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A Whole Life Costing Approach for Rainwater Harvesting SystemsRichard Roebuck PhD, Bradford University
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5.0 Rainwater Harvesting Model Development
5.1 Introduction
This chapter describes the development of a model for predicting the financial
performance of RWH systems using a whole life costing approach. It has been
implemented as a spreadsheet application using Microsoft Excel and is a
deterministic model based on discrete timesteps of one day. It contains both
empirical and process model elements. The water saving reliability is predicted
using a mass-balance transfer model based on the YAS reservoir operating
algorithm described by Latham (1983), as discussed in chapter three. The
model was developed using the concepts and information presented in chapters
two, three and four.
This chapter is divided into two sections. The first provides an overview of the
modelling tool and describes its main features, scope, analysis capabilities, data
requirements and limitations. The second provides details on the underlying
algorithms that drive the hydrological and financial analysis engine.
Referring to the flowchart presented previously in figure 3.1, this chapter can be
considered to cover the following model development stages: formulation of
equations (where these have not already been presented), creation of model
structure, formulation of methods for solving and formulation of computational
methods.
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5.2 Model overview
The spreadsheet developed during this research is a mass-balance transfer
model that represents RWH systems which supply non-potable water to
residential, commercial, industrial and institutional buildings. The primary
purpose of the application is to provide an assessment of the hydrological and
WLC performance of these systems for individual buildings. The model
simulates and then compares two scenarios: a building with a mains-only
supply and the same building with a RWH system plus mains top-up function.
This allows the user to judge the relative cost effectiveness of a proposed RWH
system compared to relying solely on mains-only water. It is also possible to
predict its technical performance under a range of operating conditions and
configurations. For example, a range of tank sizes (and associated
costs/benefits) can be assessed and the results compared in order to determine
which size optimises the financial performance under a given set of
circumstances.
5.3 Model scope
A daily timestep has been employed and simulations can be run for up to 100
years. This upper limit was chosen as it represents a long enough time period
over which to judge the performance of any system, and in any case for
reasons of practicality most financial assessments would not be conducted on
timescales of this length. The selection of a daily timestep was discussed and
justified previously in chapter three. Any RWH system can be assessed
providing that the configuration does not vary significantly from that shown later
in figure 5.3. This configuration corresponds to most contemporary systems and
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virtually all domestic ones. A range of key input parameters have been identified
and most are user-definable, for example rainfall patterns, catchment size,
storage tank capacity, water demand profiles, pump and UV unit characteristics
(including electricity costs). Mains supply and sewerage systems are included
as boundary conditions and only the volume of water passing to and from these
is considered, along with any associated costs.
Both new-build and retro fit systems can be modelled, although this thesis only
considers new-build situations.
Operating costs can be entered on a yearly basis and these include water
supply and sewerage charges, electricity costs and the discount rate. This
allows gradual long-term changes in costs to be taken into account. For
instance there is a general trend of increasing water supply and sewerage
charges in real terms. The same is also true of energy costs (see chapter four).
These increases can be modelled in detail and it does not have to be assumed
that prices remain static over time, a trait that was deemed to be a limitation of
many of the existing models reviewed in the previous chapter. Maintenance
activities and associated costs can be modelled on a temporal scale of at least
one month, although costs for a given year are aggregated to give an overall
annual expenditure. Maintenance activities can be programmed so that they
occur only once or repeatedly at a specified time interval, e.g. once at five
years, once every six months. It is possible to exclude a given financial cost
from the analysis if it is not required, e.g. decommissioning costs.
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5.4 Model structure
To recap from chapter three, the hydrological components explicitly modelled
consist of rainfall depth, catchment surface (runoff characteristics), first flush
diverter, coarse filter, pump, UV unit, potable (mains) water supply and
sewerage systems (volumes to and from), storage tank and non-potable supply
and demand. To this can be added the associated financial parameters
identified in chapter four which consist of capital and decommissioning costs,
volumetric water supply and standing charges, volumetric sewerage disposal
and standing charges, electricity supply, maintenance frequencies plus
associated expenses and the selected discount rate and discount period. Figure
5.1 shows a picture of the main navigation screen from which the rest of the
application is accessed.
Figure 5.1 RWH system model: main navigation screen
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The application is modular in design and broadly consists of three types of
modules: input, analysis and computational. The input modules are where the
user enters the data required by the program to perform an analysis. These can
be further divided into hydrological and financial input modules and each has its
own set of associated parameters that require user input, as shown in tables 5.1
and 5.2. In total there are 7 hydrological and 4 financial input modules.
