UK; Rainwater Harvesting Model Development - Bradford University

8/3/2019 UK; Rainwater Harvesting Model Development - Bradford University

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A Whole Life Costing Approach for Rainwater Harvesting SystemsRichard Roebuck PhD, Bradford University

Rainwater harvesting software from:www.SUDSolutions.com

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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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243

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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244

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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246

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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247

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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248

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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249

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.

Documents

UK; Rainwater Harvesting Model Development - Bradford University