# Enabling Efficient and Sustainable Transitions of Water Distribution Systems under Network Structure Uncertainty

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## Abstract

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## 1. Introduction

## 2. Modelling Framework

**Task 1**describes the generation of networks according to the approach presented by Mair et al. [18]. The generation algorithms are implemented in C++ and distributed as open source. (Available online: https://github.com/iut-ibk/DynaVIBe (accessed on 15 August 2017)) The software includes: 1) a spanning tree-based algorithm for network structure design, 2) algorithms for future demand projection and 3) an automated pipe-sizing algorithm to create WDSs based on GIS data [20,21]. Previous studies showed the high colocation of street and water distribution networks [14], which offers the opportunity to use that information for the WDS design. The required input data are the digital elevation map (DEM) of the town, the positions and the supply ratio (%) of the water sources, the street network, the nodal demands and – optional - the known pipe sections (see “set” pipe in Figure 2). In case the WDS and/or the nodal demands are incomplete or even unknown, the missing information represent variables in the stochastic WDS generation process. This principle applies for all unknown WDS parts, regardless of existing and/or future WDS. For this reason, the WDS is designed for the initial (existing) and the final (planning) stage. For example, in a WDS only the pipes with a diameter greater than 200 mm are known. In that case, the missing pipe connections to demand nodes can be stochastically generated on basis of the overlying street network, by assuming the WDS network |P| being a subset (|P| ⊆ |S|) of the street network |S|. Resulting WDSs, using different a different level of detail in the input data, are shown in Figure 2 on the right. With this modelling approach, a robust network structure can be identified for the future, not only for newly planned WDSs, but also for the redesign of existing systems (e.g., closing loops for redundancy).

_{h,max}as design value and b) an assumed pressure surface inclination of 5 m/km. The pipe diameters are then divided into discrete diameter classes. Let |P

^{i}| = {p

_{1}, p

_{2}, …, p

_{ni}}

^{i}be the set of all pipes at initial stage i, where ni is the number of pipes at stage i. Conversely, |P

^{f}| = {p

_{1}, p

_{2},…, p

_{nf}}

^{f}is the set of all pipes at final stage f, where nf is the number of pipes at stage f. Then the intersection of the sets |P

^{i}| ∩ |P

^{f}| is built and the designed diameters compared. Pipes with a changing diameter are added to the new pipe set |P

^{up}| = {}, representing the necessary pipe upgrades. According to Mair et al. [14] the generated WDS set is classified with the cycle index (CI), describing the degree of loops (alternative flow paths) in the network. With this approach sufficiently working “engineering” solutions, rather than optimal WDS are generated with adequate computational capacity. For the target application to large case studies (with several thousand elements), the reduced computational effort is a compelling argument.

**Task 2**presents the creation of transition stage models to describe the detailed step-by-step progress of construction and deconstruction phases on basis of the master plan. In doing so, specific points in time between initial stage i and final stage f, i.e., intermediate stages, are investigated. Figure 4 shows an example of an intermediate stage j where some parts of the initial WDS are disconnected, while other parts are added at the same time. Not only the pipe structure is changed, also a shifting of the nodal demand from the disconnected to the new connected WDS parts occurs. The transition stage models comprise the initial, intermediate and final stages of the WDS. The number of intermediate stages is a model input parameter and depends on the temporal definition within the master plan (e.g., phased construction and deconstruction zones of new building blocks).

**Task 3**). In the current work, the physical location and attributes of WDS components that are unaffected from the deconstruction and the construction processes are maintained over time, i.e., the intermediate and final-stage WDS are dependent on their previous transition stages and originate from the initial stage (network structure and pipe diameter). The scheduling of the determined pipe upgrades (|P

^{up}|) to achieve high performances at final stage is part of a design strategy. In this work, we test a simple “doing-all-at-the-end” approach, where necessary pipe upgrades are performed at the final stages of the transition process.

**Task 3**, a model interface to a hydraulic solver is implemented where each transition stage model (see

**Task 2**) is simulated under different scenarios. In WDS modelling, it is state-of-the-art to use extended period simulations to consider the diurnal demand patterns of several representative days [24]. In this work, the hydraulic solver EPANET 2 [25] is used, where each transition stage model (

**Task 2**) is simulated under different scenarios. In a first simulation run, the system is solved for one day with high water consumption to identify supply problems. Then, the simulation is repeated for a period of low water usage (six consecutive days of low water consumption are simulated to determine maximum water age and potential stagnation problems). The water age is calculated from the residence time of the storage tank and the travel time in the network from the source node(s) to the demand nodes at low flow conditions. For this purpose, we used the water quality analysis tool of EPANET 2 [25].

