The behavior of a rainwater harvesting system depends on some variables that cannot be controlled, such as precipitation, building roof size and water demand. The selection regarding rainwater tank-size will affect the performance of the system and the cost-benefit ratio. The criterion employed for this selection is based on the need for volume-storage and typically, yield large-sized rainwater-tanks, especially when the amount of rainwater is higher during rainy seasons. This article presents a methodology for modelling the rainwater harvesting, storage, and water consumption, for different configurations of a set of buildings, called clusters, where all buildings collect, store and same collected water. This methodology allows for analyzing based on different indicators what is the best recommended configuration and tank sizing, based on configuration and storage ratio exhibited, thus avoiding the situation of being underutilized. The proposed methodology is applied to case of study at a university (Mexico). In this study case, the dynamics per day is modeled over a year, considering monthly rainfall averages, over 2 groups made up of 4 buildings with different collecting capabilities and consumption each, allowing for the analysis of 9 cluster configurations and 4 tank sizing dimensions. The results are analyzed by means of annual indicators such as: the decrease in the volume of water used from the public network, the days of autonomy of the system, and a coefficient R (which relates the volume spilled to the empty volume). This coefficient is then used selection regarding tank sizing and the most recommended cluster configuration.
Research Article
Methodology to optimize rainwater tank sizing and cluster configuration for a group of buildings
https://doi.org/10.21203/rs.3.rs-1626723/v1
This work is licensed under a CC BY 4.0 License
Version 1
posted 05 May, 2022
You are reading this latest preprint version
rainwater harvesting cluster
optimal tank size
water balance model
performance annual indicators
In the 21st century, due to population growth and a constant increase in population density in large cities, have generated a crisis of water scarcity in the main metropolises of the world. In Mexico 107 of the 653 aquifers were overexploited (CONAGUA 2018). The study case of this article is centered in the Metropolitan area of Mexico City (CDMX), where the aquifer is overexploited even though it supplies only 55% of water for consumption. Other sources for the supply are the Lerma system, which supplying 14%, and the Cutzamala system supplying 29%. In these systems, the water is imported into the basin and must be raised from its origin into its destination up to 1,000 m located 127 km away. This situation implies that 86% of operating costs are spent in electricity (Breña 2009). The remaining 2% of the water supply is therefore taken from local open to surface sources (springs and Magdalena River). Precipitation in CDMX concentrates 68% between June and September, generating some floods in this period.
This justifies the importance of taking advantage of rainwater for consumption in different activities. Rainwater harvesting (RWH) consists of collecting from selected surfaces, especially roofs and terraces, then storing, and finally employment of collected rainwater. Although this collected water, due to its quality, does not meet the parameters to be considered as drinking water, with the application of simple processes, generally only filters, can achieve the quality of drinking water. This collected water can also be used for non-potable uses, such as flushing toilets, washing clothes, cleaning, and for watering the gardens. RWH has proved to be an excellent tool seen from perspectives, such as: stakeholders, water supply operators, policy makers, and entrepreneurs (Concha et al. 2020). Because they generate savings in billing costs, access to this resource, reduction of supply interruptions, improve health, and even business opportunity by selling and maintaining RWH systems. Social benefits can also be considered, such as long-term availability of water, improvement of water quality, reduction of flooding and mitigation of environmental impacts.
Concha et al. (2020) carried out an evaluation of the potential RWH in CDMX, considering various types of users, local rainfall, and the costs of paying for water. This study focuses on financial benefits, considered as savings on the bill paid by property owners and entrepreneurs. RWHs are more beneficial for homeowners and entrepreneurs that have larger demands, large rooftop areas, and more users paying the high tariff (Concha et al. 2020), and not for small home users, who are often targeted to address a small escalation of RWH. The previous occurs as a direct consequence of the non-linear rate of water collection. This results in turns out that RWHs are economically attractive for domestic users, uncommon in CDMX, with catchment areas up to ranging from 150 to 300 m2 and with a high demand for potable water (> 1,500 L/day). Other economically attractive sites have large catchment areas, for instance, the case studied by Zavala et al. (2018), which corresponds to a logistics company in CDMX, where the sum of the different catchment areas accounts for accounts for more than 17,000 m2 and is sufficient to supply the water demand for the entire company. On the other hand, Ward et al (2010) found that in the UK, RWH in large commercial buildings may be more financially viable than smaller domestic systems. Other RWH study that have found feasible conditions to implement in groups of buildings is that of Cook et al. (2013) in which a group of 46 homes in a peri-urban area of Brisbane, Australia, was considered.
