What process is simulated by these moving dots ? a)- Diffusion b)- Dispersion c)- Advection d)- Free...

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What process is simulated by these moving dots ? a) - Diffusion b) - Dispersion c) - Advection d) - Free convection e) - Something else f) - This is NO groundwater flow Groundwater Flow/Transport Model ? ?

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Transcript of What process is simulated by these moving dots ? a)- Diffusion b)- Dispersion c)- Advection d)- Free...

Page 1: What process is simulated by these moving dots ? a)- Diffusion b)- Dispersion c)- Advection d)- Free convection e)- Something else f)- This is NO groundwater.

What process is simulatedby these moving dots ?

a) - Diffusion b) - Dispersion c) - Advection d) - Free convectione) - Something elsef) - This is NO groundwater flow

Groundwater Flow/Transport Model

??

Page 2: What process is simulated by these moving dots ? a)- Diffusion b)- Dispersion c)- Advection d)- Free convection e)- Something else f)- This is NO groundwater.

Groundwater Flow/Transport Model

The same model, now showing the

tracks followed by the moving dots

a) - Diffusion b) - Dispersion c) - Advection d) - Free convectione) - Something elsef) - This is NO groundwater flow

??

Page 3: What process is simulated by these moving dots ? a)- Diffusion b)- Dispersion c)- Advection d)- Free convection e)- Something else f)- This is NO groundwater.

Groundwater Flow/Transport Model

Advection

2D projections of 3D streamlines

The model simulates 3D groundwater flow in a layered anisotropic aquifer

Page 4: What process is simulated by these moving dots ? a)- Diffusion b)- Dispersion c)- Advection d)- Free convection e)- Something else f)- This is NO groundwater.

Complex Groundwater Whirl

Systems Kick Hemker & Mark Bakker

Groundwater flow in layered anisotropic aquifers

Introduction• Flow in layered aquifers • Anisotropy • Solution techniques

Some Numerical results• Parallel flow models• Well flow model

Analytical models • Solution for Well flow

• Parallel flow in heterogeneous

systems• Patterns of connected whirls• Complex whirl systems

Conclusions

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Flow in confined layered aquifers

Parallel flow

Well flow well discharge

layer 1

layer n r

layer 1

layer n

0 x

y

z

high head

low head

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Flow in anisotropic aquifers

Anisotropy of the hydraulic conductivity

K1

K2

K3

h Kv

z

y

x

v

v

v

v

z

h

y

hx

h

h

zzzyzx

yzyyyx

xzxyxx

KKK

KKK

KKK

K

K1

K2

y

h

v

Page 7: What process is simulated by these moving dots ? a)- Diffusion b)- Dispersion c)- Advection d)- Free convection e)- Something else f)- This is NO groundwater.

Analytical and Numerical solutions

Numerical solution:• Finite element method• Finite difference method

MicroFEM software: ĥ = f (i,x,y)• horizontal flow -> triangular finite elements• vertical flow components -> finite differences

Analytical solutions: Fully 3-dimensional: h = f (x, y, z) Multilayer approximation: h = f (i, x,

y) Dupuit approximation: h = f (x, y)

layer i

layer 1

layer n

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Finite element model + parallel

flowSimple two-layer model- a box-shaped confined aquifer- homogeneous isotropic- no-flow west and east sides- steady-state flow to the north

Page 9: What process is simulated by these moving dots ? a)- Diffusion b)- Dispersion c)- Advection d)- Free convection e)- Something else f)- This is NO groundwater.

