Optimisation and reliability assessment of water distribution networks are complicated processes. Most of the research focuses only on the pipes without considering other network components, such as tanks. Despite the benefits that the tanks may bring, they are usually omitted in the optimisation process or in reliability considerations. Various indices from the literature that describe network reliability are calculated exclusively based on pipe failure analyses for single demand scenario, without taking into consideration the volume of possibly existing balancing tanks. The research discussed in this paper aims to incorporate the demand balancing tanks to the optimisation process and also find out their influence on the total cost and reliability of the network. A tool called NORAT (Networks Optimisation and Reliability Assessment Tool) has been used, which determines the required balancing volume, optimises pipe diameters and tank elevations and finally calculates the total cost of supply. NORAT further assesses the hydraulic reliability of the network. The tool has been tested on a synthetic network by applying different combinations of topography, supply schemes and locations of water sources and tanks. The results prove the ability of NORAT to employ balancing tanks, both in optimisation and reliability assessment processes.

## INTRODUCTION

Demand balancing tanks in water distribution networks (WDN) are mostly relevant for their role during regular supply. The balancing volume will be designed based on the diurnal patterns under normal conditions, and some emergency provision will be added depending on the local safety requirements. Consequently, the final choice of appropriate volume will need to be in tune with the selection of pumps and pipe diameters in the network.

Despite the fact that they can be a significant buffer during various calamities, the balancing tanks are rarely considered in the network optimisation and reliability assessment. It is a bit confusing, because generally the reliability can be defined as an ability of the network to provide an acceptable level of service under all supply conditions. The researchers define this acceptable level of service based on the most appropriate parameter that reflects it, being nodal demands and pressures, or water quality. Hence, in periods of deficient demand, the tank volume can compensate the deficit for at least a limited period of time, delaying negative consequences of the calamity. There are many methods introduced in the literature for assessment of WDN reliability, lacking this aspect. On the other hand, the proper quantification of WDN reliability is an uneasy task, because it depends on a combination of factors, such as the overall network conditions, uncertain and variable demands and other different standards related to water consumption (Trifunović 2006). It is therefore difficult to pick the most appropriate measure of reliability, as it requires weighing of the true relevance of the assessment measure against the ability to compute it (Wagner et al. 1988). More recent terminology views WDN reliability through an assessment of network resilience, robustness and sustainability (Lansey 2012).

Owing to a complex computational process, most researchers initially focussed exclusively on the piping system while optimising the network design, omitting other network components, such as balancing tanks, pumps or valves. In the next generation of optimisation algorithms, pump optimisation was considered but mostly geared towards the minimisation of energy consumption. Finally, the more recent research on the role of valves deals with network topology, i.e., segmentation for optimal location of valves to minimise isolated parts of the network during calamities (Giustolisi & Savić 2010; Giustolisi et al. 2014). Still, the WDN hydraulic reliability will be mostly assessed without incorporating the volume of balancing tanks, despite the benefits they may bring. This can also be attributed to the fact that the network reliability is commonly assessed for one (given) demand scenario, i.e., by running snapshot simulations.

Abunada et al. (2014) made an attempt to include the balancing tanks into the optimisation of network design by developing a tool called NORAT (Networks Optimisation and Reliability Assessment Tool). This paper offers an extended description of that research and adds more insight to the tool including some thoughts on reliability considerations from the perspective of demand balancing volume, to find out their influence on the total cost and service levels for a given demand scenario on a typical consumption day. The additional relevance of this attempt lies in the fact that many networks in arid areas of the world operate intermittently at regular intervals and with the support of numerous roof tanks; such is the case, e.g., in the Middle East and North Africa region (Abu-Madi & Trifunović 2013).

### Optimisation of water distribution networks

The optimisation process of WDN aims at finding the best way to transfer water from the source to the customers while respecting given constraints. These could be the minimum and maximum nodal pressures or demands, maximum and minimum pipe velocity or unit head-loss, or any other design criterion required to be satisfied. The optimal solution should consider the best combination of network components (pipes, valves, pumps, tanks, etc.), which satisfy the constraints. For instance, the optimisation may include selecting pipe diameters, sizing tanks, selecting valves settings and locations and/or pumps number and locations (Banos et al. 2010).

There are two types of optimisation. The first one is a single-objective optimisation in which a single criterion is optimised to its minimum or maximum, such as minimising cost or maximising the benefit. The second is a multi-objective optimisation in which multi-conflicting objectives are optimised and compromised, such as minimising the cost and maximising the benefit simultaneously (Weise 2009). The early studies mostly focussed on single-objective optimisation that minimises the total cost. This optimisation is simple and quickly indicates the nature of the problem, but it is not entirely suitable for WDN applications, as it does not compromise with other objectives such as water quality and/or network reliability. Because of this, researchers further gave considerable attention to the multi-objective optimisation as being more flexible and realistic for WDN applications. Nevertheless, both the conventional single- and multi-objective optimisations require a huge number of simulation runs, which makes them not practical for applications on large WDN (Vamvakeridou-Lyroudia et al. 2005; Di Pierro et al. 2009; Batchabani & Fuamba 2012).