Choice for rainwater tank size for RWH does not obey any practical rule, because it depends on the criterion considered to achieve a certain objective, but mostly, on the relationship capture-consumption which in turn is defined based on the amount of rainfall of the place, and the number of user consumption habits. In most cases, the cost of a single rainwater tank (RWT) represents a significant portion of the initial investment. In the case studied by Zavala et al. (2018), the cost of the RWT represented more than half of the total cost of the system; however, despite this, it resulted in a feasible, reliable, and economically viable solution. Hanson and Vogel (2014) employed a method to estimate the volume of storage required by using regional regression equations considering climatic differences at 231 locations throughout the continental United States. These authors conducted continuous simulations of several days with information on the demand, the collection area, and values for local precipitation. This information allowed to determine the storage-reliability-yield (SRY) relationships and how large the RWT should be. Lawrence and Lopes (2016) determined the reliability of RWT in a performance analysis for three Texas cities under different rainfall conditions and multiple scenarios. The previous highlights demonstrate the importance of optimizing RWT sizing. A simple technique for the selection of RWT sizing is called the Rippl method and has been used by various authors (Matos et al. 2014; Santos and Taveira-Pinto 2013; Shadeed and Alawna 2021). In this method, the optimal storage size is determined by calculating the maximum cumulative positive difference in the dynamics of the RWT with regards to inlets and outlets. As a result of this methodology, the size obtained for the tank is large, and for the areas where the rainy season is dominant, it means that the collected water could be stored for weeks. This situation is an unwanted condition when considering water quality. Sultana (2022) studied the optimum tank size to maximize water savings considering potential of a RWH with a 10,000 m2 rooftop area in a college campus located in California, USA, where weather is semi-arid. The study consisted of a simple daily water balance model comparing the intended capability to capture 100% of the water, against the scenario of sizing the tank using reliability curves (efficiency, spill, and reliability), in which this last case leads to a significant reduction in the tank size of about 40%.
In this article, a daily estimation of the balance between inputs such as rainwater harvesting, storage (different RWTs dimension) and outputs such as water consumption, is performed. In addition, in this study a new approach is pursued in which the behavior of isolated buildings as well as groups of buildings, called clusters, are modeled, and then compared. All these connected buildings, can collect, store, and finally consume water as a single RWH system
Study Case
Azcapotzalco campus of the Metropolitan Autonomous University (UAM Azc) is in the north of CDMX and has presented problems with the availability of drinking water between the months of March to May. The university community is made up of approximately 18,000 people, including academics personnel, students, and workers. This problem has encouraged adoption of water saving actions, and additionally, has enforced the purchase of water in trucks, a situation that implies increasing expenditures, as opposed to obtaining the water supply from the public network.
All activities conducted in UAM-Azc induce different amounts of water consumption which can be considered through different periods: quarterly, inter-quarterly and vacation. In the quarterly period, due to lectures there is a major attendance of students representing the largest group of the University. During the inter-quarterly period there are no lectures, only a small number of students attend to conduct other minor activities. During the vacation period only the presence of security personnel and reduced number of students and academics can be seen. The campus community, according to data from UAM (2019), accounts for 14,839 students (67.2%); 6,063 academics (27.5%) and 1,170 workers (5.3%).
Solorzano et al. (2019) proposed a methodology to model the amount of collected water, storage, and consumption of rainwater in a RWH located the W building of UAM Azc. This building has an atypical behavior that generates a surplus in the intake-consumption ratio; this is a consequence of the fact that it houses a reduced number of users in both lecture rooms and research laboratories, also owns a vast roof area (1,974 m2). The results of Solórzano et al. (2019) allows to suggest that the excessive volume of water in building W can be used in one or more neighboring buildings that have a deficit, because their catchment area is small or because the number of users is large.
This proposal aims to be a tool that solves or at least mitigates the local problem of water scarcity, but at the same time it is a methodology that can be applied in other places. The proposed system consists of collecting rainwater on the surface of 8 buildings in UAM Azc, to subsequently store it, and use it for non-drinking purposes.
