## Abstract

The widespread uptake of household water-saving systems (i.e. appliances, fittings, rainwater harvesting tanks, etc.) usually aims to reduce the gap between water demand and supply without considering the performances of downstream sanitary sewers (SSs). This paper presents an analysis approach that examines the lifespan interaction of water-saving schemes (WSSs) and operation of existing SSs. Examined are three probable ways of using (or not using) these water systems, including the conventional (baseline), full application and optimal selection of efficient WSSs. For optimality, a method that maximises the WSS potential efficiency (overall) and minimises the cost of WSSs including the associated savings across the entire existing SS subject to constraints at the end of the planning horizon has been formulated. The problem is solved using a non-dominated genetic algorithm to obtain optimal solutions. Decision variables include various water use (or saving) capacities of water-saving schemes at different inflow nodes (locations). The method was demonstrated on the subsystem of the Tsholofelo Extension SS. The results indicate impactful and revealing interactions between water use efficiency, instantaneous hydraulic performances and existing SS upgrade requirements due to different applications of WSSs. The impacts and revelations observed would inform decisions during lifespan operations and management of SSs.

## HIGHLIGHTS

• Conventional, optimal and maximum water savings have been analysed considering existing sanitary sewers.

• Trade-offs between cost, cost savings and water efficiency have been analysed.

• Water-saving related sanitary sewer (SS) upgrade postponement has been articulated.

• Flows across the SS lifespan are quantified using the proposed velocity violation factor.

• Spatial and temporal considerations would inform existing SS upgrades.

## INTRODUCTION

Globally, the widespread manufacturing and uptake of water-saving schemes (WSSs) at household levels is currently on the rise. These developments reduce the gap between water demand and supply. Household water sources (rainwater harvesting and greywater recycling and/or reuse systems) and water-saving products (appliances and fittings) all referred to as WSSs in this paper, are progressively being developed, promoted and used in households. In the context of water supply in general, as much as reducing water demand may have benefits (i.e. less wastewater generated), there are potential adverse effects on the performances of sanitary sewers (SSs) downstream. The adverse effects may arise because existing networks would be subjected to less amounts of wastewater than they were designed to dispose of.

According to the sewer design principle, SS (pipe) flow velocities mainly depend on the pipe slopes, diameters and demands (or wastewater flows). Changing one or more of these parameters would prompt appropriate adjustment(s) of others to maintain the required levels of service in existing sewers. However, for existing networks, it is worth noting that slopes and conduit diameters remain the same (fixed) while wastewater inflows and velocities change, thus leading to questions that motivate the current study. This principle implies that a potential decrease in wastewater flows subjects existing sewers to potential risks such as those of blockages that are associated with the infringement of pipe flow self-cleansing velocities (see McGhee 1991; Mattsson et al. 2015). These velocities are generally used as design constraints (or objectives) that are necessary for obtaining the acceptable performances of sewers, i.e. SSs are required to meet certain hydraulic standards.

The aforementioned principles show the need to analyse WSSs (and their associated benefits) in the context of technical aspects of SSs. This analysis is necessitated by the link that exists between the use of WSSs and SSs (i.e. WSSs affect hydraulics of SSs), which suggests that the benefits (e.g. cost savings) of saving water in households may conflict with the hydraulic performances of existing SSs. WSSs also present challenges in terms of various lifespans that require cautious decision making in order to find more viable and cost-effective schemes. On the other hand, reduction of water supplied, and wastewater generated can contribute significantly to reduction in the capital and operation costs. Water saving decreases treatment by reducing the need for storage of effluent water, untreated waste overflows and providing for increased efficiency of the plant processes by reducing flow rates (Robinson et al. 1984). However, reduced flow rates can also impact wastewater treatment facilities negatively. In this regard, McKenna et al. (2018) predicted a significant increase in effluent total ammonia nitrogen, nitrates, nitrites and total inorganic nitrogen concentrations, and thus higher costs when the influent flow rates were reduced by more than 43% in the treatment plants they studied. Therefore, the modern trends of implementing WSSs require proactive management and integrated water system approaches to obtain sustainable solutions. Despite the principles discussed here, many studies (e.g., Fidar et al. 2010; Proenca et al. 2011; Campisano & Modica 2015) have considered water demand management separately without taking into account water network (e.g., SS) technical issues or vice versa (e.g., Austin et al. 2014; Duque et al. 2016).

The aim of this study is to develop and demonstrate a method that consists of analysis approaches, which examine, compare and reveal lifespan interactions of existing SS hydraulics and different levels of WSS uptake resulting from conventional, optimal and full applications of WSSs. This approach should provide efficiencies and SS upgrade requirements. The method would therefore support timely and appropriate decisions for system upgrades and promote incorporation of the widespread use of WSSs in the management of SSs because reduction of water consumption becomes the main priority both economically and environmentally. The method evaluates how the required hydraulic performance(s) of existing SSs may be violated by the selection of WSSs (i.e. certain level of water use efficiency) during their service life. In the uptake of WSSs, the existing SS operational performances would be basically tested against technical standards amidst the resultant benefits such as cost savings for SS wastewater treatment. However, water quality implications of WSSs are not considered. After the background of WSS applications, the proposed method is explained and applied to a subsystem of a SS network.

