Features of POLLUSOLFeatures of POLLUSOLFlow modelFlow model

Homogeneous, Isotropic, Homogeneous, Isotropic, Heterogeneous and Anisotropic Heterogeneous and Anisotropic mediummedium

Saturated as well as Unsaturated Saturated as well as Unsaturated subsurface environmentsubsurface environment

Multiple layersMultiple layersTransient and Steady flow simulationTransient and Steady flow simulationPressure head and / or Flux boundary Pressure head and / or Flux boundary

conditionsconditions

Features of POLLUSOL (contd..)Features of POLLUSOL (contd..)Solute transport modelSolute transport model

Multiple layersMultiple layersForecasting of the future effects of Forecasting of the future effects of

groundwater pollutiongroundwater pollutionHomogeneous, Isotropic, Homogeneous, Isotropic,

Heterogeneous and Anisotropic Heterogeneous and Anisotropic mediummedium

Saturated as well as Unsaturated Saturated as well as Unsaturated subsurface environmentssubsurface environments

Constant concentration and/or Flux Constant concentration and/or Flux boundary conditionsboundary conditions

Transient and Steady state simulationTransient and Steady state simulation

CASE STUDIES (Flow cases)CASE STUDIES (Flow cases)

4. Earth and rock-fill 4. Earth and rock-fill dam using Gardner dam using Gardner permeability function permeability function (nonhomogeneous (nonhomogeneous earth and rock-fill earth and rock-fill dam)dam)

1. Flow 1. Flow around around the the cylindercylinder

3. Steady-state 3. Steady-state seepage analysis seepage analysis through through saturated-saturated-unsaturated soilsunsaturated soils

2. Confined 2. Confined flow under flow under dam dam foundatiofoundationn

Case1: Flow around the cylinderCase1: Flow around the cylinderIntroductionIntroduction

This study examines the problem of uniform fluid flow This study examines the problem of uniform fluid flow around a cylinder of unit radiusaround a cylinder of unit radius

,

θ

r

X

Y

Φ1 Φ2

L

L

Analytically, The total head values at any point in the Analytically, The total head values at any point in the problem domain can be given as :problem domain can be given as :

U U is the uniform undisturbed velocity is the uniform undisturbed velocity ==

a a is the radius of cylinderis the radius of cylinder, ,

is the anti-clockwise angle measured is the anti-clockwise angle measured from the from the x-axisx-axis to the field point to the field point

5.0cos2

r

arU

L21

22 yxr

Owing to the symmetry of problem only half of Owing to the symmetry of problem only half of domain is discretized in the modeldomain is discretized in the model

MeshMesh2-dimensional zone with 2-dimensional zone with

quadrilateral elements which quadrilateral elements which comprises of 223 cells and 472 nodescomprises of 223 cells and 472 nodes

Porous MediumPorous MediumFully saturated material with Fully saturated material with

hydraulic conductivity of 1e-05 m/shydraulic conductivity of 1e-05 m/sWaterWater

Incompressible with density=1000 Incompressible with density=1000 Kg/mKg/m33

Boundary conditionsBoundary conditions Constant head of 1 m is applied at the left Constant head of 1 m is applied at the left

boundary and Zero head is applied at boundary and Zero head is applied at right boundaryright boundary

The remaining boundaries are no flow The remaining boundaries are no flow boundaries those could be considered as boundaries those could be considered as adiabatic walls. adiabatic walls.

ResultsResultsFlow vector (m/s) with meshFlow vector (m/s) with mesh

Total pressure head (m) contours in the domain

Comparison of total heads calculated using Pollusol with that of other Models

Coordinates of points on problem domain

Pollusol

Phase2*

analytical

Ref.**

X Y

4 1 0.585 0.4999 0.5000 0.500 4.5 0.866 0.388 0.3810 0.3743 0.378

0 5 0 0.255 0.2626 0.2500 0.276

5 6 0 0.19 0.2031 0.1875 0.213

2 8 0 0.056 0.0000 -0.0312 0.000

* Groundwater Module in Phase2 , 2D finite element program for ground water analysis, Version 6.0, 2005 , Rocscience Inc.