Simple two-layer model- a box-shaped confined aquifer- homogeneous isotropic- no-flow west and east sides- steady-state flow to the north

- long anisotropic block - two homogeneous layers - different horizontal anisotropies

Finite element model + parallel

flow

Page 10: What process is simulated by these moving dots ? a)- Diffusion b)- Dispersion c)- Advection d)- Free convection e)- Something else f)- This is NO groundwater.

published

in

Ground

Wat

er

(mar

ch 2

004)

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Finite-element gridof 2470 nodes and4800 elements

Model built with MicroFEM

Page 12: What process is simulated by these moving dots ? a)- Diffusion b)- Dispersion c)- Advection d)- Free convection e)- Something else f)- This is NO groundwater.
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Results:- five spiralling streamlines- rotating counter-clockwise

- one axis in the general flow direction,

at the layer interface

Groundwater Whirla bundle of spiral-shaped streamlines

rotating clockwise or counter-clockwise

Page 14: What process is simulated by these moving dots ? a)- Diffusion b)- Dispersion c)- Advection d)- Free convection e)- Something else f)- This is NO groundwater.

- a confined aquifer with 20

sublayers

- no-flow west and east sides

- steady-state flow to the north

- isotropic layers K = 1 m/day - anisotropic block 10 by 10 m

Kmax = 1 m/day

Kmin = 0.1 m/day

30 m30 m

20 m

10

Finite element model + parallel

flow

Page 15: What process is simulated by these moving dots ? a)- Diffusion b)- Dispersion c)- Advection d)- Free convection e)- Something else f)- This is NO groundwater.

Results:- 3 groundwater whirls- 3 axes in the general flow direction, at the layer interfaces- adjacent whirls rotate in opposite directions

• Layered aquifer

• Different anisotropiesWhirls

Page 16: What process is simulated by these moving dots ? a)- Diffusion b)- Dispersion c)- Advection d)- Free convection e)- Something else f)- This is NO groundwater.

Well flow in a two-layer aquiferwith cross-wise anisotropy

Aquifer:- a single confined aquifer- two homogeneous hor.-anisotropic layers- cross-wise anisotropy

Well:- fully penetrating

Flow- steady state

Computation:- finite elements (MicroFEM)

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T1 = 10 T2 = 1 m2/d

T1 = 10 T2 = 1 m2/d

Page 18: What process is simulated by these moving dots ? a)- Diffusion b)- Dispersion c)- Advection d)- Free convection e)- Something else f)- This is NO groundwater.
Page 19: What process is simulated by these moving dots ? a)- Diffusion b)- Dispersion c)- Advection d)- Free convection e)- Something else f)- This is NO groundwater.
Page 20: What process is simulated by these moving dots ? a)- Diffusion b)- Dispersion c)- Advection d)- Free convection e)- Something else f)- This is NO groundwater.
Page 21: What process is simulated by these moving dots ? a)- Diffusion b)- Dispersion c)- Advection d)- Free convection e)- Something else f)- This is NO groundwater.

Q

N

Schematic representation of four whirls induced by flow to a well

in a two-layer aquifer

Page 22: What process is simulated by these moving dots ? a)- Diffusion b)- Dispersion c)- Advection d)- Free convection e)- Something else f)- This is NO groundwater.

Analytical solution using Dupuit

- a single (semi)confined aquifer- m homogeneous layers- anisotropic transmissivity in each layer

layer 1 layer

2

layer 3 laye

r 4

x

y

layer i

layer m

aquifer

z

Dupuit approximation: h = f (x, y)

Page 23: What process is simulated by these moving dots ? a)- Diffusion b)- Dispersion c)- Advection d)- Free convection e)- Something else f)- This is NO groundwater.

- fully confined aquifer- two homogeneous layers top layer = isotropic

base layer = anisotropic

- fully penetrating well- steady-state flow

Example of two-layer well flowcomparison analytical

numerical

12 m

eter

12 m

eter

1

2

T1 =120 T2 =24 m2/d = -30

T1 =120 T2 =120 m2/d

Q

1

2

3

4

5

6

Page 24: What process is simulated by these moving dots ? a)- Diffusion b)- Dispersion c)- Advection d)- Free convection e)- Something else f)- This is NO groundwater.