## BACKGROUND

In the past, the predominant approach to water management has been supply development rather than integrated supply and demand management (Robinson et al. 1984). Household demand management increasingly play a key role in water supply sustainability. The demand management interventions considered include the use of water-saving appliances and fittings together with some measures, which provide alternative sources of water that promote water use efficiency. Trends in water research put emphasis on household WSSs because of their potential benefits to communities (e.g., Fidar et al. 2010; Basupi et al. 2014). Regarding the water source perspective, Campisano & Modica (2016) evaluated the potential of rainwater harvesting systems (RWHS) to mitigate peak roof runoff due to rainfall and found that a significant peak runoff reduction exists. In another study, GhaffarianHoseini et al. (2015) ascertain that accurate design and configuration, simulation, localisation and proper maintenance are expected to accomplish the goal of using RWHSs. Furthermore, Campisano et al. (2017) reviewed the practical, theoretical and social aspects of RWHSs to ascertain state-of-the-art after noticing that RWHSs have not been implemented with systems that maximise the benefits. They found out that the degree of RWHS implementation and technology solutions are strongly influenced by economic constraints and local regulations. In this study, the proposed method assumes social acceptance of all the WSSs. Therefore, the effects of RWHSs among other WSSs are also evaluated in the hydraulic performance and the related upgrade requirements of SSs in this study.

One of the most relevant studies to the current research was carried out by Penn et al. (2013b) who modelled the effects of on-site greywater reuse and low-flush toilets on municipal sewer systems. Later, Penn et al. (2013a) optimised types of greywater recycling systems that were combined with different flush volumes of toilets, but a full range of household WSSs and the ranges of product capacities that require attention as WSSs increasingly become popular were not examined. In the similar context, Basupi (2019) integrated WSSs in the design of SSs where new decisions of the SS components and/or functions were made, together with the selection of WSSs. However, considering that most SSs have already been constructed (fixed) and WSSs are generally implemented in the vicinity of such existing SSs, a different scope, which include analyses that are most appropriate for existing SSs rather than SS designs is therefore considered in this paper. In terms of objectives considered, Basupi (2019) optimised cost (minimised) and cost savings (maximised) without the explicit inclusion of system-wide water efficiency (%), which would further enhance trade-offs (i.e. further influencing SSs) as it has been herein addressed accordingly. In terms of SS performance analyses, Basupi (2019) and other earlier studies did not articulate and use the novel timescale and hydraulic performance indicators associated with the implementation of WSSs such as the SS upgrade requirements and self-cleansing velocity violation factor. Therefore, consequent implications of WSSs on the proposed instantaneous SS hydraulics and SS upgrade requirements of SSs, during their entire service period and beyond, respectively, have not been quantified and/or explored yet. Performance indicators that include self-cleansing velocity violation factor, upgrade postponement, and system wide WSS efficiency considering instantaneous demands in the interaction of existing SSs and different WSS applications are therefore articulated as shown in the following section and demonstrated in the case study.

## METHODOLOGY

The integrated modelling and analysis approaches considered in this paper include fiscal, SS hydraulic and the related upgrade deferral performances of different water-saving interventions. These interventions include optimal solutions, conventional and full application of WSSs. The conventional approach is associated with options of standard intervention measures while the full application of WSSs refers to the use of the most efficient components of WSSs available. An informative methodology that captures the interaction effects of WSSs and SSs is articulated and explained in the following sections.

### Performances of WSSs and SSs

In order to understand and reasonably compare the interactions of WSS interventions with existing SSs, different existing water-saving models (products) and their characteristics form part of the options evaluated. The WSSs consist of local water sources such as RWHSs (i.e. different tank sizes), water-saving appliances (washing machines, dishwashers) and fittings (toilets, kitchen taps, basin taps, baths, and showerheads). Further details of water-saving products are presented in the case study section.

#### Economic cost and benefits

Among other performance indicators, WSSs are analysed in terms of costs (i.e. in any currency). The total cost includes the cost of WSSs, together with cost savings in the system. The cost is expressed as equivalent annual worth (EAW) (McGhee 1991) because costs of WSS investments have different lifespans, i.e. capital expenditures are basically related by lifetime to operational expenditures. In this cost method, the capital recovery factor is used to convert the capital costs of the interventions to comparable quantities. In other words, the EAW method allows rational comparisons of intervention options that do not have equal lifespans. This method may incorporate costs of transport, treatment and final disposal of wastewater. The annual total cost () of WSSs in any currency is therefore estimated as follows:
(1)
(2)
(3)
where is the total number of SS inflow nodes; is the total number of households and/or any other water use entities in the catchments of the SS inflow nodes; is the total number of WSS components; is the capital recovery factor; r is the interest rate of the k-th WSS investment; nk is the lifespan of the k-th WSS component under consideration; and are the capital and annual operational costs of the k-th WSS component, respectively; and is the total cost saving. Note that all costs/benefits are added regardless of cost ownership because the approach used is a holistic method, which considers the general cost to the society:
(4)
where and are the unit costs of energy () and billed water required by a particular WSS, respectively; and (used to determine Bss,op) are the volumes of water used by the k-th WSS component and the total (or system) volume, respectively. The energy required for heating water that is apportioned according to water use of fixtures and appliances is estimated in kWh using the equation below:
(5)
where m is the mass (kg) of water that requires heating. Well documented proportions of WSS components that use hot water are used to estimate m, and also ratios between cold and hot water use for components are required (e.g., equal use); c is the specific heat capacity of water (J/kg/oC); is the change in water temperature (oC); and is the efficiency of the heating system that is used. The constant in the equation is a factor that converts Joules to kWh. The benefits (cost savings) that are eventually subtracted from the total cost are calculated as functions of water-saving efficiencies of a specific WSS () and the overall system () as follows:
(6)
(7)
where and correspond with standard products in this instance; and are the WSS component and SS operational savings, respectively, i.e. annual operational cost savings, which are generally equivalents of the differences between the costs and/or losses that would be incurred assuming no water efficient measures applied () and the corresponding costs with efficient measures () as follows:
(8)
where is the general operational benefit of a water system. The total daily water consumption per household or other entities is required in the evaluation of water use efficiency.