** Desai, C. S., Kundu T., (2001) Introductory Finite Element Method, Boca Ration, Fla. CRC Press

Case2: Confined flow under dam foundationCase2: Confined flow under dam foundationIntroductionIntroduction

It examines the confined flow under dam It examines the confined flow under dam which rest on homogeneous isotropic soil which rest on homogeneous isotropic soil with dimensions (40m*10m).The walls with dimensions (40m*10m).The walls and base of dam are considered and base of dam are considered imperviousimpervious

MeshMeshThe domain is modeled as a 2-dimensional The domain is modeled as a 2-dimensional zone with quadrilateral elements. The zone with quadrilateral elements. The mesh comprises of 10800mesh comprises of 10800 cells and 15004 cells and 15004 nodesnodes

Porous MediumPorous MediumFully saturated material with hydraulic Fully saturated material with hydraulic conductivity of 1e-05 m/sconductivity of 1e-05 m/s

WaterWaterIncompressible with density=1000 Kg/mIncompressible with density=1000 Kg/m33

Boundary conditionsBoundary conditionsNo flow occurs across the impermeable No flow occurs across the impermeable

surfaces. These were considered as surfaces. These were considered as isotropic walls. isotropic walls.

Total pressure head between A and B is Total pressure head between A and B is equal to 5 m and between C and D is equal equal to 5 m and between C and D is equal to 0.0 m.to 0.0 m.

ResultsResultsFlow vector (m/s) with meshFlow vector (m/s) with mesh

Total pressure head (m) Total pressure head (m) contourscontours in the in the domaindomain

Comparison of total head variation along section 1-1 obtained Comparison of total head variation along section 1-1 obtained using Pollusol with that of other modelsusing Pollusol with that of other models

PollusolPollusol Phase2Phase2** and Ref and Ref****

* Groundwater Module in Groundwater Module in Phase2 , Phase2 , 2D finite element 2D finite element program for ground program for ground water analysis, Version 6.0, 2005 , Rocscience Inc.water analysis, Version 6.0, 2005 , Rocscience Inc.** Rushton K.R., Redshaw S.C. (1979) ** Rushton K.R., Redshaw S.C. (1979) Seepage and Seepage and Groundwater FlowGroundwater Flow, John Wiley & Sons, U.K., John Wiley & Sons, U.K.

Comparison of total head variation along section 2-2 obtained Comparison of total head variation along section 2-2 obtained using Pollusol with that of other modelsusing Pollusol with that of other models

PollusolPollusolPhase2Phase2** and Refand Ref****

* Groundwater Module in * Groundwater Module in Phase2 , Phase2 , 2D finite element 2D finite element program for program for ground water analysis, Version 6.0, 2005 , Rocscience Inc.ground water analysis, Version 6.0, 2005 , Rocscience Inc.** Rushton K.R., Redshaw S.C. (1979) ** Rushton K.R., Redshaw S.C. (1979) Seepage and Seepage and Groundwater FlowGroundwater Flow, John Wiley & Sons, U.K., John Wiley & Sons, U.K.

Case3: Steady-state seepage analysis through Case3: Steady-state seepage analysis through saturated-unsaturated soilssaturated-unsaturated soils

IntroductionIntroductionThis study considers the problem of This study considers the problem of seepage through an earth dam. seepage through an earth dam.

MeshMeshThe domain is modeled as a 2-dimensional The domain is modeled as a 2-dimensional zone with quadrilateral elements. The mesh zone with quadrilateral elements. The mesh comprises of 1404comprises of 1404 cells and 2906 cells and 2906 nodes nodes

WaterWaterIncompressible with density=1000 Kg/mIncompressible with density=1000 Kg/m33

Porous MediumPorous Medium Four types of cases are considered:Four types of cases are considered:

1.1. Isotropic earth dam with a horizontal Isotropic earth dam with a horizontal drain (length 12 m)drain (length 12 m)

2.2. Anisotropic earth dam with a horizontal Anisotropic earth dam with a horizontal draindrain

3.3. Isotropic earth dam with a core and Isotropic earth dam with a core and horizontal drainhorizontal drain

4.4. Isotropic earth dam with a steady state Isotropic earth dam with a steady state infiltrationinfiltration

5.5. Isotropic earth dam with a seepage faceIsotropic earth dam with a seepage face

1.00E-11

1.00E-10

1.00E-09

1.00E-08

1.00E-07

-200000 -150000 -100000 -50000 0

Pressure ( Pa)

Perm

eability

(m

/s)

For Anisotropic earth damFor Anisotropic earth dam horizontal horizontal direction is nine times larger than in the direction is nine times larger than in the vertical direction. The permeability vertical direction. The permeability function for vertical direction is same as function for vertical direction is same as that of isotropic earth dam.that of isotropic earth dam.