Harvested rainwater estimation
Average daily rainfall per month is estimated averaging daily data corresponding to the amount of rainfall recorder at the 9 closest weather stations, all located within a radius of 10 km. The data was retrieved from 8 stations belonging the CLICOM System (CICESE 2020), and from a station located in UAM Azc, which belongs to the Hydrological Observatory of Engineering Institute (OHIIUNAM 2020), the data can be consulted in Table 1.
| Name | ID | Period |
|---|---|---|
| UAM – Azc | UAM AZC | 2018–2019 |
| Vaso Regulador Carretas | 15154 | 2013–2015 |
| Molino Blanco | 15059 | 1961–2010 |
| Aquiles Serdán | 9003 | 1933–1988 |
| Molinito | 15058 | 1969–2014 |
| Totolica San Bartolo | 15127 | 1961–2013 |
| Arboledas | 15047 | 1970–2014 |
| Amealco | 15137 | 1997–2014 |
| Calacoaya | 15013 | 1961–2014 |
The criterion for grouping buildings is the proximity between them because this will represent a reduce in the cost of installation and separation of a RWH system. For instance, having a single group with 8 buildings implies up to 500 m between buildings R and D (see Fig. 1). For this reason, it was decided to employ two RWHs. Group 1 (G1) considering of buildings C, D, E and G, with a total combined roof size of 7,595 m2. Group 2 (G2) consisting of buildings K, P, R and W, with a total combined roof size of 7,060 m2. Modelling the dynamics of the different configurations of clusters make it possible to identify which of these best uses the availability and consumption of water. This assumption is that some buildings with RWH will have a water surplus, such as that of building W, according to the results of Solorzano et al. (2019), thus enabling sharing water with other buildings exhibiting water deficit. Figure 1 shows an aerial view of the location of the buildings considered in this study. Table 2 shows roof size (\(A\)), type of roof (Roof), runoff coefficients (\(C\)) representing the amount of water that is collected, and main activities conducted in the building (Building use).
| Grup | Building | \({A}\) (m2) | Roof | \({C}\) | Building use |
|---|---|---|---|---|---|
| 1 | C | 2,565 | waterproofed slab | 0.8 | Offices, auditorium, meeting rooms, gallery, and bookstore |
| D | 1,291 | waterproofed slab | 0.8 | Auditoriums, offices, and postgraduate classrooms | |
| E | 1,344 | waterproofed slab | 0.8 | Auditoriums and classrooms | |
| G | 2,310 | waterproofed slab | 0.8 | Teaching laboratories, and teacher cubicles | |
| 2 | K | 1,236 | waterproofed slab | 0.8 | Auditorios y salones de licenciatura |
| P | 2110 | waterproofed slab | 0.8 | Auditoriums and bachelor's rooms | |
| R | 1740 | waterproofed slab | 0.8 | Multipurpose gym | |
| W | 1974 | covered slab and polycarbonate | 0.9 | Research laboratories |
The data corresponding to precipitation is used to calculate the average precipitation per day \({P}_{m}\) in each month \(m\). The roof size \({A}_{j}\) and the corresponding runoff coefficient \({C}_{j}\) allows the calculation of the mean values of harvested rainwater \({V}_{HRj}\) for the \(j-th\) building in a day, according to Eq. 1.
$${V}_{HRj}={P}_{m}\bullet {A}_{j}\bullet {C}_{j}$$
1
Data corresponding to harvested rainwater for several days allows for estimating the volumes associated with longer periods of time (e.g. week, month or year); per building, group of buildings, or cluster (later explained). This results from adding the volumes of the buildings under consideration, according to Eq. 2:
$${V}_{HRC}=\sum {V}_{HRj}$$
2
Clusters configuration
Groups of buildings are evaluated in different possible combinations, called clusters: 4 buildings working as a single system; 3 together and 1 working in isolation; 2 and 2 together; or the 4 buildings working as separate entities. All these combinations are shown in Table 3.
| Group | Combinations | Clusters |
|---|---|---|
| G1 | 1 | C-D-E-G |
| 3 − 1 | CDE-G, CDG-E, CEG-D, DEG-C | |
| 2–2 | CD-EG, CE-DG, CG-DE | |
| 4 | CDEG | |
| G2 | 1 | P-K-R-W |
| 3 − 1 | PKR-W, PKW-R, PWR-K, KRW-P | |
| 2–2 | PK-RW, PR-KW, PW-RK | |
| 4 | PKRW |
Rainwater demand
Rainwater demand for harvested rainwater depends on the type of consumption in each building, which in turn depends on the number and type of users, the number and type of sanitary furniture allocated, the day of the week and the activities by the users. The amount of volume demanded in the toilets (\({V}_{b}\)) is estimated with Eq. 3, according to the furniture installed in each toilet and with the usage factor \(F\), as proposed by Solorzano et al. (2019).
