Computer Modelling of Water Distribution...

transcript

Computer Modelling of Water

Distribution Networks

N.Trifunović, Associate Professor

UNESCO-IHE

Delft, The Netherlands

N. Trifunovic Chapter 0: Module Introduction

About my CareerEDUCATION

BSc Civil Engineering (1984) (Faculty of Civil Engineering, University of

Belgrade, Yugoslavia),

MSc in Hydraulic Engineering (1990) (Faculty of Civil Engineering,

University of Belgrade, Yugoslavia)

PhD on reliability assessment of WDN (2012) (Faculty of Civil Engineering

and Geosciences, Delft University of Technology, the Netherlands)

SPECIALISATION

Water supply engineering (urban water distribution, computer modelling)

EXPERIENCE

Over 25 years of professional and academic experience in planning,

design, implementation, and O&M of urban water transport and distribution

systems.

Worked as researcher, water supply company development engineer and

lecturer at UNESCO-IHE since 1990. Current position: Associate

Professor. Recent experience in design and moderation of innovative

learning programmes.

N. Trifunovic Chapter 0: Module Introduction

About my Work

TEACHING

Water Transport and Distribution: general aspects, hydraulic performance,

operation and maintenance, development and application of hydraulic

models.

Applied hydraulics, Unit Operations (Sedimentation), Engineering Economy

On-line programme in Water Distribution

RESEARCH

Reliability assessment of water distribution systems.

Optimisation of water distribution system operation.

PROJECTS

Director of capacity building projects (Mozambique, South Africa, Ghana).

Team member in training, advisory and consulting assignments in water

distribution in various countries in Africa, Asia and Middle East.

N. Trifunovic Computer Modelling of Water Distribution Networks

Contents

• Principles

• Main Features

• Classification

• Designer’s Tips

• New Generation

• Further Information

Main DefinitionsSteady and Uniform Flow

12211 tttt

Steady flow in a pipe of constant

diameter is at the same time uniform.

Mass Conservation LawThe Continuity Equation

Qinp Qoutt1 V1

VQQ outinp

After t ...

Qinp Qoutt2

Mass Conservation LawThe Continuity Equation

Node ‘n’

ni QQ1

Q1- Q2+ Q3= Qn

Energy Conservation LawThe Bernoulli Equation

EEE 21

becomes:

Grade LinesEnergy, Hydraulic

Reference level

Energies, HeadsSummary

Reference level

Elevation Head (potential)

Pressure Head

Piezometric Head

Energy Head (total)Velocity Head (kinetic)

Energies, HeadsWater Distribution Practice

Reference level

Elevation

Pressure

Velocity head becomes relevant

only for velocities well above 1

m/s (example: pumping stations)

Hydraulic GradientSlope of The Hydraulic Grade Line

Flow rate in pipes under

pressure is related to the

hydraulic gradient!

Hydraulic GradientSlope of The Hydraulic Grade Line

Hydraulic LossesFriction, Minor

E results from a friction between

the water and the pipe wall,

and/or a turbulence developed by

obstructions of the flow.

fmf QRQRhhE

hf,m = Friction, Minor loss (respectively)Rf,m = Pipe resistanceQ = Flownf,m = Exponents

Friction LossesDarcy-Weisbach

52 1.12

LQRh fn

λ = Friction factor (-)L = Pipe length (m)D = Pipe diameter (m)Q = Pipe flow (m

or proportional to the kinetic energy:

Friction FactorColebrook-White

λ = Friction factor (-)Re = Reynolds number (-)k = Absolute roughness (mm)D = Pipe diameter (mm)

Simplified form of Barr (error ±1%):

51.2log2

1286.5log2

Reynolds Number

v = Flow velocity (m/s)D = Pipe diameter (m)ν = Kinematic viscosity (m

Kinematic viscosity:

T Temperature,T(ºC)

Laminar flowThe Reynolds number falls under 2000

Transitional zoneThe Reynolds number falls between 2000 and 4000

Turbulent flowThe Reynolds number is above 4000 with two zones:

1. Zone of transitional turbulence

2. Zone of developed (or rough) turbulence

Flow Regimes

For laminar flow:

Flow Regimes

1286.5log2

For transitional zone:

89.0Re

1286.5log2

For zone of transitional turbulence:

7.3log2

For zone of developed turbulence:

The Moody Diagram

Absolute Roughness

Pipe material

(mm) Asbestos cement Galvanised/Coated cast iron Uncoated cast iron Ductile iron Uncoated steel Coated steel Concrete Plastic, PVC, PE Glass fibre Brass, cooper, lead

0.015 - 0.03 0.03 - 0.15 0.15 - 0.6 0.03 - 0.06 0.015 - 0.06 0.03 - 0.15 0.06 - 1.5 0.02 - 0.05

0.06 0.003

Source: Wessex Water, 1993

The Best Formula?

51.12Q

87.4852.1

68.10Q

229.10Q

Darcy-Weisbach

(the most accurate)

Hazen-Williams

(straight-forward)

Manning

(straight-forward)

Hazen-Williams Factors

Source: Bhave, 1991

Pipe material / D (mm)

Uncoated cast iron Coated cast iron Uncoated steel Coated steel Galvanised iron Uncoated asbestos cement Coated asbestos cement Concrete, min. values Concrete, max. values Prestressed concrete PVC, brass, cooper, lead Wavy PVC Bitumen/cement lined

121 129 142 137 129 142 147 69 129

- 147 142 147

125 133 145 142 133 145 149 79 133

- 149 145 149

130 138 147 145

- 147 150 84 138 147 150 147 150

132 140 150 148

- 150 152 90 140 150 152 150 152

134 141 150 148

95 141 150 153 150 153

Manning Factors

Source: Bhave, 1991

Pipe material

(m-1/3

s) PVC, brass, lead, copper, glass fibre Prestressed concrete Concrete Welded steel Coated cast iron Uncoated cast iron Galvanised iron

0.008 - 0.011 0.009 - 0.012 0.010 - 0.017 0.012 - 0.013 0.012 - 0.014 0.013 - 0.015 0.015 - 0.017

Source: Prof. V.L. Snoeyink, University of Illinois

Friction LossesCorrosion from Magnesium Silicate

What is the right roughness factor (diameter)?

Friction LossesSummary

Choice of adequate roughness value is more

important than the choice of the friction formula.

In theory, the friction losses grow by:•increase of discharge

•increase of pipe roughness

•reduction of pipe diameters

•increase of pipe lengths

•decrease of water temperature

In practice, this happens by:•higher consumption or leakage

•corrosion growth

•network expansion

Minor Losses

ξ = Minor loss factor (-) D = Pipe diameter (m) Q = Pipe flow (m

or proportional to the kinetic energy:

v is the velocity downstream the

obstruction.

42 1.12

gDQRh mn

Minor LossesGeneral Formula

Minor Loss FactorsValve Characteristics (1)

Source: Erhard

Minor Loss FactorsElbows, Bends, Knees

Source: KSB

Minor Loss FactorsBranches

Source: KSB

Minor Loss FactorsEnlargers, Reducers

Source: KSB

Minor Loss FactorsInlets, Outlets

Source: KSB

Minor LossesSlope of The Hydraulic Grade Line

Substantial minor losses are measured

only if the flow velocity is high or/and

there is a valve throttling in the system.

Single Pipe CalculationBasic Parameters

Single Pipe CalculationDerived Parameters

Single Pipe CalculationStandard Input Parameters

Single Pipe CalculationPipe Pressure

Single Pipe CalculationMaximum Pipe Capacity

Single Pipe CalculationOptimal Diameter

1286.5log

Iterative calculation is necessary!

Assume v (1 m/s)

1286.5log

vcal=vassNo

YesStart

Iteration 1: v = 1 m/s

Iteration 2: v = 1.59 m/s

1286.5log

Iterative calculation is necessary!

Assume v (1 m/s)

1286.5log

vcal=vassNo

StartEnd

Iteration 1: v = 1 m/s

Branched SystemsSupply at One Point

• Pipe Flows

– For known nodal demands, the rates can be easily determined (the

Continuity Equation).

