Analysis of Potable Water Savings Using Behavioural Models

The availability of drinking water in reasonable amounts is currently considered the most critical natural resource of the planet (United Nations Educational, Scientific and Cultural Organization [UNESCO], 2003). Studies show that systems of rainwater harvesting have been implemented in different regions such as Australia (Fewkes, 1999a; Marks et al., 2006), Brazil (Ghisi et al., 2009), China (Li & Gong, 2002; Yuan et al., 2003), Greece (Sazakli et al., 2007), India (Goel & Kumar, 2005; Pandey et al., 2006), Indonesia (Song et al., 2009), Iran (Fooladman & Sepaskhah, 2004), Ireland (Li et al., 2010), Jordan (Abdulla & Al-Shareef, 2009), Namibia (Sturm et al., 2009), Singapore (Appan, 1999), South Africa (Kahinda et al., 2007), Spain (Domenech & Sauri, 2011), Sweden (Villareal & Dixon, 2005), UK (Fewkes, 1999a), USA (Jones & Hunt, 2010), Taiwan (Chiu et al., 2009) and Zambia (Handia et al., 2003). One of the most important steps in planning a system for rainwater harvesting is a method for determining the optimal capacity of the rainwater tank. It should be neither too large (due to high costs of construction and maintenance) nor too small (due to risk of rainwater demand not being met). This capacity can be chosen from economic analysis for different scenarios (Chiu et al., 2009) or from the potential savings of potable water for different tank sizes (Ghisi et al., 2009). Several methodologies for the simulation of a system for rainwater harvesting have been proposed. The approaches commonly used are behavioural (Palla et al., 2011; Fewkes, 1999b; Imteaz et al., 2011; Ward et al., 2011; Zhou et al., 2010; Mitchell, 2007) and probabilistic (Basinger et al., 2010; Chang et al., 2011; Cowden et al., 2008; Su et al., 2009; Tsubo et al., 2005). One advantage of the behavioural methods is that they can measure several variables of the system over time, such as volumes of consumed and overflowed rainwater, percentage of days in which rainwater demand is met (Ghisi et al., 2009), etc. The main disadvantage of these methods is that as the simulation is based on a mass balance equation, there is no guarantee of similar results when using different rainfall data from the same region (Basinger et al., 2010). This problem can be avoided, in part, with the use of long-term rainfall time series. Probabilistic methods have the advantage of their robustness, for example, by using stochastic precipitation generators. A disadvantage of these methods is their portability. Several models adequately describe the rainfall process in one location but may not be satisfactory in another (Basinger et al., 2010).


Introduction
The availability of drinking water in reasonable amounts is currently considered the most critical natural resource of the planet (United Nations Educational, Scientific and Cultural Organization [UNESCO], 2003). Studies show that systems of rainwater harvesting have been implemented in different regions such as Australia (Fewkes, 1999a;Marks et al., 2006), Brazil (Ghisi et al., 2009), China (Li & Gong, 2002;Yuan et al., 2003), Greece (Sazakli et al., 2007), India (Goel & Kumar, 2005;Pandey et al., 2006), Indonesia (Song et al., 2009), Iran (Fooladman & Sepaskhah, 2004), Ireland (Li et al., 2010), Jordan (Abdulla & Al-Shareef, 2009), Namibia (Sturm et al., 2009), Singapore (Appan, 1999), South Africa (Kahinda et al., 2007), Spain (Domènech & Saurí, 2011), Sweden (Villareal & Dixon, 2005), UK (Fewkes, 1999a), USA (Jones & Hunt, 2010), Taiwan (Chiu et al., 2009) and Zambia (Handia et al., 2003). One of the most important steps in planning a system for rainwater harvesting is a method for determining the optimal capacity of the rainwater tank. It should be neither too large (due to high costs of construction and maintenance) nor too small (due to risk of rainwater demand not being met). This capacity can be chosen from economic analysis for different scenarios (Chiu et al., 2009) or from the potential savings of potable water for different tank sizes (Ghisi et al., 2009). Several methodologies for the simulation of a system for rainwater harvesting have been proposed. The approaches commonly used are behavioural (Palla et al., 2011;Fewkes, 1999b;Imteaz et al., 2011;Ward et al., 2011;Zhou et al., 2010;Mitchell, 2007) and probabilistic (Basinger et al., 2010;Chang et al., 2011;Cowden et al., 2008;Su et al., 2009;Tsubo et al., 2005). One advantage of the behavioural methods is that they can measure several variables of the system over time, such as volumes of consumed and overflowed rainwater, percentage of days in which rainwater demand is met (Ghisi et al., 2009), etc. The main disadvantage of these methods is that as the simulation is based on a mass balance equation, there is no guarantee of similar results when using different rainfall data from the same region (Basinger et al., 2010). This problem can be avoided, in part, with the use of long-term rainfall time series. Probabilistic methods have the advantage of their robustness, for example, by using stochastic precipitation generators. A disadvantage of these methods is their portability. Several models adequately describe the rainfall process in one location but may not be satisfactory in another (Basinger et al., 2010).
A way of comparing different models for rainwater harvesting systems is by assessing their potential for potable water savings and optimal tank capacities. The objective of this study is to compare the potential for potable water savings using three behavioural models for rainwater harvesting in buildings. The analysis is performed by varying rainwater demand, potable water demand, upper and lower tank capacities, catchment area and rainfall data. Studies which consider behavioural models generally use either Yield After Spillage (YAS) or Yield Before Spillage (YBS) (Jenkins et al., 1978). This study aims to compare them with a software named Neptune (Ghisi et al., 2011). A method for determining the optimal tank capacity will also be presented based on the potential for potable water savings.