Table 5.1 Hydrological input modules and associated parameters
Module Associated parameters UnitsRainfall profiles Historic daily rainfall data
UKCIP-02 scenarios1mm/daymm/day
Catchment surfacedetails
Catchment (plan) areaInitial lossesRunoff coefficientFirst-flush device
m2mm-litres
Coarse rainwater filter Filter coefficient -
Storage tank Tank storage capacityInitial degree of fillingMains top-up location
(storage tank or in-buildingheader tank)Drain-down intervals
m3%-
Date
Pump Pump installed? (yes/no)Power ratingPumping capacity
-kWlitres/min
UV unit UV unit installed (yes/no)Power ratingOperating time
-Whrs/day
Water demand Daily demand m3/day1Climate change scenarios generated from historic data usingUKCIP (2002b) methodology
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Table 5.2 Financial input modules and associated parameters
Module Associated parameters Units
Capital/decommissioningexpenses
Capital costsDecommissioning costs
Water and seweragecharges
Volumetric supply chargeSupply standing chargeVolumetric seweragechargeSewerage standing chargeHarvested water disposalcharge1
/m3
/yr/m3
/yr/m3
Operating expenses Electricity costDiscount rate2
p/kWhr%
Maintenance activities3 Activity frequencyAssociated cost
Months/years/activity
1
Not yet applicable in the UK but this situation may change in the future2Selected discount rate applies to allcost components including mains-only system3Specify up to 20 maintenance activities and associated costs/frequencies
There are three separate analysis modules available that allow the user to
conduct a range of investigations of increasing complexity (and therefore of
increasing data requirements). A range of analysis options was included
because the user may not wish to perform a detailed assessment at the outset,
which would require a large amount of data to be gathered. At first they may
wish to perform a simpler scoping exercise in order to determine the feasibility
of a system in terms of its ability meet a given set of design criteria, e.g. be able
to supply a minimum amount of water or be financially viable. Once the
feasibility of a system has been confirmed then time and resources can be
dedicated to collecting the information required to perform a more detailed
analysis. The available analysis modules are summarised in table 5.3.
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Table 5.3 Description of available analysis modules
Module Description Parameters requiring dataAssess tanksizes
For a given system,predicts the percentage of
demand likely to be met byassessing the performanceof a range of tank sizes(0.1-1000m3)
Analysis time horizon, tank sizes,rainfall profile, catchment area, initial
losses, runoff coefficient, coarse filtercoefficient, water demand and first-flush volume
Assess savings As above but also predictsthe WLC of both the RWHsystem and an equivalentmains-only system andcalculates the financialsavings associated with arange of tank sizes
As above plus capital anddecommissioning costs, water supplyand sewerage charges, discount rate,electricity charge, pump power ratingand capacity, UV unit power ratingand operating time and maintenanceitems (frequency and associatedcosts)
Detailed analysis Similar to the assesssavings module but onlyassesses one system at atime. However, results areavailable in much greaterdetail
Same as for assess savings module
The assess savings module determines the WLC performance of a range of
tanks during the same simulation run. That is, for a given building and set of
conditions (climate, building characteristics, water demand) the module will
perform a comparative simulation for different tank sizes and their associated
capital/decommissioning costs. All other costs are assumed to be the same, for
instance water supply and sewerage charges, maintenance requirements,
electricity costs. This allows the user to optimise the financial performance of
the RWH system by selecting the most cost effective tank size from the
available range. Figure 5.2 shows the results from an analysis conducted for a
proposed school system in the West Yorkshire region. The graph clearly shows
an initially increasing profitability as tank size increases but this peaks at about
30m3 and then declines for all tank sizes after that. The optimisation results
would therefore indicate that, under the assumptions used in the analysis, a
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tank size of approximately 30m3 represents the best investment from a financial
perspective.