– Flow directions are known based on the pipes’ connectivity.

• Velocities

– For known flow rates and pipe diameters can be easily determined.

– The velocity directions are known.

• Pressures

– If there is at least one point of reference (fixed) piezometric head, the

pressures can be easily determined from known nodal elevations.

– The fixed piezometric head should be specified either at the source or

a node where certain (minimum) pressure is to be maintained

• Hydraulic calculation

– It follows the principles of single pipe calculation for pipe pressures and

optimal diameters (at fixed hydraulic gradient).

Single SourceDiameters & Nodal Elevations

Single SourceFlows & Nodal Demands

Single SourceVelocities & Nodal Demands

Single SourceHead Losses & Piezometric Heads

Reference

Single SourceHead Losses & Pressures

Single SourceSpreadsheet Application

Branched SystemsSupply at Several Points (1)

Branched SystemsSupply at Several Points (2)

Branched SystemsSupply at Several Points

• Pipe Flows

– For known nodal demands, the rates can be partially determined.

– Flow rates & directions in the pipe routes connecting the sources

depend on the piezometric heads at the sources and the distribution of

nodal demands.

• Velocities

– Also partially known.

• Pressures

– Conditions are the same as in case of the single source, once the

flows and velocities have been determined.

– Single pipe calculation can only partially solve the system.

– Additional condition is necessary.

Multiple SourceSource 1 (60 msl) & Source 11 (75 msl)

Multiple SourceDemand Shifting From Node 8 to Node 4

Multiple SourceSource 1 (60 msl) & Source 11 (70 msl)

Looped Networks

• Pipe Flows

– Flow rates and directions are unknown.

• Velocities

– The velocities and their directions are known only after the flows have

been calculated.

• Pressures

– Conditions are the same as in case of branched networks once the

flows and hydraulic losses have been calculated for each pipe.

– The equations used for single pipe calculation are not sufficient.

– Additional conditions have to be introduced.

– Iterative calculation process is needed.

Branched NetworkDiameters & Nodal Elevations

Looped NetworkDiameters & Nodal Elevations

Branched NetworkFlows & Nodal Demands

Looped NetworkFlows & Nodal Demands

Branched NetworkHead Losses & Pressures

Looped NetworkHead Losses & Pressures

Kirchoff’s Laws

Flow continuity at junction of pipesThe sum of all ingoing and outgoing flows in each node equals

zero (SQi = 0).

Head loss continuity at loop of pipesThe sum of all head-losses along pipes that compose a

complete loop equals zero (SΔHi = 0).

• Hardy Cross Methods

– Method of Balancing Heads

– Method of Balancing Flows

• Linear Theory

• Newton Raphson

• Gradient Algorithm

Hardy CrossMethod of Balancing Heads

Step 1Arbitrary flows are assigned to each pipe; (SQi = 0).

Step 2Head-loss in each pipe is calculated.

Step 3The sum of the head-losses along each loop is

checked.

Step 4If SΔHi differs from the required accuracy, a flow

correction δQ is introduced in loop ‘i’.

Step 5Correction δQ is applied in each loop (clockwise or anti-

clockwise). The iteration continues with Step 2

Hardy CrossMethod of Balancing Heads - Example

Iteration 1

Iteration 2

Iteration 3

Iteration 4

Iteration 7

Hardy CrossMethod of Balancing Flows

Step 1Arbitrary and unique piezometric head is assigned to

each node; head-loss in each pipe is determined from

these piezometric heads.

Step 2Flow in each pipe is calculated.

Step 3Flow continuity is checked in each pipe junction.

Step 4If SQi differs from the required accuracy, a piezometric

head correction δH is introduced in node ‘i’.

