Flow and TransportFlow and Transport in in NaturalNatural and and Man MadeMan Made

SystemsSystems

M.S.Mohan KumarM.S.Mohan Kumar

Department of Civil Engineering,Indian Institute of Science, Bangalore 560 012, India

Acknowledgements

1.1. ShibaniShibani JhaJha2.2. Mini MathewMini Mathew3.3. G R G R MunavalliMunavalli4.4. VeenaVeena SoraganviSoraganvi5.5. M M PrasannaPrasanna KumarKumar6.6. HarsadHarsad ParateParate7.7. SibteySibtey hasanhasan8.8. IndoIndo--French Cell for Water SciencesFrench Cell for Water Sciences

Today’s Presentation IncludesToday’s Presentation Includes

Ground water flow and transportGround water flow and transportUnsaturated flow and transportUnsaturated flow and transportMultiphase flow and transportMultiphase flow and transport

Flow and Transport in Natural (geological) Systems

Man Made Systems

Flow and transport in channels Flow and transport in piped systems

Flow and Transport in Natural Flow and Transport in Natural (geological) Systems(geological) Systems

Geological systems

Porous Media

Fractured Media

Conservative and Reactive flow

Miscible and Immiscible flowCoastal Systems

Variably saturated flow: Saturated-Unsaturated

Ground Water ResourceGround Water Resource

More than 70 More than 70 -- 80 % of drinking 80 % of drinking water is through ground waterwater is through ground water

Extremely Important resourceExtremely Important resource

In many places In many places -- the only sourcethe only source

Ground Water ContaminationGround Water ContaminationSource of ground water contaminationSource of ground water contamination

AgricultureAgricultureFertilizersFertilizersPesticides Pesticides

Leading to non point source pollution Leading to non point source pollution

IndustriesIndustriesPollution depends on type of industryPollution depends on type of industryUntreated effluentUntreated effluentEffluent treated to some level Effluent treated to some level -- not sufficientnot sufficientStarts as a point source pollution Starts as a point source pollution -- can become acan become anon point source non point source

Over exploitationOver exploitation -- Sea water intrusionSea water intrusion

Flow and Transport Through Flow and Transport Through PorousPorous and and Fractured MediaFractured Media

Ground water contamination by Ground water contamination by NAPLNAPL release to the surface and its release to the surface and its

further infiltration to the further infiltration to the subsurfacesubsurface

NAPL Release

Porous Media Fractured Rocks

Groundwater Contamination Risks

Study of

Behavior of NAPL Migration

Contamination Evaluation

Aquifer Remediation

Two/ Three Phase Flow Modelling

Reduce the field investigation effort

and cost

Requires

NAPL Migration NAPL Migration –– Porous MediaPorous MediaSource of Source of NAPLsNAPLs

Subsurface leakage of Subsurface leakage of hydrocarbon fuels hydrocarbon fuels Immiscible organic Immiscible organic liquids due to leaky liquids due to leaky storage tanks or storage tanks or pipelines.pipelines.Coal tar from Coal tar from illuminating gas illuminating gas production, wastes production, wastes from steel Industry and from steel Industry and wood treating wood treating operationoperationOrganic substances Organic substances --Mineral fuels Mineral fuels

General General Migration PatternMigration Pattern and and Process Process of of NAPLsNAPLs -- Porous MediaPorous Media

Vertical migration in the Vertical migration in the vadosevadose zone zone predominantly by gravitypredominantly by gravitySome lateral spreading due to capillary Some lateral spreading due to capillary forces and media propertiesforces and media propertiesMigration occurs when enough pressure is Migration occurs when enough pressure is available to overcome the displacement available to overcome the displacement pressure of the mediapressure of the mediaIn saturated zone the movement is by In saturated zone the movement is by displacement of waterdisplacement of water

Single phase regionwater

Single phase regionwater

Two phase regionWater-NAPL

Interface region

Three phase regionWater- NAPL-Air

Two phase regionAir - WaterTwo phase region

Air - Water

Interface regionInterface region

NAPL infiltration in the subsurface

Interface region

NAPL Infiltration

Water

NAPL

Water

Air

Organiccompound

Watervapour

Organiccompound

Air

NAPL

Air

Water

Processes of Multiphase SystemProcesses of Multiphase SystemAir

Studies Done Studies Done –– Porous MediaPorous MediaModellingModelling and analysis of and analysis of NAPLsNAPLs migration in saturated migration in saturated porous medium porous medium -- Two phase Two phase NAPLNAPL--WaterWater systemsystem

Influence of air phase on the infiltration of water in Influence of air phase on the infiltration of water in unsaturated porous medium unsaturated porous medium -------- Two phase Two phase AirAir--Water Water systemsystem

ModellingModelling and analysis of NAPL migration in unsaturated and analysis of NAPL migration in unsaturated porous medium.porous medium.

-- Three phase Three phase AirAir--NAPLNAPL--Water Water systemsystem--Two phase Two phase NAPLNAPL--WaterWater system with constant air system with constant air

pressurepressure

ModellingModelling and analysis of NAPL migration and analysis of NAPL migration -- Combined Combined saturatedsaturated--unsaturated porous mediumunsaturated porous medium

Governing Equation- Multiphase flow through Porous Media

Governing EquationGoverning Equation-- Multiphase flow Multiphase flow through Porous Mediathrough Porous Media

α ∈{w, nw} in saturated porous medium nw - Nonwetting phase(NAPL) in the saturated medium

α ∈{w, nw, a} in unsaturated porous medium w - Wetting phase(water) nw - Intermediate phase(NAPL)a - Nonwetting phase(air) in the unsaturated porous medium

( ) ( )ααααα

αα

α ρφρρμ

St

QgxPkk

x j

rji

i ∂∂

=+⎟⎟⎠

⎞+

∂∂

⎜⎜⎝

⎛∂∂

i, j : Direction indices i, j : Direction indices kkijij : Intrinsic permeability of the porous : Intrinsic permeability of the porous mediummediumkkrrαα : Relative permeability of the phase : Relative permeability of the phase ααμμαα : Viscosity of the phase : Viscosity of the phase ααρραα : Density of the phase : Density of the phase ααg : Acceleration due to gravityg : Acceleration due to gravityz : Elevation taken positive from bottomz : Elevation taken positive from bottomPPαα : Pressure of the phase : Pressure of the phase ααSSαα : Saturation of the phase : Saturation of the phase ααQQαα : Source/sink term of the phase: Source/sink term of the phaseφφ : Porosity of the medium. : Porosity of the medium.