The literature includes a significant number of different optimisation algorithms, which have been applied to WDN. The most popular algorithm used in WDN optimisation is the genetic algorithm (GA). The GA is suitable for network applications as it deals with complex, nonlinear and discrete problems (Babayan et al. 2005). On the other hand, the GA has some shortcomings: one is that it requires a high number of evaluation functions to achieve convergence to the optimal solution. Second, the GA is time-consuming. For large WDN, the GA process can take up to a few days, even using a modern PC (van Zyl et al. 2004). Still, owing to the fast development of computational speed, numerous improved GA algorithms for design purposes have been developed in the past years (Farmani et al. 2006; Krapivka & Ostfeld 2009; Wang et al. 2014).

### Reliability assessment of water distribution networks

Many researchers have tried to define WDN reliability. Table 1 includes some of those frequently mentioned in the literature (Abunada et al. 2014).

Table 1

Definition of WDN reliability (Abunada et al. 2014)

Researchers Definition
Tung (1985)  Probability that flow can reach all the demand points in the network
Cullinane et al. (1992)  Ability of the system to provide service with an acceptable level of interruption in spite of abnormal conditions of the water distribution system to meet the demands that are placed on it
Goulter (1995)  Ability of a water distribution system to meet the demands that are placed on it where such demands are specified in terms of the flows to be supplied (total volume and flow rate) and the range of pressures at which the flows must be provided
Xu & Goulter (1999)  Ability of the network to provide an adequate supply to the consumers, under both regular and irregular operating conditions
Tanyimboh et al. (2001)  Time-averaged value of the flow supplied to the flow required
Lansey et al. (2002)  Probability that a system performs its mission under a specified set of constraints for a given period of time in a specified environment
Researchers Definition
Tung (1985)  Probability that flow can reach all the demand points in the network
Cullinane et al. (1992)  Ability of the system to provide service with an acceptable level of interruption in spite of abnormal conditions of the water distribution system to meet the demands that are placed on it
Goulter (1995)  Ability of a water distribution system to meet the demands that are placed on it where such demands are specified in terms of the flows to be supplied (total volume and flow rate) and the range of pressures at which the flows must be provided
Xu & Goulter (1999)  Ability of the network to provide an adequate supply to the consumers, under both regular and irregular operating conditions
Tanyimboh et al. (2001)  Time-averaged value of the flow supplied to the flow required
Lansey et al. (2002)  Probability that a system performs its mission under a specified set of constraints for a given period of time in a specified environment

Ostfeld (2004) classifies the assessment methods of WDN reliability into three categories: analytical (connectivity/topological) methods, hydraulic (simulation) methods and heuristic (entropy) methods. Analytical (connectivity/topological) methods refer to the measures associated with the probability that a given network remains physically connected. However, he mentions that the analytical methods do not provide a comprehensive coverage of reliability considerations and are useful only for initial screening of the system to identify serious problems. He refers this to two reasons. The first reason is that, in practice, connection of a fully operational path to a source is not sufficient condition to ensure that the demand nodes in the system are functional. If insufficient pressure exists in the system, some of the demand nodes may not receive water. The second reason is that the analytical methods do not consider the system failure conditions. Hydraulic (simulation) methods deal with the main purpose of the WDN, which is to convey the required quantity and quality of water with given pressures to the required locations at any times. These methods require good details about the network layout and operation including the failure records of the network components. These are the most widely explored methods nowadays. Heuristic (entropy) methods use entropy as a surrogate measure for reliability. By that approach, the distribution systems designed to carry maximum entropy flows are generally reliable. However, the question still arises what a given level of entropy means in terms of reliability for a given system.

Lansey (2012) attempts to ‘decompose’ the network reliability by introducing the definitions of the US National Science Foundation on sustainability, resilience and robustness of various infrastructure, which includes drinking water systems. Accordingly, the distribution network ‘sustainability’ ‘implies providing adequate and reliable water, … supplies of desired quality – now and for future generations – in a manner that integrates economic well-being, environmental protection and social needs'. Furthermore, infrastructure ‘resilience’ is ‘the ability to gracefully degrade and subsequently recover from a potentially catastrophic disturbance that is internal or external in origin’. Lastly, ‘the “robustness” of a system to a given class of disturbances is defined as the ability to maintain its function when it is subject to a set of disturbances of this class'. To distinguish the terminology is important for two reasons: (1) systems can be defined as reliable if they are robust and/or resilient but they can be robust and not resilient, and as well they can be resilient and not robust; and (2) often in the literature, the network reliability is assessed by actual analysis of its resilience (indices) as is the case in Todini (2000), Prasad & Park (2004) and Trifunović (2012).

### Demand balancing tanks

Demand balancing tanks play an essential role in WDN making a significant impact on the overall network performance in regular and irregular situations. If they are well-designed and located, they should improve the overall network performance and reduce the total cost (Vamvakeridou-Lyroudia et al. 2007). Batchabani & Fuamba (2012) discuss different approaches used in the design of demand balancing tanks. Tanks have been traditionally designed based on the local design guidelines (regulations) of the country. The weakness of the guidelines is that they usually focus on tank volume and not on the other variables, such as elevation and location. In addition, they may cause a risk of tank over-sizing even if the WDN can operate efficiently with less storage volume. Common optimisation algorithms are suitable in principle to design the tanks considering the main decision variables (volume, minimum and maximum level, shape, etc.). However, with increased numbers of decision variables, the number of possible solutions grows exponentially. On the other hand, if too many decision variables are ignored, the optimisation model can produce solutions that may be inapplicable technically and commercially.

