Transcript POLLUSOL - Fluidyn

Features of POLLUSOL
 Flow model
 Homogeneous, Isotropic, Heterogeneous and
Anisotropic medium
 Saturated as well as Unsaturated subsurface
environment
 Multiple layers
 Transient and Steady flow simulation
 Pressure head and / or Flux boundary
conditions
Features of POLLUSOL (contd..)
 Solute transport model
 Multiple layers
 Forecasting of the future effects of groundwater
pollution
 Homogeneous, Isotropic, Heterogeneous and
Anisotropic medium
 Saturated as well as Unsaturated subsurface
environments
 Constant concentration and/or Flux boundary
conditions
 Transient and Steady state simulation
CASE STUDIES (Flow cases)
2. Confined
1.4.Flow
around
Earth and rock-fill dam using Gardner
flow under
the
cylinder function (nonhomogeneous
permeability
dam
earth and rock-fill dam)
foundation
3. Steady-state seepage
analysis through
saturatedunsaturated soils
,
Case1: Flow around the cylinder
 Introduction
This study examines the problem of uniform fluid flow
around a cylinder of unit radius
Y
r
Φ1
Φ2
θ
X
L
L
Analytically, The total head values at any point in the
problem domain can be given as :
2

a
  U  r   cos  0.5

r 


1   2
U is the uniform undisturbed velocity =
L
a is the radius of cylinder,
r  x 2  y 2 is the anti-clockwise angle measured
from the x-axis to the field point
Owing to the symmetry of problem only half of domain
is discretized in the model
 Mesh
 2-dimensional zone with quadrilateral
elements which comprises of 223 cells and
472 nodes
 Porous Medium
 Fully saturated material with hydraulic
conductivity of 1e-05 m/s
 Water
 Incompressible with density=1000 Kg/m3
 Boundary conditions
 Constant head of 1 m is applied at the left boundary
and Zero head is applied at right boundary
 The remaining boundaries are no flow boundaries
those could be considered as adiabatic walls.
 Results
 Flow 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
X
Y
4
4.5
5
6
8
1
0.866
0
0
0
Pollusol Phase2*
0.585
0.388
0.255
0.19
0.056
0.4999
0.3810
0.2626
0.2031
0.0000
analytical Ref.**
0.5000
0.3743
0.2500
0.1875
-0.0312
0.500
0.3780
0.2765
0.2132
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 foundation
 Introduction
It examines the confined flow under dam which
rest on homogeneous isotropic soil with
dimensions (40m*10m).The walls and base of
dam are considered impervious
 Mesh
The domain is modeled as a 2-dimensional zone
with quadrilateral elements. The mesh comprises
of 10800 cells and 15004 nodes
 Porous Medium
Fully saturated material with hydraulic
conductivity of 1e-05 m/s
 Water
Incompressible with density=1000 Kg/m3
 Boundary conditions
 No flow occurs across the impermeable surfaces.
These were considered as isotropic walls.
 Total pressure head between A and B is equal to 5 m
and between C and D is equal to 0.0 m.
 Results
 Flow vector (m/s) with
mesh
 Total pressure head (m) contours in the domain
Comparison of total head variation along section 1-1 obtained
using Pollusol with that of other models
Pollusol
Phase2* and Ref**
* Groundwater Module in Phase2 , 2D finite element program for
ground
water analysis, Version 6.0, 2005 , Rocscience Inc.
** Rushton K.R., Redshaw S.C. (1979) Seepage and Groundwater Flow,
Comparison of total head variation along section 2-2 obtained
using Pollusol with that of other models
Pollusol
Phase2* and Ref**
* Groundwater Module in Phase2 , 2D finite element program for
ground water analysis, Version 6.0, 2005 , Rocscience Inc.
** Rushton K.R., Redshaw S.C. (1979) Seepage and Groundwater Flow,
John Wiley & Sons, U.K.
Case3: Steady-state seepage analysis through
saturated-unsaturated soils
 Introduction
This study considers the problem of seepage
through an earth dam.
 Mesh
The domain is modeled as a 2-dimensional zone
with quadrilateral elements. The mesh comprises
of 1404 cells and 2906 nodes
 Water
Incompressible with density=1000 Kg/m3
 Porous Medium
Four types of cases are considered:
1. Isotropic earth dam with a horizontal drain
(length 12 m)
2. Anisotropic earth dam with a horizontal drain
3. Isotropic earth dam with a core and horizontal
drain
4. Isotropic earth dam with a steady state infiltration
5. Isotropic earth dam with a seepage face
The permeability function used for isotropic earth
dam
Pressure ( Pa)
-200000
-150000
-100000
-50000
0
1.00E-08
1.00E-09
Perme abi lity (m /s)
1.00E-07
1.00E-10
1.00E-11
For Anisotropic earth dam horizontal direction is
nine times larger than in the vertical direction. The
permeability function for vertical direction is same
as that of isotropic earth dam.
An isotropic dam having core with lower coefficient
of permeability. The permeability function used for
the core of the dam
Pressure ( Pa)
-100000
-80000
-60000
-40000
-20000
0
1.00E-09
1.00E-10
1.00E-11
1.00E-12
Permeability (m/s)
-120000
 Boundary conditions
1.
Isotropic earth dam with a horizontal drain
•
•