Governing Equation (symbols)Governing Equation (symbols)Governing Equation (symbols)

Internal conditions

The governing equation is subjected to the followinginternal constraints

11

=∑=

αα

SN

( ) { } { }{ } { } mediumdunsaturateforgnwwgnww

mediumsaturatedfornwwnwwSkk rr

βαβββαβαααα

≠∈∈≠∈∈=,,,,,,

,,,,

( ) { } { }{ } { } mediumsaturatedfornwwnww

mediumdunsaturateforgnwwgnwwPPSPC

βααβ

βααββαααβ

≠∈∈

≠∈∈−=

,,,,

,,,,,,

Typical capillary pressure saturation relation

Constitutive Relationships

BC Relationship

VG Relationship

PC = Pd Sew -1/λ

PC ≥ Pd

Wr

WrW

ew S

SSS

−

−=

1 λ : Pore size distribution index Pd : Displacement pressure

Swr: Residual wetting phase saturation Sew : Effective wetting phase saturation

ά : Capillary fringe parametern : Soil texture parameter

Capillary Pressure - Saturation Relationships

Parker’s Relationships

For 3 phase systems air, water, NAPL

( ) nmweC SP

/1/1 11−= −

βα

Capillary pressure saturation relation

β - Ratio of interfacial tension between phases

Relative permeability - saturation relationships

Due to the concept of Burdine , Mualemthese relations are derived from the capillary saturationrelationships

B rook s & C orey w ettin g an d n on w ettin g p h ase re lativep erm eab ility is

λλ32 +

= ewrW Sk

( ) ⎟⎠⎞

⎜⎝⎛ −−=

+λλ22 11 ewewrNW SSk

Van Genuchten wetting & nonwetting relation

( )[ ] 2/12/1 11 mewewrw SSk −−=

Saturation front at the Macroscale & in Microscale

Relative permeability - saturation relationships for 3 phase system - due to Parker

[ ( ) ( ) ]2/1/1 111

mmt

mmwe

wr

nnr SS

SSk −−−⎥

⎦

⎤⎢⎣

⎡−

=

⎟⎟⎠

⎞⎜⎜⎝

⎛−

−+=

wr

wrwnt S

SSSS1

krn - relative permeability of intermediate phase

relative permeability of wetting and nonwetting is same as two phase system

Typical relative permeability saturation curve- Three Phase System

Linearization methods adopted

Approaches of linearization

•Newton Raphson method

•Picard's method

•Modified Newton Raphson method

Multiphase through geological systems are highly nonlinear systems

Solution Methodologies Solution Methodologies AdoptedAdopted

Conventional simultaneous method Conventional simultaneous method

Modified sequential methodModified sequential method

Adaptive solution fully implicit Adaptive solution fully implicit modified sequential methodmodified sequential method

Methodologies used to solve linearizedalgebraic systems

Model studiesModel studies(Numerical tests)(Numerical tests)

Multiphase through porous Multiphase through porous mediummedium

Density of NAPL : 1460kg/m3

Viscosity of NAPL : 0.0009pa-sec

Migration in Saturated Porous Medium – NAPL- Water SystemMigration in Saturated Porous Medium – NAPL- Water System

Experimental resultsPresent model

Sand 1 Sand 2 Sand 3 Sand 4Φ 0.4 0.39 0.39 0.41k 5.04E-10 2.05E-10 5.26E-11 8.19E-12 Swr 0.078 0.069 0.098 0.189λ 3.86 3.51 2.49 3.3

Pd 369 434 1324 3246

Migration in Saturated Porous Medium – NAPL- Water SystemMigration in Saturated Porous Medium – NAPL- Water System

Two phase (Air-Water) in heterogeneous porous mediaTwo phase (Air-Water) in heterogeneous porous media

Initial pressure = -100cmFlux at the inflow end = 9.5E-05cm/sec

Impermeable layer

150cm

20 cm

40cm

lens

Sand and sandy loam

Open column

One phase model Two phase model

Bounded column

One phase model Two phase model

Sand and sandy loam

20cm

15cm

Initial pressure = -150cm

100 cm

50cm

60cm

10cm

Low permeability soil

sand

Flux = 1.13x10-5 cm/sec

Two phase (Air-Water) in heterogeneous porous mediaTwo phase (Air-Water) in heterogeneous porous media

Sand and Sandy loam

Infiltartion rate- 5.07E-05m/sec

3 Phase NAPL distribution in the subsurface

Bounded column

DNAPL

Effect of with and without air pressureEffect of with and without air pressure

Multiphase flow (Porous Media) – key points•For simulation of water infiltration in homogeneous soils effect of air pressure has to take into account, if the air phase does not have free movement

•In heterogeneous media, the effect of air phase has to taken into account for the water infiltration irrespective of the boundary conditions and the media properties both in one dimensional and two dimensional simulations.

•For the simulation of NAPL in the unsaturated and in combined saturated-unsaturated porous medium, the effect of air pressure has to taken into account if the air does not have free phase movement.

• The effect of capillary pressure has to be taken into account at the interface for heterogeneous media

Multiphase flow Multiphase flow –– Fractured MediaFractured Media

Accidental release of DNAPL

Unconsolidated sediments

Ground water flow

DNAPL Pooling

Fractured RockFractures

Dissolved Plume

DNAPL

Ground water flow

Schematic representation of groundwater Schematic representation of groundwater contamination by NAPL Migration through contamination by NAPL Migration through

FractureFracture

Two phase (DNAPLTwo phase (DNAPL--Water) Water) --Fracture flowFracture flow

DNAPL DNAPL -- Water as immiscible system through a Water as immiscible system through a fracture with aperture, e, (assuming laminar flow fracture with aperture, e, (assuming laminar flow along smooth parallel plates as given by along smooth parallel plates as given by cubic lawcubic law) ) can be written as:can be written as:

These equations are coupled through capillary These equations are coupled through capillary pressure relation and subject to the constraint:pressure relation and subject to the constraint:

tS

exzg

xPke

xW

jW

j

W

W

rW

i ∂∂

=⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛

∂∂

+∂∂

∂∂ φρ

μ12

3

tS

exzg

xPke

xNW

jNW

j

NW

NW

rNW

i ∂∂

=⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛

∂∂

+∂∂

∂∂ φρ

μ12

3

0.1=+ NWW SS

Capillary pressure and entry pressure Capillary pressure and entry pressure condition in condition in Parallel PlateParallel Plate Fracture Fracture

FlowFlowThe capillary pressure is the difference between the phase The capillary pressure is the difference between the phase pressures at the interface, as given belowpressures at the interface, as given below

