Development and validation of a drinking water temperature model in domestic drinking water supply systems

Abstract

Domestic drinking water supply systems (DDWSs) are the final step in the delivery of drinking water to consumers. Temperature is one of the rate-controlling parameters for many chemical and microbiological processes and is, therefore, considered as a surrogate parameter for water quality processes. In this study, a mathematical model is presented that predicts temperature dynamics of the drinking water in DDWSs. A full-scale DDWS resembling a conventional system was built and run according to one year of stochastic demands with a time step of 10 s. The drinking water temperature was measured at each point-of-use in the systems and the data-set was used for model validation. The temperature model adequately reproduced the temperature profiles, both in cold and hot water lines, in the full-scale DDWS. The model showed that inlet water temperature and ambient temperature have a large effect on the water temperature in the DDWSs.

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Development and validation of a drinking water
temperature model in domestic drinking water
supply systems
Ljiljana Zlatanovic, Andreas Moerman, Jan Peter van der Hoek, Jan Vreeburg
& Mirjam Blokker
To cite this article: Ljiljana Zlatanovic, Andreas Moerman, Jan Peter van der Hoek,
Jan Vreeburg & Mirjam Blokker (2017): Development and validation of a drinking water
temperature model in domestic drinking water supply systems, Urban Water Journal, DOI:
10.1080/1573062X.2017.1325501
To link to this article: http://dx.doi.org/10.1080/1573062X.2017.1325501
© 2017 The Author(s). Published by Informa
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URBAN WATER JOURNAL, 2017
https://doi.org/10.1080/1573062X.2017.1325501
RESEARCH ARTICLE
Development and validation of a drinking water temperature model in domestic
drinking water supply systems
Ljiljana Zlatanovica, Andreas Moermanb, Jan Peter van der Hoeka,c, Jan Vreeburgb,d and Mirjam Blokkerb,e
aDepartment of Water Management, Delft University of Technology, Delft, The Netherlands; bDepartment of Water Infrastructure, KWR Watercycle
Research Institute, Nieuwegein, The Netherlands; cWaternet, Strategic Centre, Amsterdam, The Netherlands; dSub- department of Environmental
Technology, Wageningen University, Wageningen, The Netherlands; eDepartment of Civil and Structural Engineering, University of Sheffield, Sheffield,
United Kingdom
ABSTRACT
Domestic drinking water supply systems (DDWSs) are the nal step in the delivery of drinking water to
consumers. Temperature is one of the rate-controlling parameters for many chemical and microbiological
processes and is, therefore, considered as a surrogate parameter for water quality processes. In this study,
a mathematical model is presented that predicts temperature dynamics of the drinking water in DDWSs.
A full-scale DDWS resembling a conventional system was built and run according to one year of stochastic
demands with a time step of 10s. The drinking water temperature was measured at each point-of-use in the
systems and the data-set was used for model validation. The temperature model adequately reproduced
the temperature proles, both in cold and hot water lines, in the full-scale DDWS. The model showed that
inlet water temperature and ambient temperature have a large eect on the water temperature in the
DDWSs.
Introduction
The domestic drinking water system (DDWS) is dened as the
part of the drinking water distribution system that includes
plumbing between a water meter and consumer’s tap, and thus,
represents the nal section of a drinking water supply system.
Apart from being made from a wide range of materials that are
not commonly present in the distribution mains (copper, brass,
high-density polyethylene, stainless steel), the factors that addi-
tionally distinguish DDWSs from the distribution mains are the
magnitude of residence time, temperature gradient, surface
area to volume ratio and loss of disinfectant residual (NRC 2006).
Among the above-mentioned factors, temperature is one of
the most important parameters aecting the quality of drinking
water. The signicance of drinking water temperature is based
upon its role in physical, chemical and biological processes.
Viscosity of drinking water, for instance, tends to fall as tem-
perature increases. A rise from 5 to 25°C causes the viscosity to
drop by almost 40% resulting in a decrease in ow resistance,
which aects the transport phenomena in pipes (Blokker and
Pieterse-Quirijns 2013). Chemically speaking, water temperature
is important due to its eects on copper solubility, the rate of
corrosion, lead leaching from brass xtures, bulk chlorine decay
rate and formation of disinfection by-products. Higher water tem-
peratures aggravate the corrosion of pipes. As an example, an
increase in water temperature to 60°C in copper pipes results in
nearly three times higher copper levels (Singh and Mavinic 1991,
Boulay and Edwards 2001). Leaching of brass may signicantly
be increased by temperature rise leading to increased lead lev-
els that leached from brass elements (Sarver and Edwards 2011).