Step 5Correction δH is applied in each node and new head

losses determined. The iteration continues with Step 2

Hardy CrossMethod of Balancing Flows - Example

Iteration 1

Iteration 2

Iteration 3

Iteration 4

Iteration 8

Linear Theory

UQQQRRH mf )(51.12

iji QQ

Linear TheoryJunction of Three Pipes (1)

iiii QQQQ 312

Linear TheoryJunction of Three Pipes (2)

Linear TheoryGeneral Format

iji HfQQ

System of linear equations that is equal to the number of

nodes in the network, ‘m’, creates a matrix ‘m×n’ where ‘n’

is the maximum number of pipes that can meet in any

junction of the network. This system can also be solved by

the Newton Raphson method.

Newton Raphson MethodGeneral Format

)()()1(

)( 1)(

)( 1)('

Iterative Process

Step 1 - PreparationSetting of initial values for pipe flows and nodal piezometric heads in the

1st iteration; calculation of U-values.

Step 2 – Internal cycleIterations of the piezometric heads; the calculation is repeated until H(k+1) -

H(k) < εH in each node, or the number of iterations has reached the

maximum specified number.

Step 3 – External cycleCalculation of pipe flows Qi = ΔHi/Ui. Check the flows in each node (Q(l+1) -

Q(l) < εQ ). ‘No’: recalculation of the U-values with the flows from the

current iteration and restart of the iterative process in Step 2. ‘Yes’: Step 4

Step 4 – Determination of pressures The iterative process is finished; the pressures are calculated for each

node based on its elevation and the final value of the piezometric head.

Linear TheorySpreadsheet Example

Fixed Demand Conventional Approach

Reference level

S2ΔH2

Q=const

ΔH1=ΔH2

Fixed head point(s) influence(s)

the pressure distribution in a

system of fixed demands.

Fixed Demand Pressure Change (1)

Q1=Q2=Q3

S1=S2=S3

Any specified demand is

satisfied while the pressure

can have negative value.

Pressure Related Demand Pressure Dependant Leakage

51.12Q

Source: Wessex Water, 1993

Pressure Related Demand Pressure & Demand Change (1)

Pressure Related Demand Pressure & Demand Change (2)

Pressure Related Demand Pressure Change (3)

Q1>Q2>Q3

S1>S2>S3

The specified demand

gradually drops based

on the pressure drop.

Pressure Related Demand Similarity With The Discharge Through Orifice

ghCAQ 2

Pressure Related Demand Practical Application

Source: KIWA, 1993

Types of Hydraulic Calculation

• Demand-Driven– Any nodal demand is satisfied

– Pressures can be negative

• Pressure-Driven– Nodal demand depends on the pressure

– Pressures can never be negative

• Optimisation (Genetic Algorithms)

116116

Demand Driven CalculationRegular Supply

117117

Demand Driven CalculationRepair Pipe 6-9

118118

Pressure Driven CalculationRegular Supply

119119

Pressure Driven CalculationRepair Pipe 6-9

Types of Models

• For Network Design– Major pipes and valves, reservoirs and pumps

– Not for tertiary networks

• For Network Operation and

Maintenance (GIS)– Calamities

– Flushing

– Water quality

121121

Network Model of Amsterdam

122122

Modelling ProcessMain Steps

1. Input data collection

2. Network schematisation

(skeletonisation)

3. Model building

4. Model testing

5. Problem analysis

123123

Input Data CollectionMain Categories

1. General data

2. Water demand

3. Network layout

4. Network operation and monitoring

5. Network maintenance

6. Water company organisation

124124

Input Data CollectionGeneral Data

1. Layout of the system – pipe routes and

junctions; location of the main components.

2. Topography - ground elevations in the area of the

system; some specific natural barriers.

3. Type of the system - distribution scheme: gravity,

pumping, combined; role of each system

component.

4. Population - distribution and estimated growth.

125125

Input Data CollectionWater Demand

1. Demand categories present in the system: average

domestic consumption, industry, tourism, etc.

2. Patterns of variation: daily, weekly, and seasonal.

3. Type of domestic water use: direct supply, roof

tanks, etc.; average household size, habits with

respect to water use.