Where capillary pressure developed within the fracture is Where capillary pressure developed within the fracture is calculated in terms of saturation, as given by Brooks and calculated in terms of saturation, as given by Brooks and Corey, 1964Corey, 1964

Considering flow in a fracture with aperture, e and opening Considering flow in a fracture with aperture, e and opening as parallel plates, and considering water as perfectly wetting as parallel plates, and considering water as perfectly wetting with respect to DNAPL, then the entry pressure criteria is with respect to DNAPL, then the entry pressure criteria is given as:given as:

WNWC PPP −=

ePE

σ2=

λ/1)( −= eEC SPP

Parameters of InfluenceParameters of InfluenceEntry aperture (geological parameter) Entry aperture (geological parameter) -- controls the controls the invasion of DNAPL into the fracturesinvasion of DNAPL into the fractures

Variability in aperture Variability in aperture -- higher values of residual higher values of residual wetting phase saturationwetting phase saturation

DNAPL flow in fractures DNAPL flow in fractures -- preferential paths of least preferential paths of least capillary resistancecapillary resistance

Real fractures Real fractures -- rough walls through variability of rough walls through variability of apertures along surfaceapertures along surface

Real fracture Real fracture -- aperture variations in both the flow aperture variations in both the flow direction and the direction normal to flow.direction and the direction normal to flow.

Challenges in fracture flowChallenges in fracture flowPrimary concern Primary concern -- examine the impact of aperture examine the impact of aperture variation on the flow of one or more fluid phases variation on the flow of one or more fluid phases

Difficulty arises Difficulty arises -- flow within fractures is flow within fractures is dominated by preferential pathwaysdominated by preferential pathways

Mathematical Mathematical modellingmodelling –– depends on scale of depends on scale of interestinterest

Local problems Local problems -- twotwo--phase flow near sources and phase flow near sources and sinkssinks

Flow through a Flow through a single single fracturefracture

To enable accurate To enable accurate modellingmodelling of the of the multiphase flow and transport in fractured multiphase flow and transport in fractured domains, using discrete fracture or domains, using discrete fracture or continuum approaches, a great deal of continuum approaches, a great deal of effort has been directed towards studying effort has been directed towards studying the the behaviourbehaviour of flow within a of flow within a single single fracture with fracture with constant/ variableconstant/ variableapertureaperture

Factors which control flow through single joint

Flow through a single fracture

Surface roughness

Apertures/Variable

apertures

Orientation Of fractures

External stressesThermal stresses

Loading & Unloading behavior

solutions

Numerical and analytical

Experimental verification

Model ConceptualizationModel Conceptualization

Parallel plateParallel platePPee=(2=(2σσcoscosθθ)/e)/e

CircularCircularPPee=(4=(4σσcoscosθθ)/e)/e

Entry condition for DNAPLEntry condition for DNAPLPPcc > > PPee

Height of DNAPL pooled above Height of DNAPL pooled above the fracture opening needed to the fracture opening needed to enter the fractureenter the fractureHHdd=(2=(2σσ)/()/(ΔρΔρge)ge)

Height of Height of DNAPL PoolDNAPL Pool versus versus ApertureAperture InvadedInvaded

10−2

10−1

100

101

102

103

10−1

100

101

102

HEIGHT OF DNAPL POOL (m)

FR

AC

TU

RE

AP

ER

TU

RE

INV

AD

ED

( μ

m )

σ = 0.045 N/m

σ = 0.035 N/m

σ = 0.025 N/m

σ = 0.015 N/m

σ = 005 N/m

Shallow DNAPL pools are capable of invading fractures of 100 microns, while relatively high pools are required to invade the extremely small apertures.

One Dimensional ModelOne Dimensional ModelSingle fracture with Single fracture with

equivalent aperture eequivalent aperture e

RoughnessRoughness of fracture is of fracture is incorporated and permeability incorporated and permeability is modified as:is modified as:

k=ek=e22/12(1.0+8.8R/12(1.0+8.8Rrr1.51.5))

((MarshilyMarshily, 1986), 1986)

For For moderately rough fracturemoderately rough fractureplane plane RRrr = 0.1= 0.1

Solution domain adopted for numerical tests

Sensitivity with Sensitivity with DNAPL PoolDNAPL Pool,,ApertureAperture and and Fracture DipFracture Dip

0 1 2 3 4 5 6 7 8 9 100

0.5

1

1.5

2

2.5

Time (hours)

Poo

l Hei

ght (

met

ers)

present model for density = 1460 kg/m3

Kueper’s model for density = 1460 kg/m3

present model for density = 1200 kg/m3

Kueper’s model for density = 1200 kg/m3

DNAPL pool vs time

•Traverse time for DNAPL is inversely proportional to the fracture aperture, dip and DNAPL pooled above the fracture

Sensitivity with Sensitivity with DNAPL PoolDNAPL Pool,,ApertureAperture and and Fracture DipFracture Dip

0 5 10 15 20 25 300

20

40

60

80

100

120

140

160

180

200

Time (hours)

Ap

ertu

re (

mic

ron

s)

present model for density = 1460 kg/m3

Kueper’s model for density = 1460 kg/m3

present model for density = 1200 kg/m3

Kueper’s model for density = 1200kg/m3

0 1 2 3 4 5 60

10

20

30

40

50

60

70

80

90

Time (hours)

Fra

ctu

re D

ip (

deg

rees

)

Kueper’s ResultPresent Model

Aperture vs time Fracture dip vs time

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

Length of Fracture (m)

DN

AP

L S

atur

atio

n

DNAPL pool = 0.50 mDNAPL pool = 0.40 mDNAPL pool = 0.30 mDNAPL pool = 0.35 m

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

Length of Fracture (m)

DN

AP

L S

atur

atio

n

e = 25 μme = 50 μme = 75 μme = 100 μm

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

Length of Fracture (m)

DN

AP

L S

atur

atio

n

Dip = 0o

Dip = 15o Dip = 30o

Dip = 45o

Dip = 60o

Dip = 90o

Higher the DNAPL pool greater the portion of fracture invaded

Smaller the aperture more sensitive to DNAPL migration

Shallower the fracture dip more sensitive the DNAPL migration

One dimensional fracture One dimensional fracture --variable aperture fieldvariable aperture field

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

Length of Fracture (meters)

Ap

ertu

re (

mm

)

Aperture distribution along the length of fracture (mean-75 μm, std. dev-0.734)

DNAPL and Water Migration through DNAPL and Water Migration through Variable Aperture FractureVariable Aperture Fracture

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Length of Fracture (meters)

DN

AP

L S

atur

atio

n

Time = 5000 sTime = 10000 s Time = 25000 sTime = 50000 s

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

Length of Fracture (meters)