Figure 5.2 Example of a WLC optimisation analysis
0
2,000
4,000
6,000
8,000
10,000
12,000
14,000
16,000
18,000
0 10 20 30 40 50 60
Tank size (cu.m)
Saving
s@N
PV()
Notes: results are for school building with 200 male and 200 female pupils, harvestedwater uses were urinal and toilet flushing, yearly demand = 1,226m3, roof area =1,150m2, runoff and filter coefficients = 0.9, mains water supply and sewerage charges
as described in chapter four. Discount rate = 3.5%, discount period = 50 years
Once the optimum tank size has been determined then the associated
capital/decommissioning costs are transferred to the detailed analysis module,
if a more in-depth study is required. This module outputs assessment results as
a series of performance indicators. The primary indicators consist of the total
water demand over a systems lifetime and percentage of demand met by
harvested water, WLC of the RWH system at present value, WLC of an
equivalent mains-only system at present value, financial savings (if any) of the
RWH system compared to the equivalent mains-only system, and the pay-back
period (if any). It is also possible to examine system performance in greater
detail than with the other modules. For example a detailed breakdown of the
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WLC contribution from each maintenance item is available whereas in the
assess savings module maintenance costs are aggregated each year into a
single figure. More hydrological performance details are also available, e.g.
number of overflows, overflow volume, number of empty tank days, maximum
consecutive empty tank days, total water to tank, water utilised as percentage of
total catchment runoff.
There is one computational module plus associated Visual Basic for
Applications (VBA) code. This can be considered as the engine of the model
as it links the other modules together and contains the algorithms that represent
the physical components of the RWH system. The operation of the
computational module is covered in greater detail later in this chapter.
5.5 Model limitations
There are a number of limitations with the current version of the model. It does
not explicitly take account of water quality although it does include a
representation of components that are known to improve it, such as coarse
filters and UV units. It was shown in chapter two that coarse filtration is
considered sufficient treatment for most non-potable applications. The addition
of UV sterilisation would further reduce any associated risks but would also
increase costs. The assumption therefore is that the harvested water will always
be of sufficient quality for the non-potable uses considered during this research
project.
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There is an implicit assumption that mains top-up water will always be available
for those times that the RWH storage tank runs empty. This is a reasonable
supposition as the literature review showed that the vast majority of
contemporary systems located in urban areas have a mains top-up function.
5.6 Assessment procedure
The model consists of two analysis components. One assesses the hydrological
performance and the other the financial performance. Both the proposed RWH
system and an equivalent mains-only system are simulated. For a given time
period tthe hydrological performance is evaluated first. The model operates on
a daily time-step and, for the RWH system, simulates the water fluxes
associated with the storage tank in a 24 hour period. In order to keep the
volume of data produced to manageable levels the application was
programmed so that it performs a single years worth of daily analysis and then
aggregates the outputs and records the key daily results from that current year,
e.g. percentage of demand met, volume of mains top-up required. Daily results
for the current year are then deleted before proceeding to the next year. The
equivalent mains-only system is modelled in a similar fashion. However, the
process is less complex than for the RWH variant and it is simply assumed that
all non-potable demand is met by mains supply water.
The financial aspects are evaluated on an annual basis after the hydrological
calculations have been performed and aggregated for a particular year. Some
financial components are dependant on the results from the hydrological
analysis whilst others are affected only by the passage of time, i.e. costs are
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incurred on a daily basis or on a specific calendar date regardless of
hydrological performance. The former include pump operating, mains top-up
and harvested water disposal costs. The latter include capital, decommissioning
and UV operating costs, supply and sewerage standing charges as well as any
maintenance activities.
This process is repeated until the number of years simulated have reached the
value specified by the user, up to a maximum of 100 years. Figures 5.3-5.5
show schematic representations of the hydrological and financial components
and demonstrate how they are linked to produce a complete systems model.
