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 flow Groundwater Flow / Transport Model ?

2. The same model, now showing the tracks followed by the moving dots a)- Diffusion b)- Dispersion c)- Advection d)- Free convection e)- Something else f)- This is NO groundwater flow ?

3. Groundwater Flow / Transport Model Advection 2D projections of 3D streamlines The model simulates 3D groundwater flow in a layered anisotropic aquifer

4. 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

5. 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

6. Flow in anisotropic aquifers Anisotropy of the hydraulic conductivity K1K1 K2K2 K3K3 K1K1 K2K2 v

7. 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

8. Finite element model + parallel flow Simple two-layer model - a box-shaped confined aquifer - homogeneous isotropic - no-flow west and east sides - steady-state flow to the north

9. 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

10. published in Ground Water (march 2004)

11. Finite-element grid of 2470 nodes and 4800 elements Model built with MicroFEM

13. Results: - five spiralling streamlines - rotating counter-clockwise - one axis in the general flow direction, at the layer interface Groundwater Whirl a bundle of spiral-shaped streamlines rotating clockwise or counter-clockwise

14. - 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 K max = 1 m/day K min = 0.1 m/day 30 m 20 m 10 Finite element model + parallel flow

15. Results: - 3 groundwater whirls - 3 axes in the general flow direction, at the layer interfaces - adjacent whirls rotate in opposite directions Layered aquifer Different anisotropies Whirls

16. Well flow in a two-layer aquifer with 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 )

17. T 1 = 10 T 2 = 1 m 2 /d

21. Q N Schematic representation of four whirls induced by flow to a well in a two-layer aquifer

22. Analytical solution using Dupuit - a single (semi)confined aquifer - m homogeneous layers - anisotropic transmissivity in each layer layer 1 layer 2 layer 3 layer 4 x y layer i layer m aquifer z Dupuit approximation: h = f (x, y)

23. - fully confined aquifer - two homogeneous layers top layer = isotropic base layer = anisotropic - fully penetrating well - steady-state flow Example of two-layer well flow comparison analytical  numerical 12 meter 1 2 T 1 = 120 T 2 = 24 m 2 /d  = -30  T 1 = 120 T 2 = 120 m 2 /d Q 1 2 3 4 5 6

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

25. Streamlines to a well in a two-layer aquifer Numerical results using MicroFEM

26. - 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 K max = 1 m/day K min = 0.1 m/day 30 m 20 m 10 Analytic model + parallel flow

27. Streamlines starting at depths of -8 and -12 m Streamlines starting at depths of -7, -8 and -9 m

28. Streamlines starting at depths of -8 and -12 m Streamlines starting at depths of -7, -8 and -9 m

29. 20 Streamlines and their projections

30. Projected streamlines Stream function contours Ψ = stream function Ψ = 0 m 2 /d at model boundary and whirl interfaces max = 0.0015 m 2 / day at upper and lower whirl axis min = -0.0091 m 2 / day at central axis

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

32. Patterns of connected whirls Two whirls rotating counter-clockwise X saddle point Two whirls rotating in opposite directions o----o whirl interface

33. Patterns of connected whirls Two whirls rotating in opposite directions o----o whirl interface Two whirls rotating in opposite directions X saddle point

34. - 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 m 18 m 100 m More complex analytic model

35. A heterogeneous block of 9 layers 10 strips 90 cells with different horizontal anisotropies Conductivities of all cells K 1 = 10 m/day K 2 = 5 m/day K z = 1 m/day All principal directions randomly distributed between northeast (45°) and northwest (135°) within each layer K2K2 K1K1 α N KzKz E W

36. Cross-section with hydraulic heads in 9 layers west east west east Cross-section with lateral flux in 9 layers

37. Stream function contours Cross-section showing 9 * 20 streamlines

38. 16 + 18 whirl axes ( and ) 28 saddle points (x) and 10 boundary points ( ) Clockwise and counter-clockwise whirl systems

39. 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

40. 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 ?

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

42. Groundwater flow in layered anisotropic aquifers Parallel Flow Radial Flow Numerical solution MicroFEM Hemker, v.d.Berg & Bakker: 2001-2004 Ground Water Analytical solution 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/