DN

AP

L V

elo

city

(m

/s)

T=5000sT=10000sT=25000s T=50000s

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

Length of Fracture (meters)

Wat

er V

elo

city

(m

/s)

T=5000sT=10000sT=25000sT=50000s

DNAPL distribution at various times

DNAPL velocity

Water velocity

Rough walled fractureRough walled fracture plane plane –– variable variable aperture fractureaperture fracture

Aperture in mm

Solution domain for a rough walled fracture plane

Aperture distribution for a rough walled fracture plane

DNAPL Migration DNAPL Migration –– Preferential Preferential butbut fasterfasterflow, some portion remains flow, some portion remains void of DNAPLvoid of DNAPL

0 0.1 0.2 0.3 0.4 0.5

0 0.5 1 1.5 2 2.5 3 3.5 4 4.50

0.5

1

1.5

Length of Fracture along x−axis (m)

Leng

th o

f Fra

ctur

e al

ong

y−ax

is (m

) Time = 5000s

0 0.1 0.2 0.3 0.4 0.5

0 0.5 1 1.5 2 2.5 3 3.5 4 4.50

0.5

1

1.5

Length of Fracture along x−axis (m)

Len

gth

of

Fra

ctu

re a

lon

g y−a

xis

(m) Time = 10000.0 seconds

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

0 0.5 1 1.5 2 2.5 3 3.5 4 4.50

0.5

1

1.5

Length of Fracture along x−axis (m)

Leng

th o

f Fra

ctur

e al

ong

y−ax

is (m

) Time = 50000.0 seconds

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

0 0.5 1 1.5 2 2.5 3 3.5 4 4.50

0.5

1

1.5

Length of Fracture along x−axis (m)

Len

gth

of

Fra

ctu

re a

lon

g y−a

xis

(m) Time = 100000.0 seconds

DNAPL distribution at t = 5000s

DNAPL distribution at t = 10000s

DNAPL distribution at t = 50000s

DNAPL distribution at t = 100000s

Multiphase flow through fracture Multiphase flow through fracture –– key key points points

Fractures provides preferential and faster Fractures provides preferential and faster pathwayspathways

DNAPL enters the fracture at the points of DNAPL enters the fracture at the points of largest aperture and continue to migrate largest aperture and continue to migrate through the larger aperture regionsthrough the larger aperture regions

Certain regions of the fracture may remain Certain regions of the fracture may remain void of DNAPL at all times void of DNAPL at all times

Multiphase flow (fracture) Multiphase flow (fracture) –– key pointskey points

The ability of DNAPL to enter smaller aperture The ability of DNAPL to enter smaller aperture regions of fracture increases as a function of regions of fracture increases as a function of depth of penetrationdepth of penetration

Traverse time for DNAPL is inversely proportional Traverse time for DNAPL is inversely proportional to the fracture aperture, fracture dip and DNAPL to the fracture aperture, fracture dip and DNAPL pooled above the fracturepooled above the fracture

Shallow dipping fractures (30Shallow dipping fractures (30o o to 0to 0oo) shows ) shows sensitive to DNAPL migrationsensitive to DNAPL migration

Coupling of Coupling of deformationdeformationwith with twotwo--phase phase modelmodel

Coupling of deformation with two phase model

DNAPL-Water Flow

Joint alteration

1. Confining stresses2. Pore pressure

3. Joint inclination

Thermal stresses

Compressibility of fluids

Primary concern

Influences: flow quantities

Influences: thermal energy

transport

Influences: Miscibility of NAPL in water

Fracture deformability

Normal compressive

stress

Hydraulic,mechanical

behavior

1. Aperture distribution 2. Contact area distribution

3. Spatial connectivity

Govern the hydraulic

conductivity

Hydraulically induced fractures

Orientedvertically

Orientation Understood in terms of:

normal state of stress Shown next

Coupling of deformation with two phase Coupling of deformation with two phase modelmodel

Stress element showing preferred plane of fracture orthogonal Stress element showing preferred plane of fracture orthogonal to the least principal stress, as shown in the sketch below:to the least principal stress, as shown in the sketch below:

Idealized fracture plane

Fracture plane developed due to external stresses

Coupling of deformation with two phase model

Rock discontinuity

Closure points

Rock material: impermeable

Rock matrix: isotropic and linearly elastic

within

DNAPL-WaterFlow

Aperture of discontinuity, et

nt ee δ±= 0

Normal deformationcomponents of a joint

Shear deformation components of a joint

[ ]βσβσδ 23

21 sincos1

+=n

n k

[ ]βσβσδτ2

12

3 sincos1−=

sk

DNAPL and waterpressures

Normal to thefracture surface

Incompressible Act against thein situ stress

Tend to stiffen the rock mass reaction

Coupling of deformation with fluid pressures

Modifiednormal

deformation

If PW >PNW

If PW <PNW

[ ]Wn

n Pk

−+= βσβσδ 23

21 sincos1

[ ]NWn

n Pk

−+= βσβσδ 23

21 sincos1

DNAPL saturation profile for non-deformable and deformable fracture

1. Dispersion dominated flow2. Saturation increased to more than thrice

Advection dominated flow

Over Exploitation of Over Exploitation of GroundwaterGroundwater

consequencesconsequencesCoastal Aquifer Coastal Aquifer ContaminationContamination

Coastal Aquifer ContaminationCoastal Aquifer Contamination

Saline water Ingress poses Saline water Ingress poses Unique challengesUnique challenges

Complicates understanding of water quality and Complicates understanding of water quality and aquifer “aquifer “behaviourbehaviour””

Different hydrological principles must be applied Different hydrological principles must be applied (e.g., density effect)(e.g., density effect)

TimeTime--scales (usually long)scales (usually long)

The sea water intrusion process is mostly difficult The sea water intrusion process is mostly difficult to reverseto reverse

Coastal Aquifer ContaminationCoastal Aquifer Contamination --Practical perspectivePractical perspective

Coastal aquifer are complex systemCoastal aquifer are complex system

Models plays a significant roleModels plays a significant role

RegionalRegional--scale modeling of 3scale modeling of 3--D system is D system is now practically possible with the right now practically possible with the right combination of toolscombination of tools

Further adoption of management planFurther adoption of management plan

ApproachesApproaches to the solution of to the solution of saltwater intrusionsaltwater intrusion

Analytical solution on the basis of Analytical solution on the basis of GhybenGhyben--HerzbergHerzberg RelationshipRelationship (Bear,1972) and (Bear,1972) and single potential theorysingle potential theory (strack,1976)(strack,1976)

The assumption of a The assumption of a sharp interfacesharp interface between between freshwater and saltwater freshwater and saltwater –– Immiscible Immiscible multiphase flow approachmultiphase flow approach

Variable densityVariable density flowflow in both time and space in both time and space dimensiondimension

Seawater Intrusion - The Henry’s problemBoundary condition of Henry problem

parameters

Solution with modflow/mt3d

Application to Local ProblemEffect of Aquifer Heterogeneity on the Intrusion of Seawater

Effects of variable hydraulic conductivity in layers of coastal aquifers and Position of 0.2, 0.4, 0.6, 0.8 and 1.0 isochlor in (a) Layer 1 (b) Layer 2 and (c) Layer 3.