Figure 5.3 Schematic representation of the hydrological model
RtILt + RLt
ERt
FFLt
FLtQt
Mt
A
Ot
DDt
S Vt
Dt
F
Building
FF
FFt
Yt
Pu
Tank
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Where:
A = Effective catchment (roof) area (m2) Qt = tank inflow in time t(m3)
Rt = rainfall depth in time t(m) S = storage capacity of tank (m3)
ILt = Initial losses in time t(m) Vt = storage content in time t(m3)
RLt = runoff losses in time t(m3 /day) Mt = mains top-up in time t(m
3)*
ERt = effective runoff in time t(m3) Ot = overflow in time t(m
3)
FF = first flush filter DDt = drain-down in time t(m3)
FFt = first flush pass forward flow in t(m3) Pu = pump unit
FFLt = first-flush losses in time t(m3) Yt = yield in time t(m
3)
F = coarse filter Dt = water demand in time t(m3)
FLt = coarse filter losses in time t(m3)
*Mains top-up can also occur in the in-building header tank, location is user-definable
Unless otherwise stated the time interval t refers to one day, y denotes the
current simulation year and nis the analysis time horizon in years
Figure 5.4 Schematic representation of mains-only financial model
Where:
MSYSTEM = mains (public) water supply system
MSUPPLIED = volume of mains water supplied (m3/yr)
MSUPCOST/YR = volumetric mains water supply cost (/yr)
MDISPOSED = volume of mains water discharged to sewer system (m3/yr)
SupSC = mains water supply standing charge (/yr)
SewSYSTEM = public sewer system
SewCOST/YR = volumetric sewerage disposal cost (/yr)
SewSC = sewerage standing charge (/yr)
r = discount rate (%)
SewSYSTEM
MSUPPLIED
MDISPOSED
MSUPCOST/YR
SewCOST/YR
MSYSTEM
SupSC
SewSC
r
Financial model boundary
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Figure 5.5 Schematic representation of RWH system financial model
Where:
RWHSYSTEM = rainwater harvesting system
RWHCAPCOST = capital cost ()
RWHMACOST/YR = maintenance cost (/yr)
RWHDECOST = decommissioning cost ()1
PuEnt = pump energy usage (kWhrs)
PuCOST/YR = pump operating cost (/yr)UVEnt = UV unit energy usage (kWhrs)
UVCOST/YR = UV unit operating cost (/yr)
RWHDISPOSED = volume of harvested water discharged to sewer (m3/yr)
RWHDISCOST/YR = disposal charge for RWHDISPOSED (/yr)
MTOP-UP = annual volume of mains top-up required (m3/yr)
MTOP-DIS = annual volume of mains top-up to sewer system (m3/yr)
1Assumed to occur at end of analysis period (year n)
The other terms are as previously defined.
SewSYSTEM
SewCOST/YR
Financial model boundary
MSYSTEM
MTOP-UP
MTOP-DIS
MSUPCOST/YR
RWHSYSTEM
PuEntPuCOST/YR
UVEntUVCOST/YR
RWHDISPOSEDRWHDISCOST/YR
RWHCAPCOST
RWHMACOST/YR
RWHDECOST
SupSC
SewSC
r
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5.7 Hydrological model algorithms
The underlying principles of the selected hydrological modelling approaches
were discussed in chapter three. This section details their inclusion within the
developed model in terms of the algorithms used to implement them.
Figure 5.6 is a flowchart that demonstrates the order in which the hydrological
calculations are conducted. Note that the arrangement of inflow/outflow fluxes
associated with the storage tank correspond to those of a YAS operating
algorithm (Jenkins et al, 1978). Different algorithms, for instance YBS, would
have a different order of operations. The numbered boxes on the flowchart refer
to equations presented later in this chapter and demonstrate how the equations
are linked to form a complete model.
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Figure 5.6 Flowchart demonstrating order of hydrological operations
109
8
7
6
5
4
3
1 2
Collect andinput data
Read rainfalldepth for
current day
Startsimulation( =1, t=1)
Notation Keyn= analysis period in years
y= current yeart= current day in year y
Subtract initial lossesfrom daily rainfall
depth
Effective rainfalldepth and runofffrom catchment
Initial and coefficientlosses (depression
storage etc)
First-flush filterFirst-flush losses
Coarse (leaf) filterCoarse filter losses
Storage Tank(YAS)
1) Determine yield2) Inflow3) Overflow4) Extract yieldOverflow losses
Read waterdemand forcurrent day
Pump unit
Water use anddisposal / losses
In storagetank
In headertank
Mains top-up(if required)
y+ 1
Foul sewer systemand / or garden
t= 365?
y= n?
Yes
t+ 1
Simulation ends
YesNo
t= 1
t= 365AND
y= n?
No Yes
No
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5.7.1 Initial losses
The user is required to input the initial loss value in mm for a given catchment
material (e.g. roof tiles). Since the model works on a daily timestep the initial
losses are also calculated at this time scale. The program compares the initial
loss value with the rainfall depth occurring on a given day. If the rainfall depth is
greater than the initial losses then subtract the initial loss value to give the
effectiverainfall depth. See equation 5.1.
tt
tttt
t
ILR
ILRILR
RE
if0
if
(5.1)
where:
REt = effective rainfall depth in time t(m)
Rt = rainfall depth in time t(m)ILt = initial losses (m)
5.7.2 Effective runoff and runoff losses
The effective runoff is the volume of rain falling on a catchment (plan) area that
can be collected and routed into the RWH system. A coefficient is used to
represent the volume of rainfall that is lost from the system, for example due to
processes such as depression storage, surface wetting and evaporation (these
are in addition to the initial losses described in section 5.7.1). Equation 5.2
shows the algorithm employed in the model.
