Non-Revenue Water: Model for Optimal Management in Developing Countries

1

Alan S. WyattRTI International

North Carolina, USA

Water Loss 2010Sao Paulo, Brazil

June 2010

2

1. Current Situation

2. ConceptualFramework

3. New Model Mathematics

4. Running the New Model

5.Results in 27 Countries 6. Conclusions

1. Current Situation

3

Typical water kiosk in African cities

Water supply in LDCs

• 900 million people without improved water

• 1.5 million children die each year from diahrrea

• More die from diarrhea than HIV/AIDs

• Most unserved are in peri-urban poor areas - where illegal connections are rampant

• Millenium development goals call for unserved to be cut in half by 2015

4

NRW: Major resource, but...

• 45 million m3/day leakage - could serve up to half the 900 million unserved

• 30 million m3/day not paid for - utility revenues could go up 13%-40%.

• Cost of NRW reduction far less than new water plants

• Few financial or political incentives to reduce or control NRW

• Target setting not rational or based on local conditions or financial realities

5

Existing tools

•Water Balance fundamental tool for all - has been adjusted for LDCs

•BABE, FAVAD, ELL, UARL and ILI = Good tools for developed countries leakage.

• Ignore commercial losses and capital cost savings.

•Concerns about UARL flow rates and use of ILI in developing countries

6

New Financial Model Enables:

• Utilites: Find optimum total losses, find zones where losses are furthest from optimal, set targets, plan reduction and control programs

• Ministries / Regulators: Set targets for NRW and prioritize among utilities. Arrange twinning and exchanges.

• National Policy-makers and Donors: Identify utlities for NRW assistance, and develop National NRW Guidelines & Programs

7

8

2. Conceptual Framework

IWA Water Balance

9

Adjusted Water Balance

10

Steady state model....How far down do we take the losses ?

11

Loss control policies

12

NRW as a percentage of production is misleading

13

If billed water falls while losses are steady, % NRW rises !

3. Model Mathematics

14

Mathematical Framework

15

Objective Function1. Maximize utility surplus(loss), based on decision

variables: specific level of losses, lp and lc

lp = Physical Losses / System Inputlc = Commercial Losses / Consumption

S = R − [ Cv + Cc + Cpl + Ccl ]

S = Annual Surplus (loss)R = Collected Revenue (lc)

Cv = Variable cost of water production (lp)Cc = Annualized present value of future Capital cost (lp)

Cpl = Cost of physical loss control program (lp)

16

2. Develop formula for each component in terms of lp and lc.

3. Differentiate formula for surplus with respect to lc, set to zero and solve for optimal lc, lc*

4. Differentiate formula for surplus with respect to lp, set to zero and solve for optimal lp, lp*

17

Optimality Conditions

Commercial Loss: Optimality

18

R=N q r(1- lc)

Ccl=M N s / 2 lc

lc* =(M s / q r K)1/2

Physical loss components

19

EconoLeak Model Parameters

20

Leakage = α + β Ps, m3 / km / dayα = Background + Reported Lossesβ = Unreported Losses (ALC)

!

Physical losses: Optimality condition

21

4. Running the Model

22

23

!

Inputs for Sample Model Run for Southern Water Supply Co., Zambia

24

!

Physical Losses - Optimality Condition for Southern Water Supply Co., Zambia

25

Actual Conditions and Optimal Results for Southern Water Supply Co., Zambia

!

26

Optimal Results for Southern Water Supply Co., Zambia

!

Fig 15

27

Loss Components: Multiple Sites

Sensitivity of Optimal NRW to Various Inputs 59 National, Regional and Municipal LDC Utilities

28

!