Methodology
Behavioural methods are based on mass balance equations. A simplified model is given by Eq. (1).
where V is the stored volume (litres), Q is the inflow (litres), Y is the rainwater supply (litres), and O is the overflow (litres). The software named Neptune was used to perform the simulations. YAS and YBS methods were implemented only for simulations in this research, but they are not available to users. Neptune requires the following data for simulation: daily rainfall time series (mm); catchment area (m²); number of residents; daily potable water demand (litres per capita/day); percentage of potable water that can replaced with rainwater; runoff coefficient; lower tank capacity; and upper tank capacity (if any). For each day of the rainfall time series, Neptune estimates: the volume of rainwater that flows on the catchment surface area, the stored volume in the lower tank (at the beginning and end of the day), the overflow volume and the volume of rainwater consumed. If an upper tank is used, the volume stored in the upper tank and the volume of rainwater pumped from the lower to the upper tank are also estimated. The volume of rainwater that flows on the catchment surface is estimated by using Eq. (2).
where is the volume of rainwater that flows on the catchment surface (litres); is the precipitation in day t (mm); is the catchment surface area (m²); is the runoff coefficient (non-dimensional, < ≤ ). The methods Neptune, YAS and YBS differ in the way stored volumes are calculated and pumped. Details about them are shown as follows.

Neptune
The volume of rainwater stored in the lower tank at the beginning of a given day is calculated using Eq. (3).
where is the volume of rainwater stored in the lower tank at the beginning of day t (litres); is the capacity of the lower tank (litres); is the volume of rainwater that flows on the catchment surface on day t (litres); is the volume of rainwater available in the lower tank at the end of the day (litres). Next, the volume of rainwater that can be pumped to the upper tank is calculated by using Eq. (4).
where is the volume of rainwater pumped on day t (litres); is the volume of rainwater stored in the lower tank at the beginning of day t (litres); is the capacity of the upper tank (litres); − is the volume of rainwater available in the upper tank at the end of the previous day (litres). The volume of rainwater available in the lower tank at the end of a day is defined as the difference between the volume of rainwater in the beginning of the day and the volume that was pumped (Eq. (5)(4)).
where is the volume of rainwater available in the lower tank at the end of day t (litres); is the volume of rainwater stored in the lower tank at the beginning of day t (litres); is the volume of rainwater pumped on day t (litres). The volume of rainwater available in the upper tank at the beginning of a given day (after pumping) is given by Eq. (6).
where is the volume of rainwater available in the upper tank at the beginning of day t (litres); − is the volume of rainwater available in the upper tank at the end of the previous day (litres); is the volume of rainwater pumped on day t (litres). The volume of rainwater consumed daily depends on rainwater demand and volume stored in the upper tank; it is calculated by using Eq. (7).

=
( 7) where is the volume of rainwater consumed in day t (litres); is the rainwater demand in day t (litres per capita/day); is the volume of rainwater available in the upper tank at the beginning of day t (litres). The volume of rainwater available in the upper tank at the end of a given day is obtained by using Eq. (8).
where is the volume of rainwater available in the upper tank at the end of day t (litres); is the volume of rainwater available in the upper tank at the beginning of day t (litres); is the volume of rainwater consumed on day t (litres).