$${V}_{RDj}=N[\left({F}_{S}\bullet {V}_{S}\right)+\left({F}_{U}\bullet {V}_{U}\right)+\left({F}_{T}\bullet {V}_{T}\right)]$$
3
where \({V}_{Bj}\) is rainwater demand in restroom \(j\) per day; \(N\) is the number of users per restroom in a day. Eq. 3 makes a distinction between male and female restrooms, because it assigns values to the usage factors, \({F}_{T}\) (toilet) and \({F}_{RD}\) (urinal). The usage factor represents the portion of times the furniture is under use and was reported by Solorzano et al. (2019). The nominal amount of volume demanded by the furniture was taken from the manufacturers' specifications, see Table 4.
| Furniture | Usage factor | Volume (l) | |
|---|---|---|---|
| Sink | \({F}_{S}=\) 2 | \({V}_{S}=\) 0.25 | |
| Dry urinal | \({F}_{U}=\) 0.25 | \({V}_{U}=\) 0 | |
| Wet urinal | \({V}_{U}=\) 0.5 | ||
| Toilet | male | \({F}_{T}=\) 0.75 | \({V}_{T}=\) 5 |
| female | \({F}_{T}=\) 1 | ||
The amount of volume demanded per day per building \({V}_{BDi}\), results from adding the demand in restroom \({V}_{RDj}\) and the demand \({V}_{Cl}\) for cleaning purposes in the buildings; according to Eq. 4.
$${V}_{BDi}= \sum {V}_{RDj}+\sum {V}_{Cl}$$
4
The amount of volume demanded per day by group of buildings or cluster \({V}_{CDi}\) results from adding the volume demanded by the buildings, according to Eq. 5.
$${V}_{CDi}=\sum {V}_{BDi}$$
5
Cumulative water
The methodology followed for calculating the balance of harvested water in RWTs is that proposed by Mozur and Sameer (2022), where the ratio of the collection to the volume consume per day \({V}_{Ci}\), represents a water surplus in the cluster (\({V}_{Ci}>0\)), or deficit (\({V}_{Ci}<0\)).
$${V}_{Ci}={V}_{HRCi}-{V}_{RDi}$$
6
The RWT system has the objective to store water for hours, days or weeks. When the RWH is comprised integrated by a cluster, it also performs the function of communicating and integrating the collection and consumption of water in a single system. Storing water from those buildings presenting surplus, for later using it in those exhibiting deficit. The above is possible, if there is enough empty space (\({V}_{WTEi})\) in the RWT, depending on the volume currently occupied with water (\({V}_{WTi}\)) and the maximum capacity of the rainwater tank (\({V}_{WTM}\)).
$${V}_{WTEi}={V}_{WTM}-{V}_{WTi}$$
7
The volume of stored water at the end of a day \(\left(i\right),\) which is available for the following day (\(i+1\)) is:
$${V}_{WTi+1}={V}_{WTi}+{V}_{Ci}$$
8
$${V}_{SPi}={V}_{CACi}-{V}_{WTEi}$$
9
When there is a deficit in the balance, (\({V}_{Ci}<0\)), the missing volume of water is taken from the RWT only if the stored volume is sufficient (\(abs \left({V}_{Ci}\right)<{V}_{WTi}\)). In this case the volume of water stored is also calculated according to Eq. 8. When the occurring scenario when the volume of water in the balance is greater than that available in the RWT (\(abs \left({V}_{Ci}\right)>{V}_{WTi}\)), then it is considered to have reached its empty situation, and the missing portion is therefore taken from the public network (\({V}_{WNi}\)).