Bulk chlorine decay rates have also been found to increase with
temperature, and the chlorine decay coecient in water was
reported to increase more than threefold when temperature goes
from 10 to 20°C (Li et al. 2003). In case of the presence of the
organic precursors in drinking water, formation of chlorination
by-products, as trihalomethanes (THMs), is inevitable. In a study
on THMs formation it was concluded that levels of trihalometh-
anes increased considerably with elevation of water temperature
(Li and Sun 2001). Water temperature is known to promote bio-
logical processes, as biological activity increases twofold when
temperature increases by 10°C (Van der Kooij 2003). Higher water
temperatures also encourage bacterial regrowth and coliform
occurrence during the water distribution phase (LeChevallier
et al. 1996a, 1996b).
Given the substantial impact that temperature may have on
water quality, the World Health Organization recommends a
maximum value of 25°C for drinking water (WHO 2006). In the
Netherlands, where drinking water is being distributed without
persistent disinfectant residual, the temperature of drinking water
at the customers’ tap is not allowed to exceed 25°C. However,
as stated in a recent study (Blokker and Pieterse-Quirijns 2013),
during a relatively warm year (2006), 0.1% of the samples did
exceed the legislative limit.
ARTICLE HISTORY
Received 29 November 2016
Accepted27 April 2017
KEYWORDS
Drinking water; domestic
systems; water temperature;
modelling
© 2017 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group.
This is an Open Access article distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives License (http://creativecommons.org/licenses/by-nc-nd/4.0/),
which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is properly cited, and is not altered, transformed, or built upon in any way.
CONTACT Ljiljana Zlatanovic l.zlatanovic@tudelft.nl
The supplemental material for this paper is available online at http://doi.org/10.1080/1573062X.2017.1325501
OPEN ACCESS

2 L. ZLATANOVIC ET AL.
where λw symbolizes the water thermal conductivity [Wm−1K−1]
and Nuw is the Nusselt number for water.
Depending on the ow conditions (stagnant, laminar or tur-
bulent), the value of the Nusselt number changes (Janssen and
Warmoekserken 1991):
where Re is Reynolds number and Pr is Prandtl number.
The heat transfer coecient for the outer surface of the pipe
can be calculated by Equation (7):
where λa is the thermal conductivity of air [W·m−1·K−1] and Nua is
the Nusselt number for air.
The Nusselt number for air can be calculated using the Rayleigh
number (Ra), which is equal to the product of the Grashof (Gr) and
the Prandtl (Pr) number:
where α and γ are coecients which are experimentally
obtained. All pipes are treated as vertical plates in this research
and α = 0.59 and γ = 0.26 (Cengel 2002).
The Grashof number can be calculated as (Cengel 2002):
where g is the acceleration of gravity [m·s−2], β is the thermal
expansion coecient of air [K−1], Ts is the temperature at the
outer pipe wall surface [K], ν is the kinematic viscosity of air
[m2·s−1] and G is the length [m] of the characteristic geometry.
Since the characteristic geometry is positioned perpendicular to
the direction of the gravity force, for vertical pipes the charac-
teristic geometry is equal to the pipe length, while for horizontal
pipes G is considered to be equal to the pipe diameter.
The heat transfer coecient for the wall of the pipe can be
derived using the Equation (10):
where λp represents the pipe thermal conductivity [W·m−1·K−1]
and dp is the thickness of the pipe wall [m], which is considered
to be 10% of the pipe diameter in this research.