**Task 4**describes the performance evaluation of the WDS. Helpful tools to assess hydraulic and quality requirements of WDSs are global performance indicators (PIs). By definition, the PIs take values in the interval from 0 (worst performance) to 1 (best performance), depending on predefined threshold values and a performance criterion. Furthermore, statistical values complement the investigation. First, the nodal performances PI

_{k}are determined for each node k before they are averaged and weighed to one global representative value PI. For this study, we analyzed a minimum performance indicator at peak demand and the mean pressure head at average demand under normal operation conditions (e.g., no pipe breaks). The threshold values for PIs differ among case studies and design guidelines of sufficient performance, and have a strong impact on the overall performance. Therefore, they must be defined by the user [20]. The minimum pressure performance, including the selected threshold value in accordance with the Austrian Standard ÖNORM B2538 [26], is defined as:

_{k,min}is the nodal pressure head in meters. Furthermore, the water quality of the WDS model is described by the maximum water age, which is a driving factor related to microorganism growth [27]. The maximum nodal water age w

_{k,max}in hours is calculated based on flow velocities and pipe lengths and assessed after a low demand period of 144 h and contains the initial water age from the storage tank. In this work, the nodal water age performance is defined as:

_{k}to consider the hydraulic importance of node k (e.g., number of supplied customers) as follows:

_{r}is assessed [28,29]. The index is based on the power balance of the network and gives information about how much pressure surplus is available at each network node, compared to a minimum required head [30]. The pressure surplus can be seen as a “buffer capacity” that can be used under critical operation conditions (e.g., pipe breaks), when the internal energy dissipation increases. The capacity index is assessed at peak demand and defined as follows:

_{D}= $\sum _{j=1}^{{N}_{p}}{q}_{j}\u2206{H}_{j}$ is the dissipated power, and P

_{D,max}= $\sum _{s=1}^{{N}_{r}}{q}_{s}{H}_{s}-\sum _{k=1}^{{N}_{n}}{d}_{k}\overline{{H}_{k}}$ describes the maximum dissipated power to meet the minimum head constraints $\overline{{H}_{k}}$ at node i. For this case study, the minimum required nodal head $\overline{{H}_{k}}$ is adopted with the nodal elevation plus an additional pressure head of 15 metres at node k. H

_{s}refers to the nodal head of supply source s and ∆H

_{j}is the head loss along pipe j. The inflow from source s is described with q

_{s}, d

_{k}represents the nodal demand and q

_{j}is the flow in pipe j. N

_{r}, N

_{n}and N

_{p}state the number of supply sources, nodes, and pipes, respectively. A more detailed description can be found in Di Nardo et al. [31].

## 3. Case Study Application and Numeric Results

- The basic assumption for the scenario “Baseline” is that the total demand remains constant within the transition period. It represents no change in population but a change of its location (Q
_{h,max,2100}= 128 L/s). - The scenario “Growth” implies a linear increase of water usage of 30 percent until the end of the century [33]. This represents a population or demand per capita growth (Q
_{h,max,2100}= 166 L/s). - The scenario “Stagnation” describes an economic decay, where migration of labour occurs due to an assumed reduction of mining activities [33]. The water demand is taken to gradually decrease by 30 percent until 2100 (Q
_{h,max,2100}= 90 L/s).

**Task 1**). This gives the opportunity to apply and test the approach also to variety of initial WDS structures. However, more detailed and complementary information (e.g., actual WDS) can easily be integrated, if available, and allowed in terms of legal aspects.

**Task 1**describes the creation of the WDS model set. For this application the required input data are the digital elevation map (DEM) of the town, the position of the current and future water sources, and the real street networks for the initial (year 2012) and final stages (year 2100). The future street network data is taken from architecture plans. Due to the data restrictions, the population density and nodal demand distribution are assumed to be uniform over the area of interest with 1,000 implemented demand points. Elevation differences in the investigation area allow for the construction of a functioning gravity driven WDS and hence, no pumping is required (see Figure 5a). The generated WDS includes the positions of the reservoir, tank and pressure reduction valves (PRVs) and flow control valves (FCVs). The locations of the valves within the 30 stochastic WDS structures are unchanged. The FCVs are positioned between reservoir and tank, while the locations of the PRVs are chosen based on minimum and maximum pressure head requirements (30–100 m) within each pressure zone. Regarding the size of the generated networks, they consist of approximately 100 km pipe length (~4000 pipes) at the initial stage and about 75 km (~2000 pipes) at the final stage. This shows that the future network is planned to be denser as compared to the existing one at all demand projections.

^{i}| ∩ |P

^{f}| is about half the size of |P

^{i}|, which implies that 50% of pipes at the initial stage WDS keep their physical location in the final-stage WDS. Therefrom approximately 10% of the pipe diameters have to be upgraded due to changing flow conditions and to maintain a connected network (e.g., new water source). This builds the pipe set describing necessary upgrades (|P

^{up}|).