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The potential for potable water savings results from the relationship between the total volume of rainwater consumed and the potable water demand over the period considered in the analysis, according to Eq. (9).
where is the potential for potable water savings (%); is the volume of rainwater consumed on day t (litres); is the rainwater demand on day t (litres per capita/day); is the number of inhabitants; is the period considered in the analysis (the same as the duration of the rainfall time series).

YAS
In the YAS method, the volume of rainwater collected will be consumed only in the next day. Thus, in systems where there is an upper and a lower tank, rainwater will be pumped at the beginning of the next day (Chiu & Liaw, 2008). When considering the use of an upper tank, the difference between YAS and Neptune resides only in calculating the volume of rainwater pumped. It can be seen, in Eq. (10), that YAS method considers the volume stored in the tank at the previous day.
where is the volume of rainwater pumped on day t (litres); − is the volume of rainwater stored in the lower tank at the beginning of the previous day (litres); is the capacity of the upper tank (litres); − is the volume available in the upper tank at the end of the previous day (litres). The other equations are identical to those presented for Neptune.

YBS
In Neptune and YAS methods, the available volume of rainwater at the end of a given day is estimated by using Eq. (8). Thus, it is possible to notice that the tank is never full at the end of the day, no matter the amount of rainwater available. The main feature of the YBS method is the possibility that this gap does not exist. When using both upper and lower tanks, a way to fill the upper tank is pumping rainwater two times a day; the first time before or during consumption and the second one after consumption (usually at night). For YBS method, the volume of rainwater stored in the lower tank at the beginning of day t is the same as that for Neptune and YAS, given by Eq.
(3). Thus, according to YBS method, the first volume of rainwater to be pumped is calculated by using Eq. (11).
where is the volume of rainwater pumped on day t (litres); is the volume of rainwater stored in the lower tank at the beginning of day t (litres); is the volume www.intechopen.com of the upper tank (litres); − is the volume of rainwater available in the upper tank at the end of the previous day (litres). The volume of rainwater available in the lower tank after the first pumping is given by Eq. (12).
where is the volume of rainwater available in the lower tank after the first pumping (litres); is the capacity of the lower tank (litres); − is the volume of rainwater available in the lower tank at the end of the previous day (litres); is the volume of rainwater that flows on the catchment surface (litres); is the volume of rainwater pumped on day t (litres). The volume of rainwater available in the upper tank after the first pumping is given by Eq. (13).
where is the volume of rainwater available in the upper tank after the first pumping (litres); − is the volume of rainwater available in the upper tank at the end of the previous day (litres); is the volume of rainwater pumped on day t (litres). The volume of rainwater consumed in a given day is calculated by using Eq. (14).

=
( 14) where is the volume of rainwater consumed on day t (litres); is the rainwater demand on day t (litres per capita/day); is the volume of rainwater available in the upper tank at the beginning of day t (litres). After that consumption, the volume of rainwater available in the upper tank is calculated by using Eq. (15).
where is the volume of rainwater available in the upper tank after consumption (litres); is the volume of rainwater available in the upper tank at the beginning of day t (litres); is the volume of rainwater consumed on day t (litres). The volume of rainwater available for the second pumping is given by Eq. (16).
where is the volume of rainwater available for the second pumping (litres); is the volume of rainwater available in the lower tank after the first pumping (litres); is the capacity of the upper tank (litres); is the volume of rainwater available in the upper tank after consumption (litres). The volume of rainwater available in the upper and lower tanks at the end of a given day are given by Eqs. (17) and (18) where is the volume of rainwater available in the upper tank at the end of day t (litres); is the capacity of the upper tank (litres); is the volume of rainwater available in the upper tank after consumption (litres); is the volume of rainwater available for the second pumping (litres).
where is the volume of rainwater available in the lower tank at the end of the day (litres); is the volume of rainwater available in the lower tank after the first pumping (litres); is the volume of rainwater available for the second pumping (litres).

