change propagation method for the iden-tification of the design elements that require the implementation offlexibility (Suh et al., 2007). These methods are mathematical andstructured and may not facilitate a creative process for the devel-opment of flexible design solutions. Therefore, Cardin et al. (2012)suggest a simple and intuitive “directed brainstorming” techniquefor the generation of flexible design alternatives. Similarly, TRIZ(Russian for Theory of Inventive Problem Solving) methods aresuggested as an approach to generate radically new design solu-tions and transfer innovation from one field of engineering toanother (Altshuller, 1999; Vincent et al., 2006).

Finally, empirical evidence needs to be gathered to assess whichflexible technologies contribute to flexibility in urban water man-agement. In the following section we will make a first step towardsthis, by suggesting which type of design alternative to use underdifferent development scenarios.

5.2. Guidelines for choice of flexible design alternatives

For engineers and planners it is crucial to know when to applywhich flexible design alternative, particularly in the early designand planning stage, since later changes are difficult and costly toimplement. We suggest guidelines to select different designsdepending on the character of environmental change, the ability toincorporate technological progress, the speed of change and thelocation of the implementation within the urban area.

5.2.1. Flexible design e reversibility, novelty and speed of changeTo determine which design alternative to select, the first step is

to assess the changes and uncertainty which the technology orinfrastructure may encounter throughout its useful life; the secondstep is to assess whether the design should offer the ability toimplement changes after implementation.

For the first step, we suggest developing plausible develop-ment trends, for example through the construction of qualitative

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scenarios. Scenario methods are widely used to identify long termstrategies for large investment projects including municipal waterand wastewater service planning (Krueger et al., 2001). Scenarioconstruction employs a combination of expert interviews, stake-holder discussion, trend analysis, document study and modellingto develop and illustrate plausible scenarios for future develop-ment (Mahmoud et al., 2009). A common way to represent thesescenarios is as quadrants along two uncertain developmenttrends. Fig. 4 adopts this approach, showing four differentscenarios:

1. Highly dynamic environment, but with a predictable operatingrange and limited requirement for innovation and change inoperational objectives.

2. Highly uncertain and dynamic environment. Due to uncertainty,an operating range cannot be estimated.

3. Environmental change is comparatively slow (not dynamic) anda range of operating conditions can be estimated.

Fig. 4. Flexible design alternatives allocated to suitable development scenarios (the axes shchange).

4. Environmental change is comparatively slow (not dynamic) buthighly uncertain. It is not possible to estimate possibledevelopments.

The axes in Fig. 4 show the properties of the technology: speedof change and change in operating objectives. The alternativesrobust design, platform design (distinguished into component andmodular platforms), modular design, phased design and design forremanufacturing are placed in the quadrants.

Robust designs such as the dimensioning of pipe networks andtreatment works for growth predictions or low return periodevents, are most appropriate when change is very dynamic across aknown operating range. This design option it best suited herebecause it can cope with rapid load or capacity change. However,changes in operational objectives and thus implementation ofinnovation are not applicable in this quadrant. This design optionwill incur additional costs as a result of investment in idle capacityand its maintenance.

ow flexibility properties of technologies - change in operational objective and speed of

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M. Spiller et al. / Journal of Environmental Management 149 (2015) 271e281 279

Modular designs or modular platforms, such as the “modularsustainable wastewater treatment” developed by the water boardof the Province of Limburg or containerised treatment, are suitablefor future developments that are highly uncertain, dynamic andlikely to require changes in operational objectives. Modular designsare suitable for this because they can facilitate fast responses tonew developments through “plug in plug out” functionality.Furthermore, continuous incremental innovation and change canbe implemented because modules are designed to be added toexisting systems when necessary, which enables the incorporationof new operating conditions.

Platform and phased designs, such as expansion areas and MUTsare most appropriate in situations where an operating range can beanticipated, but options for innovation are to be kept open.Furthermore, the environmental change should be appropriate forslow implementation of change and innovation, as phasing andaddition to component platforms will progress slower than formodular designs. An operating range must be known because de-signs such as the use of expansion areas, central gutters or MUTswill limit future expansions. Furthermore, it is important to notethat phased designs in particular only provide flexibility forexpansion, reduction in capacity is not part of this design strategy.Therefore, phased designs are only appropriate for load/capacitygrowth scenarios.

Design for remanufacturing, as discussed for plastic pipes, areappropriate for highly uncertain but slow changing environments,because response to new conditions progresses slowly, due to thedisassembly and reconstruction process. However, uncertainty canbe addressed as new operational objectives can be adopted,because renewal is autonomous from previous implementationsteps, that is, previous decisions will not have any influence onsubsequent changes.