Effects of homogeneous hydraulic conductivity for Henry problem homogeneous hydraulic conductivity.

The Elder problem

Boundary condition of the Elder problem

MODFFLOW/MT3D

Comparison of non dimensional results 1, 4 and 20 years for the Elder problem, showing maximum concentration for SUTRA (solid curves) and (red curve) for MODFLOW and MT3D.

SUTRA

Effects of heterogeneity in Elder problem

Effects of (a) homogeneous (b) variable in layered (c) Randomhydraulic conductivity for Elder problem

Huyakorn Saltwater Intrusion Problem

Boundary condition for Huyakorn et al. problem

(a) homogeneous case (b) Effects of variable hydraulic conductivity in layers of coastal aquifers (c) heterogeneous case, for Huyakorn et al. problem.

Flow and Transport in Flow and Transport in Natural (geological) SystemsNatural (geological) Systems

Flow and Transport Flow and Transport --VadoseVadose ZoneZone

Subsurface Contamination Subsurface Contamination TransportTransport

Governing Equation of Unsaturated Flow

Stt

Sz

Kz

Kzx

Kx s

zzzzxx +

∂∂

+∂∂

=∂

∂+

⎭⎬⎫

⎩⎨⎧

∂∂

∂∂

+⎭⎬⎫

⎩⎨⎧

∂∂

∂∂ θψ

φθθψθψθ )()()(

where K = hydraulic conductivity [LT-1 ] ψ = Matric potential[L] ,θ = Volumetric moisture content [L3 L-3],

φ = porosity of the soil media[L3 L-3] ,Ss = the specific storage[L-1], t = time [T] S = Source /sink term

Scope of the Transport ModelingScope of the Transport Modeling

The study is concerned with presenting an The study is concerned with presenting an algorithm to solve the ADE in a wide range of algorithm to solve the ADE in a wide range of unsaturated flow conditions faced in the field.unsaturated flow conditions faced in the field.

The two dimensional ADE is to be solved by The two dimensional ADE is to be solved by operator split method, which uses operator split method, which uses EulerianEulerianframe work with finite volume method for frame work with finite volume method for advectiveadvective transport and fully implicit finite transport and fully implicit finite difference for dispersive transport. difference for dispersive transport.

KK-- θθ --ψψ RelationshipRelationship

Soil Constitutive Relationships (K-θ-ψ)1)Brooks and Coorey’s (1964)

λ

ψψ

⎥⎦

⎤⎢⎣

⎡=Θ b

bψψ ≤...for

1= ….for bψψ >bψ = bubbling pressureλ = pore size index

Where,rs

r

θθθθ−−

=Θ = Effective Saturation

2)Gardner (1958)

)exp()( ψβψ −= sKKWhere, β = pore size distribution index

rBrs

AA

θψθθ

ψθ ++

−=

)()(

3. Haverkamp’s Model

Ds

r CC

KKK

)100()()(

ψψψ

+==

A, B , C and D are fitting parameters

v

v

m

nv ⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

+=Θ

ψα11

21

21

)1(1)(⎥⎥⎦

⎤

⎢⎢⎣

⎡Θ−−Θ=Θ vv mm

sKK

4. Van Genuchten (1980) Model

vvv nandm,αwhere are van Genuchten coefficients

and

Governing Equation for Unsaturated Transport

⎟⎠⎞

⎜⎝⎛

∂∂

∂∂

+⎟⎠⎞

⎜⎝⎛

∂∂

∂∂

=∂

∂+

∂∂

+∂∂

zCD

zxCD

xzCv

xCv

tC

zzxxzzxx )/()/()()( θθθθ

where c is concentration of the solute and , =moisture content Dxx and Dzz are dispersivities [L2 T –1 ] in x and z direction respectively. Given by,

θcC =

θ

no avDD += λ

where

Where a=dispersivity, n is a constant

θxx

xxqv =

θzz

zzqv =

xKq xxxx ∂

∂−=

ψθ )(

)1)((z

Kq zzzz ∂∂

+−=ψθ

λ=tortuosity

•Matrix solution by Strongly Implicit Procedure

Water Table Recharge

Moisture and relative concentration (8 and18 hrs)

Transient unconfined drainage

Moisture and solute (8 and 18 hrs Drainage case)

q=3.55 m/d

Relative concentration at various depths of seepage face

Field Application of Flow ModelField Application of Flow ModelLocation of Study Area

Topo-sheet of Moole Hole watershed

Transect T3

For bore hole A8, initial and 39 days moisture

For borehole A3: moisture at 64 and 85 days

1

2

3

For borehole A1: initial moisture and after 35 days

For borehole A4: initial moisture and at 84 days

•The results of the field study validate the applicability of theRichards equation to field.

•The field study conducted over five boreholes indicate a very good match between the simulated and measured moisture content. Each bore hole exhibit different properties with respect to soil type and layers.

•Such a set of boreholes spread across the watershed can be upscaled to study the overall subsurface water movement pattern.

•Water balance studies made for one of the boreholes in the field, for 350 days time period indicate that, AET contributes towards 33% of the total rainfall of 1291 mm, and 25 % drains through bottom boundary, which will add to recharge of the groundwater. Runoff is very less and amounts to just 8 %, which is very less,but is acceptable since it is in accordance with the observations made in the field.