#### SS capacity, water use efficiency, SS upgrade postponement and hydraulics

The existing SS analysis presented here is based on the principle that existing SSs are designed for maximum inflows that satisfy flow velocities and flow depth requirements. In this regard, these performances would be achieved at the end of the planning horizon. However, SSs should also satisfy hydraulic requirements from the beginning when inflows are lower. Given these requirements, an approach that analyses the interactions of WSSs and SSs in the planning horizon is articulated.

The analysis proposed in this study establishes the intended initial and final demands at the beginning (time equals 0) and end of the design period of an existing SS by estimating the minimum and maximum demands that barely satisfy the required flow characteristics (velocities, flow depth). From known magnitudes of demands that are distributed across an existing and well-functioning SS (meeting design criteria), amounts of these demands can be decreased or increased proportionally until the minimum or maximum threshold demands that lead to acceptable hydraulics are obtained, respectively. These minimum and maximum demand thresholds correspond to the acceptable initial and final demands in the SS, respectively. The self-cleansing flow velocity requirement is necessary for obtaining both initial and final (max) demands while the flow depth ratio governs the maximum capacity of the SS at the end of the planning horizon. With initial () and final demands ), demands across the planning horizon (design period) can be determined by fitting an exponential curve of the general form , where represents an instantaneous system demand at time t; a and b are coefficients that are determined by formulating two equations and solving them simultaneously, using the known initial ( and final () points with their corresponding system water demands. In this notation, d is the design period of the SS. These simultaneous equations eventually simplify to a general curve as follows:
(9)

The maximum flow depth ratio would not be exceeded with optimal WSSs obtained for the maximum demand, which corresponds to the maximum flow depth ratio. Varying over time would be costs, water demands, water use efficiencies and the system violation factor () of pipe flow self-cleansing velocity.