From an engineering point of view, the tanks will be mostly operated in combination with pumping stations, located on the pumps' suction (as a source tank) or their pressure side (as a service tank within the distribution area). The balancing volume will depend entirely on the operation of the pumps and the nature of the diurnal pattern and will be maximised for the constant operation of pumps at average flow conditions. Trifunović (2006) developed a spreadsheet application for simplified and straightforward design of balancing volume without applying the optimisation tools, and this is illustrated in Figures 1,23. Figure 1 shows the situation of pumping at constant capacity (of 1,455.24 m3/hour), which represents the average flow. The table shows the balance of inflow and outflow, and cumulative volume of the tank based on the valid diurnal pattern.

Figure 1

Tank balancing volume based on the constant pumping and diurnal demand pattern (adapted from Trifunović (2006)).

Figure 1

Tank balancing volume based on the constant pumping and diurnal demand pattern (adapted from Trifunović (2006)).

Figure 2

Tank balancing volume based on the variable pumping and diurnal demand pattern (adapted from Trifunović (2006)).

Figure 2

Tank balancing volume based on the variable pumping and diurnal demand pattern (adapted from Trifunović (2006)).

Figure 3

Tank balancing volume based on the intermittent pumping and diurnal demand pattern (adapted from Trifunović (2006)).

Figure 3

Tank balancing volume based on the intermittent pumping and diurnal demand pattern (adapted from Trifunović (2006)).

More pumping will demand less of the balancing volume, as shown in Figure 2, and as well, the balancing volume will have to grow significantly in case of interrupted pumping, which can be a choice for optimal use of block electricity tariffs, as shown in Figure 3.

In summary, for the same system, i.e., the diurnal pattern and pump characteristics, based only on the different pump schedules, the three figures show three substantially different balancing volumes: 3,594.42, 908.30 and 18,554.30 m3, respectively. Hence, only the complete cost–benefit analysis including the investment, operation and maintenance costs can give the answers about optimal design of balancing volume.

## METHODOLOGY AND FRAMEWORK OF NORAT

NORAT is a decision support tool developed by Abunada et al. (2014) with the objective to (1) optimise, (2) calculate the cost and (3) assess the hydraulic reliability of WDN. The tool consists of two modules: network optimisation module (‘NetOpt’) and network reliability assessment module (‘NetRel’). NORAT has been developed in C ++ language code by integrating the EPANET programmer's toolkit functions for hydraulic analyses. The optimisation algorithm used is Evolving Objects (EO) of Keijzer et al. (2002). This GA algorithm is in the public domain and was randomly selected by the fact that the choice of the most effective GA was not among the objectives of this research. Nevertheless, the EO has proven to be fairly effective and fast in the analyses done.

### NetOpt module

The framework of the NetOpt module is shown in Figure 4, and its components are further detailed in Table 2.

Table 2

NetOpt module components

Component Description
Network input file The EPANET input file (*.inp) that includes the network to be optimised
Optimisation parameters A text file that includes the EO input parameters. Some of these parameters can be changed (usually by trial and error approach) based on the case study, while the others are fixed
Costs structure A text file that includes the data required for costs' calculation, such as pipe unit costs, interest rate, project life, etc.
Optimised network file An EPANET file that includes the optimised network
Outputs report file An Excel file that contains the total cost of the optimised network in addition to the total process duration and all the settings entered during the model process
Optimisation constraints The constraints, which the optimisation will be based on: both the minimum nodal pressure and the maximum pipe unit head-loss, or only on the minimum nodal pressure
Optimisation hour The demand hour, which the optimisation process will use: the maximum demand hour or any other specific hour
Tank settings If the network includes a tank, the following settings are required to be set:
• Maximum allowed tank elevation

• Maximum tank volume depth

• Demand balance control hours (hours required to match the target demand balancing curve)

Partial optimisation An alternative option to deliberately exclude selected pipes and/or a tank (volume and elevation) from the optimisation process, which will then keep their original properties in the network input file
Component Description
Network input file The EPANET input file (*.inp) that includes the network to be optimised
Optimisation parameters A text file that includes the EO input parameters. Some of these parameters can be changed (usually by trial and error approach) based on the case study, while the others are fixed
Costs structure A text file that includes the data required for costs' calculation, such as pipe unit costs, interest rate, project life, etc.
Optimised network file An EPANET file that includes the optimised network
Outputs report file An Excel file that contains the total cost of the optimised network in addition to the total process duration and all the settings entered during the model process
Optimisation constraints The constraints, which the optimisation will be based on: both the minimum nodal pressure and the maximum pipe unit head-loss, or only on the minimum nodal pressure
Optimisation hour The demand hour, which the optimisation process will use: the maximum demand hour or any other specific hour
Tank settings If the network includes a tank, the following settings are required to be set:
• Maximum allowed tank elevation

• Maximum tank volume depth

• Demand balance control hours (hours required to match the target demand balancing curve)

Partial optimisation An alternative option to deliberately exclude selected pipes and/or a tank (volume and elevation) from the optimisation process, which will then keep their original properties in the network input file
Figure 4

NetOpt module framework.

Figure 4

NetOpt module framework.

The process starts with the calculation of required tank volume. In the next step, the optimisation of the pipe diameters and tank elevation takes place. Finally, the total cost of the network will be calculated. The composition of the tank volume is shown in Figure 5, which consists of the following:
1. Demand balancing volume: calculated based on the diurnal pattern, according to the principles elaborated in Figures 1,23.

2. Emergency volume for maintenance works, pipe failure events, fire fighting, etc.: assumed arbitrarily at twice the average hourly demand.