While water ows in pipes, air ow develops around the pipes,
and thus, Nusselt numbers are averaged along the characteristic
geometry for which the Nusselt number equals (Cengel 2002):
Substituting Equations (5), (7) and (11) in Equation (4) and
assuming d = 0.1D we end up with the Equation (12):
(5)
h
water =
𝜆
w
Nuw
D
(6)
Nu
w=
⎧
⎪
⎨
⎪
⎩
Re <10 5.8
10 <Re ≤2300 3.66
Re >2300 0.023Re0.8Pr1/3
⎫
⎪
⎬
⎪
⎭
(7)
h
out =
𝜆
a
Nu
a
D
(8)
Nua=𝛼Ra𝛾=𝛼(Gr
⋅
Pr)𝛾
(9)
Gr
=g𝛽(T∞−Ts)G
3
𝜈
2
(10)
h
wall =
𝜆
p
d
p
(11)
Nua
=0.59 R
0.25
a
(12)
hoverall
=D(𝜆
−1
w
Nu
−1
w
+0.1𝜆
−1
p
+𝜆
−1
a
Nu
−1
a)
Even though the drinking water temperature has been rec-
ognized as one of the crucial parameters aecting the drinking
water quality, most research on modelling of water quality in
distribution systems have considered water temperature to be
constant (DiGiano and Zhang 2004, Rubulis et al. 2007). In a recent
study, a model that predicts the temperature of the water in dis-
tribution networks was proposed (Blokker and Pieterse-Quirijns
2013). To our knowledge, the temperature dynamics have not
been modelled yet for the DDWSs. In this research a model,
intended to predict the temperature dynamics in DDWSs, was
developed and validated.
Methodology
Model development
Temperature model
The temporal change of water temperature inside the pipes is
governed by the dierence between water temperature and
ambient temperature. Calculation of the temperature change
over the time step ∆t can be done by solving the energy balance
equation for a control volume with arbitrary length ∆x:
where
ET,t
and
ET,t+Δt
[J/m] symbolize the amount of thermal
energy in the control volume at time t and time t+∆t, respec-
tively, while
ΔET
represents the change of thermal energy in
the control volume over the time interval ∆t. By introducing
the geometry of the control volume and physical properties of
water, the dierential equation is generated:
where T is the actual temperature of water, which is averaged
over the pipe diameter, [K], T∞ is the ambient temperature [K],
hoverall is the overall heat transfer coecient [Wm−2K−1], ρ the
water density [kgm−3], cp the heat capacity of water [Jkg−1K−1]
and D the pipe diameter [m].
To obtain the overall heat transfer coecient, it is essential to
establish the dierent heat transfer processes that occur along
the pipe. These processes can be divided into three phases: con-
vective heat transfer phase inside the pipe (Rconv,1), conductive
heat transfer phase through the pipe wall (Rc) and convective heat
transfer phase outside the pipe (Rconv,2) (Cengel 2002).
The overall thermal resistance can be described as Equation
(3):
The overall heat transfer coecient can be related to the ther-
mal resistance and can be dened as shown in Equation (4):
The variables hwater, hout and hwall are the heat transfer coe-
cients for the inner (hwater) and outer pipe surface (hout) and the
pipe wall (hwall) in Wm−2K−1 (Cengel 2002).
The heat transfer coecient for the inner surface of the pipe
is calculated as (Cengel 2002):
(1)
ET,t+Δt−ET,t=ΔET
(2)
dT
dt=
4h
overall
𝜌c
p
D(T∞−T
)
(3)
Roverall =Rconv,1 +Rc+Rconv,2
(4)
h
overall =
1
1
h
water
+1
h
out
+1
h
wall

URBAN WATER JOURNAL 3
Hydraulic model
To model the temperature dynamics in DDWSs it is essential to
have: (1) information on the lay-out of the system to be mod-
elled, in terms of pipe diameters, lengths of pipes and pipe
materials; (2) a set of demand patterns for each tap point in the
systems; (3) a hydraulic simulation software; (4) an extension
to the hydraulic software to implement the equations from the
temperature model.
In this research, the layout of the DDWSs was done accord-
ing to a plan of a terraced house, so-called Typical Dutch House
(Supplemental Figure S1), as terraced houses account for approx-
imately 62% of all residential properties in The Netherlands (as
cited in Majcen et al. 2013)
The demand patterns were generated by SIMDEUM (SIMulation
of water Demand, an End Use Model) for a two-person house-
hold. SIMDEUM, developed by KWR Watercycle Research Institute
(Nieuwegein, The Netherlands), is a stochastic model which is
grounded on statistical information of water appliances and water
consumers. SIMDEUM generates water demand patterns based
on consumers’ behaviour, considering the dierences in DDWSs
and water appliances (Blokker et al. 2006, 2010). In total, 365dif-
ferent demand patterns for a two-person household (including
104weekend patterns) were generated.