Total head of 10m at the left side.
Zero pressure head at horizontal drain.
No flow occurs at the rest of the boundary of geometry
that could be considered as adiabatic walls in model.
2. Anisotropic earth dam with a horizontal drain
•
Same as that of case1.
3. Isotropic earth dam with a core and horizontal
drain
•
Same as that of case1.
 Boundary conditions (contd..)
Isotropic earth dam with a steady state infiltration
3.




Total head of 10m applied at the left side
Flux boundary of 1e-8 m/s applied at the right side in
order to consider the effect of infiltration
Zero pressure head at horizontal drain
No flow occurs at the rest of the boundary of the geometry
that could be considered as adiabatic walls in model
4. Isotropic earth dam with a seepage face

Total head of 10m applied at the left side of the dam

Pressure is zero at right bottom of the slope surface

No flow occurs at the rest of the boundary of the geometry
that could be considered as adiabatic walls in model
Results
 Isotropic earth dam with a horizontal drain
Flow vector (m/s) with mesh
 Total pressure head (m) contours in the domain
 Total pressure head along the section1-1
 Anisotropic earth dam with a horizontal drain
Flow vector (m/s) with mesh
 Total pressure head (m) contours in the domain
 Total pressure head along the section1-1

Isotropic earth dam with a core and horizontal
drain
Flow vector (m/s) with mesh
 Total pressure head (m) profile in the domain
 Total pressure head along the section1-1
 Isotropic earth dam with a steady state
infiltration
Flow vector (m/s) with mesh
 Total pressure head (m) contours in the domain
 Total pressure head along the section1-1
 Isotropic earth dam with a seepage face
Flow vector (m/s) with mesh
 Total pressure head (m) contours in the domain
 Total pressure head along the section1-1
Case4: Earth and rock-fill dam using Gardner
permeability function (nonhomogeneous earth and
rock-fill dam)
 Introduction
This study examines seepage flow rate through the
nonhomgeneous earth and rock fill dam.
 Mesh
The domain is modeled as a 2-dimensional zone
with triangular elements. The mesh comprises of
3616 cells and 3890 nodes
 Water
Incompressible with density=1000 Kg/m3
 Porous Medium
The porous medium was unsaturated. Gardner nonlinear equation between permeability function and
pressure head was used as given below
Ks
Ku 
(1  ahn )
where a and n are the model parameters,
h is pressure head (suction),
Ku is unsaturated permeability, and
Ks is saturated permeability.
Models parameters
usedLayer
K (m/s)
Dam
Foundation
Toe drain
s
1e-7
1.25e-5
1e-3
a
0.15
0.15
0.15
n
2
6
6
 Boundary conditions
 Total pressure head of 28 m was applied at the left
of the dam
 Total pressure head of 10 m was considered at the
right of the dam.
 No flow was occurred at the rest boundaries of the
geometry that could be treated as adiabatic walls
 Results
 Flow vector with mesh
 Total pressure head contours in the domain
CASE STUDIES (Flow and Solute transport
cases)
1. Areal Constant Density Solute Transport
(Example at Rocky Mountain Arsenal)
2. Three-dimensional contaminant transport
through the porous medium
Case1: Areal Constant Density Solute Transport
(Example at Rocky Mountain Arsenal)
 Introduction