3. ‘Dead’ volume/depth to protect the tank from staying dry: assumed arbitrarily at 20 cm.

Figure 5

Required tank volume – left, and demand balancing volume – right (adapted from Trifunović (2006)).

Figure 5

Required tank volume – left, and demand balancing volume – right (adapted from Trifunović (2006)).

By assuming the maximum height of the tank, the model determines the required pipe diameters, minimum water level and initial water level at the beginning of the simulation. After calculating the required tank volume, NetOpt starts the optimisation process, performed by using the EO algorithm. The optimisation includes the pipe diameters and tank elevation based on minimising the total cost. The optimisation is constrained by minimum nodal pressure, maximum pipe unit head-loss and tank inflow/outflow that preserve the target demand balancing curve in the network.

The optimisation process is done by generating many solutions (populations) and then selecting the best solution based on the objective function. In each population generation, the objective function first calculates the total cost of the pipes. Then, the function checks if the optimisation constraints are satisfied or not with this population. If the constraints are not satisfied, the objective function will add a proportional penalty cost to the total cost. Finally, the objective function returns the total cost (including the penalty costs) to be evaluated. The optimal solution will be in this case the least-cost one that satisfies the optimisation constraints. The whole process of the objective function is summarised in Figure 6. There: D and L are the diameter and length of m pipes, respectively; Qavl/req is the available/required tank flow (inflow/outflow), where the required tank flow is determined during calculating the demand balancing volume; Pavl/min is the available/required minimum nodal pressure; Havl/max is the available/maximum pipe unit head-loss. F1, F2 and F3 are factors determined in advance by trial and error approach until reaching the best values that guide to the optimal solution.

Figure 6

Objective function in EO algorithm (NetOpt module).

Figure 6

Objective function in EO algorithm (NetOpt module).

Finally, the NetOpt module calculates the total cost of the network based on the unit cost of each component, interest rate and design/repayment period. Cost calculations include the total investment cost, operation and maintenance costs (O&M). The annual loan repayment is calculated using the annuity equation:
1
where A is the equivalent annual cost of the present investment cost P, n is the project life in years and r is the interest rate.

### NetRel module

NetRel module assesses exclusively the hydraulic reliability of WDN, by using the following three indices: (1) the available demand fraction (ADF) of Ozger & Mays (2003); (2) the network resilience (In) of Prasad & Park (2004); and (3) the network buffer index (NBI) of Trifunović (2012). The module framework is shown in Figure 7 and the module components in Table 3.

Table 3

NetRel module components

Component Description
Network input file The (optimised) EPANET input file (*.inp)
Outputs report file An Excel file that includes all the calculations details and final results in addition to the total process duration and all the settings entered during the process
Threshold pressure Minimum pressure value that reflects the level of service. It is required in the PDD simulation
Emitter exponent Emitter exponent value. It is required in the PDD simulation
Assessment duration Selected times to assess the network: a snapshot hour, minimum and maximum demand hours, or the full extended time period
Full pumping operation An option to operate all the existing pumps including the stand-by units in the assessment of the network reliability
Multipliers definition An option to multiply the baseline demands, pipe diameters and lengths by selected factors in order to analyse their impact (gradual increase or reduction) on the network performance
Initial link status Checking if there is any link (pipe or valve) initially closed. The model includes four options to deal with links, which are initially closed, as follows:
• 2. Open the link and exclude it from the assessment

• 2. Keep the link closed and exclude it from the assessment

• 3. Open the link and include it in the assessment

• 4. Keep the link closed and include it in the assessment

Component Description
Network input file The (optimised) EPANET input file (*.inp)
Outputs report file An Excel file that includes all the calculations details and final results in addition to the total process duration and all the settings entered during the process
Threshold pressure Minimum pressure value that reflects the level of service. It is required in the PDD simulation
Emitter exponent Emitter exponent value. It is required in the PDD simulation
Assessment duration Selected times to assess the network: a snapshot hour, minimum and maximum demand hours, or the full extended time period
Full pumping operation An option to operate all the existing pumps including the stand-by units in the assessment of the network reliability
Multipliers definition An option to multiply the baseline demands, pipe diameters and lengths by selected factors in order to analyse their impact (gradual increase or reduction) on the network performance
Initial link status Checking if there is any link (pipe or valve) initially closed. The model includes four options to deal with links, which are initially closed, as follows:
• 2. Open the link and exclude it from the assessment

• 2. Keep the link closed and exclude it from the assessment

• 3. Open the link and include it in the assessment

• 4. Keep the link closed and include it in the assessment

Figure 7

NetRel module framework.

Figure 7

NetRel module framework.

ADF is a reliability index that expresses the demand proportion still available in the network after pipe failure events. The calculation starts with non-failure condition and then failing the pipes in sequence, calculating the network ADF for each one (Equation (2)), and finally calculating the average value of ADF for the entire network (Equation (3)).
2

3
In the above equations, Qavl is the available demand after pipe failure, Q is the demand under normal conditions, ADFnet,j is the ADFnet corresponding to the failure of pipe j, and m is number of pipes.
Prasad & Park (2004) upgraded the resilience index Ir of Todini (2000) to their network resilience In, based on the concept of the power balance:
4
where Hs/i indicates the piezometric heads at l sources (which includes all the reservoirs and tanks that supply the network) and the piezometric heads at n nodes (which includes all the demand nodes and tanks supplied from the network), respectively. is the minimum piezometric head required to satisfy the demand at node i. Furthermore, Qs/p/i is the corresponding supplying flow (s), pump flow (p) and nodal demand flow (i), respectively. The adaptation of the Todini index includes the index Ci, which takes care of the nodal uniformity, according to Equation (5) where Dj is the diameter of m pipes connected to node i:
5
NBI of Trifunović (2012) is derived graphically from his hydraulic reliability diagram. By adding the weighting proportional to the pipe flows under regular supply conditions, NBI can be calculated as in Equation (6):
6
where Qtot is the total demand in the network under normal supply, Qtot,j is the total demand in the network after the failure of pipe j, Qj is the flow in pipe j under normal condition and m is the total number of pipes.