4. Demand forecasting.

126126

Input Data CollectionNetwork Layout – Nodes and Pipes

1. Nodes (discharge points) - concerns predominantly the

supply points of at least a few hundred consumers or major

industry. Relevant for each point are:

- location (X,Y) in the system,

- ground elevation (Z), and

- average consumption and dominant categories.

2. Pipes - concerns predominantly the pipes D > 80-100 mm.

Relevant for each pipe are:

- length,

- diameter (internal),

- material and age,

- assessment of corrosion level (description of roughness)

127127

Input Data CollectionNetwork Layout - Storage

1. Service reservoirs - type (ground, elevated),

capacity, minimum and maximum water level,

shape (e.g. described through the volume-depth

curve), inlet/outlet arrangement.

2. Individual roof tanks (where applicable) - type

and height of the tank, capacity, inflow/outflow

arrangements, average number of users per

house connection, description of house

installations (existence of direct supply in the

ground floor).

128128

Input Data CollectionNetwork Layout – Pumping Stations and Others

1. Pumping stations - number and type (variable,

fixed speed) of pumps; duty head and flow and

preferably the pump characteristics for each unit;

age and condition of pumps.

2. Others - description of appurtenances that may

significantly influence the system operation (e.g.

valves, measuring equipment, etc.)

129129

Input Data CollectionNetwork Operation and Monitoring

Important and preferably simultaneous measurements:

• The pressure in a number of points covering the

entire network

• Level variations in the service reservoirs and roof

tanks (where applicable)

• Pressures and flows in the pumping stations

• The flows in a few main pipes in the network

• Valve operation (where applicable)

130130

Network SchematisationBenefits

Advantages:

• It saves computer time.

• It allows model building in steps i.e. easier tracing

of possible errors.

• It provides a clearer picture about global operation

of the system.

Reduction of the model size with acceptable

reduction of the model accuracy.

131131

Network SchematisationDo’s and Don’t’s

1. Combination of a few demand points close to each

other into one node.

2. Exclusion of a hydraulically irrelevant part of the

network such as branches and dead ends at the

borders of the system.

3. Neglecting small pipe diameters.

4. Introduction of equivalent pipe diameters.

5. Omit demand of excluded parts of the network.

6. Elimination of major loops.

7. Neglect the impact of existing pumps, storage and

valves.

132132

Network SchematisationPipe Elimination

133133

Network SchematisationElimination of Small Pipes

1. When laying perpendicular to the usual direction of

2. If conveying flows with extremely low velocities.

3. When located in the vicinity of large diameter pipes.

4. When located faraway from the supply points.

134134

Model BuildingMain Information

1. Junctions

• sources

• nodes

• reservoirs

2. Links

• pipes

• pumps

• valves

135135

Model BuildingInformation for Junctions

1. Sources: identification, location and elevation of water

surface level.

2. Nodes: identification, location and elevation, average

demand and pattern of demand variation.

3. Reservoirs: identification, position, top & bottom water

level, description of the shape (cross-section area, either

the volume-depth diagram), initial water level at the

beginning of the simulation, inlet/outlet arrangement.

136136

Model BuildingInformation for Links

1. Pipes: identification, length, diameter, description of

roughness, minor loss factor .

2. Pumps: identification, description of pump

characteristics, speed, operation mode .

3. Valves: identification, type of valve, diameter, head-

loss when fully open, operation mode .

137137

Input Data CollectionNetwork Layout - Pipes

1. Water quality parameters:

– initial concentrations,

– patterns of variation at the source,

– decay coefficients, etc.

2. Simulation run parameters:

– duration of the simulation,

– time intervals,

– accuracy,

– preferred format of the output, etc.

