Residential water demand modelling and hydraulic reliability in design of building water supply systems: a review

The building water supply system is a fundamental unit in water supply systems as it is directly associated with end users. However, the studies available on its efficient design are limited. Water demand estimation continues to be an important issue in water supply systems’ design because of its multifaceted nature. Hunter’s curve, or Fixture Unit method, is widely used for estimating the load on plumbing. Regardless of its popularity, it has a few drawbacks and is arbitrarily modified in some plumbing codes. Fixture-use probability, a basic entity in the Fixture Unit and some other methods, is a difficult parameter to estimate. Commonly, high-resolution field data is used for stochastic modelling of residential water demand which may not be always available. The paper reviews important residential water demand models in view of their applicability in building water supply system design. The irregular nature of water demand in buildings is due to uncertainty in water-use behaviour of users at fixture level. Use of soft-computing techniques can provide an advantage over the other methods in modelling such behaviour. The paper also discusses reliability of building water supply systems and applicability of some common indices for estimating reliability of building water supply systems.


INTRODUCTION
Water distribution system (WDS) is a term used to represent a system of collection, storage and transportation of water from treatment plant to the point of house service connection. Beyond the municipal water meter, water is carried to end users by the plumbing system, herein referred to as the building water supply system (BWSS) (Gad & Abd-Elaal ). Some basic input parameters required for design of both the above hydraulic systems are common, like pipe layout, nodal demands, nodal elevations, head at source and residual head at nodes, etc. Analysis and design of WDS is characterized by water demand estimation and subsequent demand allocation to nodes. Variation in water demand at a node in WDS may be moderate due to the large population served by the respective node. On the contrary, in the BWSS, the demand at water supply fixtures is intermittent and quite uncertain as it is directly affected by consumers. Water demand at different household fixtures is dependent on user habits, and a number of demographic and socio-demographic characteristics (Blokker et  Pipe sizing in BWSS is conventionally based on the principle of simultaneous demand. The probability of using certain number of fixtures simultaneously is considered in the calculation of maximum flow through a pipe supplying water to these fixtures. Fixture-use probability (p) is a basic entity used to calculate probable maximum simultaneous demand (PMSD) as a design flow through a pipe in BWSS, assigning the probability distribution for the number of fixtures being used simultaneously (Hunter ; Murakawa ). The estimation of load on the plumbing system of a building in terms of water demand is a critical step after which the hydraulic analysis is performed to ensure the minimum residual head at user end (Cole ).

Majority of the National and International Codes utilize
Hunter's curve () for pipe sizing in plumbing, using the concept of Fixture Units. Because of the sound probabilistic approach and easy calculations of PMSD, Hunter's Fixture Unit method is popularly used in plumbing system design.
However, it is an extensively accepted fact that Hunter's curve overestimates water demand in plumbing pipe sizing Apart from this, some other issues associated with the Fixture Unit method are highlighted in the paper.
There are a number of models and methods proposed by various researchers for estimating residential water demand.
For BWSS design, end-use models can be effective as they study water use events at fixtures (Blokker et al. ).
Often, such stochastic end-use water demand models require a huge amount of high-resolution field data, which may not be always available for every region or locality, especially in developing countries. Some of the models and methods in literature are effective in estimating the instantaneous residential water demand (Hunter ; Wistort ; Omaghomi ), but they are based on p-values.
Obtaining the p-values of fixtures might be a difficult and extensive task. Nevertheless, residential water use habits change over time and location. This change in water-use behaviour needs to be considered by a timely update on values of fixture-use probability (p), to be used in the water demand models for BWSS pipe sizing in the respective locality.
Water demand pulse models use probability distribution for fitting the data of arrival of the water demand pulse Scrupulous statistical analysis is required to develop such models from the field data.
As water demand is a subjective event, its deterministic models are difficult to build and might involve incomprehensible parameters. Soft-computing, or Grey-box approaches, have been used by some researchers to overcome this prob- Also, accurate estimation of water demand is practically unattainable due to several factors affecting the event. With the use of soft-computing techniques such as fuzzy logic, subjective behaviour of users can also be modelled mathematically to estimate water demand (Oliveira et al. ). Such models can include user characteristics along with the other demographic and climatic factors affecting water demand.
Reliability studies on the water supply system (WSS) are required to be done to ensure its functioning under abnormal conditions of operations. Majorly, estimation of reliability of WSS consists of two aspects, viz. evaluating possibility of failure of its components and calculating the degree of demand dissatisfaction at nodes during infrequent operating conditions. Latterly referred to as hydraulic failure, is the inability of the WSS to satisfy the required quantity of water with a specified head during periods of high demand.
Hydraulic failure may occur due to inadequate design of components, changes in demand over a period of time and reduction in heads available at nodes due to increased roughness of pipes (Bao & Mays ). As hydraulic reliability (HR) quantifies demand satisfaction at nodes, estimation of water demand is crucial for a reliability analysis. The improper design of BWSS may lead to inefficient use of water, compromise with the quality of water reaching the user, large maintenance costs and waste of energy too.
With the growing concern about sustainability and water management, improving BWSS design is inevitable.
All the above aspects call for an investigation into the design of BWSS with emphasis on water demand modelling and due consideration to estimating its HR for effective urban water management and sustainable development.
The important water demand modelling approaches for residential water use, including the commonly used Fixture Unit method, are briefly discussed in this paper. Hydraulic reliability and its indices to estimate reliability of BWSS are also discussed.