$${V}_{WTi+1}=0$$
10
$${V}_{WNi}=abs \left({V}_{Ci}\right)-{V}_{WTi}$$
11
Optimal rainwater tank sizing
The reliability of a RWH lies within its ability to provide water when it is needed, and this is related to the reduction in the amount of water taken from the public network, this can be done by measuring with different indicators, for example, the autonomy of a RWH system can be measured with the AAA parameter, representing the number of days in a year in which this system achieves autonomy. Which a larger sized RWT induces an increase in the reliability but implies higher costs, and if the objective is to store the entire volume of precipitated water, the RWT will be halted in periods of drought. This situation will generate an underuse of the RWT. Other indicators affecting the size of a RWT and thus on the performance of the RWH, are the volume spilled \({V}_{SP},\) or the number of days that water spills occur, due to it express the lack of capacity of the volume of the RWT. Optimal rainwater tank sizing (ORWTS) is defined as the size of the tank that induces the smallest spilled water volume (\({V}_{SP}\)), as well as the smallest empty volume (\({V}_{WTEi})\) over a certain period. This relationship is known as spill-empty \({R}_{S-E}\), and is exhibited in the following equation.
$${R}_{S-E}={V}_{WTEi-}{V}_{SPi}$$
12
Potential of harvesting rainwater
Precipitation occurs mainly along the summer, between the months of June and September accumulating 620 mm, equivalent to 75% of the total annual of 829 mm. Maximum precipitation occurs in July, registering a value of 167.3 mm (Fig. 2). The daily month average precipitation is obtained by dividing monthly average by the number of days corresponding in each month (in the case of February, 28.25 days).
The potential amount of volume of harvested rainwater per building (\({V}_{HR}\)) and per group of buildings (\({V}_{HRC}\)) for each month and for an entire year, can be consulted in table A1 of the appendix. The potential amount of volume for harvested rainwater in each month (\({V}_{HRC}\)) showed in Fig. 3, allows for identifying the contribution of each building with respect to the others. In G1, the uptake depends only on the uptake areas A, because C is constant on all surfaces. The building with the highest potential collection volume \({V}_{HR}\) is C, followed by G, E and finally D. In G2, building W has the second largest collection area \({A}\), which combined with its surface type (highest value of C) generates the largest potential amount of volume of collected rainwater. Followed by buildings P, R and K.
Demand for rainwater
Characterization of the infrastructure demanding rainwater
A census for the number of toilets by gender and by the type of urinal allocated, was performed (see Table 4). Furniture of the same type is considered to have the same water demand. It should be noted that most of the restrooms have dry urinals 
, except for the W building.
| Building | Male | Female | Total | |
|---|---|---|---|---|
| Dry urinal | Wet urinal | |||
| C | 4 | 4 | 8 | 16 |
| D | 3 | 0 | 3 | 6 |
| E | 3 | 0 | 3 | 6 |
| G | 6 | 0 | 6 | 12 |
| K | 3 | 0 | 3 | 6 |
| P | 2 | 0 | 2 | 4 |
| R | 1 | 0 | 1 | 2 |
| W | 0 | 3 | 3 | 6 |
The number \(N\) corresponding to the number of users per bathroom per day was determined based on the concurrence, with gauging that and allowed for identifying six behavior routines. Routines R1, R2 and R3 correspond to the quarterly period. R1 is the routine with the highest consumption and occurs on Mondays, Wednesdays, and Fridays. R2 occurs on Tuesdays and Thursdays, R3 occurs on Saturdays. In the interquartile period, routine R4 is presented from Monday to Friday, and routine R5 occurs on Saturdays. All these routines have the presence of academics and workers. Routine R6 corresponds to the vacation period, sundays, and holidays when the university is closed.
The amount of water demanded for cleaning purposes in the toilets (\({V}_{Cl}\)), was estimated based on interviews with personnel belonging to the cleaning staff. The amount of water used by a single person belonging to this staff is 0.4 m3 per day, from monday to friday.
The amount of water demanded by routine and group is shown in Fig. 4 and in table A2 of the appendix, on which routines with the highest consumption is R1 and R2, followed by R4, R3 and R5. Water consumption between groups of buildings is despair, twice as much in G1, compared to G2. This is associated with the use and availability of restrooms in each building, as well as the presence of students. The building with the highest consumption is G, followed by C, D and E, all belonging to G1, which are the buildings with the highest concurrence people, mostly.
Water demanded from the public water network
If the amount of water demanded is bigger than that the RWT is capable to provide, then the difference in volume (\({V}_{WNi}\)) is taken from the public water network (PWN), which is sought to be reduced with the implementation of an RWH system. Figure 5 shows the annual amount of water demanded: with RWH and without RWH for the different dimensions considered for the RWTs, and for the different cluster configurations.