It consists of an areal model of a rectangular
alluvial aquifer with a constant transmissivity
and two impermeable bedrock outcrops which
influence groundwater flow.
Three wells pump from the aquifer (at a rate of
QOUT each), and contamination enters the system
through a leaking waste isolation pond (at a rate
of QIN, with concentration, C).
 Mesh
The domain is modeled as a 2-dimensional zone
with quadrilateral elements. The mesh comprises
of 32000 cells and 64722 nodes
 Water
Incompressible with density=1000 Kg/m3
Viscosity of water =0.001 Pa.s
 Parameters used
• Porosity (n)=0.2
Hydraulic conductivity (Kx= Ky= Kz) = 7.76e-12 m2
Longitudinal dispersivity (αL) = 152.4 m
Transverse dispersivity (αT) = 30.48 m
Leakage rate through pond (QIN) = 0.0283 m3/s
Concentration entered through pond (C) = 1000
ppm
• Pumping rate from each well (QOUT) = 0.005663
m3/s
• Half life period = 20 years
•
•
•
•
•
 Initial conditions
 Initial pressures are zero for steady-state simulation
of pressure. Initial concentration is zero ppm
 Boundary conditions
 No flow occurs across any boundary except where
constant heads are specified at 76.2 m and 11.43 m at
the top of the mesh and at the bottom of the mesh
respectively.
 A source is specified at the leaky pond node, and a
sink is specified at each well node.
Results
Total Pressure head contours
Solute concentration contours after 1000 years
Solute concentration (with solute half life ~ 20
years) after 1000 years
Case2: Three-dimensional contaminant transport
through the porous medium
 Introduction
The study area consists of homogeneous and
isotropic confined aquifer. A horizontal source
200m*100m*0.1m (i.e. red color indicated in figure
1.0) on the upper surface of the computational
domain continuously releases a contaminant into
the aquifer, which is initially free of the
contaminant
56m
200m
100m
800m
700m
3700m
 Mesh
The domain is modeled as a 2-dimensional zone
with hexa elements. The mesh comprises of 80000
cells and 23042 nodes
 Water
Incompressible with density = 1000 Kg/m3
Viscosity of water = 0.001 Pa.s
 Parameters
 Porosity of the porous medium=0.1
 Longitudinal dispersivity = 91 m
 Transverse dispersivity = 20 m
 The release of contaminant in to aquifer is 2.5e-4
kg/m3s.
 The velocity component in the x-direction is 1.4x106 m/s everywhere
 Initial conditions
 The velocity component in the x-direction is 1.4x10-6
m/s everywhere
 Initial concentration is zero ppm
 Boundary conditions
 The flow entering the recharge boundary at left (i.e.
at x=0) is free of any contaminant; thus the
concentration at that boundary is zero.
 All other boundaries are set to conditions of zero
flux.
Results
Contour plots of Solute concentration (g/m3)
at 5 years
Concentrations of the solute (g/m^3) at different
locations in the domain
Trace1 at (850m, 50m, 0.05m)
Trace2 at (850m, 300m, 0.05m)