Vadose zone Flow and Transport (Field Study) – key points

Flow and Transport in Man Made Flow and Transport in Man Made SystemsSystems

(Conservative and Reactive flow systems)

Piped systemsPiped systems

Flow controlsFlow controls

Piped systemsPiped systems

Water Quality Simulation Water Quality Simulation

Parameter EstimationParameter Estimation

Source Strength Identification Source Strength Identification

Bacteriological Growth Bacteriological Growth

Needs of the Study in a Water Distribution System

Water Quality SimulationWater Quality Simulation

Water Quality Deterioration Water Quality Deterioration BlendingBlendingAge, type and maintenance of the distribution systemAge, type and maintenance of the distribution systemChemical and biological transformationsChemical and biological transformations

Water Quality Expressed in terms of Water Quality Expressed in terms of Constituent concentration (generally chlorine) Constituent concentration (generally chlorine) Water ageWater ageSource traceSource trace

Water Quality ModelingWater Quality ModelingHydraulic analysis is prerequisiteHydraulic analysis is prerequisiteSteady state (ultimate values of water quality)Steady state (ultimate values of water quality)Dynamic state (spatial and temporal distribution of Dynamic state (spatial and temporal distribution of water quality)water quality)

Chlorine Reaction KineticsChlorine Reaction Kinetics

Bulk Flow ReactionsBulk Flow ReactionsDue to organic content in water Due to organic content in water First order or non first order kineticsFirst order or non first order kinetics

Wall Reaction KineticsWall Reaction KineticsDue to materials at pipe wall and corrosion Due to materials at pipe wall and corrosion productsproductsFirst or zero order kineticsFirst or zero order kinetics

Total Chlorine DecayTotal Chlorine DecayCombination of bulk and wall reactionsCombination of bulk and wall reactions

Mass transfer from bulk flow to pipe wallMass transfer from bulk flow to pipe wall

The extent of work doneThe extent of work doneDevelopment of Basic Water Quality Simulation Development of Basic Water Quality Simulation

parameter estimation and parameter estimation and Source strength Identification problems Source strength Identification problems

Steady State Water Quality ModelSteady State Water Quality ModelTo incorporate non first order (bulk and wall) reactions with To incorporate non first order (bulk and wall) reactions with analytical expressions wherever possibleanalytical expressions wherever possibleExtending the available hydraulic model (Extending the available hydraulic model (NiranjanNiranjan Reddy 1994) Reddy 1994) to a to a water quality model water quality model

Dynamic State Water Quality ModelDynamic State Water Quality ModelAn alternative hybrid method is proposed to eliminate the An alternative hybrid method is proposed to eliminate the deficiencies of the existing deficiencies of the existing LagrangianLagrangian modelsmodelsTo study the effect of concentration tolerance and water qualityTo study the effect of concentration tolerance and water qualitytime step on the performance of all time step on the performance of all LagrangianLagrangian models models Modifying available static hydraulic model to handle dynamic Modifying available static hydraulic model to handle dynamic conditions using extended period simulation and development of conditions using extended period simulation and development of dynamic models TDM, EDM and EDMNET dynamic models TDM, EDM and EDMNET Comparison of TDM with EPANETComparison of TDM with EPANET

Dynamic Water Quality ModelDynamic Water Quality Model

Comparative Study of Existing Models TDM and EDM with new Hybrid Method (EDMNET)• For analytical solutions• For application on network examples

Model Formulation• Static hydraulic model (Niranjan Reddy 1994) modified to handle extended period simulation

• Water quality model1. Transport in pipes

Expressions for Reaction Rate and Concentration

Conservative Chemical: R[ci(x,t)]=0Reactive Chemical

• First order bulk and first order wall reactions

•First order bulk and zero order wall reactions

2. Modeling water age• Modeled as reactive constituent of zero order

growth and R[ci(x,t)]=13. Modeling source trace• Modeled as simulating conservative constituent

of 100 units concentration at desired source

4. Dilution Equation

5. Mass balance equation at storage tank

Model ApplicationModel ApplicationTest Problem Used for Conservative and Reactive Constituent

Tank detailsDiameter 15.24 mInitial height 17.29 mMinimum height 15.24 mMaximum height 21.34 mFirst order chlorine reaction constants usedBulk reaction constant 0.55 /dWall reaction constant 0.15 m/d

Conservative Constituent

Reactive Constituent

Water Quality Parameter EstimationWater Quality Parameter EstimationWater Quality (Chlorine) Reaction Parameters

• Bulk reaction parameters (determined by bottle tests) • Wall reaction parameters (product of calibration)

Inverse Modeling Techniques are Useful to Estimate the Unknown Wall Reaction Parameters and Hence to Calibrate the Water Quality Model

Unknown Reaction Parameters are Expressed as• Overall first order reaction parameter• First order wall reaction parameter• Zero order wall reaction parameter• First order wall reaction-pipe roughness parameter• Zero order wall reaction-pipe roughness parameter

Present Work Done Present Work Done

Development of Inverse Models for Auto calibration of Steady State Water Quality Model

Development of Inverse Models for Auto calibration of a Typical Dynamic Water Quality Model (TDM)• To incorporate all types of unknown reaction parameters involved in

first or non first order reaction kinetics• Free from numerical diffusion

Simulation-Optimization Inverse Modeling Technique is Used with• Gauss-Newton Sensitivity Analysis Technique (GNSAT)• Genetic Algorithm Technique (GAT) in the optimization module

Model Verification and ApplicationModel Verification and ApplicationModel is verified using Bangalore Water Transmission Network Model using Error Free Data

Model is Applied to Estimate Wall ReactionParameters under noisy measurements

GNSAT Results

Comparison of GNSAT and GAT ResultsComparison of GNSAT and GAT Results

GA Parameters

GAT Convergence

Performance of Reaction Kinetics Models

For hypothetically assumed data it is tried to identify appropriate reaction kinetics

Performance of Reaction Kinetics Models

Water Quality Parameter EstimationWater Quality Parameter Estimation(Dynamic State)(Dynamic State)

Model Formulation

Solution by GNSAT• Corrections to parameters are obtained by solving Nup

(number of unknown parameters) linear equations given by

• Sensitivity coefficients are determined by parameter perturbation technique

• Calibration error statisticso Stastical parameters are computedo Parameter uncertainty is obtained using posterior parameter

covariance matrix given by

where, Jf = final Jacobian of sensitivity coefficients; s2=estimated error variance

Parameter confidence limits are given by

• Choice of weightso Weight based on measured values

Solution by GAT• Exactly similar to steady state case except dynamic water quality model

TDM is used in the forward simulation

∑ −=M

jNupjNE )(

Model Verification /PerformanceModel Verification /PerformanceModel is verified and tested its performance under noisy conditions for over- and underdetermined cases First order chlorine

reaction constants usedBulk reaction constant 0.31 /d (Lake)0.03 /d (River)Wall reaction constant Zone 1 0.3048 m/dZone 2 1.5244 m/dZone 3 3.0488 m/dZone 4 6.0976 m/dChlorine Conc. AtLake: 0.49 mg/LRiver: Varies between

0.23 and 0.31 mg/L

Data Used for Verification and PerformanceData Used for Verification and PerformanceGA Parameters