Computer simulations
In order to compare Neptune, YAS and YBS, computer simulations were carried out for different cases. In all three cases a runoff coefficient of 0.8 was taken into account, i.e., 20% of rainwater is discarded due to dirt on the roof, gutters, etc. The capacity of the upper tank is given by the daily rainwater demand. It is calculated by using Eq. (19).
where is the capacity of the upper tank (litres); is the potable water demand (litres); is the number of inhabitants; is the percentage of potable water that can be replaced with rainwater. Three cities with different rainfall patterns were considered in the simulations: Santana do Ipanema, Florianópolis and Santos. The monthly average rainfall for the three cities are shown in Figure 1

Optimal capacity for the lower tank
To calculate the ideal capacity for the lower tank, simulations were performed for tank capacities ranging from 0 to 10,000 litres, at interval of 250 litres. Then graphs of potential for potable water savings as a function of tank capacities were drawn. For each two points in the graph, the difference between potable water savings was estimated by using Eq. (20).

∆ =
where ∆ is difference between potable water savings (%/m³); is the potential for potable water savings (%); is the lower tank capacity (m³). Eq. (20) represents the resulting increase in for a given increase in . As "%/litre" usually results in very small values, the tank capacities are expressed in m³. The tank capacity chosen as optimal is the one in which ∆ ≤ %/ . This means that, for that interval, an increase of 1 m³ in the capacity of the lower tank results in an increase less or equal to 1% in the potential for potable water savings. This ensures that the tank capacity will not be too small (such that the rainwater demand will not be met) or too large (such that the tank will not be filled for most of the time).

Results
In this section, results for the three cases and three cities are shown. The optimal capacities for the lower tank are determined for YAS, YBS and Neptune. It will be seen that the potential for potable water savings, in %, obtained with Neptune is always greater than YBS and smaller than YAS. Thus, to compare results for a given capacity, the reference will be that estimated by Neptune.

Low rainwater demand
The simulation for Santana do Ipanema gives the results shown in Figure 4. Due to low rainfall, even with a low rainwater demand (90 litres/day), it can be seen that the maximum percentage of rainwater demand, 30%, is not reached within the range of tank capacities simulated. The ideal capacities for the lower tanks are: Neptune -4500 litres; YAS -4750 litres; YBS -4500 litres. The potential for potable water savings are, respectively, 25.15%, 25.31% and 25.24%. Considering a tank capacity of 4500 litres, additional results are obtained (  The difference between average rainwater consumption for Neptune and YAS is 0.32 litres/day, which is equivalent to 0.36% of daily rainwater demand. Similarly, the difference between YBS and Neptune is 0.28 litres/day, which corresponds to 0.31% of daily rainwater demand. For Florianópolis, the potential for potable water savings as a function of the volume of lower tank is presented in Figure 5. For Florianópolis, which has greater rainfall than Santana do Ipanema, one sees that, with tank capacity around 3000 litres the maximum potential for water savings is reached. The ideal capacities for the lower tanks are: Neptune -2000 litres; YAS -2000 litres; YBS -1750 litres. The potential for potable water savings are, respectively, 29.24%, 29.15% and 29.08%.  The difference between average rainwater consumption for Neptune and YAS is 0.28 litres/day, which is equivalent to 0.31% of daily rainwater demand. Similarly, the difference between YBS and Neptune is 0.18 litres/day, which corresponds to 0.20% of daily rainwater demand. The potential for potable water savings for Santos is presented in Figure 6. In this case, the maximum potential for potable water savings is reached for a lower tank capacity of about 2000 litres. The ideal capacities for the lower tanks are: Neptune -1500 litres; YAS -1500 litres; YBS -1500 litres. The potential for potable water savings are, respectively, 29.76%, 29.67% and 29.84%. Table 4 presents additional results for the three methods using a lower tank of 1500 litres.  The difference between average rainwater consumption for Neptune and YAS is 0.27 litres/day, which is equivalent to 0.27% of daily rainwater demand. Similarly, the difference between YBS and Neptune is 0.21 litres/day, which corresponds to 0.23% of daily rainwater demand.