MODELLING RESIDENTIAL WATER DEMAND
Water demand in residential buildings is a quite probabilistic yet important variable in BWSS pipe sizing. Estimation of water demand is difficult because of the number of factors affecting water demand and the dynamic nature of the variable itself. The uncertainty in water demand at various common fixtures in residential buildings causes a great deal of complexity in appropriate pipe sizing. Being on the conservative side in estimating demand might not only affect the economy of the design, but can also be a great threat to the quality of water reaching consumer ends due to increased residence time of water in the system causing growth of harmful micro-organisms like Legionella. The interaction between user and water fixture and the study of simultaneous use of fixtures is important in the pipe sizing in BWSS.
Various methods and models are available in literature for the estimation of residential water demand, as discussed in this section. Some of the methods are used by the standards and codes (e.g. the Fixture Unit method, Loading Unit method) while the other models are not so popular among plumbing designers and practitioners (e.g. pulse models, end-use models).

Fixture Unit method and related issues
Hunter () introduced the concept of Fixture Units to estimate demand in BWSS using a methodical probabilistic approach. Using the idea of Fixture Units, Hunter was able to present combined effects of different types of fixtures on a flow through a pipe serving them. The curve of demand in gallons per minute (gpm) against Fixture Units was developed ( Figure 1). The Hunter's curve can be easily used for estimating PMSD for BWSS pipe sizing.
Hunter applied binomial probability distribution for number of fixtures operating simultaneously in BWSS. Fixture-use probability (p) was used considering the operating condition of a fixture as On or Off. It was calculated as a ratio of duration of use of a fixture (t) and average time interval between its two consecutive uses (T ). A failure rate of 1% was considered while calculating PMSD; that is, a confidence limit (CL) of 99%. The assumption of 'congested  Apart from the methods adopted by Codes and Standards, methods proposed by researchers to estimate residential water demand still need some simplification for using them in BWSS pipe sizing. Some important types of models are discussed in the further sub-sections. It is important to note that the number and type of fixtures served by different pipes in BWSS vary as per building planning, pipe layout and size of building. Thus, use of an end-use model for design of BWSS would be effective as compared to models generating water demand at household level. Such end-use models are discussed in the next sub-section.

End-use models
In BWSS, the study of demand at each fixture facilitates modelling of water demand for pipe sizing effectively as the flow of water in a pipe is directly associated with use of fixtures served by it. End-use models require detailed information on water use at each fixture type by users in the households. The relation between users and different water consuming appliances can be understood through such models.
A GIS based end-use residential water demand models As water use habits keep changing with the time, the models for demand estimation need regular updating when used for BWSS design. The difference between the actual and theoretical values is always found. Implementation of Bayes' theorem may be useful for this purpose.
Bayes' theorem has been applied in many research areas such as the thermal comfort of buildings (Wong et al. As design of components of any WSS is based on water demand as an inevitably important input, its accurate estimation may supposedly lead to efficient design of the system. But, the variations in instantaneous water demand are unavoidable in any circumstances. Consequently, the endeavour to estimate accurate instantaneous water demand is most likely to result in a complex analytical model. Any changes in water use occurring over a period of time due to several climatic, technological, behavioural and socio-economic factors may not be accommodated in such a model. Also, it is highly difficult to consider all the factors affecting water demand simultaneously in an analytical or mathematical model. The fact to be highlighted here is that water demand can never be predicted accurately but can be estimated with certain probability (Hunter ).
As most of the hydraulic systems and models are nonlinear (Tabesh & Dini ), a grey-box approach or soft computing tools may be effective in water demand modelling.
Noting the fact that the user is the most important factor in water demand modelling, its subjective behaviour and water use habits can be used to model the residential water demand. Ultimately, fuzzy modelling and neural network techniques can comprehend such subjective behaviour of users, incorporating the uncertainty of water use.