Modelling the hydraulics within the DDWSs was done by apply-
ing a free water distribution system modelling software EPANET.
EPANET was developed by the United States Environmental
Protection Agency (EPA) in 1993 (Rossman 2000). The simulation
outputs provide hydraulic information such as, ows in pipes,
pressures and water residence times at various locations in the
systems.
An extension to EPANET called EPANET-MSX (Multi-Species
eXtension), was used to implement the temperature model equa-
tions. This extension uses a Lagrangian time-based approach, i.e.
‘follows’ the trajectory of water parcels throughout the system
and considers concentrations, in this case temperature, as a func-
tion of time and their prior coordinates.
Model validation
Experimental rig
To validate the temperature model (and to study the inuence
of the DDWS’s extension for re sprinklers system integration,
which is a topic of a parallel research carried out by the authors),
two full-scale test rigs were built using standard copper pipes.
One experimental rig was built in a way to resemble a conven-
tional DDWS, while the other was constructed with the extension
of the plumbing for the residential sprinkler accommodation. In
this paper, only the results from the conventional DDWS rig are
presented.
The rigs were located in an old elevator shaft at the Water
Laboratory of the Faculty of Civil Engineering and Geoscience at
the Delft University of Technology and they were directly con-
nected to the drinking water line in the Water Laboratory. The
distance between the connection point to the drinking water
supply line and the beginning of the test rigs at the water meters
was 40m. The 40-m supply pipe with a diameter of 35mm was
insulated using 10mm Armaex AF2 insulation foam, with ther-
mal conductivity of 33W·m−1·K−1 (12times smaller than copper
thermo conductivity).
Conguration of the conventional experimental rig, which was
used for model validation (Supplemental Figure S1), complies
with the Dutch home plumbing codes NEN 1006 (NEN1006 2002).
The conventional DDWSs consisted of two vertical lines and four
horizontal branches of copper (manufactured in accordance with
European Standard EN 1057), namely vertical copper composite
of 22 mm diameter – carrying cold water to the upper oors,
vertical copper tube of 15mm (ID) – delivering hot water from a
50-L water heater and copper tubing’s of 15mm- supplying cold
and hot water from the vertical lines to the 11plumbing xtures
(solenoid valves), as given in Supplemental Figure S2. The total
length of the pipes was 48.6m in the conventional system and
the volume of the plumbing rig was 6L.
Water consumption pattern
To be able to mimic a realistic drinking water consumption at the
household level, the test rigs included 11solenoid valves (point
of use) per system. The valves were congured to run automati-
cally (‘on’ and ‘o’ mode) according to one-year demand patterns
with a time step of 10 s, which were generated by SIMDEUM
model. For the sake of validation of the temperature model, a
SIMDEUM pattern for a weekend day was used. In Supplemental
Figure S3 the measured ows are given.
In the DDWS experimental rig, the magnetic valves operated
only in ‘on’ and ‘o’ mode. This means that the valves were either
fully open or fully closed, which is not common in real DDWSs.
In addition to this, in experimental DDWSs opening a tap to the
full extent took longer than in real water systems (from ‘o’ to ‘on’
mode – the magnetic valve response is 0.1–4s). What was also
specic for the experimental set-up is that all magnetic valves
were of the same discharge capacity of 4 tapping units (TU),
where capacity of 1TU is equal to 5L/min. Having a slow response
and the same capacity for all valves in the systems resulted in
larger discharge on the weekend day, as the total measured daily
water use was 1000L.
The length of the pipe that delivers water from the connection
point to the lab rigs is 40m. Despite the fact that the pipe has
been thermo-insulated, stagnant water in the pipe heated up by
2.5°C per hour, until it got equal to the ambient temperature. For
the purpose of model validation, the 40-m long pipe was ushed
for 5min before the opening of each tap in the system. This was
done in order to ensure a stable inlet water temperature prole,
for the purpose of drinking water temperature model validation.
Every point of use in the systems was equipped with a ow
sensor and a temperature probe. A temperature probe was also
mounted before the water meters, to measure the inlet water
temperature. Moreover, three ambient temperature sensors
were installed on every ‘oor’ of our virtual Typical Dutch House.