The efficiency of implementing a WSS is estimated relative to the known standard product. In other words, the maximum flow for any water use component corresponds with a standard product. When a lower flow product is used, the standard flow becomes the base used to measure the level of efficiency of such a product. This computation requires prior knowledge of water consumption and the typical proportions of water use components (see Alliance for Water Efficiency 2015), i.e. assuming standard products were used. The rainwater use efficiencies that are required in the evaluation of WSSs are obtained by simulating different sizes of rainwater tanks using hydrological models such as RainCycle (Roebuck 2007). Different sizes of rainwater tanks with their corresponding performances are subsequently used as opportunities towards water security. Therefore, the estimation of the overall system water-saving efficiency contributed by the WSSs in percentage (%) form is formulated as follows:
(10)
where is the corresponding nodal water demand at the i-th node;
(11)
(12)
(13)
where i,wss is the collective WSS efficiency (%) at a demand node. The formulation of the i,wss shown may also explicitly take into account greywater reuse. The RainCycle software used here can analyse RWHSs that accommodate the combined quantities of rainwater and greywater. Rainwater and/or recycled water is used in the washing machines (WMs), flushing of the toilets (WCs) and any outdoor/outside water activity/event that contributes to water demand; and represent the efficiencies for RWHSs, showerheads (SHs), bathtubs (Bs), dishwashers (DWs), kitchen taps (KTs) and basin taps (BTs), respectively; and are the collective water use efficiencies of toilets and washing machines, respectively, in the case where rainwater is used for flushing the toilets and in washing machines (i.e. non-potable use) according to the assumptions made in the formulation. Other assumptions can be made and the same procedure can be followed. It should be noted that while RWHSs contribute to the overall water use efficiency in the network, they do not affect the sewer inflows because the water used would still be discharged; and are water-saving efficiencies for toilets (i.e. WC) and washing machines (i.e. WM), respectively. The resultant efficiencies of WSSs directly influence the amounts of sewer inflows. Therefore, the sewer nodal inflow () that is generated in households can be estimated as follows:
(14)
where is the effective system efficiency of WSSs that reduces inflow, i.e. less the effect of WSSs that do not reduce sewer inflows, although this is not the case in this study; is any other household water use event that reduces the inflows received in the sewer's i-th node.
The estimation of the effective service roof area () that is necessary for obtaining the potential potable water-saving efficiencies of RWHSs is based on the following assumptions as adapted from Ghisi et al. (2007):
(15)
where is the number of dwellings estimated from nodal and per capita/day water demands. is multiplied by a weighted average roof area per dwelling; and are the percentages of houses and flats in the service area; is the number of people per dwelling; is the assumed area of a house and is the area per person in flats (e.g., 3.75 m2).
The energy consumption of RWHS local pumps is estimated in kWh as follows (adapted from Ward et al. 2012):
(16)
(17)
(18)
where is the total energy consumed (kWh); is the RWHS pump efficiency; is the RWHS pump power rating (kW), which is a function of head and flow. The head is considered to be equivalent to the minimum head required for water distribution and the flow is taken as the RWHS pump capacity, (m3/h), which is the nodal non-potable water demand; is the start-up duration and is the operating duration; is the start-up energy factor; V is the daily (i.e. 24 h) volume of rainwater pumped to serve non-potable water use; , is the percentage of water that is pumped during operation; , is the percentage of water pumped on start-ups and is the number of RWHS pump start-ups; is the percentage of water pumped per start-up. With daily volume V, , and , hence and , the average flow rate pumped at the operating point and the average flow rate in the start-up can be estimated.
When the existing SS capacity explained earlier is reached, there would be upgrade requirements. Reducing inflows would postpone SS upgrade requirements, which is derived as in the following formulation:
(19)
(20)
where is the compound annual growth rate; and that correspond to and , respectively, are the initial and final times, with indicating the duration (if the initial time is zero) required by the SS to serve adequately until the next upgrade requirement. Taking logarithms on both sides of Equation (19) and solving for t yields:
(21)
If is the maximum water demand that can be served by the SS, its upgrade postponement would be formulated as follows:
(22)
where is any lower demand managed by WSSs. At different ages of the SS, the velocity violation factor is obtained by averaging the accumulated pipe flow violations () across all the sewer pipes considered as follows:
(23)
(24)
where is the number of pipes considered, which depends on the standard adopted; is the required pipe flow velocity in the i-th sewer conduit according to design criteria (i.e. regulation); must be reached (or exceeded) at least once a day; pipe flow velocities and flow depths are obtained by running the EPA Storm Water Management Model (SWMM) 5.0 hydraulic simulator/solver (Rossman 2004) using the kinematic wave routing method or an alternative over a defined period (e.g., 24 h) while storing values at specified intervals. The maximum instantaneous velocity stored over the entire simulation for the i-th sewer conduit is referred to as .

It should be noted that the analyses proposed here are applicable on existing networks where appropriate conditions (e.g., diameters and slopes) would have been decided during the design phase, i.e. other design conditions would already have been met for a certain level of water demand. For analysis of existing SSs, slopes and conduit diameters remain the same (fixed) while wastewater inflows and velocities change, hence only the pipe flow self-cleansing velocity violations are the focus of this analysis. With fixed diameters and slopes, pipe flow velocities would mainly be affected by the changes in water demand, which is directly associated with WSSs.

### Optimisation problem

For the optimal WSS application, the solutions sought are those with minimised total cost of WSSs (both capital and operational) in any currency, while household water-saving efficiencies (%) are maximised using the demand that can be served at the maximum capacity of the SS. The methodology utilises efficiencies of water-saving technologies that are available on the market. The decision variables consist of different water-saving appliances, fittings and local water sources with their corresponding range of water-saving capacities. As much as we want to save water, there is a cost associated with it that we need to minimise. The optimisation model is formulated with two objectives as follows:
(25)
(26)
The proposed approach ensures that the optimisation problem for selection of WSSs is subjected to decision variable constraints as follows:
(27)
where Di is the value of the i-th discrete decision variable; D is a discrete set of available WSS capacities/variables; and is the number of decision variables. The approach used to derive the minimum and maximum water demands ensures that the maximum allowed flow depth ratio is not exceeded, while may be violated. Worth observing is that can be optimised without the term in Equation (25). The optimisation problem formulated in this study is solved by using the well-known non-dominated sorting genetic algorithm (NSGA-II) (Deb et al. 2002).

## CASE STUDY

The methodology presented in this study has been demonstrated on a subsystem (Figure 1) of the newly developed Tsholofelo Extension SS system whose components and physical characteristics were obtained from the ‘As built’ drawings provided by the Water Utilities Corporation of Botswana. Physical characteristics include fundamental features such as invert levels of the inflow nodes that also provide the sewer slopes. The description of the sewer system, data and the necessary assumptions required in the demonstration of the methodology discussed next.

Figure 1

A subsystem of the Tsholofelo Extension sanitary sewer.

Figure 1

A subsystem of the Tsholofelo Extension sanitary sewer.

### Network and WSS descriptions

The Tsholofelo Extension SS is in Gaborone, which is the capital city of Botswana. For demonstration, an adequate portion of this sprawling development area is considered in this study. The sewer considered consists of 113 inflow nodes (manholes) and 138 links (i.e. 200, 110- and 160-mm uPVC pipes for conduits 33–36 that are adjacent to the outfall, conduits 113–116 and the rest of conduits across the network, respectively) with a total length of approximately 4.5 km. The existing sewer system should serve about 271 dwellings and/or properties. Household sewer pipes connect and discharge inflows into the immediate manholes of known characteristic levels/elevations. In the evaluation of hydraulic performance, calibration of the sewer model could not be performed because the location is still developing. Moreover, with appropriate data assumptions, the hydraulic characteristics of the sewer lead to informative results, i.e. the focus of the study is the comparative differences that arise when implementing WSSs rather than actual values.