To determine the available demand in both ADF and NBI considerations, the hydraulic analysis should be performed by the pressure-driven demand simulation (PDD). The PPD simulation in NetRel is done by using the algorithm of Pathirana (2010). This algorithm considers three demand conditions as follows:

1. Full demand: if Pi ≥ ECUP, Qi,PDD = Qi,DD

2. Partial demand: if 0 < Pi < ECUP,

3. No demand: Pi ≤ 0, Qi,PDD = 0

Pi is the pressure at node i, ECUP is threshold pressure, Qi,PDD/DD is the demand at node i, which is calculated by PDD and DD simulation, respectively, and k is the emitter coefficient, which can be estimated by Equation (7) as follows:
7

## NORAT APPLICATION AND DISCUSSION OF RESULTS

The case study selected to apply NORAT is Safi town network demonstrated as a design exercise in Trifunović (2006). The layout of the network is shown in Figure 8(a) including the baseline demands (l/s) and pipe lengths (m). All the nodes follow the diurnal demand pattern shown in Figure 8(b), except the factory that is working from 7 a.m. to 7 p.m. with constant consumption. The seasonal peak factor is 1.406, which includes 10% water loss.

Figure 8

(A) Layout of Safi town network (including nodal base demands and pipe lengths) and (B) domestic demand pattern.

Figure 8

(A) Layout of Safi town network (including nodal base demands and pipe lengths) and (B) domestic demand pattern.

### Simulation scenarios

The original network layout has been transformed into 12 variants by combining the following:
1. Three topographic terrains: flat, hilly and valley, as shown in Figure 9.

2. Two pipe configurations: fully looped and quasi-looped, shown in Figures 10(a) and 10(b). The quasi-looped cases have an adjusted total demand as the factory node has been removed. To avoid possible confusion, the fully looped and quasi-looped schemes are further named as ‘looped’ and ‘branched’, respectively.

3. Two source locations: at the edge (E) and in the middle (M) of the area, shown in Figure 10.

Figure 9

Topographic terrains.

Figure 9

Topographic terrains.

Figure 10

(A) Looped scheme with source and tank locations and (B) branched scheme with source and tank locations.

Figure 10

(A) Looped scheme with source and tank locations and (B) branched scheme with source and tank locations.

In each of the 12 cases, the network is first analysed with the existing water source and then by incorporating demand balancing tank at different locations in the network; nine locations in the looped networks (total 10) and six locations in the branched networks (total seven).

The locations of the tanks are selected at the border and in the middle of the network, to be close/far from the water source. The sources and tanks are connected by 300 and 500 m pipe, respectively, and have elevations equal to the network nodes they connect. In this way, a total of 102 network variants are generated from the original network.

Each network is named as XYZN, where X denotes the topography (F – flat, H – hilly and V – valley), Y is the network scheme (L – looped and B – branched), Z is the source location (E – edge and M – middle), and N is the tank location number as in Figures 10(a) and 10(b) (N equals 1 if there is no tank incorporated in the network).

### Application steps

Each network variant is subject to the following steps:

1. The required pumping capacity: number of pumps, duty heads and flows and pumping operation schedule have been specified and based on the pump efficiency pattern as shown in Table 4.

2. NetOpt optimisation based on the arbitrary settings shown in Table 5 (randomly selected, only for the sake of the software demonstration).

3. Checking if the optimisation constraints are satisfied. If not, the source pumping capacity is not sufficient and steps 1 and 2 must be repeated with new pumping capacity. The penalty cost factors can also provide unsatisfactory results, but these were tested in advance.

4. The target demand balancing pattern was matched four times; at every 1, 2, 4 and 6 hours (the network optimised four times), where the least-cost design that satisfies the constraints will be selected.

5. The reliability of the optimised network assessed by NetRel based on the settings in Table 6. The minimum tank volume in the optimised network includes the dead- and emergency volumes. The minimum volume in the reliability analyses is reduced to the dead volume to enable NetRel to consider the emergency volume.