HYDRAULIC RELIABILITY OF BWSS
The reliability of a system lies in its smooth functioning under varying operating conditions. For WDS and BWSS, water demand is an input that has an inherent characteristic of uncertainty and shows variation with numerous known and unknown factors. Thus, it becomes important to know if the system can accommodate these variations in water demand and serve its purpose of supplying water to users with required flow and specified head. This tolerance in demand variation can be quantified by estimation of HR.
Tanyimboh () presented three major scenarios while defining failure of WDS as its the inability to perform satisfactorily (Table 1). Scenario 3 was found to be relevant in defining the HR, and accordingly Tanyimboh () defined it as the ratio of mean value of flow delivered to the flow required at nodes.
In the case of BWSS, the availability of required flow at fixtures with sufficient head is a major concern while design- where, R -Reliability; • M -Number of pipes; • p(0) -Probability of no pipe being out of service; • p(m) -Probability of pipe m out of service; • p(m, n) -Probability of pipes m and n out of service; • T(0) -Total flow with no pipe out of service; and • T -The sum of the nodal demands.
The modification of Equation (1) can be used for estimating HR of BWSS with a looped pipe network considering different base demand values of each fixture. In a branched pipe layout, which is commonly observed in BWSS, the case of a pipe being out of service will be more significant as it can affect the water supply of few or more users simultaneously. A significance factor has to be associated with the type of pipe while calculating the reliability of BWSS using Equation (1); for example, a fixture supply pipe will have a lesser significance factor than a branch pipe or service pipe.
( 2) where, S -Entropy of WDN; • INset of source and demand nodes; • T -Total supply; • T j -Total flow reaching node j; • q ij -Flow rate in pipe ij; • Q j -Nodal demand; • N j -Number of adjacent nodes connected to node j.
Nodal entropy is important for BWSS as an end node in BWSS represents a fixture where a water-use event occurs.

CONCLUSION
A relevant literature on residential water demand modelling and hydraulic reliability is reviewed with the aim of exploring into efficient design of BWSS. Use of water is a subjective and user-dependent event affected by several factors and user characteristics. The common basic parameter, fixture-use probability (p) used in many models for instantaneous residential water demand estimation, including the Fixture Unit approach, is a very difficult variable to determine and requires a large amount of high-resolution field data. Most of the stochastic water demand estimation models use such fine-scaled data collected from a large number of households for quite a long period of time (around 1-15 years), which may not be available for a region under consideration. Thus, an alternative approach is required to model residential water demand to circumvent the need for high-resolution field data. The location-specific studies for characterizing water-use behaviour of users might be tedious, but can prove to be a more rational way to estimate water demand for the efficient design of BWSS in the respective locality. The size of an area or region under consideration for characterizing user-behaviour remains an aspect open for investigation.

Soft computing techniques like fuzzy logic and ANN
can simplify the modelling of uncertainties and irregularities in residential water demand more compared to other mathematical modelling approaches. The subjective information on use of different fixtures can be obtained from users and used for developing an interaction between the user and plumbing fixtures using fuzzy logic. The water demand model based on such a data will require no costly field measurements, as its parameters such as instance, duration and frequency can be retrieved from approximate information given by users. The feasibility of such an end-use water demand model in BWSS design may be strengthened by giving due consideration to estimation of its hydraulic reliability during design. Moreover, estimation of hydraulic reliability of BWSS is essential as there are significantly higher demand variations in BWSS than those of WDS.
The amalgamation of these two aspects, viz. modelling of water demand using soft-computing techniques and consideration to estimation of hydraulic reliability in the design of BWSS, can prove to be very useful to overcome problems of selecting appropriate method of pipe sizing in BWSS and efficient design of BWSS. Nonetheless, applicability and consequent use of available reliability indices, viz. entropy, RI, MRI, NR, etc. for estimating the hydraulic reliability of BWSS needs to be studied in detail.

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