### Data and assumptions

Water demands were distributed according to ‘As built’ drawings, which show property plots that correspond with water consumption categories (WUC 2014) and manholes into which each property will discharge wastewater. Demands of about 3.61 and 4.51 litres/second were derived as explained earlier for initial and final values, respectively. The water consumption pattern required for hydraulic simulations was obtained from WUC (2014). The wastewater generated from households was approximated at 90% of the household indoor water use. The technical aspects of the sewer used for demonstrating the proposed approach include a maximum pipe flow depth ratio of 0.5 and a pipe flow self-cleansing velocity of 0.6 m/s (pipes 19–36; 67–71) at least once a day (Department of Sanitation and Waste Management 2003). The demands stated here lead to the performances that meet the criteria stipulated by the Botswana design manual for certain pipe sizes considered.

The study considered the WSS product capacities available on the market and typical costs as presented in Table 1. Due to lack of local data and importation of most fixtures and appliances, typical values considered reasonable were adopted. The lifespans of fixtures and appliances were obtained from the International Association of Certified Home Inspectors, while RWHSs are expected to serve for 25 years, approximately. Standard capacities of household water use components such as WCs (6.06 litres), SHs (0.16 litres/second), Bs (192.5 litres), WMs (628 litres/cycle/m3), DWs (18.9 litres/cycle), KTs (0.14 litres/second) and BTs (0.14 litres/second) were assumed (Alliance for Water Efficiency 2014). It is also assumed that each household has two toilets and two basin taps. On the other hand, water use appliances and other fittings (shower head, bath, washing machine, dishwasher and a kitchen tap) are single in each household.

Table 1

Summary of typical WSS capacities, water use proportion, lifespans and adapted costs used for analysis (National Renewable Energy Laboratory 2002; Alliance for Water Efficiency 2014; Alliance for Water Efficiency 2015; Plastic-mart 2017)

WSS componentCapacitiesWater use proportion (%)Lifespan (years)Costs (US$) Rainwater harvesting system 2.5; 5.0; 10 (m3– 25 495; 790; 1,360 Toilet 6.06; 4.85; 4.16 (litres/flush) 26.7 100 356; 427; 467 Showerhead 0.16; 0.13; 0.09; 0.05 (litres/second) 16.8 100 46; 55; 64; 78 Bath 192.5; 149 (litres) 1.8 100 1,030; 1,263 Washing machine 628; 495; 428; 374 (litres/cycle/m321.7 10 1,260; 1,401; 1,462; 1,482 Dishwasher 18.9; 16.1; 15.7; 13.2 (litres/cycle) 1.4 1,037; 1,193; 1,213; 1,348 Kitchen tap 0.14; 0.08 (litres/second) 9.8 17.5 489; 711 Basin tap 0.14; 0.09; 0.08; 0.06 (litres/second) 5.9 17.5 489; 645; 711; 756 WSS componentCapacitiesWater use proportion (%)Lifespan (years)Costs (US$)
Rainwater harvesting system 2.5; 5.0; 10 (m3– 25 495; 790; 1,360
Toilet 6.06; 4.85; 4.16 (litres/flush) 26.7 100 356; 427; 467
Showerhead 0.16; 0.13; 0.09; 0.05 (litres/second) 16.8 100 46; 55; 64; 78
Bath 192.5; 149 (litres) 1.8 100 1,030; 1,263
Washing machine 628; 495; 428; 374 (litres/cycle/m321.7 10 1,260; 1,401; 1,462; 1,482
Dishwasher 18.9; 16.1; 15.7; 13.2 (litres/cycle) 1.4 1,037; 1,193; 1,213; 1,348
Kitchen tap 0.14; 0.08 (litres/second) 9.8 17.5 489; 711
Basin tap 0.14; 0.09; 0.08; 0.06 (litres/second) 5.9 17.5 489; 645; 711; 756

The energy cost of US$0.12/kWh (U.S. Department of Energy 2015) was used to calculate the cost of operation energy utilised by RWHS pumps (i.e. assuming a realistic efficiency of 0.65). This unit energy cost was also used to estimate energy cost savings of different WMs and DWs. The start-up energy factor of 0.6 (Ward et al. 2012) was used. The energy uses and the efficiencies of WMs and DWs were estimated using the cost-saving calculators obtained from the U.S. Department of Energy (2015). The energy required for water heating (geysers) and/or savings were calculated assuming the specific heat capacity of water equal to 4,190 J/kg/°C and the temperature rise of 40°C. In the case of WSS components such as taps (basin and kitchen), baths and showerheads, hot and cold water uses were assumed to be equal (Fidar et al. 2010). RWHS pumps were expected to meet a conservative pressure head of 15 m, which is above the required water distribution system minimum pressure (WUC 2014). The cost of US$2.2/m3 (U.S. Department of Energy 2015) paid by customers for both water and sewerage services was used. The energy required per unit of water (0.505 kWh/m3) in WWTPs was obtained from EPRI (2002). This energy requirement assumes insignificant cost effects of wastewater concentrations on operation considering the relatively little maximum water efficiency (i.e. <30%) compared to the significant magnitude (>43%) observed by McKenna et al. (2018). The effects of wastewater concentrations would have even lesser effects on a centralised WWTP considered in this study.