Rtt CARER (5.2)
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where:
ERt = effective runoff in time t(m3)
Rt = rainfall depth in time t(m)
A = effective catchment area (m
2
)CR = catchment runoff coefficient
5.7.3 First flush device
First flush devices capture a predefined volume of the effective runoff
originating from the catchment surface. It is possible for the effective runoff
volume to be less than that of the first flush volume (such as on a day with little
or no rainfall) and this condition requires evaluation. The first flush pass forward
flow (volume of water bypassing the device) is given by equation 5.3.
0if0
0if
VOLt
VOLtVOLt
t
FFER
FFERFFER
FF (5.3)
where:
FFt = first flush pass forward flow in time t(m3)
FFVOL = first flush volume (m3)
5.7.4 Coarse filter
The volume of water passing into the storage tank via the coarse filter is
represented by a coefficient as shown in equation 5.4. It is assumed that no
further components exist between the coarse filter and the storage tank and so
the cleaned water from the filter is routed directly to the tank (equation 5.5).
Ftt CEFF (5.4)
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tt FQ (5.5)
where:
Ft = course filter pass forward flow in time t(m3)
CF = coarse filter coefficient
Qt = inflow to storage tank in time t(m3)
5.7.5 Storage tank water fluxes
The operation of the storage tank was modelled using the generalised
YAS/YBS algorithm described by Latham (1983). The storage operating
parameter was set to zero, meaning that the model behaved the same as the
YAS variant. A more detailed explanation of the YAS/YBS operating rules can
be found in chapter three. The generalised YAS/YBS algorithm is shown here in
equations 5.6 and 5.7.
tt
t
t
QV
DY min (5.6)
t
tttt
t
YS
YYQVV
)1(
)1()(min
1
(5.7)
where:
Yt = yield from system in time t(m3)
Dt = demand from system in time t(m3)
Vt = storage content in time t(m3)
Vt-1 = storage content in time t-1 (m3)
= Storage operating parameter coefficient
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Note that in equation 5.6 the daily demand Dt is automatically extracted from the
Demand Generator module (see chapter three).
5.7.6 Overflow
An overflow algorithm was developed using the same principles as that used by
Latham (1983) to derive the generalised YAS/YBS equations, as shown in
equation 5.8.
SYQV
O
ttt
t
1
0
max (5.8)
where:
Ot = overflow in time t(m3)
5.7.7 Mains top-up
The volume of mains top-up required is determined by subtracting the yield
obtained on a given day, Yt, from the demand occurring on the same day, Dt.
The difference between the two parameters is the daily shortfall which is
assumed to be compensated for by mains top-up water (equation 5.9).
ttt YDM (5.9)
where:
Mt = mains top-up in time t(m3)
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5.7.8 Pump unit
Pump unit operating time per day is given in equation 5.10. The volume of water
which requires pumping can be affected by the location of the mains top-up
function (storage tank or in-building header tank) and so this condition requires
evaluation.
tankheaderinup-topif
tankstorageinup-topif
CAP
t
CAP
tt
TIME
PuY
Pu
MY
PU (5.10)
where:
PUTIME = pump operating period in time t(hrs)
PUCAP = pump capacity (m3/hr)
5.8 Financial model algorithms
The underlying principles of the selected financial modelling approaches were
discussed in chapter four. This section details their inclusion within the model in
terms of the algorithms used to implement them.
The selected financial assessment method is fundamentally a comparison
between two possible options: one in which a building uses a metered mains
supply to satisfy potable and non-potable demand, and one in which a RWH
system with mains top-up is used to satisfy some (or potentially all) of the non-
potable demand. In the latter case water is still drawn from the mains for
potable uses. Both options have associated costs. For the metered mains-only
scenario water supply and sewerage charges are incurred, as are standing
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charges. These may also apply to the RWH system due to the use of mains top-
up water. The rainwater system also incurs expenses that the mains-only
system does not and these consist of capital, operation, maintenance and
(possibly) decommissioning costs. The financial analysis procedure for both the
mains-only and RWH systems are demonstrated in figures 5.7 and 5.8. The
numbered boxes refer to equations from this chapter and demonstrate how they
are linked.