Streamlines to a well in a two-layer aquiferBakker & Hemker, Adv. Water Res. 25 (2002)

Page 25: What process is simulated by these moving dots ? a)- Diffusion b)- Dispersion c)- Advection d)- Free convection e)- Something else f)- This is NO groundwater.

Streamlines to a well in a two-layer aquiferNumerical results using MicroFEM

Page 26: What process is simulated by these moving dots ? a)- Diffusion b)- Dispersion c)- Advection d)- Free convection e)- Something else f)- This is NO groundwater.

- a confined aquifer with 20

sublayers

- no-flow west and east sides

- steady-state flow to the north

- isotropic layers K = 1 m/day - anisotropic block 10 by 10 m

Kmax = 1 m/day

Kmin = 0.1 m/day

30 m30 m

20 m

10

Analytic model + parallel flow

Page 27: What process is simulated by these moving dots ? a)- Diffusion b)- Dispersion c)- Advection d)- Free convection e)- Something else f)- This is NO groundwater.

Streamlines starting at depths of -8 and -12 m

Streamlines starting at depths of -7, -8 and -9

m

Page 28: What process is simulated by these moving dots ? a)- Diffusion b)- Dispersion c)- Advection d)- Free convection e)- Something else f)- This is NO groundwater.

Streamlines starting at depths of -8 and -12 m

Streamlines starting at depths of -7, -8 and -9

m

Page 29: What process is simulated by these moving dots ? a)- Diffusion b)- Dispersion c)- Advection d)- Free convection e)- Something else f)- This is NO groundwater.

20 Streamlines and their projections

20 25 30 35 40 45 5020

10

0

x (m)

depth

(m

)

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Projected streamlines

Stream function contours

Ψ = stream function

Ψ = 0 m2/d at model boundary and whirl

interfaces

max = 0.0015 m2/day at upper and lower whirl

axis

min = -0.0091 m2/day at central axis

Page 31: What process is simulated by these moving dots ? a)- Diffusion b)- Dispersion c)- Advection d)- Free convection e)- Something else f)- This is NO groundwater.

Conclusions:- numerical and analytical results are very similar- analytical models are easier to build- whirls are best visualized as stream function contour plots

Page 32: What process is simulated by these moving dots ? a)- Diffusion b)- Dispersion c)- Advection d)- Free convection e)- Something else f)- This is NO groundwater.

Patterns of connected whirls

50 100 150 200 250-18

-12

-6

0 o

o

50 100 150 200 250-18

-12

-6

0

Two whirls rotating counter-clockwise X saddle point

Two whirls rotating in opposite directions o----o whirl interface

Page 33: What process is simulated by these moving dots ? a)- Diffusion b)- Dispersion c)- Advection d)- Free convection e)- Something else f)- This is NO groundwater.

Patterns of connected whirls

50 100 150 200 250-18

-12

-6

0

c

o o

50 100 150 200 250-18

-12

-6

0

Two whirls rotating in opposite directions o----o whirl interface

Two whirls rotating in opposite directions X saddle point

Page 34: What process is simulated by these moving dots ? a)- Diffusion b)- Dispersion c)- Advection d)- Free convection e)- Something else f)- This is NO groundwater.

- a layered confined aquifer

- no-flow west and east sides

- steady-state flow to the north

- long anisotropic block - with many homogeneous cells in

the general flow direction- cells have varying anisotropies

100 m100 m

18 m

100 m

More complex analytic model

Page 35: What process is simulated by these moving dots ? a)- Diffusion b)- Dispersion c)- Advection d)- Free convection e)- Something else f)- This is NO groundwater.