The cost data for water-saving appliances were obtained from the National Renewable Energy Laboratory (2002). The costs of RWHSs were guided by Plastic-mart (2017). The discount rate of 5% was used for the cost of interventions. Note that all the costs were converted to a common year as shown in Table 1 for sensible comparisons using the online inflation calculator (CoinNews Media Group LLC 2015).

The potential water-saving efficiencies of appliances were estimated using standard capacities according to the U.S. federal standards (Alliance for Water Efficiency 2014) and a variety of other commercially available water-saving models (see Alliance for Water Efficiency 2015). As for RWHSs, the efficiency of demand reduction is modelled by performing separate hydraulic analyses of each RWHS size (i.e. discrete sizes of 2.5, 5 and 10 m3) under each nodal catchment using the RainCycle Standard model (Roebuck 2007). An approximated average rainfall of 490 mm/annum was expressed and input into the model in terms of mm/day, together with the catchment area that differs for each network node. The effective rooftop catchment area for each node is estimated according to Equation (15). Additional key parameter inputs are catchment runoff coefficient (0.85), filter coefficient (0.9), recycled greywater and the daily non-potable water demand. Non-potable water demand differs for each network node. The water use components excluded from Table 1 are outdoor water use (2.2%) and leakages (13.7%) (Alliance for Water Efficiency 2015).

It should be noted that more efficient WSSs with smaller proportions of water use can influence pipe flows more than those with larger proportions. For instance, the most efficient showerheads presented in Table 1 would influence the pipe flows much more than the volumes of the toilet flushes despite toilets having a bigger share of water use. The total water use of taps was shared between the kitchen and basin taps according to the ratio of UK kitchen tap to basin tap water use (i.e. 5:3). The output of the RainCycle model is the overall water-saving efficiencies (%) of the non-potable water demand. Uncertainties that are associated with rainfall, demand and other parameters that influence efficiency of RWHSs are beyond the scope of the methodology presented here. In the case of optimisation, the NSGA-SWMM model was run with a population of 100 for 5,000 generations. Multiple (six) independent runs (with different initial seeds) were carried out to obtain and confirm the best convergence whose solutions are shown and analysed in this paper.

## RESULTS AND DISCUSSION

The impacts of conventional and full application of WSS approaches on the SS are presented and compared against each other and the non-dominated solutions obtained from the formulated two-objective optimisation problem as shown in Figures 25 and Table 2. Table 1 shows characteristics and costs of WSSs used. These approaches are herein referred to as conventional, full application of WSSs and optimal WSS solutions, respectively. They are all evaluated in the same model presented in this study to make comparable discussions. It should be noted that the full application of WSSs is also referred to as the maximum efficiency intervention, i.e. the application of maximum efficiency of each WSS component at every node in the network. Optimal WSS solutions form a trade-off curve, which suggests that there are many optimal solutions A – C that represent arbitrary low, medium and high efficiency WSSs were selected for comparative discussions.

Table 2

Cost breakdown, water use efficiencies and pipe hydraulic performances due to conventional, full application of WSSs and selected optimal interventions

WSS interventions
Performance measureABCConventionalMax efficiency
Overall cost (× US$1056.080 6.030 6.022 7.018 6.286 RWHS capital cost (× US$1034.686 4.645 4.666 10.90
RWHS pumping cost (× US$1030.282 0.282 0.282 0.280 Total cost of fittings & appliances (× US$1056.786 6.729 6.712 7.018 6.941
Fittings & appliance operational cost savings (× US$1047.379 7.315 7.233 7.505 Wastewater treatment savings (× US$1040.171 0.170 0.169 0.171
Water-saving efficiency (%) 19.81 19.68 19.56 0 19.80
Self-cleansing velocity deficit (factor)
WSS interventions
Performance measureABCConventionalMax efficiency
Overall cost (× US$1056.080 6.030 6.022 7.018 6.286 RWHS capital cost (× US$1034.686 4.645 4.666 10.90
RWHS pumping cost (× US$1030.282 0.282 0.282 0.280 Total cost of fittings & appliances (× US$1056.786 6.729 6.712 7.018 6.941
Fittings & appliance operational cost savings (× US$1047.379 7.315 7.233 7.505 Wastewater treatment savings (× US$1040.171 0.170 0.169 0.171
Water-saving efficiency (%) 19.81 19.68 19.56 0 19.80
Self-cleansing velocity deficit (factor)
Figure 2

Comparative WSS solutions including low (solution C), medium (solution B) and high (solution A) water-saving interventions in terms of cost and water use efficiency.

Figure 2

Comparative WSS solutions including low (solution C), medium (solution B) and high (solution A) water-saving interventions in terms of cost and water use efficiency.

Figure 3

Comparative conventional, low (solution C), medium (solution B), high (solution A) and maximum water-saving interventions in terms of (a) water use efficiency and service duration (b) water demand and service duration, and (c) water use efficiency and water demand.