Results of Overdetermined CaseFor error free data

For noisy concentrations

GAT Convergence

Bacteriological Modeling in Distribution SystemBacteriological Modeling in Distribution SystemBacterial Growth

• Increase in the cell number by utilizing organic carbon is as a energy source

• Organic matter in drinking water is natural in origin resulting from decaying vegetation (e.g. humic and fulvic acids)

• Given the presence of nutrients regrowth is theoretically possible• May result in biofilm formation

Factors Affecting Bacterial Growth• Attachment to and shearing from the surfaces• Age of biofilm• Disinfectant levels

Multicomponent Reaction Transport Model• Used as tool to study the bacterial growths• Components incorporatedo Organic carbon (Substrate)o Bacterial content (Biomass)o Disinfectant (Chlorine)

Present WorkPresent Work

Development of Multicomponent Reaction Transport Model as Applicable to a Network

• Through simplified expressions for the processes such as bacterial growth, substrate consumption, attachment, detachment and disinfectant action• Which can predict the spatial and temporal spread of contaminant intruded into the system• Development of numerical Eulerian and Lagrangian solution methods to solve multicomponent model

Development of Multicomponent Reaction Transport Model as Applicable to Pilot Loop Experiments

MulticomponentMulticomponent Reaction Transport Model Reaction Transport Model Conceptual Basis

MulticomponentMulticomponent Reaction Transport Model Reaction Transport Model

Governing Equations for Plug Flow• Bulk flow

MulticomponentMulticomponent Reaction Transport Model Reaction Transport Model • Wall Zone

• Mixing at Node

Governing Equations for Perfectly Mixed Reactor• Pipe loop arrangement

• Bulk flow

• Wall zone

• Solved numerically using Runge-Kutta procedure

Model Validation Model Validation

Model Predictions Model Predictions

Influent ConcentrationsBDOC 0.5 mg/LBiomass 0.0006 mg/L Chlorine 0.0 mg/L to 2.0 mg/L

Hypothetical Network

•A serial network consisting of 300 mm, 250 mm, 200 mm, 150 mm, 100 mm and 80 mm each pipe has residence time of 12 h

Model Predictions Model Predictions

Model Predictions Model Predictions

Model Predictions Model Predictions

Key pointsKey points

Water Quality Simulation•In dynamic models, TDM dependent on concentration tolerance and Qstep, EDM on concentration tolerance and EDMNET predicts the concentrations better even at relatively higher concentration tolerances

• TDM results - compatible with EPANET results

Water Quality Parameter Estimation •The parameter estimation procedures for steady and dynamic statedeveloped are applicable for any type of reaction kinetics

o useful to identify the appropriate reaction kinetics for a system

o able to handle group or zoned estimates of the parameters

Key pointsKey points

• (GNSAT and GAT) - compute the parameters with comparable degree of accuracy

• GAT more appropriate method - estimating large number of parameters (not need the initial estimate of parameters)

• The inverse models (steady and dynamic) - a good tool for the water supply authorities to calibrate the water quality model, having either a first order or non first order chlorine reaction kinetics, for their system

Key pointsKey points

Source Strength Identification

•In dynamic strength identification model GNSAT is suitable for simple cases involving single monitoring node whereas GAT for multiple monitoring nodes

o GA approach is well suited for source strength identification problem

o Application of the optimally determined source strength(s)will reduce the total mass of chlorine and at the same time maintains a more uniform chlorine residuals throughout the system

•The steady and dynamic state strength identification models developed are very much useful in deciding the operational strategies with respect to chlorine inputs at the source(s) in a real life network

Key PointsKey Points

Bacteriological Modeling in Distribution System

•The results of sensitivity study on the hypothetical network shows that the model can adequately predict the various relationships among the components used the maintenance of the minimum chlorine residuals all the time throughout the network effectively controls the microbial growth

o The developed model can also be used to describe the spreading of contaminant throughout distribution system

Flow controlsFlow controls

Need for flow controls in Need for flow controls in piped systemspiped systems

Why Why flow controlsflow controls in water supply systems?in water supply systems?

To reach the targets/set points (reservoir flows / To reach the targets/set points (reservoir flows / levels)levels)

To reach the targets as fast as possibleTo reach the targets as fast as possible

To ensure the smoothest possible operation of To ensure the smoothest possible operation of valves/pumpsvalves/pumps

To control the slow transientsTo control the slow transients

For real time operation monitored by SCADA For real time operation monitored by SCADA

Particularly useful for complex pipe networksParticularly useful for complex pipe networks

Control system configurations: openControl system configurations: open--loop and loop and closedclosed--looploop

Closed-Loop System (also known as Feedback Control System)

Open loop system

Performance CriteriaPerformance Criteria

PID/PD/PI controllersPID/PD/PI controllers

-- Proportional Integral (PI) controller, Proportional Proportional Integral (PI) controller, Proportional Derivative (PD) controller and Proportional Integral Derivative (PD) controller and Proportional Integral Derivative controller (PID)Derivative controller (PID)--most commonly used most commonly used controllers.controllers.

--Have been in use in different forms since long Have been in use in different forms since long time.time.

--Works well for linear systemsWorks well for linear systems

Dynamic inversion based controllers:

- Nonlinear control design

- Technique of feedback linearisation

- Output tracking problems

- May be implemented as PD, PI or PID

Controller EquationsController Equations

PD ControllerPD Controller

PID ControllerPID Controller

DI based nonlinear controllerDI based nonlinear controller

dtdeKeKu dp +=

dtdeKdteKeKu dip ++= ∫

⎥⎦⎤

⎢⎣⎡ −= − )()(

.1 XfXXgu des uXgXfX )()(

.+=

Schematic diagram of the Gaziantep (Turkey) water supply system- Test Problem 1

llp1p1 = 669.27m= 669.27m hhs1s1 = 113.4m= 113.4m D=1.4 mD=1.4 m

llp2p2 = 13805.04m= 13805.04m hhs2s2 = 210.4m= 210.4m AA00 = 0.0001433= 0.0001433

llp3p3 = 20094.69m= 20094.69m hhs3s3 = 283.4m= 283.4m BB0 0 = 0.005015= 0.005015

llp4p4 = 4689.04m= 4689.04m hhs4s4 = 279.7m= 279.7m CC00 = 3.98= 3.98

AApipi= 1.5394 m= 1.5394 m22 AAtt= 475 m= 475 m22 n = 1n = 1

Pump Rated Discharge 2830 lit/sec

Pump Rated Speed 985 rpm

Initial Reservoir levels 3.20 m,2.15 m,4.20 m

Targeted Reservoir levels 4.0 m,2.50 m,3.91 m

Data for Gaziantep water supply system

Target outflow rate (Qo*): 2.4 m3s-1

Target reservoir levels (ht1*, ht2

*, ht3

*): 4.0 m, 2.5 m and 3.91 m

1st Initial condition:X(0) =

= (2.83, 3.20, 2.83, 2.15, 2.83, 4.20, 2.83)T

2nd Initial condition:X(0) =

= (2.20, 3.50, 2.20, 2.70, 2.20, 3.80, 2.20) T

[ ] 123T

atbtcto QhQhQhQ

[ ] 123T

atbtcto QhQhQhQ

Case 1: Constant set point over the time period

Error plots and Variation in pump speeds Error plots and Variation in pump speeds