The permeability function used for The permeability function used for isotropic earth damisotropic earth dam

1.00E-12

1.00E-11

1.00E-10

1.00E-09

-120000 -100000 -80000 -60000 -40000 -20000 0

Pressure ( Pa)

Per

mea

bilit

y (m

/s)

An isotropic dam having core with lower An isotropic dam having core with lower coefficient of permeability. The coefficient of permeability. The permeability function used for permeability function used for the core of the core of the damthe dam

Boundary conditionsBoundary conditions1.1. Isotropic earth dam with a horizontal Isotropic earth dam with a horizontal

drain drain • Total head of 10m at the left side. Total head of 10m at the left side. • Zero pressure head at horizontal drain. Zero pressure head at horizontal drain. No flow occurs at the rest of the boundary of No flow occurs at the rest of the boundary of

geometry that could be considered as geometry that could be considered as adiabatic walls in model.adiabatic walls in model.

2.2. Anisotropic earth dam with a horizontal Anisotropic earth dam with a horizontal draindrain• Same as that of case1.Same as that of case1.

3.3. Isotropic earth dam with a core and Isotropic earth dam with a core and horizontal drainhorizontal drain• Same as that of case1.Same as that of case1.

Boundary conditions (contd..)Boundary conditions (contd..)3.3. Isotropic earth dam with a steady state Isotropic earth dam with a steady state

infiltrationinfiltration Total head of 10m applied at the left side Total head of 10m applied at the left side Flux boundary of 1e-8 m/s applied at the right Flux boundary of 1e-8 m/s applied at the right

side in order to consider the effect of infiltrationside in order to consider the effect of infiltration Zero pressure head at horizontal drain Zero pressure head at horizontal drain No flow occurs at the rest of the boundary of the No flow occurs at the rest of the boundary of the

geometry that could be considered as adiabatic geometry that could be considered as adiabatic walls in modelwalls in model

4.4. Isotropic earth dam with a seepage faceIsotropic earth dam with a seepage face Total head of 10m applied at the left side of the Total head of 10m applied at the left side of the

dam dam Pressure is zero at right bottom of the slope Pressure is zero at right bottom of the slope

surface surface No flow occurs at the rest of the boundary of the No flow occurs at the rest of the boundary of the

geometry that could be considered as adiabatic geometry that could be considered as adiabatic walls in modelwalls in model

ResultsResults

Isotropic earth dam with a horizontal drainIsotropic earth dam with a horizontal drain

Flow vector (m/s) with meshFlow vector (m/s) with mesh

Total pressure head (m) contours in the Total pressure head (m) contours in the domaindomain

Total pressure head along the section1-1Total pressure head along the section1-1

Anisotropic earth dam with a horizontal drainAnisotropic earth dam with a horizontal drain

Flow vector (m/s) with meshFlow vector (m/s) with mesh

Total pressure head (m) contours in the domainTotal pressure head (m) contours in the domain

Total pressure head along the section1-1Total pressure head along the section1-1

Isotropic earth dam with a core and horizontal drainIsotropic earth dam with a core and horizontal drain

Flow vector (m/s) with meshFlow vector (m/s) with mesh

Total pressure head (m) profile in the domainTotal pressure head (m) profile in the domain

Total pressure head along the section1-1Total pressure head along the section1-1

Isotropic earth dam with a steady state infiltrationIsotropic earth dam with a steady state infiltration

Flow vector (m/s) with meshFlow vector (m/s) with mesh

Total pressure head (m) contours in the domainTotal pressure head (m) contours in the domain