6. Analysing the output results of both NetOpt and NetRel models.

Table 4

Pump efficiency

Flow (Q0.25 Qduty 0.5 Qduty 1.0 Qduty 1.5 Qduty 1.75 Qduty
Efficiency (%) 20 60 75 65 30
Flow (Q0.25 Qduty 0.5 Qduty 1.0 Qduty 1.5 Qduty 1.75 Qduty
Efficiency (%) 20 60 75 65 30
Table 5

NetOpt model settings

Parameter Value
Minimum nodal pressure constraint 20 m
Maximum pipe unit head-loss constraint 5 m/km
Optimisation hour Maximum demand hour
Maximum tank elevation 30–40 m
Maximum tank volume height 7 m
Pipe laying costs, in USD/m:
D = 80 mm 60
D = 100 mm 70
D = 150 mm 90
D = 200 mm 130
D = 300 mm 180
D = 400 mm 260
D = 500 mm 310
D = 600 mm 360
Investment cost pumping station (USD) 5 × 103 × Q0.8, Q = maximum installed flow (m3/hour)
Constructing tanks (USD) 35 × 104 + 150 × V, V = tank volume (m3
Elevated tank, supporting structure (USD) 3 × H × V, V = volume (m3), H = elevation (m)
O&M cost of pipes 0.5% of total pipe investment cost
O&M cost of pumping stations 2.0% of pump investment cost
O&M cost of tanks 0.8% of tank investment cost
Energy cost 0.15 USD/kWh
Interest rate 8%
Design period 20 years
Parameter Value
Minimum nodal pressure constraint 20 m
Maximum pipe unit head-loss constraint 5 m/km
Optimisation hour Maximum demand hour
Maximum tank elevation 30–40 m
Maximum tank volume height 7 m
Pipe laying costs, in USD/m:
D = 80 mm 60
D = 100 mm 70
D = 150 mm 90
D = 200 mm 130
D = 300 mm 180
D = 400 mm 260
D = 500 mm 310
D = 600 mm 360
Investment cost pumping station (USD) 5 × 103 × Q0.8, Q = maximum installed flow (m3/hour)
Constructing tanks (USD) 35 × 104 + 150 × V, V = tank volume (m3
Elevated tank, supporting structure (USD) 3 × H × V, V = volume (m3), H = elevation (m)
O&M cost of pipes 0.5% of total pipe investment cost
O&M cost of pumping stations 2.0% of pump investment cost
O&M cost of tanks 0.8% of tank investment cost
Energy cost 0.15 USD/kWh
Interest rate 8%
Design period 20 years
Table 6

NetRel model settings

Parameter Value
Assessment hour Maximum demand hour
Minimum pressure 20 m
Emitter exponent 0.5
Parameter Value
Assessment hour Maximum demand hour
Minimum pressure 20 m
Emitter exponent 0.5

### Results and discussion

The optimisations based on running extended period simulations (EPS) took anything between 5 (FBM3) and 64 minutes (FLE7) depending on the variant, and using a standard laptop computer. For the applied GA settings, all 102 simulations resulted in the minimum pressures in the networks ranging from 19.38 m (HBM5) up to 21.78 m (HLM3), the vast majority being in the vicinity of the targeted minimum pressure of 20 m. The range of maximum unit head-loss was between 1.55 m/km (FBE6 and FBM7) and 5.02 m/km (HLM9). Based on the same demand in all the cases, the calculated volume of balancing tanks was also the same. Regardless of the location, the satisfactory balancing pattern was maintained in all the cases, which is first illustrated in Figure 11 showing HLE, HBE, VLE and VBE cases.

Figure 11

Tank volume variation for E-source cases: Y – tank depth (m), X – time (hours).

Figure 11

Tank volume variation for E-source cases: Y – tank depth (m), X – time (hours).

As expected, in virtually all the cases, the costs of branched configurations were lower than the costs of loped configurations; this is illustrated in Figure 12 showing the same cases as in Figure 11. Finally, the overview of the reliability indices for the given variants is shown in Figure 13. Despite the discrepancies between the values of In on one side, and ADFavg and NBI on the other side, it is visible in all the categories that the variant without tank (the first in the bar charts) is less reliable than the rest. Significantly, different values in Figure 13 originate from the nature of the indices, which has been discussed by Trifunović (2012).

Figure 12

Total costs per variant| (USD) for E-source cases.

Figure 12

Total costs per variant| (USD) for E-source cases.

Figure 13

Reliability measures per variant for E-source cases.

Figure 13

Reliability measures per variant for E-source cases.

The trends of ADFavg and NBI comply in most of the cases, because both indices are based on the loss of demand calculated in the PDD; this loss is generally lower in better connected networks. On the other hand, the value of In index is influenced by the surplus head (i.e., the supplying head), as Equation (4) shows. Hence in looped configurations, the lower source head results in lower In values than those of NBI, while the opposite will be the case in branched configurations (also because the NBI for branched networks equals zero).

The same results for the networks with centralised source (M) are further shown in Figures 14,1516.

Figure 14

Tank volume variation for M-source cases: Y – tank depth (m), X – time (hours).

Figure 14

Tank volume variation for M-source cases: Y – tank depth (m), X – time (hours).

Figure 15

Total costs per variant (USD) for M-source cases.

Figure 15

Total costs per variant (USD) for M-source cases.

Figure 16

Reliability measures per variant for M-source cases.

Figure 16

Reliability measures per variant for M-source cases.

The demand balancing function has also been preserved more or less in a similar way in all the cases. The comparison of the costs and the reliability indices shows lower operational and therefore also lower total costs in the case of the centralised source in the hilly terrain and looped configurations (HLM), while the reliability is generally higher. The branched networks in the same terrain configurations and the same location of the source (HBM) also showed lower operational but higher investment costs, making the total costs comparable to the HBE category. However, the reliability in the case of the source located at the edge was expectedly lower. On the other hand, the networks located in the valley configuration appeared to be more expensive, due mostly to higher operational costs in the case of the centralised source, while their reliability is still generally higher.

Last but not least, the results for the flat terrain configuration are shown in Figures 17,1819.
Figure 17

Tank volume variation for flat terrain configuration: Y – tank depth (m), X – time (hours).