Figure 5.7 Flowchart demonstrating order of financial operations for
mains-only system
11
11
11
12
11
Collect andinput cost data
Startsimulation
( y= 1)
Notation Keyn= analysis period in yearsy= current yeart= current day in year yPV = present value
Sum daily waterdemand volumes fort=1 to 365 inclusive
y+ 1 y= n?
Simulation ends
Yes
No
Annual demand xvolumetric supply &sewerage charges
Sum costs to givetotal annual cost at
current prices
Yearly supply andsewerage standing
charges
Calculate and record
PV of costs for yeary
Daily waterdemandvalues
Sum present valuesfor all years to givemains-system WLC
Vol. seweragecharges, account for
non-return losses
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Figure 5.8 Flowchart demonstrating order of financial operations for
RWH system
24 23
19
17
15
13
Start
simulation( = 1)
Collect andinput data
y+ 1
Simulation ends
Yes
Supply andseweragecharges
y= 1?Add capital cost toRWH system WLC
sum
Calculate and recorddecommission cost
at PV
No
Calculate and recordpump operating cost
at PV
Sum pump annualoperating time and
energy usage
Calculate and recordUV operating cost at
PV
Sum UV annualoperating time and
energy usage
Calculate and recordmains top-up costs
at PV
Calculate volume ofmains top-up
required
Electricityunit charges
Calculate and recordharvested water
disposal cost at PV
Calculate volume ofharvested water to
public sewer
Maintenanceactivitiesand costs
Calculate and recordyearly maintenance
cost at PV
y= n?
Yes
No
Notation Keyn= analysis period in yearsy= current yeart= current day in year yPV = present value
21
14, 16, 18,20, 22, 25,26
Sum present valuesfor all years to giveRWH system WLC
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All future costs are related back to their equivalent present values using
standard discounting techniques.
5.9 Mains-only system financial calculations
Mains-only system costs are limited to the non-potable fraction which harvested
water is intended to substitute, for example the volume of mains water used to
flush the WC, wash clothes and/or irrigate the garden. The costs of other non-
potable and potable uses are not included in the analysis since they are
independent of the RWH system. The algorithms that calculate the yearly cost
and total WLC of the mains-only system are given in equations 5.11 and 5.12.
)()]1[(
)()(
%
%/
SCSCUNITCOSTLOSSESSUPPLIED
SCSCUNITCOSTSUPPLIEDYRCOST
SewSewSewSewM
SupSupMMM
(5.11)
ny
y
YRPVCOSTNPV MM1
/ (5.12)
where:
MCOST/YR = annual mains water cost (/yr)
MSUPPLIED = annual volume of mains water supplied (m3/yr)
MUNITCOST = volumetric supply charge for mains water (/m3)
SupSC = supply standing charge (/yr)
SupSC% = fraction of supply standing charge applicable
SewLOSSES = fraction of non-return to sewer losses
SewUNITCOST = volumetric disposal charge for sewerage (/m3)
SewSC = sewerage standing charge (/yr)
SewSC% = fraction of sewerage standing charge applicable
MNPV = discounted NPV value of mains supply over nyears ()
MPVCOST/YR = discounted annual mains water costs (/yr)
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It would have been technically acceptable to disregard the supply and sewerage
standing charges since these apply equally to both the mains-only and RWH
systems. The selected WLC approach allows costs that are common to all
options to be ignored since ultimately they do not affect the WLC difference
between the modelled scenarios. However, it can still be useful to include the
standing charges since this gives a better indication of the total cost of each
system and also the true unit cost of water supplied from each, not just the
difference between the two.
Supply and sewerage standing charges were assigned to the RWH system by
estimating the totalwater demand (potable plus non-potable) of a building, and
then calculating the percentage of the total demand that could potentially be
met by harvested rainwater. The same percentage of the supply and sewerage
standing charges were then assigned to the RWH system. For example if half of
all water demand could met by harvested water then 50% of the supply and
sewerage charges would be assigned to the RWH system costs. In all cases
the daily per capita internal water use was assumed to be 120 litres (see
chapter three).
