What process is simulated by these moving dots ? - Diffusion - Dispersion - Advection

1. Groundwater Flow/Transport Model • What process is simulated • by these moving dots ? • - Diffusion • - Dispersion • - Advection • - Free convection • - Something else • - This is NO groundwater flow ?

2. Groundwater Flow/Transport Model • The same model, now showing the • tracks followed by the moving dots • - Diffusion • - Dispersion • - Advection • - Free convection • - Something else • - 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. low head layer 1 high head z y layer n x 0 Flow in confined layered aquifers Parallel flow Well flow well discharge layer 1 r layer n

6. K1 v K2 Flow in anisotropic aquifers Anisotropy of the hydraulic conductivity K1 K3 K2

7. layer i layer 1 layer n Analytical and Numerical solutions • Analytical solutions: • Fully 3-dimensional: h = f (x, y, z) • Multilayer approximation: h= f (i, x, y) • Dupuit approximation: h = f (x, y) • 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

8. N 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. N 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 • - long anisotropic block • two homogeneous layers • different horizontal anisotropies

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. 20 m N 30 m 10 30 m • isotropic layers K = 1 m/day • anisotropic block 10 by 10 m • Kmax = 1 m/day • Kmin= 0.1 m/day Finite element model + parallel flow - a confined aquifer with 20 sublayers - no-flow west and east sides - steady-state flow to the north

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. T1 = 10 T2 = 1 m2/d T1 = 10 T2 = 1 m2/d

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

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

23. Q 1 1 2 12 meter T1=120T2=120 m2/d 3 2 4 5 12 meter 6 T1=120T2=24 m2/d = -30 Example of two-layer well flow comparison analytical  numerical - fully confined aquifer - two homogeneous layers top layer = isotropic base layer = anisotropic - fully penetrating well - steady-state flow

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. 20 m N 30 m 10 30 m • isotropic layers K = 1 m/day • anisotropic block 10 by 10 m • Kmax = 1 m/day • Kmin= 0.1 m/day Analytic model + parallel flow - a confined aquifer with 20 sublayers - no-flow west and east sides - steady-state flow to the north

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

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

29. 20 Streamlines and their projections

30. 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

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----owhirl interface

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

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

35. A heterogeneous block of 9 layers 10 strips 90 cells with different horizontal anisotropies 90 125 85 75 55 105 115 95 65 135 45 90 90 65 55 125 75 135 95 115 85 105 45 90 90 125 65 105 115 95 75 85 135 45 55 90 90 125 55 85 115 75 95 45 65 105 135 90 90 75 95 65 135 55 45 85 125 105 115 90 90 135 125 65 115 85 105 75 55 95 45 90 90 65 135 95 55 115 85 75 105 45 125 90 90 55 85 105 125 65 135 115 75 45 95 90 90 45 115 125 95 105 75 85 135 55 65 90 All principal directions randomly distributed between northeast (45°) and northwest (135°) within each layer Conductivities of all cells K1 = 10 m/day K2 = 5 m/day Kz = 1 m/day N K2 K1 α E W Kz

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

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

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

39. 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 Conclusions

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 For a complete list of publications on groundwater whirls see: http://www.microfem.com/download/gwwhirl-papers/