Medium rainwater demand
Considering a daily rainwater demand of 320 litres and a catchment surface of 200 m², the shape of the curves on the graphs remain the same, with an asymptotic tendency. For Santana do Ipanema, the maximum potential for potable water savings (40%) cannot be reached due to small amounts of rainfall. The ideal capacity for the lower tank with method Neptune is 5000 litres. YAS estimated a capacity 250 litres bigger, while YBS estimated a capacity 250 litres smaller. The potential for potable water savings are, respectively, 23.29%, 23.26% and 23.36%. With a lower tank with capacity of 5000 litres, the difference between average rainwater consumption for Neptune and YAS is equivalent to 0.78% of daily rainwater demand. Similarly, the difference between YBS and Neptune corresponds to 0.73% of daily rainwater demand. The ideal capacities for the lower tank using Neptune and YAS were the same as those estimated for Santana do Ipanema. YBS had an optimal capacity of 4500 litres. However, due to higher rainfall the potential for potable water savings are, respectively, 36.34%, 36.27% and 36.17%. With a lower tank capacity of 5000 litres, the difference between average rainwater consumption for Neptune and YAS corresponds to 0.82% of daily rainwater demand. Similarly, the difference between YBS and Neptune is equivalent to 0.71% of daily rainwater demand. As an example, Figure 7 shows the potential for potable water savings as a function of the lower tank capacity for Santos. litres. The ideal capacities, however, are considerably smaller. The estimated capacities for Neptune, YAS and YBS were, respectively, 4000 litres, 4250 litres and 3750 litres. For these lower tanks, the potential for potable water savings are 38.49%, 38.42% and 38.56%. With a lower tank capacity of 4000 litres, the difference between average rainwater consumption for Neptune and YAS is equivalent to 0.89% of daily rainwater demand. Likewise, the difference between YBS and Neptune corresponds to 0.68% of daily rainwater demand.

High rainwater demand
The third case considers a higher rainwater demand, i.e., 750 litres/day. The catchment surface is also larger, i.e., 300 m². For Santana do Ipanema, which has the lowest rainfall, the simulation gives the results shown in Figure 8. Due to low rainfall in Santana do Ipanema, and the high rainwater demand, the highest potential for potable water savings obtained in the interval 0-10000 litres is less than 25%. Differences in the lower tank capacity are greater than the ones obtained in the previous sections. The ideal capacities for Neptune, YAS and YBS are 5500 litres, 6250 litres and 4750 litres, respectively. The potential for potable water savings, on the other hand, are very similar: respectively 20.90%, 20.97% and 20.90%. Considering a lower tank capacity of 5500 litres, the difference between average rainwater consumption for Neptune and YAS corresponds to 1.46% of daily rainwater demand. Similarly, the difference between YBS and Neptune is equivalent to 1.43% of daily rainwater demand. For Florianópolis, a potential for potable water savings of 40% is the most that can be obtained in the interval 0-10000 litres, due to the high rainwater demand. The ideal capacities for the lower tanks are: Neptune -8250 litres; YAS -9000 litres; YBS -7500 litres. The potential for potable water savings, however, are almost equal: 39.63%, 39.65% and 39.63%, respectively. The biggest difference in the average rainwater consumption occurs between Neptune and YAS, and is equivalent to 1.50% of daily rainwater demand. Because of higher amounts of rainfall, lower tank capacities estimated for Santos are smaller than those obtained for Florianópolis. For Neptune, it is 7750 litres. YAS and YBS estimated volumes of 8500 litres and 7000 litres, respectively. The potential for potable water savings are, respectively, 46.10%, 46.11% and 46.79%. With a lower tank capacity of 7750 litres, the difference between average rainwater consumption for Neptune and YAS is equivalent to 1.65% of daily rainwater demand. Similarly, the difference between YBS and Neptune corresponds to 1.35% of daily rainwater demand. As noted in the previous sections, the differences between methods are very small compared to the daily rainwater demand.

Conclusions
Three behavioural models for rainwater harvesting analysis were investigated. Two rainwater tanks were considered, i.e., a lower and an upper one, so that the water is pumped from the lower to the upper tank. A methodology for determining the optimum lower tank capacity was presented, based on variations in the potential for potable water savings as a function of the tank capacity. Results showed that the method estimates a capacity for the lower tank that is not too small so as to allow for a great amount of rainwater to be wasted; and neither too large so as to allow for the increase in construction and maintaining costs to surpass the increase in potential for potable water savings. Simulations were performed for three rainwater demands and three cities. Results showed that, due to the modelling, the YAS method always estimates the smallest potential for potable water savings, followed by Neptune and YBS, respectively. It was also found that the differences between the methods increase as increases the rainwater demand. Despite the potential for potable water savings obtained with YBS being slightly higher than the other two methods, one should take into account that two pumpings per day can occur; and this causes an increase in system maintenance and energy costs. The greatest difference of daily average rainwater consumed obtained between Neptune and YAS was 1.65%. Similarly, the greatest difference between Neptune and YBS was 1.35%. Thus, it can be concluded that, for practical purposes, the methods are equivalent.