Figure 17

Tank volume variation for flat terrain configuration: Y – tank depth (m), X – time (hours).

Figure 18

Total costs per variant (USD) for flat terrain configuration.

Figure 18

Total costs per variant (USD) for flat terrain configuration.

Figure 19

Reliability measures per variant for flat terrain configuration.

Figure 19

Reliability measures per variant for flat terrain configuration.

What can be immediately observed in these results is that not that much cheaper branched networks are significantly less reliable, compared to the looped ones. The price difference in the case of the centralised sources becomes smaller, although the difference in the reliability is smaller, as well. Also, the networks in the flat terrain appear to be generally less reliable than those in the hills and valleys, but they are also somewhat cheaper.

Finally, the results per group are indicated in Table 7, displaying the range of costs and reliability indices. The peak values do not necessarily correspond to the same network; the subscript number in each figure indicates the ID of the network. The values in bold represent the absolute minimum and maximum, respectively.

Table 7

The range of costs and reliability indices for various groups of networks

Nets Investment cost (US$) O&M cost (US$) Total cost (US$) ADFavg NBI In HLEx 539,5111–598,9325 203,96810220,2651 749,33010805,7085 0.9211–0.9923 0.44510.9233 0.5131–0.6693 HBEx 465,0301–524,6392 187,0603–189,4955 653,9271–713,4762 0.8011–0.9702 0.0821–0.8102 0.66710.7892 VLEx 591,2792637,5245 137,12210–149,1551 725,87810–777,3045 0.9181–0.9894 0.4181–0.8944 0.4261–0.5773 VBEx 479,4421–551,0957 122,1564–124,9267 603,4231–676,0217 0.7961–0.9592,7 0.0561–0.7382 0.5931–0.6457 HLMx 478,5531–557,0945 132,8648–138,5551 617,1071–693,1685 0.94210.9933 0.4381–0.9203 0.4681–0.6383 HBMx 521,3031–588,0865 123,5323–126,8275 647,3551–714,9125 0.7321–0.9827 0.0471–0.9047 0.6671–0.7675 VLMx 507,2751–581,7606 202,78210–218,6691 721.82510–787,9786 0.9351–0.9843 0.3671–0.8156 0.4721–0.5823 VBMx 529,5293–567,9517 189,2084–192,4841 718,7553–759,3627 0.7321–0.9567 0.0441–0.7567 0.6041–0.7236 FLEx 595,0709–636,3255 137,3809–149,3051 732,4509–775,9285 0.9081–0.9834 0.3741–0.8494 0.1713–0.3118 FLMx 507,28310–576,6175 133,17510–145,1041 640,45810–713,3825 0.9441–0.9823 0.4541–0.7863 0.2252–0.3725 FBEx 488,4561–552,0387 122,9334–124,8517 612,8801–676,8897 0.7941–0.9482 0.0481–0.6732 0.2611–0.3563 FBMx 546,1634–589,6527 124,2344–127,9551 670,3984–716,3867 0.7291–0.9597 0.0361–0.7797 0.2711–0.5097 Nets Investment cost (US$) O&M cost (US$) Total cost (US$) ADFavg NBI In
HLEx 539,5111–598,9325 203,96810220,2651 749,33010805,7085 0.9211–0.9923 0.44510.9233 0.5131–0.6693
HBEx 465,0301–524,6392 187,0603–189,4955 653,9271–713,4762 0.8011–0.9702 0.0821–0.8102 0.66710.7892
VLEx 591,2792637,5245 137,12210–149,1551 725,87810–777,3045 0.9181–0.9894 0.4181–0.8944 0.4261–0.5773
VBEx 479,4421–551,0957 122,1564–124,9267 603,4231–676,0217 0.7961–0.9592,7 0.0561–0.7382 0.5931–0.6457
HLMx 478,5531–557,0945 132,8648–138,5551 617,1071–693,1685 0.94210.9933 0.4381–0.9203 0.4681–0.6383
HBMx 521,3031–588,0865 123,5323–126,8275 647,3551–714,9125 0.7321–0.9827 0.0471–0.9047 0.6671–0.7675
VLMx 507,2751–581,7606 202,78210–218,6691 721.82510–787,9786 0.9351–0.9843 0.3671–0.8156 0.4721–0.5823
VBMx 529,5293–567,9517 189,2084–192,4841 718,7553–759,3627 0.7321–0.9567 0.0441–0.7567 0.6041–0.7236
FLEx 595,0709–636,3255 137,3809–149,3051 732,4509–775,9285 0.9081–0.9834 0.3741–0.8494 0.1713–0.3118
FLMx 507,28310–576,6175 133,17510–145,1041 640,45810–713,3825 0.9441–0.9823 0.4541–0.7863 0.2252–0.3725
FBEx 488,4561–552,0387 122,9334–124,8517 612,8801–676,8897 0.7941–0.9482 0.0481–0.6732 0.2611–0.3563
FBMx 546,1634–589,6527 124,2344–127,9551 670,3984–716,3867 0.7291–0.9597 0.0361–0.7797 0.2711–0.5097

Without any intention to draw general conclusions on the impact of topography, network configuration and location of sources and tanks on the network costs and reliability, the following is a summary related to the table:

1. HLM1 and VLE5 are the networks with the lowest and highest investment costs, respectively.

2. VBE4 and HLE1 are the networks with the lowest and highest operational costs, respectively.

3. VBE4 and HLE1 are the networks with the lowest and highest total costs, respectively.

4. FBM1 and HLM3 are the networks with the lowest and highest ADFavg values, respectively.

5. FBM1 and HLE3 are the networks with the lowest and highest NBI values, respectively.

6. FLE3 and HBE2 are the networks with the lowest and highest In values, respectively.

The selected networks and calculation results served only to demonstrate the ability of the tool. Applying different energy tariffs, interest rates, range of altitudes, or any other parameter would obviously yield different ranking of the networks, but one thing that can confidently be verified is that tanks significantly contribute to the hydraulic reliability, regardless of the index applied.