Total pressure head along the section1-1Total pressure head along the section1-1

Isotropic earth dam with a seepage faceIsotropic earth dam with a seepage faceFlow vector (m/s) with meshFlow vector (m/s) with mesh

Total pressure head (m) contours in the domainTotal pressure head (m) contours in the domain

Total pressure head along the section1-1Total pressure head along the section1-1

Case4: Earth and rock-fill dam using Gardner Case4: Earth and rock-fill dam using Gardner permeability function (nonhomogeneous earth and permeability function (nonhomogeneous earth and rock-fill dam)rock-fill dam) IntroductionIntroduction

This study examines seepage flow rate through This study examines seepage flow rate through the nonhomgeneous earth and rock fill dam.the nonhomgeneous earth and rock fill dam.

MeshMeshThe domain is modeled as a 2-dimensional The domain is modeled as a 2-dimensional zone with triangular elements. The mesh zone with triangular elements. The mesh comprises of 3616 comprises of 3616 cells and 3890 nodes cells and 3890 nodes

WaterWaterIncompressible with density=1000 Kg/mIncompressible with density=1000 Kg/m33

Porous MediumPorous MediumThe porous medium was unsaturated. The porous medium was unsaturated. Gardner non-linear equation between Gardner non-linear equation between permeability function and pressure head permeability function and pressure head was used as given belowwas used as given below

)1( ns

u ah

KK

where where a a and and n n are the model parameters, are the model parameters, hh is pressure head (suction), is pressure head (suction), KKuu is unsaturated permeability, and is unsaturated permeability, and

KKss is saturated permeability. is saturated permeability.

Layer Ks (m/s) a nDam 1e-7 0.15 2

Foundation 1.25e-5 0.15 6Toe drain 1e-3 0.15 6

Models Models parameters usedparameters used

Boundary conditionsBoundary conditionsTotal pressure head of 28 m was applied at Total pressure head of 28 m was applied at

the left of the dam the left of the dam Total pressure head of 10 m was Total pressure head of 10 m was

considered at the right of the dam.considered at the right of the dam. No flow was occurred at the rest No flow was occurred at the rest

boundaries of the geometry that could be boundaries of the geometry that could be treated as adiabatic wallstreated as adiabatic walls

ResultsResultsFlow vector with meshFlow vector with mesh

Total pressure head contours in the domainTotal pressure head contours in the domain

1.1. Areal Constant Density Solute Areal Constant Density Solute Transport (Example at Rocky Mountain Transport (Example at Rocky Mountain Arsenal)Arsenal)

2.2.   Three-dimensional contaminant Three-dimensional contaminant transport through the porous mediumtransport through the porous medium

CASE STUDIES (Flow and Solute transport CASE STUDIES (Flow and Solute transport cases)cases)

Case1: Areal Constant Density Solute Transport Case1: Areal Constant Density Solute Transport (Example at Rocky Mountain Arsenal)(Example at Rocky Mountain Arsenal)IntroductionIntroduction

It consists of an areal model of a It consists of an areal model of a rectangular alluvial aquifer with a rectangular alluvial aquifer with a constant transmissivity and two constant transmissivity and two impermeable bedrock outcrops which impermeable bedrock outcrops which influence groundwater flow. influence groundwater flow.

Three wells pump from the aquifer (at a Three wells pump from the aquifer (at a rate of Qrate of QOUT OUT each), and contamination each), and contamination enters the system through a leaking enters the system through a leaking waste isolation pond (at a rate of Qwaste isolation pond (at a rate of QININ, , with concentration, C). with concentration, C).

MeshMeshThe domain is modeled as a 2-dimensional The domain is modeled as a 2-dimensional zone with quadrilateral elements. The zone with quadrilateral elements. The mesh comprises of 32000 mesh comprises of 32000 cells and cells and 64722 nodes64722 nodes

WaterWaterIncompressible with density=1000 Kg/mIncompressible with density=1000 Kg/m33

Viscosity of water =0.001 Pa.sViscosity of water =0.001 Pa.s

Parameters usedParameters used• Porosity (n)=0.2Porosity (n)=0.2• Hydraulic conductivity (KHydraulic conductivity (Kxx= K= Kyy= K= Kzz) = 7.76e-12 m) = 7.76e-12 m22