When characterising the change dynamics of the water andwastewater sectors, it is possible to indicate which design alter-natives are most appropriate. Much of the research onmodules anddesign for flexibility is available in highly dynamic sectors with realmarket competition such as IT and car manufacturing. The productlifetime and the timespan between releases of new products inthese sectors can be measured in month or few years (Andrae andAndersen, 2010). Contrary to this, the water sector constitutes anatural monopoly with less rapid technological change and anexposure to “slower” change drivers, including climate change,behavioural change and urban development (Milly et al., 2008).Thus it appears that design alternatives in the bottom quadrants i.e.component platforms, phased design and design for remanu-facturing, can perform sufficiently well for the water and waste-water sector.

5.2.2. Spatial application e urban core and urban fringeThe dynamics, uncertainties and challenges faced by water and

wastewater operators differ as a function of urbanisation and thecurrent state of the infrastructure. Developing countries experiencefaster urban growth but lack the centralised water and wastewatersystems common in the western world. Similarly, cities may growat the urban-rural interface (urban fringe) while the key challengein the urban core is maintenance of infrastructure. Thus, the re-quirements for flexibility differ within urban areas and across citiesof the world.

Evidence suggests that at the urban fringe a phased extensionor decentralised growth of the network is recommended to in-crease efficiency, ensure functionality and reduce economic risk(Tsegaye, 2013). Experiences from an urban-rural area in Germanyshow that decentralised wastewater collection and treatmentwould have been better suited to respond to population decline,industrial collapse and increased water efficiencies (Panebianco

and Pahl-Wostl, 2006). In core urban areas, platform designs area preferred option, since it can be expected that a baseline ca-pacity will always be required, but the specific demand maychange over time. MUTs could offer a cost effective and environ-mentally and socially acceptable option in these areas (Hunt et al.,2014).

Modular sanitation and water supply, as now pioneered in theNetherlands (Pelzer et al., 2012), appears to be the optimal solutionfor highly dense urban areas with unpredictable changes in futuredevelopment. Alternatively, or in combination with modulardesign, centralised treatment plants for larger urban areas shouldphase their development (Maurer, 2009; Wang, 2014). This willreduce costs to the customer and allow the incorporation of tech-nological progress in later expansions. Decentralised wastewatersystems are seen as a good alternative in less densely populatedareas in developed as well as in developing countries (Massoudet al., 2009).

6. Conclusions

Flexibility describes the property of technology and infrastruc-ture to change operational objectives after implementation as aresponse to unknown future developments. We showed that,despite the recognised need for flexible technologies, there is littleacademic research on flexible technological design and evaluationin water and wastewater engineering. The exception is NPVmethods which have been more widely used recently. We sug-gested that further research should focus on exploring whetherdesign and evaluation methods used in other sectors, includingproduct design and car manufacturing, can be adapted to waterinfrastructure and technology engineering.

We also offered a framework for planners and engineers tochoose flexible design alternatives under different developmentscenarios and for different development objectives:

� Robust design e scenarios where operating range can be esti-mated and change in operating conditions is highly dynamic; nofocus on the implementation of novelty.

� Modular and modular platforms design e scenarios wheredevelopment is highly uncertain and dynamic; implementationof innovation has priority.

� Component platforms and phased design e scenarios whereoperating range can be estimated and change in operatingconditions is not dynamic; implementation of innovation isdesired.

� Design for remanufacturing - scenarios where development ishighly uncertain and not dynamic; implementation of innova-tion has priority but progresses slowly.

Of these alternatives it was argued that component platformsand phased design and design for remanufacturing, can performsufficiently well for the water and wastewater sector, becausechange in the water sector is not driven by market dynamics butslow variables including climate change, behavioural change andurban development. The capacity of design for remanufacturing todeliver flexibility needs to be explored; at present it is more likelyto be a method for efficient resource use. Finally, the characteristicsof urban development were shown to affect the choice of flexibledesign alternatives.

Acknowledgements

The authors would like to thank the water board of Limburg forproviding insights into their approach to modular wastewater

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M. Spiller et al. / Journal of Environmental Management 149 (2015) 271e281280

treatment. We also thank Roger Seaton and Sophie Rickebusch forreading and commenting on drafts of this paper.

Appendix

Equation (1) was used to generate load and capacity growth/shrinkage scenarios in MS excel with variability around a growthtrend.loadðcapacityÞwith random variationtn ¼

loadðcapacityÞtn*variabilitytn(1)

The variables in equation (1) are generated as follows:

loadðcapacityÞtn ¼ loadðcapacityÞtn*growth rateþ loadðcapacityÞtn�1

(2)

variabilitytn ¼ ð1� variability%Þ þ 2*variability%*4tnÞ (3)

where 4 denotes the random parameter, a number between 0 and 1generated with the RAND() command in MS excel.

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