In G1, the annual demand without a PWH system is 8,413 m3. With the implementation of a system with a RWT of 1 m3 a reduction the amount of water taken from the PWN, is of about 31% for the different clusters considered. When the size of the RWT is enlarged up to 5 m3, the amount demanded from the PWN is reduced by an average of 33%; when enlarged up to 10 m3 it is reduced by 35% and when enlarged up to 20 m3 the amount reduced is 38%. The cluster confirmation that provides the greatest volume reduction is CE-DG, a quantity ranging from 38% up to 46% for the different dimensions of the PWT. In the G2 cluster, the annual demand without PWH is 4,031 m3. When the PWH system is implemented together with a RWT of 1 m3, the volume taken from the PWN is reduced by an average of 48% for any given cluster. When the size of the RWT is enlarged up to 5 m3, then the amount of water taken from the PWN is reduced by an average of 51%, when enlarged up to 10 m3, then a reduction of 53% can be expected; when enlarged up to 20 m3, then a reduction of about 55% can be expected. The cluster configuration providing the greatest reduction is the KRW-P, with values ranging from 53% up to 59%, for the different dimensions of RWT. The G2 demands smaller quantities of water from the PWN. In addition, G2 presents a higher percentage of reduction in the demand of water from water from the PWN, compared to G1 cluster.
Autonomous days
Another indicator of the impact induced by the implementation of the RWH system, is the number of days per year that the cluster operates autonomously and refers to the days in which the water that is demanded comes entirely from rainwater harvesting and it is not required to be taken from UWN. A cluster AAA is computed by adding the days in which all the buildings or subgroups achieve autonomy, see Fig. 6.
The AAA value for G1 is 42% (151 to 155 days) for the RWT of 1 \({m}^{3}\). With the RWT of size 5 \({m}^{3}\), the autonomy reaches 45% (from 162 to 167 days). With the RWT of 10 \({m}^{3}\), the autonomy increases up to 47% (165 to 177 days). With the RWT of 20 \({m}^{3}\), an autonomy of 49% is achieved (from 175 to 188 days). The CE-DG cluster configuration exhibits the highest average annual autonomy with 177 days (48%) and 188 days (52%) for the RWTs of 10 \({m}^{3}\) and 20 \({m}^{3}\), respectively. The AAA value for G2 is 50% (from 155 to 206 days) considering the RWT of 1 \({m}^{3}\). In the case of the RWT of size 5 \({m}^{3}\), autonomy reaches 54% (from 171 to 215 days). With the RWT of size 10 \({m}^{3}\), it reaches 57% (180 to 233 days). When considering the RWT of size 20 \({m}^{3}\), an autonomy of 59% is achieved (from 182 to 237 days). The KRW-P cluster configuration has the highest AAA values corresponding to 233 days (64%) and 237 days (65%) for the RWTs of sizes 10 \({m}^{3}\) and 20 \({m}^{3}\), respectively.
Optimal rainwater tank sizing
The optimal rainwater tank sizing considered in this study, corresponds to those commercially available by a manufacturer of capacities: 1, 5, 10 and 20 m3 (Rotoplas 2018). Figure 7 shows the relationship \({R}_{S-E}\) (see Eq. 12), for all subgroups of buildings.
An ideal zero value for the relationship \({R}_{S-E}\) occurs for sizes not manufactured by the provider, for this reason, the relationship \({R}_{S-E}\) yielding a positive value considering the smallest magnitude is then selected. This allows for choosing the immediately superior ORWTS, favoring this way water storage capacity. The \({R}_{S-E}\) of the clusters results from adding the \({R}_{S-E}\) of the subgroups. Table 5 and Fig. 8 show optimal cluster configurations with their respective tank size.