**Task 2**describes the generation of the transition stage models. For this purpose, the master plan defining the phased transition process of the town is used. The transition stages represent the years 2012, 2013, 2018, 2023, 2033, 2050 and 2100. Figure 8 presents an example of the creation of six transition stage models for one planning option. It can be seen that the town is step-by-step moved by a simultaneous deconstruction of the initial WDS and construction of a new piping system. The resettlement progress of people living in the deformation zones is modelled by transferring the demand nodes to the new city centre, assuming the same uniform spatial distribution as for the final design stage. The total demand is dependent on the investigated scenario.

^{up}|) from initial and final network design (see

**Task 1**), a simple “doing-all-at-the-end” approach is investigated: Pipe upgrades for achieving the efficient final-stage WDS are performed at the stages in 2050 (pipe replacement rate on average 2%) and the final stage 2100 (pipe replacement rate on average 8%). This means that until stage 2050, the pipe diameters of the WDS remain unchanged, while all of the newly constructed pipes are designed for the final stage. With this approach it can be determined, (a) whether the WDS can tolerate the occurring changes or not, and (b) at which transition stage additional redesign (e.g., pipe replacements) might be necessary for the 3 scenarios and the 30 planning options.

**Tasks 3**and

**4**present the hydraulic simulations and the performance evaluations of the WDSs. The application of the developed approach is shown with the outcome of the performance analysis during the WDS transition of Kiruna as a model. In Figure 9, we firstly show example contour plots of the pressure distributions at peak demand for three different stages (2012, 2033 & 2100) and two scenarios (Baseline & Growth).

**Task 1**).

^{i}|\|P

^{f}|), must be redesigned at the intermediate stages 2033 and 2050 to maintain acceptable service pressures.

## 4. Discussion

^{up}|, and/or (2) network redesign of overloaded WDS components that are already deconstructed at the final-stage WDS (|P

^{i}|\|P

^{f}|). Future work will also address the integration of the real WDS in the network generation procedure.

## 5. Conclusions

^{i}| ∩ |P

^{f}|) was insufficient. The performance drops revealed that the pressure surplus (quantified by the capacity index) of the remaining WDS after a major disconnection was not high enough to cope with the occurring changes (“loss of capacity”). At the stages of year 2033 and 2050, an improved design strategy with additional pipe redesign in the pipe set (|P

^{i}|\|P

^{f}|) must be performed for the future scenarios of constant demand and demand increase (e.g., population growth).

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 2.**Concept of the stochastic generation of water distribution systems (WDSs). Following the idea from Sitzenfrei et al [22].

**Figure 3.**Long-term network dynamics in the concept of network generation by integrating stages in the design of the WDS.

**Figure 4.**Creation of intermediate stage WDSs on basis of the master plan and the initial and final stage.

**Figure 5.**(

**a**) Current Kiruna with digital elevation map (DEM); (

**b**) Current and future street networks (planned) with the step-by-step expansion of deformation zones, according to the master plan.

**Figure 6.**Future demand scenarios (

**a**) and two possible planning options (WDS1 & WDS2) with different network structure (

**b**) and (

**c**).

**Figure 7.**One of thirty created planning options representing (

**a**) the initial and (

**b**) the final stage.

**Figure 9.**Pressure distributions at peak demand for the Baseline scenario for the initial stage 2012 (

**a**), the final stage 2100 (

**b**), the transition stage 2033 (

**c**), and the Growth scenario for transition stage 2033 (

**d**).

**Figure 10.**Performance developments for three demand scenarios and WDS structure variations; (

**a**) System capacity, (

**b**) Mean pressure head, (

**c**) Minimum pressure performance and (

**d**) Maximum water age performance.

**Figure 11.**(

**a**) Threshold exceedances of unit head loss (top) and velocity (bottom) at peak load for scenario “Growth”, (

**b**) WDS with maximum water age for scenario “Baseline” at transition stage 2033.

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## Share and Cite

**MDPI and ACS Style**

Zischg, J.; Mair, M.; Rauch, W.; Sitzenfrei, R.
Enabling Efficient and Sustainable Transitions of Water Distribution Systems under Network Structure Uncertainty. *Water* **2017**, *9*, 715.
https://doi.org/10.3390/w9090715

**AMA Style**

Zischg J, Mair M, Rauch W, Sitzenfrei R.
Enabling Efficient and Sustainable Transitions of Water Distribution Systems under Network Structure Uncertainty. *Water*. 2017; 9(9):715.
https://doi.org/10.3390/w9090715

**Chicago/Turabian Style**

Zischg, Jonatan, Michael Mair, Wolfgang Rauch, and Robert Sitzenfrei.
2017. "Enabling Efficient and Sustainable Transitions of Water Distribution Systems under Network Structure Uncertainty" *Water* 9, no. 9: 715.
https://doi.org/10.3390/w9090715