Before starting the experiments, all sensors were manually cali-
brated. The drinking water temperatures, ambient temperatures
and ows were continuously measured, every 10s. The ambient
temperature around the pipes was also manually measured three
times a day during the ‘model validation’ day. The control of the
solenoid valves and data logging was achieved by using the data
acquisition, control and analysis software LabView.
Overview of the input parameters
The overview of the parameters used to validate the tempera-
ture model is given in Table 1.

4 L. ZLATANOVIC ET AL.
Nash-Sutclie eciencies are found in the range from −∞ to 1.
An eciency of 1 (N–S=1) shows a perfect t between simu-
lated and measured values. An eciency of lower than zero
suggests that the mean value of the measured data would have
been a better predictor than the model itself.
As for the error index, root mean square error (RMSE) –
which is described as the mean of the squares of errors, is
commonly used in model evaluation. This error measurement
is valuable because it indicates the extent of error among the
simulated and measured values. RMSE is calculated based on
Equation (15):
A RMSE value of 0 indicates a perfect goodness of t.
Sensitivity analysis
In order to identify the most relevant parameters involved in the
DDWS temperature model, a sensitivity analysis was carried out.
The sensitivity analysis included a variation of the selected input
parameters by 10% from their initial values. The selected input
parameters for water were: temperature of inuent water (Tw),
thermal conductivity (λw), Prandtl number (Prw) and heat capac-
ity (cp). The selected input parameters for air were: ambient tem-
perature (T∞), thermal conductivity (λa), Prandtl number (Pra)
and thermal expansion coecient β, while thermal conductivity
of copper pipes (λp) was selected for the sensitivity analysis for
the pipes. The percentage of the output dierence was meas-
ured for the data-set at the kitchen tap.
Results and discussion
A graphical visualization of the simulated and measured values
can give a rst valuable feedback whether the model outcomes
are realistic. Figure 1 depicts measured ows and temperature
proles for the kitchen tap in the experimental rig.
As can be seen from Figure 1, the dynamics of the measured
temperatures are predicted well by the temperature model for
(14)
N
−S=1−
∑n
i=1(yi−xi)
2
∑
n
i=1
(x
i
−−
x)
2
(15)
RMSE
=
�∑
n
i=1(xi−yi)2
n
Statistical analysis
The goodness of t between measured and modelled values
was assessed using the following statistical measures: standard
regression (correlation coecient (R)), dimensionless (Nash-
Sutclie eciency (N-S)) and error measurements (root mean
square error (RMSE)) (Nash and Sutclie 1970, Willmott et al.
1985).
The correlation coecient indicates the strength of a linear
relationship between the model outputs and observed values.
The correlation coecient is derived by dividing the covariance
of the two variables by the product of their standard deviations,
as given by Equation (13):
where xi are the observed and yi are the modelled values and
̄
x
and
̄
y
refer to the sample mean values.
The value of the correlation coecient ranges from −1 to+1.
If R=0, there is no linear relationship between the simulated and
observed values, while if R=1 or −1, there is a prefect positive
or a perfect negative linear relationship between the variables.
The Nash-Sutclie eciency N–S is used to evaluate hydro-
logic models and to study the ability of a model to reproduce the
verication data-set (Nash and Sutclie 1970). This coecient is
calculated as shown in Equation (14):
(13)
R
=
∑n
i=1(xi−̄
x) ⋅(yi−̄
y)
�∑
n
i=1(xi−̄
x)2⋅
∑
n
i=1(yi−̄
y)
2
Table 1.Overview of the parameters used in the DDWS temperature model.
Parameter Symbol Value Unit Source
Water
Temperature of influent water Tw9 °C Measured
Thermal conductivity at 15°C λw0.589 W·m−1·K−1 Cengel 2002
Prandtl number at 15°C Prw8.09 – Cengel 2002
Heat capacity cp4185 J·kg−1·K−1 Cengel 2002
Air
Ambient temperature T∞14.5–16 °C Measured
Thermal conductivity at 15°C λa0.02476 W·m−1·K−1 Cengel 2002
Prandtl number at 15°C Pra0.7323 – Cengel 2002
Thermal expansion coefficient
at 15°C
β0.00349 K−1 http://www.
mhtl.uwa-
terloo.ca
Kinematic viscosity at 15°C ν1.47 x 10−5 m2·s−1 Cengel 2002
Pipes
Thermal conductivity of
copper pipes
λp403 W·m−1·K−1 Cengel 2002
Figure 1. Left: Flow measured at the kitchen tap. Right: Modelled and measured temperature profiles at the kitchen tap plus modelled water residence time in the system.