Case 2: Three changes of set point

Targets:

Outflow: 2.3 to 2.7 m3s-1

2.7 to 2.8 m3s-1

2.8 to 2.6 m3s-1

For every 2 hrs

1st reservoir level: 4.0m

2nd reservoir level: 2.5m

Outflow, reservoir levels and pump speeds for the case Outflow, reservoir levels and pump speeds for the case of step changes in target outflow (of step changes in target outflow (QQoo

**) using DI ) using DI

Case 3: Reservoir levels and pump speeds for the Case 3: Reservoir levels and pump speeds for the case of constant target outflow (case of constant target outflow (QQoo

**) with different ) with different initial conditions using DI initial conditions using DI

Reservoir levels and speed change of the variable speed pump, Na for ±5% outflow disturbance (Q o) - Test problem 1.

Schematic diagram of the Faridabad water supply Schematic diagram of the Faridabad water supply system system –– Test problem 3Test problem 3

Details of nodes and pipes – Faridabad water supply system

Node Node no.no.

Head Head (m)/ (m)/

ElevatElevation ion (m) (m)

Node Node no.no.

Head Head (m)/ (m)/

ElevatiElevation (m) on (m)

Pipe Pipe no.no.

Length Length (m)(m)

DiameDiameter ter (mm) (mm)

Pipe Pipe no.no.

Length Length (m)(m)

DiamDiameter eter (mm) (mm)

RES 1RES 1 195.2195.2 1616 199199 11 11341134 250250 1616 12731273 300300

RES 2RES 2 203.4203.4 1717 199199 22 775775 300300 1818 23092309 400400

RES 3RES 3 199.8199.8 1818 199199 33 657657 900900 1919 17921792 400400

RES 4RES 4 202.6202.6 1919 199199 44 68506850 900900 2020 12371237 500500

RES 5RES 5 201.9201.9 2020 199199 55 29872987 500500 2121 15011501 600600

RES 6RES 6 201.6201.6 2121 201201 66 360360 450450 2222 17251725 700700

RES 7RES 7 197.2197.2 2222 200.5200.5 77 608608 400400 2323 16721672 750750

RES 8RES 8 205.7205.7 2323 200.5200.5 88 908908 300300 2424 23402340 800800

99 201201 2424 200200 99 638638 200200 2525 10151015 200200

1010 201201 2525 199199 1010 854854 250250

1111 201.5201.5 2626 197197 1111 703703 200200

1212 201201 2727 197197 1414 15971597 900900

1313 201201 2828 197197 1515 22652265 350350

1414 199199 2929 200200

1515 199199 3030 200200

3131 200200

PipesPipesNodes Nodes

Case 1: Case 1:

Error plots for 70% of initial flows as Error plots for 70% of initial flows as targets targets

Variation in valve loss coefficients for 70% of initial Variation in valve loss coefficients for 70% of initial

flows as targetsflows as targets

Case 1:Case 1:

Error plots for 30% of initial flows as Error plots for 30% of initial flows as targets targets

Case 2: Constant targets

Variation in valve loss coefficients for 30% of initial Variation in valve loss coefficients for 30% of initial

flows as targetsflows as targets

Variation in inflows for the case of step changes Variation in inflows for the case of step changes

in target inflowsin target inflows

Case 3: Case 3:

Variation in valve loss coefficients for the case Variation in valve loss coefficients for the case of step changes in target valuesof step changes in target values

The Concept of control systems has been applied for water The Concept of control systems has been applied for water network operations. Control design procedures are proposed network operations. Control design procedures are proposed to reach target reservoir levels/ target inflows.to reach target reservoir levels/ target inflows.

It is observed that linear controller PID has shown better It is observed that linear controller PID has shown better performance than PD controller. PD controller has failed to performance than PD controller. PD controller has failed to reach some of the targets.reach some of the targets.

A nonlinear robust controller DI has been tested on different A nonlinear robust controller DI has been tested on different real world problems of water networks and shown that it real world problems of water networks and shown that it has outperformed PD/PID controllershas outperformed PD/PID controllers

It has been observed that the gains of the above discussed It has been observed that the gains of the above discussed controllers play an important role in their performance and controllers play an important role in their performance and hence the different gain tuning approaches have been hence the different gain tuning approaches have been developeddeveloped

Flow controlsFlow controls –– key pointskey points

Future DirectionsFuture DirectionsModellingModelling of processes involving fluids moving underground through of processes involving fluids moving underground through complicated, soils and rocks media. Fluids could be water, oil,complicated, soils and rocks media. Fluids could be water, oil, gas gas –– One needs One needs the following coupled modeling approaches to be adoptedthe following coupled modeling approaches to be adopted

1.1. SingleSingle--phase/multiphase/multi--phase fluid flow through geological systems phase fluid flow through geological systems -- coupled with coupled with heat transport and phase changesheat transport and phase changes

2.2. SingleSingle--phase/multiphase/multi--phase fluid flow through geological systems phase fluid flow through geological systems -- under hydrounder hydro--mechanical couplingmechanical coupling

3.3. Modeling approaches to a humanModeling approaches to a human--intervened geological system intervened geological system -- a potential a potential underground radioactive waste repository.underground radioactive waste repository.

4.4. Abandoned aquifers as carbon dioxide storage reservoirs to redAbandoned aquifers as carbon dioxide storage reservoirs to reduce climatic uce climatic emissions.emissions.-- carbon sequestrationcarbon sequestration

5.5. Understanding of the linkage between smallUnderstanding of the linkage between small--scale and fieldscale and field--scale processesscale processes6.6. Coupling across regimes at large scales (e.g., surface water anCoupling across regimes at large scales (e.g., surface water and ground water, d ground water,

sea water)sea water)

Pilot loop experiments to understand the chemical and biologicalPilot loop experiments to understand the chemical and biological processes in processes in model building model building Soft computing tools to model large scale piped flow processesSoft computing tools to model large scale piped flow processes

THANK YOUTHANK YOU