5. Results in 27 Countries

29

Leak repair crew in Kampala

30

Optimal NRW: African National Water Utilities

DRC

Niger Cote d'Ivoire

Benin

Uganda

Senegal

Burkina Faso Ghana

Tunisia

Lesotho

Mali

Togo

Rwanda

Burundi

Gabon

NRW = 2.3913 D + 61.772 R2 = 0.8744

0

50

100

150

200

250

300

0 10 20 30 40 50 60 70 O

ptim

al N

RW

: L /

Con

nect

ion

/ Day

Dsitribution Mains Length / Connection, m

31

Optimal Physical Losses: 15 African National Water Utilities

DRC

Niger Cote d'Ivoire

Benin

Uganda

Senegal

Burkina Faso Ghana

Tunisia

Lesotho

Mali

Togo Rwanda

Burundi

Gabon

y = 1.9031x + 43.576 R2 = 0.8293

0

50

100

150

200

250

300

0 10 20 30 40 50 60 70 O

ptim

al P

hysi

cal L

osse

s: L

/ C

onne

ctio

n / D

ay

Distribution Mains Length / Connection, m

32

Optimal Commercial Losses: 15 African National Water Utilities

DRC Niger

Cote d'Ivoire Benin Uganda Senegal

Burkina Faso Ghana Tunisia Lesotho

Mali

Togo Rwanda

Burundi Gabon

y = 0.4882x + 18.196 R2 = 0.3216

0

50

100

150

200

250

300

0 10 20 30 40 50 60 70 O

ptim

al P

hysi

cal L

osse

s: L

/ C

onne

ctio

n / D

ay

Distribution Mains Length / Connection, m

33

Actual and Optimal NRW: African National Water Utilities

34

y = 2.9384x + 71.254 R2 = 0.6905

0

50

100

150

200

250

300

0 10 20 30 40 50 60 70 O

ptim

al N

RW

, L/

Con

nect

ion/

Day

Distribution Mains Length / Connection, m

Optimal NRW: 44 LDC Municipal and Regional Utilities

35

Optimal ILI vs Pressure59 National, Regional and Municipal LDC Utilities

y = 38.128x-0.775 R! = 0.66342

0

2

4

6

8

10

12

14

16

18

20

0 5 10 15 20 25 30 35 40 45

Opt

imal

Phy

sica

l ILI

Pressure, m

36

Optimal ILI vs Line Length59 National, Regional and Municipal LDC Utilities

0

2

4

6

8

10

12

14

16

18

20

0 10 20 30 40 50 60 70 O

ptim

al P

hysi

cal I

LI

Length per Connection, m

37

Comparison of LDC Optimal to Developed Country Actual

38

y = 23.877x-0.494 R2 = 0.9989

0

2

4

6

8

10

12

$0 $5 $10 $15 $20 $25 $30 $35 $40 R

epla

cem

ent P

erio

d, Y

ears

Monthly revenue per connection, 2005 $US

Optimal Meter Replacement Period44 LDC Municipal and Regional Utilities

39

y = 1.8454x-0.5364 R2 = 0.5407

0 3 6 9

12 15 18 21 24

$0.00 $0.05 $0.10 $0.15 $0.20 $0.25 $0.30 $0.35 Le

ak S

urve

y P

erio

d, M

onth

s Variable Water Production Cost, 2005 $US

Optimal Leak Detection Survey Period44 LDC Municipal and Regional Utilities

40

Optimal NRW: Zambia Commercial Utilities, 2006-2007

Nkana

Lusaka Kafubu

Southern

Lukanga Mulonga

Chambesi

Chiapata

NorthWestern

Western

y = 2.2317x + 108.72 R2 = 0.8222

0

50

100

150

200

250

300

0 10 20 30 40 50 60 70

Opt

imal

NR

W,

L/C

onne

ctio

n/D

ay

Distribution Mains Length / Connection, m

41

Actual and Optimal NRW: Zambia Commercial Utilities 2006/2007

Nkana (B)

Lusaka (C) Kafubu (C)

Southern (B)

Lukanga (B)

Mulonga (C)

Chambesi (B)

Chipata (A)

NorthWest (A)

Western (B)

0

250

500

750

1000

1250

1500

1750

2000

2250

2500

0 10 20 30 40 50 60 70

Non

Rev

enue

Wat

er,

L/C

onne

ctio

n/D

ay

Distribution Mains Length / Connection, m

Actual

Optimal

Financial AnalysisTransition to Optimal NRW, Sales of Saved Water

42

Class C Class B Class A Total

NRW Level High Medium Low

Current Coverage 72% 69% 71% 71%

Current Revenue $20.3M $19.0M $2.04M $41.4 M

Potential New Coverage 100% 88% 81% 94%

Optimal Revenue $40.0M $30.0 M $2.6 M $72.0 M

Est. Transition Investment $45 M $11 M 0.5 M $80.3 M

Payback Period, years 1.9 3.1 1.7 2.3

6. Conclusions

43

Water transport in peri-urban Uganda

44

The New Model .....•Produces good estimates of optimal losses, operational

guidelines, and information for financial assessment, without excessive data needs.

•Has a moderate to low sensitivity to model inputs.

•Includes commercial losses and capital savings, giving a more complete analysis

•Shows that large revenue increases are likely

•Helps utilities, policy makers and donors focus their efforts and prepare “bankable” projects.

45

Next Steps1) Country specific models 2) National programs including:

• NRW guidelines, • training, • incentives for NRW reduction and control,

new financing approaches, • performance-based contracts, • seminars, twinning and exchange programs.

46

The Future....

The new model can help countries: •save water, •increase utility revenue, •expand coverage •reach or pass MDGs•reduce health and economic impacts

Obrigado47

O Fim

48

Would you like to collaborate on model application or refinement ?

If you would like to see what the model shows for your utility, email ASW@RTI.ORG

I will send you a data template to complete and send back. I will send you the results. We can decide where to go from there.

If you have comments, suggestions, questions, PLEASE be in touch !