URBAN WATER JOURNAL 5
As is evident from Figure 2, both addition of supplementary
ows of 10s (Tmodelled - tuned ow 10s in Figure 2) and distributing the
ow over 5s (Tmodelled tuned - ow 5s in Figure 2) result in more ade-
quate trends of the temperature proles for kitchen cold tap.
This implies that better hydraulic performance in EPANET 2.0
was accomplished with the aid of the ow adjusting procedure.
Validation was also done for hot water line as is given in Figure
2 (bottom). Because the demands of the hot bathroom tap were
long enough (>20s), the pattern was not tuned by assigning
extra ows. However, an additional simulation was done with
tuned 5s time step, to assess the dierence in temperature pro-
les if shorter time steps are applied. Graphical comparison, pre-
sented in Figure 2 shows that the model is able to adequately
reproduce temperature proles at the hot water taps, as well.
The ability of the temperature model to reproduce the temper-
ature dynamics in DDWSs was assessed by statistical measures,
applying the raw and tuned ow input, shown in Table 2.
Table 2 shows that tuning the ow input improved model
performance in terms of all three statistical measures for cold
water line. The values of both correlation coecient – R and
DDWSs. However, some irregularities were spotted, i.e. where no
temperature drop was predicted by the model, but was measured
in the rig (see the ellipse in Figure 1). No change in the residence
time was also observed at the same interval, which indicates that
EPANET didn’t recognize the measured extraction of water at the
kitchen tap around 07:30 in the morning.
The explanation for this phenomenon is that the hydraulic
network solver EPANET was primarily designed to predict the
hydraulics within a drinking water distribution system (Rossman
2000). Drinking water distribution systems consist of pipes with
larger diameters, longer pipe sections and higher water ows
compared to a DDWS. In the hydraulic models of DDWSs, apart
from small diameters (13mm), the lengths between the junctions
and the tap points are as small as ~1m. Thus, the mathematical
engine most likely starts losing the power to converge accurately
with ows over a single time step (10s), resulting in non-recogni-
tion of the real water consumption. To overcome this drawback,
an attempt was made to tune the ow input.
The tuning of the input ow included the process of deter-
mining best estimates for unknown ows by comparing model
outcomes and measured temperature record. Wherever the irreg-
ularities between modelled and measured temperatures were
found, the measured input demand patterns were manually
modied by:
(1) assigning 10 s of the additional ow of the same
magnitude
(2) distributing the ow over a shorter time step, i.e. 5s.
The graphical visualization of the results and the cumulative
probability curves that were generated before and after tuning
the input ow are presented in Figure 2.
Figure 2. Water temperature profiles and cumulative probability curves for observed and simulated data at the kitchen cold water tap (up) and bathroom sink hot water
tap (down).
Table 2.Statistical measures for temperature model performance.
Flow input R N-S RMSE
Cold water tap
Raw data – time step 10s 0.822 0.662 0.867
Tuned flow input – time step 10s 0.899 0.783 0.695
Tuned flow input – time step 5s 0.923 0.809 0.651
Hot water tap
Raw data – time step 10s 0.978 0.955 1.384
Tuned flow input – time step 5s 0.982 0.955 1.382

6 L. ZLATANOVIC ET AL.
place (Supplemental Figure S3). Therefore, if the drinking water
temperature is determined by sensors in drinking water distri-
bution networks, the temperatures at the points of use can be
underestimated.
The sensitivity analysis (Figure 3 (left)) for all-day simulation
data revealed that the most relevant parameters are the tempera-
ture of inlet water (T
w
), the temperature of air (T
∞
) and the thermal
conductivity of air (λa). If only extraction hours are included in the
sensitivity analysis (from 06.00 to 19:00), the inlet water tempera-
ture is found to play a more important role, as variation of±10%
in the input temperature leads to±2.5% of relative change in
the output temperature (Figure 3 (right)). Here again, the most
sensitive parameters were found to be the temperature of inlet
water, the temperature of air and the thermal conductivity of air,
and, hence, these values need to be put in the model with high
accuracy. From the sensitivity analysis it can be concluded that,
when modelling water temperature in DDWSs, the most impor-
tant transfer process is the exchange process of heat between
water and air through the pipe wall.