5.10 RWH system financial calculations
The key RWH system cost components include capital, operating, maintenance
and decommissioning costs. The operating costs consist of pump and UV
electricity charges as well as any main top-up required.
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ny
y
YRMACOSTNPV RWHMa1
/ (5.14)
where:
RWHMACOST/YR = annual RWH system maintenance cost (/yr)
MaiCOST/YR = annual maintenance cost for item i, where i= 1-20
MaNPV = discounted NPV of total maintenance costs over nyears ()
5.10.3 Decommissioning costs
Decommissioning is assumed to occur during the final year of the selected
analysis period. The user is required to input the estimated decommissioning
costs at current prices in the Decommissioning Cost module. During analysis of
the final simulation year (y=n) the program calculates the present value of the
decommissioning cost and adds this to the WLC of the RWH system.
5.10.4 Pump operating costs
The operating (electricity) cost of the pump is related to the energy usage,
which in turn is dependant on the pump operating time and power rating. The
determination of pump operating time was given previously in this chapter
(equation 5.10). Pump power usage was covered in chapter three (equation
3.5). Equations 5.15 and 5.16 below demonstrate how annual and lifetime pump
operating costs were calculated.
365
1
/
100
t
t
UNITCOSTtYRCOST
ElPuEnPu (5.15)
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ny
y
YRCOSTNPV PuPu1
/ (5.16)
where:
PuEnt = pump energy usage in time t(kWhrs)
ElUNITCOST = unit cost of electricity (p/kWhr)
PuNPV = discounted NPV of pump operating costs over nyears ()
5.10.5 UV unit operating costs
The operating (electricity) cost of the UV unit is related to the energy usage,
which in turn is dependant on the units operating time and power rating .
Equations 5.17, 5.18 and 5.19 below demonstrate how the energy usage,
annual and lifetime UV operating costs were calculated in the model.
UVEnt= UVPOWx UVTIME (5.17)
365
1
/
100
t
t
UNITCOSTtYRCOST
ElUVEnUV (5.18)
ny
y
YRCOSTNPV UVUV1
/ (5.19)
where:
UVEnt = UV unit energy usage in time t(kWhrs)
UVPOW = lamp power rating (kW)
UVTIME = UV unit operating time (usually 24 hours/day) (hrs)
UVCOST/YR = UV unit operating cost (/yr)
ElUNITCOST = unit cost of electricity (p/kWhr)
UVNPV = discounted NPV of UV unit operating costs over nyears ()
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5.10.6 Harvested water disposal costs
A disposal charge can be applied to any harvested water discharged to the foul
sewer system and this in effect replicates the volumetric sewerage charge
associated with mains supply water. Currently no UK water utility charges for
harvested water discharged to the sewer system but it is not inconceivable that
this situation may change in the future if the use of RWH systems were to
become more widespread. Water utilities are required to cover their operating
costs and with zero harvested water disposal charge they are essentially
treating a portion of a customers foul flow without recovering their own costs.
The algorithm used in the model allows the user to route only a fraction of used
harvested water into the sewer system. This enables the model to take into
account situations in which not all of the harvested water goes to the sewer, for
example where non-potable uses include an element of garden watering.
However, this does require an estimation to be made regarding the percentage
of water that will remain outside of the sewer system and it is unlikely that the
selected value will be completely accurate. Equations 5.20 and 5.21
demonstrate how the disposal volume and associated costs are calculated.
UNITCOST
t
t
DIStYRDISCOST DisSewYRWH365
1
%/ (5.20)
ny
y
YRDISCOSTNPV RWHDis1
/ (5.21)
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yearly cost to supply MTOP-UP is calculated as shown in equation 5.25 and the
total mains top-up cost over the whole analysis period, at NPV, is given in
equation 5.26.
365
1
t
t
tUPTOP MM (5.24)
)]1[(
)(/
UNITCOSTLOSSESUPTOP
UNITCOSTUPTOPYRTOPCOST
SewSewM
MMM(5.25)
ny
y
YRTOPCOSTNPV MTopUp1
/ (5.26)
where:
MTOP-UP = annual volume of mains top-up required (m3/yr)MTOPCOST/YR = annual mains top-up cost (/yr)
TopUpNPV = discounted NPV of mains top-up over nyears ()
5.10.9 Net present value of RWH system
The NPV of the RWH system is given by summing the NPV of the individual
cost items presented in sections 5.10.1 to 5.10.8, as shown in equation 5.27.