138138

Demand ModellingGraphical Method

139139

Demand ModellingCalculation Method

qA = QA / (L1-2 + L4-5+L1-4+L2-5)

qB = QB / (L2-3+L5-6+L2-5+L3-6)

140140

Q1-2= qA×L1-2

Q4-5 = qA×L4-5

Q1-4 = qA×L1-4

Q2-5,A = qA×L2-5

Q2-3= qB×L2-3

Q5-6 = qB×L5-6

Q2-5,B = qB×L2-5

Q3-6,A = qB×L3-6

141141

Q1 = (Q1-2+Q1-4) / 2

Q2 = (Q1-2+Q2-3+Q2-5,A+Q2-5,B) / 2

Q3 = (Q2-3+Q3-6) / 2

Q4 = (Q1-4+Q4-5) / 2

Q5 = (Q4-5+Q5-6+Q2-5,A+Q2-5,B) / 2

Q6 = (Q5-6+Q3-6) / 2

142142

Model TestingValidation and Calibration

• the model has a logical response to the altering of the

input data; the simulation runs are in this case functioning

in the model validation,

• the model is behaving in relation to the real system;

comparison of the calculation results with the hydraulic

measurements is part of the model calibration.

Once the first simulation run has been completed, the

immediate concern is whether the results match reality. In

this phase, several runs have to be executed which must

confirm that:

143143

Model TestingValidation and Calibration Errors

There can be different reasons why the validation and

calibration cannot be achieved. The input file can be

accepted by the programme as correct in syntax, but:

• Some input data were (badly) estimated, because the real values

were not known.

• The network was transferred to the model with some typing errors or

data was omitted.

• The format of the input file was incorrect but the error was not

(clearly) defined in the error library: e.g. too high a calculation

accuracy, insufficient maximum number of iterations, impossible

operation mode specified, etc.

• The field measurements used for the model calibration were

inaccurate.

144144

Problem AnalysisPossibilities

1. Selection of optimal pipe diameters for a given layout and demand

scenario

2. Selection of optimal models for pumps

3. Selection of optimal position, elevation and volume of the reservoir(s)

4. Optimisation of the pump scheduling (to minimise energy consumption)

5. Optimisation of the reservoir operation (water depth variation)

6. Optimisation of the valve operation

7. Simulation of fires

8. Planning of pipe flushing in the system

9. Analysis of failures of the main system components (risk assessment)

10. Analysis of water quality in the system (chlorine residuals, water age

and mixing of water from various sources)

145145

Computer Modelling SoftwareMain Features

1. PC based applications.

2. Allow extended period hydraulic simulations.

3. Posses integrated module for water quality

simulations.

4. Can handle virtually unlimited size of network.

5. Have excellent graphical interface for

presentation of results.

6. Have link/interface with GIS.

7. Have integrated modules that allow on-line

operational decisions

8. Have built-in optimisation algorithms.

Present MarketSome Offers

1. EPANET 2 (US Environmental Protection Agency)

Price Range: 0 to approx. 60,000 USD

147147

Network ModelsEpanet 2

148148

Network ModelsInfoWorks WS

149149

WaterGEMS©

150150

More Information

• US Environmental Protection Agency

– www.epa.gov (EPANET 2)

• Bentley

– www.bentley.com (WaterCAD, WaterGEMS)

• Wallingford Software

– www.wallingfordsoftware.com (InfoWorks WS)

• Advantica Stoner

– www.advanticastoner.com (SynerGEE Water)

Model Input - Pumps

Model Input - Demands

Model Layout

Model Data Filtering

Tracing of Connectivity

Demand Allocation

Demand Concentration

Model Link With GIS

Model Labels

Longitudinal Profiles

Pump Energy Costs

Simulation Run Parameters

1 day, 15 min. time step

38.500 pipes in 6 min.

PIII, 1.2 MHz Notebook

Network Model of Amsterdam

Model Calibration

Valve Operation

Operation of Storage and Pumps

Time Series Results

Water Quality Model

Sediment Transport Assessment

Source Tracing

171171

The Best Software?

1. Cheaper software often solves the same problems as the more expensive one.

2. It is the quality of input data rather than the quality of software that is a limiting factor: what goes in, goes out!

3. Model calibration is essential and requires properly working monitoring equipment.

4. Advanced software will be fully utilised only in an advanced water distribution system.

172172

Friction LossesIron Corrosion

Source: Prof. V.L. Snoeyink, University of Illinois

Percentage of the original cross-section (the same network)

What is the right roughness factor (diameter)?

Computer Modelling of Water Distribution...

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