• Longitudinal dispersivity (αLongitudinal dispersivity (αLL)) = 152.4 m= 152.4 m• Transverse dispersivity (αTransverse dispersivity (αTT)) = 30.48 m= 30.48 m• Leakage rate through pond (QLeakage rate through pond (QININ) = 0.0283 m) = 0.0283 m33/s/s• Concentration entered through pond (C) = 1000 Concentration entered through pond (C) = 1000

ppmppm• Pumping rate from each well (QPumping rate from each well (QOUTOUT) = 0.005663 ) = 0.005663

mm33/s/s• Half life period = 20 yearsHalf life period = 20 years

Initial conditionsInitial conditionsInitial pressures are zero for steady-state Initial pressures are zero for steady-state

simulation of pressure. Initial concentration simulation of pressure. Initial concentration is zero ppm is zero ppm

Boundary conditionsBoundary conditionsNo flow occurs across any boundary except No flow occurs across any boundary except

where constant heads are specified at 76.2 where constant heads are specified at 76.2 m and 11.43 m at the top of the mesh and at m and 11.43 m at the top of the mesh and at the bottom of the mesh respectively. the bottom of the mesh respectively.

A source is specified at the leaky pond node, A source is specified at the leaky pond node, and a sink is specified at each well node. and a sink is specified at each well node.

ResultsResults

Total Pressure head Total Pressure head contourscontours

Solute concentration contours after 1000 years Solute concentration contours after 1000 years

Solute concentration (with solute half Solute concentration (with solute half life ~ 20 years) after 1000 yearslife ~ 20 years) after 1000 years

Case2: Three-dimensional contaminant transport Case2: Three-dimensional contaminant transport through the porous mediumthrough the porous mediumIntroductionIntroduction

The study area consists of homogeneous and The study area consists of homogeneous and isotropic confined aquifer. A horizontal source isotropic confined aquifer. A horizontal source 200m*100m*0.1m (i.e. red color indicated in 200m*100m*0.1m (i.e. red color indicated in figure 1.0) on the upper surface of the figure 1.0) on the upper surface of the computational domain continuously releases a computational domain continuously releases a contaminant into the aquifer, which is initially contaminant into the aquifer, which is initially free of the contaminantfree of the contaminant

3700m

800m

56m

700m

200m100m

MeshMeshThe domain is modeled as a 2-dimensional The domain is modeled as a 2-dimensional zone with hexazone with hexa elements. The mesh elements. The mesh comprises of 80000 cells and 23042comprises of 80000 cells and 23042 nodesnodes

WaterWaterIncompressible with density = 1000 Kg/mIncompressible with density = 1000 Kg/m33

Viscosity of water = 0.001 Pa.sViscosity of water = 0.001 Pa.s

ParametersParametersPorosity of the porous medium=0.1Porosity of the porous medium=0.1Longitudinal dispersivity = 91 mLongitudinal dispersivity = 91 mTransverse dispersivity = 20 mTransverse dispersivity = 20 mThe release of contaminant in to aquifer is The release of contaminant in to aquifer is

2.5e2.5e-4-4 kg/m kg/m33s. s. The velocity component in the x-direction is The velocity component in the x-direction is

1.4x10-6 m/s everywhere1.4x10-6 m/s everywhere

Initial conditionsInitial conditionsThe velocity component in the x-direction is The velocity component in the x-direction is

1.4x10-6 m/s everywhere1.4x10-6 m/s everywhere Initial concentration is zero ppm Initial concentration is zero ppm

Boundary conditionsBoundary conditionsThe flow entering the recharge boundary at The flow entering the recharge boundary at

left (i.e. at x=0) is free of any contaminant; left (i.e. at x=0) is free of any contaminant; thus the concentration at that boundary is thus the concentration at that boundary is zero. zero.

All other boundaries are set to conditions of All other boundaries are set to conditions of zero flux.zero flux.

ResultsResults

Contour plots of Solute concentration (g/m3) at 5 years

Concentrations of the solute (g/m^3) at Concentrations of the solute (g/m^3) at different locations in the domaindifferent locations in the domain

Trace1 at (850m, 50m, 0.05m)

Trace2 at (850m, 300m, 0.05m)