| Cluster | ORWTS (\({{m}}^{3}\)) | \({{R}}_{{S}-{E}}\) |
|---|---|---|
| C-D-E-G | 5-5-5-5 | 438 |
| CD-EG | 5–5 | 102 |
| CE-DG | 5–5 | 92 |
| CG-DE | 10 − 5 | 1453 |
| CDE-G | 10 − 5 | 1474 |
| CDG-E | 10 − 5 | 1504 |
| CEG-D | 10 − 5 | 1485 |
| DEG-C | 10 − 5 | 1426 |
| CDEG | 10 | 103 |
| K-P-R-W | 5-5-10-10 | 2289 |
| KP-RW | 5–20 | 1307 |
| KR-PW | 10–10 | 1120 |
| KW-PR | 20 − 5 | 1797 |
| KPR-W | 10–10 | 685 |
| KPW-R | 10–10 | 570 |
| KRW-P | 20 − 5 | 1208 |
| PRW-K | 20 − 5 | 1937 |
| KPRW | 20 | 1121 |
The optimal cluster in G1 is CE-DG, with both RWTs of size 5 \({\mathbf{m}}^{3}\). In G2, KPW-R configuration with both rainwater tanks of size 10 \({\mathbf{m}}^{3}\) can be considering as optimal. With these ORWTS, the CE-DG cluster configuration reduces its volume demanded by the UWN by 41%, starting from 8,413 \({\mathbf{m}}^{3}\) down to 5,004 \({\mathbf{m}}^{3}\) in a year, implying an autonomy of 163 days. This cluster configuration spills only 2,299 \({\mathbf{m}}^{3}\) in 106 days with a relationship \({\mathbf{R}}_{\mathbf{S}-\mathbf{E}}\) of 92 \({\mathbf{m}}^{3}\). In G2, the KPW-R cluster configuration reduces the consumption of the UWN by 53%, starting from 4,031 \({\mathbf{m}}^{3}\) down to 1,911 \({\mathbf{m}}^{3}\), with an autonomy of 213 days (equivalent to 58% of a year). This cluster spills 2,713 \({\mathbf{m}}^{3}\) over a span of 200 days, with an \({\mathbf{R}}_{\mathbf{S}-\mathbf{E}}\) of 570 \({\mathbf{m}}^{3}\).
The proposed methodology allows for modelling the dynamics of a rainwater collection-storage system over a period. This methodology can be applied to groups of buildings each working in isolation, or in groups of buildings working in clusters. This methodology yields various indicators for the performance of the buildings, clusters, or groups. These indicators correspond to the potential harvested rainwater; the Water demanded from the public water network; the days or percentage of autonomy; the volume or days of spilled water, and the volume corresponding to an emptied rainwater tank. The methodology is applied to 2 groups of buildings located in different catchment areas, and with different water demand requirements; all located in the Azcapotzalco campus of the Universidad Autonoma Metropolitana in Mexico City, Mexico. Group 1 comprised by buildings C, D, E and G. Group 2 comprised by buildings K, P, R and W. Daily modeling over a period of one year, resulted in a comparison of the performance of the different plausible clusters: 4 separate buildings (CDEG; KPRW), 3 buildings together and 1 other separate (CDE-G, CDG-E, CEG-D, DEG-C; KPR-W, KPW-R, KRW-P, PRW-K), 2 and 2 buildings (CD-EG, CE-DG, CG-DE; KP-RW, KR-PW, KW-PR) and all 4 buildings working altogether (CDEG; KPRW). Additionally, to the above 4 different dimensions of rainwater tanks are considered 1, 5, 10 and 20 \({m}^{3}\) .
In this methodology, the optimal size for the water tank is selected based on the best spilled-emptied ratio (it spills the least amount of water and, in turn, the least empty volume). In group 1, the CE-DG cluster configuration is the optimal, using 2 tanks of 5 \({m}^{3}\). This configuration reduces the water taken from the public water network by 41%, inducing an autonomy of 163 days (45%) and a spilled-emptied volume ratio of 92 \({m}^{3}\). In group 2, the optimal configuration is KPW-R, considering a tank size of 10 \({m}^{3}\), because it reduces the volume of water taken from the public water network by 53%, inducing an autonomy of 213 days (58%) and a relationship spill-emptied volume of 570 \({m}^{3}\).
This methodology is applied daily, but precipitation corresponds to monthly averaged data, a situation that is simplified. For future studies with daily rainfall recorded should be of interest. Another interesting scenario emerges from evaluating the clusters with data corresponding to years in which drought is present, as well as with years abundant precipitation. This methodology is fitted for locations where precipitations is concentrated in one season of the year, as opposed to methodologies focused in storing the biggest possible amount of water, only possible considering large dimensions in the dry season.
Funding
The authors declare that no funds, grants, or other support were received during the preparation of this manuscript.
Competing Interests
The authors have no relevant financial or non-financial interests to disclose.
Author Contributions
GNJ and MGM proposed and coordinated the general methodology of the article, as well as collected the field data regarding the water demand censuses. MR oversaw calculating the Rainwater Capture Potential. GBBA programmed the calculation algorithms that allowed to determine the Optimal rainwater tank sizing of the different cluster configurations. BQID developed the methodology to conduct water demand censuses. All authors read and approved the final manuscript.
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