### Available demand fraction for extended period simulations

As mentioned in Table 6, all three measures applied for reliability assessment were calculated for the maximum demand hour. Usually, this is the moment when the balancing tanks are nearly full and therefore a more critical situation may in theory occur at another moment when they are nearly empty, despite the fact that the demand is lower. To encapsulate the volume of the tank(s) into the calculation of network reliability in the right manner, additional information would also be necessary, which deals with the reaction time (from the moment the failure occurred until the moment the repair started), and the repair time (duration). In that case, the reliability measure does not only depend on the volume of the tank but also how quickly the regular supply can be restored by doing proper intervention in the network. Equally, such an index will depend on the overall duration of EPS. This needs mentioning in view of the fact that normal EPS durations are 24 hours; however, if the failure is modelled to occur later during the simulation period, the restoration of normal service may stretch into the following day, (or even later, in the case of serious calamities).

To illustrate this concept, an extended version of ADF index has been proposed as a reliability measure, which takes into consideration the storage volume and calculates the actual loss of demand over entire period of EPS based on the suggested reaction and repair times. The ADFsv (sv index denoting ‘storage volume’) can be calculated in two possible ways, assuming the same reaction and repair time for all links as follows:

1. Conducting a conventional single failure analysis of all available links at the same moment/hour, all for the purpose of identifying the most critical pipe(s).

2. Conducting a single failure analysis of all available links within a preselected duration of time, including the total duration of EPS, the latter leading to some sort of averaged ADFsv.

A PDD algorithm has been developed outside the NORAT environment, based on the EPS extrapolation of Equation (3), to illustrate the concept on the simple network taken from the EPANET software tutorial (Rossman 2000), shown in Figure 20.
Figure 20

EPANET tutorial example.

Figure 20

EPANET tutorial example.

Figures 21 and 22 show the impact of the failure happening in the system at 1 a.m. and 6 a.m., respectively, having the reaction time of 2 hours and the repair time of 6 hours. As expected, the effect of failures happening at 1 a.m. is less severe than if they happen at 6 a.m., which is reflected in the ADFsv values that are 0.854 and 0.832, respectively. Actually, due to low demand and enough water in the tank, the effect of the failure at 1 a.m. results in the demand shortages in the system only from 4 a.m., as seen in Figure 21. Shown in both figures is the tank depth variation that clearly shows the contribution to the supply before normal supply has been restored. Lastly, Figure 23 shows the situation when the reaction time and repair time have been shortened to 1 and 3 hours, respectively. As a result, the value of ADFsv increases from 0.832 to 0.859.
Figure 21

Failure at 1 a.m., reaction/repair time = 2/6 hours, ADFsv = 0.854.

Figure 21

Failure at 1 a.m., reaction/repair time = 2/6 hours, ADFsv = 0.854.

Figure 22

Failure at 6 a.m., reaction/repair time = 2/6 hours, ADFsv = 0.832.

Figure 22

Failure at 6 a.m., reaction/repair time = 2/6 hours, ADFsv = 0.832.

Figure 23

Failure at 6 a.m., reaction/repair time = 1/3 hours, ADFsv = 0.859.

Figure 23

Failure at 6 a.m., reaction/repair time = 1/3 hours, ADFsv = 0.859.

## CONCLUSIONS

The presented results show clearly the impact of balancing tanks on network reliability. Nevertheless, drawing more precise, i.e., general conclusions on the benefits from having a balancing tank in the network and its impact on the reliability is a much more complex task. Incorporating the demand balancing tank at an appropriate location can decrease the total cost and increase the reliability of the network, and the other way round. However, no general guidelines can be proposed to determine where the best location of the tank in the network is. This location can only be determined by generating several design scenarios while testing different tank locations based on the land configuration, availability and finally selecting the best scenario by the compromise between the total cost and the reliability of the network. Each case in practice will be specific on its own, and a tool like NORAT can be helpful to assess it thoroughly and make design choices with a higher degree of confidence.

NORAT showed the initial capability to consider the demand balancing tanks in the optimisation (NetOpt model) and reliability assessment (NetRel model) processes. NORAT also proved to be a fairly robust decision support tool providing full assessment and helping to trade off between the available design alternatives, and eventually draw a conclusion about the best compromise between the reliability and the total cost. Nevertheless, further steps in the development of NORAT are needed to include multiple tanks, as well as tanks, which have a multiple purpose in the network, such as water towers. Moreover, a need to include the volume, i.e., a duration of supply from the tank after the failure has happened, has been detected and eventually mitigated, requires redefinition of hydraulic reliability indices that are currently calculated based on the snapshot hydraulic simulations. The last example showing a hydraulic reliability measure based on extended period simulations leads to more accurate indices than is currently the case in the literature. This is to be further tested by integrating the new index into the NORAT software.

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