9065551358575105951251154590

9095457511513565125105855590

9012545105758511555951356590

9045955575105851156512513590

9011510512585455513565957590

9013510565459575115855512590

9055451358575951151056512590

9045105851159513575125556590

9045135659511510555758512590

A heterogeneous block of 9 layers 10 strips

90 cells with differenthorizontal anisotropies

Conductivities of all cells

K1 = 10 m/day

K2 = 5 m/day

Kz = 1 m/day

All principal directions randomly distributed between northeast (45°) and northwest (135°) within each layer

K2 K1

α

N

Kz

EW

Page 36: What process is simulated by these moving dots ? a)- Diffusion b)- Dispersion c)- Advection d)- Free convection e)- Something else f)- This is NO groundwater.

50 100 150 200 250-3

-2

-1

0

1

2

3x 10

-3 Heads in all layers

layer 1layer 2layer 3layer 4layer 5layer 6layer 7layer 8layer 9

50 100 150 200 250-3

-2

-1

0

1

2

3x 10

-3 Vx (m/d) in all layers

layer 1layer 2layer 3layer 4layer 5layer 6layer 7layer 8layer 9

Cross-section with hydraulic heads in 9 layers

west east

west east

Cross-section with lateral flux in 9 layers

Page 37: What process is simulated by these moving dots ? a)- Diffusion b)- Dispersion c)- Advection d)- Free convection e)- Something else f)- This is NO groundwater.

50 100 150 200 250-18

-16

-14

-12

-10

-8

-6

-4

-2

0

50 100 150 200 250-18

-16

-14

-12

-10

-8

-6

-4

-2

0

Stream function contours

Cross-section showing 9 * 20 streamlines

Page 38: What process is simulated by these moving dots ? a)- Diffusion b)- Dispersion c)- Advection d)- Free convection e)- Something else f)- This is NO groundwater.

16 + 18 whirl axes ( and )28 saddle points (x) and 10 boundary points ( )

Clockwise and counter-clockwise whirl systems50 100 150 200 250

-18

-16

-14

-12

-10

-8

-6

-4

-2

0

50 100 150 200 250-18

-12

-6

0

Page 39: What process is simulated by these moving dots ? a)- Diffusion b)- Dispersion c)- Advection d)- Free convection e)- Something else f)- This is NO groundwater.

Conclusions

1 - Simple finite element experiments

layered aquifer varying anisotropies

2 - Analytical models confirm numerical results complete view of whirl patterns easier tool for the study of whirls

3 - Heterogeneous analytical models spatially varying cell anisotropies → complex whirl patterns

whirls

Page 40: What process is simulated by these moving dots ? a)- Diffusion b)- Dispersion c)- Advection d)- Free convection e)- Something else f)- This is NO groundwater.

Consequences of whirls

a - Increased lateral and vertical

exchange of groundwater

between layers (beds)

b - Increased contaminant spreading

within aquifers ( ‘dispersion’ )

? - Can transport models do without

layering and anisotropy ?

Page 41: What process is simulated by these moving dots ? a)- Diffusion b)- Dispersion c)- Advection d)- Free convection e)- Something else f)- This is NO groundwater.

0 100 200 300 400 500 600 700 800 900 1000-100

-90

-80

-70

-60

-50

-40

-30

-20

-10

0Streamlines with times

Analytical model of 50 by 100 cells: stream function contours, 5000 streamlines

Page 42: What process is simulated by these moving dots ? a)- Diffusion b)- Dispersion c)- Advection d)- Free convection e)- Something else f)- This is NO groundwater.

Groundwater flow in layered

anisotropic aquifers

Parallel Flow

Radial Flow

Numericalsolution

MicroFEM Hemker, v.d.Berg & Bakker:

2001-2004 Ground Water

Analyticalsolution

Dupuit approx.

Bakker & Hemker:

2002-2002 Adv.Water Res.

Multi-layer approx.

1 strip

Bakker & Hemker:

2004-2004

Adv.Water Res.

Meesters, Hemker &

v.d.Berg 2003-2004

J.Hydrology

n strips

Hemker, v.d.Berg & Bakker:

(in preparation)

For a complete list of publications on groundwater whirls see:

http://www.microfem.com/download/gwwhirl-papers/


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