Figure 3

Comparative conventional, low (solution C), medium (solution B), high (solution A) and maximum water-saving interventions in terms of (a) water use efficiency and service duration (b) water demand and service duration, and (c) water use efficiency and water demand.

Figure 4

Comparative conventional, low (solution C), medium (solution B), high (solution A) and maximum water-saving interventions in terms of (a) velocity violation factor and service duration (b) water use efficiency and velocity violation factor, and (c) velocity violation factor and water demand.

Figure 4

Comparative conventional, low (solution C), medium (solution B), high (solution A) and maximum water-saving interventions in terms of (a) velocity violation factor and service duration (b) water use efficiency and velocity violation factor, and (c) velocity violation factor and water demand.

Figure 5

Comparative WSSs, including the selected low (solution C), medium (solution B) and high (solution A) water-saving solutions, together with the maximum water-saving interventions in terms of SS upgrade postponement and water use efficiency.

Figure 5

Comparative WSSs, including the selected low (solution C), medium (solution B) and high (solution A) water-saving solutions, together with the maximum water-saving interventions in terms of SS upgrade postponement and water use efficiency.

Near optimal WSS solutions are shown in Figure 2 in terms of a graph of overall cost versus water use efficiency presented by a curve for WSSs that were obtained for the SS flows. The trade-off curve indicates that increasing water use efficiency in the selection of WSS is generally associated with increasing cost because water use efficiency is attained by adding more expensive WSSs. These curves also suggest that a compromise exists between the overall cost and water use efficiency in the selection of WSSs. It is worth observing that the performance of the conventional approach is not shown in Figure 2 because it is extremely far from the full application of WSSs or WSS solutions, i.e. it is completely outcompeted by WSS interventions. For example, the conventional approach would cost US$7.018 × 105 with water use efficiency of 0% while the full application of WSSs would cost US$6.286 × 105 with water use efficiency of 19.8%. The use of maximum efficiency of each WSS component in all the nodes is clearly outperformed by optimal solutions with similar or equivalent water use efficiency in terms of cost (also see Table 2). WSS solutions outperform the full application of WSSs because the latter do not maximise the cost savings or minimise the costs that are dependent on water demands, which should vary appropriately in time and space for optimality. The selected solutions that represent low, medium and high efficiency WSS solutions are indicated in Table 2.

The nature of interventions, solutions and the in-depth analysis of factors that bring the differences between different approaches are displayed in Table 2 (two indicators considered in system evaluation are shown in bold text). This table includes WSS overall cost and benefit breakdowns of extreme approaches. The extreme interventions considered in these analyses are the conventional and full applications of WSSs. The difference between their costs (about US$7.32 × 104) is the potential benefit revealed by considering water use efficiency. In addition, for interventions with equivalent water use efficiencies, the differences between the costs are the potential benefits revealed by the optimal selection of WSSs in the context of SSs. For example, the difference between US$6.286 × 105 (full application of WSSs) and US$6.07 × 105 (WSS solution in the trade-off curve) solutions that both have water use efficiencies of about 19.8% would signify such benefit. The improvement introduced by the WSS solutions is mainly attributed to low values in the total cost of fittings and appliances, which constitute the largest part of the annual cost. In addition, the costs of RWHSs in WSS solutions are much lower than those in the case of full application of WSSs. On the other hand, the conventional approach indicates the highest total cost of fittings and appliances (US$7.018 × 105) without any water use efficiency (i.e. 0%) and the associated cost savings.

In the analyses of the likely effects of WSSs on SSs during the entire SS design period, Figure 3 illustrates the performances of WSSs in the lifespan (service duration) of the SS. The performances were analysed on three perspectives; water demand, water use efficiency and SS service duration. Figure 3(a) reveals that as the SS age across the planning horizon, water use efficiencies of all the WSS interventions decrease with visible separate graphs except for the full application and Solution A. For example, the maximum application of WSS interventions leads to water use efficiencies of 20.47% and 19.8% at the beginning and the end of the planning horizon, respectively. Similarly, the least efficient WSS intervention (Solution C), efficiency drops from 20.18% down to 19.56% at 0 and 50th years, respectively. Figure 3(b) shows that water demand increases over the planning horizon with demands associated with the conventional approach clearly differing with those of full application of WSS and WSS solutions, which are similar across the planning horizon. The increase in demands would increase with the population until the maximum SS capacity is reached. Furthermore, Figure 3(c) shows the same trends shown in Figure 3(a) for all the interventions with water efficiencies that drop as water demand increases across the planning horizon. The conventional approach is not plotted in this figure because of zero water use efficiency, which would diminish graphs of focal interventions.

Further analysis shown in Figure 4 includes four perspectives: pipe flow velocity violation factor, water use efficiency, SS service duration and system water demand. Figure 4(a) shows that the violation factors of system flow velocities decrease over the SS service duration when water demand increases (i.e. for full WSS application and WSS solutions) while the conventional (baseline) interventions generally do not violate the flow velocities. For water efficient interventions, the violation factors are similar across the planning horizon. The significance of this analysis is that, despite selecting WSSs that do not violate flow velocity requirements in SSs at the end of the planning horizon as shown in Table 2, they may violate flow velocities for the larger part of the SS service life as opposed to the conventional approach.