In the conducted research, DDWS made of copper was used
for the model validation. Because the model is based on fun-
damental thermodynamic principles, it can be used for other
DDWSs pipe materials as well. Nevertheless, the applicability of
the model for other pipe materials which are commonly applied
in DDWSs needs to be experimentally validated. If the temper-
ature model shows the same accuracy for the other pipe mate-
rials, it would be possible to couple the temperature model for
DDWSs with a model that predicts the temperature of the water
in the drinking water distribution system, fullling the goal to
model the temperature dynamics from the treatment facilities
(reservoirs) to the points of actual water use (drinking water taps
in DDWSs).
Conclusion
A temperature model for DDWSs was developed, by integra-
tion of a temperature model, a hydraulic model and a demand
pattern model (SIMDEUM). A combination of graphical and sta-
tistical techniques was used for model evaluation. A statistical
analysis showed that the model is able to adequately predict the
temperature proles within DDWSs. The most sensitive param-
eters in the model are the temperature of the inlet water, the
temperature of air and the thermal conductivity of air, imply-
ing the most dominant transfer process is the (convective) heat
Nash-Sutclie eciency N-S increased (from 0.822 to 0.923 and
from 0.662 to 0.809, respectively) while the error index, RMSE,
decreased from 0.867 to 0.651. In general, model prediction can
be judged as ‘very good’ if N-S>0.70 and R>0.90, as for the error
indices that are represented in the units of the temperature (ºC
or K), error values close to zero indicate perfect t. According to
Singh et al. (2004) if RMSE is smaller than one-half of a standard
deviation of measured time series, RMSE can be judged as low. In
our case, the standard deviation value was 1.49, implying that the
error index may be considered low for models with tuned ow.
We need to mention that discrepancies between measured
and modelled results were observed in the hours with no ow.
This was expected, as the ambient temperature uctuates by a
few degrees on a daily basis, while the model assumes constant
ambient temperature. The discrepancies also had an eect on
the statistical parameters. If the data during the daytime with
no ow are excluded from the statistical analysis (from 00:00 to
6:00 and from 19:00 to 00:00), R and N-S were improved to 0.937
and 0.992, respectively, while RMSE was of the same order, 0.704.
For the hot water line, the simulation with the tuned ow over
the time step of 5s yielded only slightly better statistical parame-
ters (Table 2), whereas R was improved from 0.978 to 0.982, while
RMSE and N-S were in the same order, 0.955 and 1.382 (1.384),
respectively. Here again, excluding the hours without the demand
from the statistical analysis (from 00:00 to 6:00 and from 19:00 to
00:00), resulted in improved R and N-S values to 0.984 and 0.999,
respectively), while RMSE was found to be larger (1.748), but still
the value of RMSE was found to be less than one-half of the stand-
ard deviation of the measured time series (6.478).
Even though the statistical measures for the temperature mod-
elling when employing tuned hydraulic models are satisfactory,
one must bear in mind that it is of high importance to have a
model with limited errors in terms of hydraulics. Thus, to obtain
representative results when having single step demands, it is
necessary to assess whether or not EPANET recognized the ow,
which can be done by analysing the extent of residence time at
a given ow.
The measured and modelled data revealed that the water
temperature dynamics in homes is mainly driven by the water
consumption pattern. Both modelled and measured data (meas-
ured data are given in Supplemental Figure S4) showed that
drinking water is being warmed up by 0.5 to 2°C within the
copper DDWSs, namely from the inlet point to the tap in use,
depending on how far from the inlet point the demand takes
Figure 3. Sensitivity of the water temperature model to the input parameters. Left Model outputs for all day simulation. Right Model outputs during extraction hours
(from 06.00 to 19:00).

URBAN WATER JOURNAL 7
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Disclosure statement
No potential conict of interest was reported by the authors.
Funding
The authors would like to acknowledge nancial support from Dutch
Automatische bluswatersystemen project (Agentschap Project No.
IMV1100047), Stichting PIT, and drinking water companies Waternet, Vitens,
Oasen, PWN and Brabant Water.
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