DECOSTNPVNPV
NPVNPVNPVNPVCAPCOSTNPV
RWHTopUpSC
DisUVPuMaRWHRWH
(5.27)
where:
RWHNPV = discounted NPV of RWH system over nyears ()
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5.11 WLC comparison between mains-only and RWH systems
Once the discounted WLC of the mains-only and RWH systems have been
calculated then the cost effectiveness of the latter can be evaluated. The model
is able to do this in a number of ways as described below.
5.11.1 Determination of WLC difference
This determines the long-term financial cost/benefit. The WLC of the mains-only
system is calculated as per equation 5.12. This equation gives the discounted
net present value of the mains-only system, i.e. this is the amount of money that
would be required now in order to meet the predicted costs of the mains-only
system as they arise over the selected analysis time horizon. The WLC of the
RWH system with mains top-up is calculated as per equation 5.27. This
equation gives the discounted net present value of the RWH system, i.e. it is the
amount of money that would be required nowin order to meet the costs of the
RWH system as they arise over the selected analysis period.
Knowing these two values allows the relative cost effectiveness of the RWH
system to be determined. Subtract the WLC of the RWH system from that of the
mains-only system (equation 5.28). If the result is positive then this represents
the financial saving arising due to the RWH system, at present value. If the
result is negative then this is the financial loss due to the RWH system, at
present value. The positive/negative sign can be used as a decision rule, as can
the magnitude of the savings achievable.
NPVNPVFCB RWHMRWH (5.28)
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where:
RWHFCB = RHW system long-term financial cost/benefit ()
It should be noted that whether the result is positive or negative can be
dependant on the selected discount rate, especially in situations where the NPV
is close to zero. In these cases care should be taken when using the NPV as a
decision rule as changing the model assumptions may give a different result. It
would be advisable to conduct a sensitivity analysis of the results in all cases.
5.11.2 Calculate average incremental cost (AIC)
This approach normalises the WLC of both systems and gives the results on a
cost per unit benefit basis, which in this case is the average discounted unit
cost of water measured in /m3 (equations 5.29 and 5.30). The RWH system
can be considered to be cost effective if the associated AIC is lower than that
for the mains-only system, or not cost effective if the reverse is true. The AIC
results can be used as decision rule regarding whether or not to implement the
rainwater harvesting system.
ny
yyr
NPVAIC
D
RWHRWH
1
(5.29)
ny
y
yr
NPVAIC
D
MM
1
(5.30)
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where:
RWHAIC = RWH system average incremental cost (/m3)
Dyr = annual demand (m3/yr)
MAIC = mains-only system average incremental cost (/m
3
)
A further advantage of this method is that it also allows the cost effectiveness of
RWH systems to be compared against various other demand measures where
AIC values are available, for instance low flush WCs, urinal controllers,
showers, rainwater butts, water efficient washing machines, water audits,
metering schemes, greywater recycling and industrial re-use schemes (National
Rivers Authority, 1995; Howarth, 1998; White & Howe, 1998; Foxon et al, 2000;
Grant, 2003).
5.11.3 Payback period
The initial (financial year zero) cost of a RWH system will usually be greater
than that of an equivalent mains-only system due to the required capital
expenditure. Providing that the RWH system has lower operating and
maintenance costs than the mains-only alternative then over time the cost
difference between the two will narrow and may converge. This is the payback
period, the point at which the WLC of the RWH system becomes equal to that of
the mains-only equivalent. This condition is evaluated in the spreadsheet model
once an analysis is complete and the results have been compiled. It is possible
that payback is never achieved, for example if the running costs of the rainwater
system are always higher than that of the mains-only system. In this case
payback can never be achieved and the model returns a value of N/A. This
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result is also given if payback is possible but lies outside the selected analysis
time horizon.
5.12 RWH model development: summary
This chapter has explained the structure, functioning, purpose and limitations of
the RWH assessment model developed as part of this research project. The key
underlying hydrological and financial algorithms have been presented and
described. Methods for comparing the cost performance of a RWH system and
equivalent mains-only system were given and it was shown how these can be
used as a decision rule when deciding whether or not to implement a rainwater
system.
In the next chapter the model is used to assess the WLC performance of a
range of domestic systems under a variety of operating conditions in order to
provide insights into the cost effectiveness of domestic rainwater harvesting in
the UK.