Figure 4(b) reveals that the velocity violation factor increases less rapidly when water use efficiency is low towards the end of the SS operation life. Differences among interventions are distinct except for high efficiency (Solution A) and the full application of WSS interventions due to their close efficiencies. Figure 4(c) confirms the velocity violations which happen due to low connections that result in lower flows in the presence of WSSs at the commissioning of the SS. Finally, an important perspective in the uptake of WSSs is the network upgrade postponement shown in Figure 5. Results of this analysis reveal that upgrade requirements of the SS studied can be postponed by a significant magnitude of about 17.6–17.8 years depending on the respective water use efficiencies achieved. The results also confirm that the maximum use of WSSs does not necessarily guarantee the best results.

Demonstrated in Figure 6 are the temporal variations of flow velocities in selected pipes of the network. The selected pipes 26 and 67 shown in Figure 1 are used to illustrate the significance of implementing WSSs in the existing SS. Considered are the extreme extents of WSS applications and the time perspective of the SS performance. Figure 6(a) reveals that full application of WSSs in the SS introduces significant reduction of pipe flow velocities, which is demonstrated by a clear visible separation of 24-h flow velocity graphs for conventional and full applications of WSSs. The differences in pipe 26 are the results of reduced SS inflows. In Figure 6(b), the time factor reveals that the application of WSS efficiency in the SS has the potential of negative effects on the hydraulics of SSs in terms of self-cleansing velocity. Even though WSSs would be satisfactory at the end (50th year) of the planning horizon, with a self-cleansing velocity of 6 m/s being met in the presence of WSSs, the SS would violate the velocity requirements in the initial stages and most of the time of its operation. This violation happens despite the SS performing adequately under the conventional approach. The results obtained should inform decision makers in terms of prioritisation and timing of system operations and/or upgrades for sustainable SSs.

Figure 6

Effects of (a) conventional and maximum WSSs on instantaneous flow velocities over 24 h in pipe 26 and (b) maximum water efficiency on instantaneous flow velocities over 24 h in pipe 67 at the start and the end of the SS operational life.

Figure 6

Effects of (a) conventional and maximum WSSs on instantaneous flow velocities over 24 h in pipe 26 and (b) maximum water efficiency on instantaneous flow velocities over 24 h in pipe 67 at the start and the end of the SS operational life.

## CONCLUSIONS

This study articulated novel approaches that examine the implications of the conventional, full application of WSSs and optimal WSS efficiencies on existing SS hydraulics and SS upgrade postponement. The proposed analysis method was demonstrated on an existing real-life sewer network in Tsholofelo Extension, Gaborone. The results obtained and the conclusions that are based on the assumptions, data and cost models used in the case study presented in this paper are as follows:

• The analysis approach revealed that cost, benefits and water use efficiency and the determining trade-off factors in different applications of WSSs in existing SSs. In this regard, the full application of WSSs (US$6.286 × 105) is more expensive than all WSS solutions while the conventional application would be the most expensive (US$7.018 × 105) due to lack of the benefits of water use efficiency, which would have reduced the overall cost of WSSs. Furthermore, water use efficiency of WSSs reduces over time when water demand increases. Despite no violation of self-cleansing velocities with a conventional approach in the entire planning horizon, WSS solutions and the full application of WSSs would lead to violation of pipe flow velocity. For instance, the full application of WSSs considered would have a maximum flow velocity violation factor of 0.012 at the beginning of the planning horizon, which could be addressed by incorporating WSSs in the design of SSs.

• Despite the pipe flow violations that may be associated with water use efficiency, the uptake of WSSs also presents desirable impacts on SS upgrade requirements. In this view, the Tsholofelo SS would require upgrades after about 17.6–17.8 years beyond its design period, which is expected to differ with other SSs. Conversely, the maximum use of WSSs does not guarantee the best results in terms of both efficiency and SS upgrade postponement.

• The impact of WSSs and existing SS interactions differ in terms of spatial and temporal variations as indicated by different pipe hydraulics. Therefore, considerable differences exist between the impacts of the conventional approach and the full use of WSSs in terms of temporal variations of pipe flow velocities in selected pipes of the SSs over 24 h (i.e. compliance to non-compliance). Similarly, the effects of WSSs on pipe flow velocities at the beginning and end of the planning horizon would differ.

The practical implications for considering the impacts of WSSs on SSs are the informed investments (rehabilitation and/or redesign decisions) or operations of SSs that guide sustainable solutions. For completeness, the significance (or insignificance) levels of flow reductions and the water quality implications on wastewater treatment operations regarding any specific SS network would be integrated in this approach. Further studies that apply the proposed method of different SSs with different levels of complexities and uncertainties should be carried out before the findings of this study can be considered unique or general.

## ACKNOWLEDGEMENTS

The author is grateful to the Water Utilities Corporation of Botswana for availing Tsholofelo SS data that supported this study. This research did not receive any specific grant from funding agencies in the public, commercial or not-for-profit sectors.

## CONFLICT OF INTEREST

There is no conflict of interest associated with this study.

## DATA AVAILABILITY STATEMENT

All relevant data are included in the paper or its Supplementary Information.

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