1. Ground Water Basics • Porosity • Head • Hydraulic Conductivity

2. Porosity Basics • Porosity n (or f) • Volume of pores is also the total volume – the solids volume

3. Porosity Basics • Can re-write that as: • Then incorporate: • Solid density: rs = Msolids/Vsolids • Bulk density: rb = Msolids/Vtotal • rb/rs = Vsolids/Vtotal

4. Cubic Packings and Porosity Simple Cubic Body-Centered Cubic Face-Centered Cubic n = 0.48 n = 0. 26 n = 0.26 http://members.tripod.com/~EppE/images.htm

5. FCC and BCC have same porosity • Bottom line for randomly packed beads: n ≈ 0.4 http://uwp.edu/~li/geol200-01/cryschem/ Smith et al. 1929, PR 34:1271-1274

6. EffectivePorosity

7. EffectivePorosity

8. Porosity Basics • Volumetric water content (q) • Equals porosity for saturated system

9. Sand and Beads Courtesey C.L. Lin, University of Utah

10. Aquifer Material (Miami Oolite)

11. Aquifer MaterialTucson recharge site

12. Aquifer Material • X-Ray Tomography

13. Data Set Burrow porosity in Miami Limestone barrier bar deposited during the last interglacial (maximum unit thickness ~ 1m) Photo: Mike Wacker/USGS Data and image produced at the High-Resolution X-ray Computed Tomography Facility of the University of Texas at Austin

14. Borehole Televiewer Data • New USGS Project Image provided courtesy of A. Manda, Florida International University and the United States Geological Survey.

15. Thresholding

16. 3-D Coordinate Extraction • Columns map to x,y • Rows map to z

17. Omnidirectional Sample Variogram 4 inch diameter Number of pairs Command file # # One variable definition: # to start the variogram modelling user interface. # data(BH1): '../BH1.dat', x=1, y=2, z=3, v=4;

18. Approximate Simple Variogram Model gstat 2.4.1 (12 March 2003), BH1.cmd enter/modify data choose variable : BH1 calculate what : semivariogram cutoff, width : 7.5, 0.1 direction : total variogram model : 0.0639973 Nug(0) + 0.178246 Exp(0.622207) fit method : OLS (unwweighted)

19. Indicator Simulation # # Unconditional Gaussian simulation on a mask # (local neigbourhoods, simple kriging) # # dummy defines empty variable: data(dummy): dummy, sk_mean=0.5,min=20, max=40; # local neighbourhood; variogram(dummy): 0.0639973 Nug(0) + 0.178246 Exp(0.622207); data(): 'grid.dat', x=1, y=2, z = 3; # prediction locations method: is; # Indicator simulation instead of kriging set output = 'is.out'; Need to remove header and extraneous information and sort by layer to run file through MATLAB script for slice generation

20. Use ImageJ for raw volume creation from slice data • Visualize with 3dView

21. (Unconditioned) Rock Simulation

22. Aquifer Material (Keys limestone)

23. Aquifer Material (Keys limestone)

24. Bioturbated Aquifer Material

25. Aquifer Material http://www.uta.edu/geology/geol1425earth_system/images/gaia_chapter_5/sedimentary_structures.htm

26. Aquifer Material (CA Coast)

27. Aquifer Material (CA Coast)

28. Aquifer Material (CA Coast)

29. Aquifer Material (CA Coast)

30. (CA Coast)

31. Karst (MN) http://course1.winona.edu/tdogwiler/websitestufftake2/ SE%20Minnesota%20Karst%20Hydro%202003-11-22% 2013-23-14%20014.JPG

32. Karst http://www.fiu.edu/~whitmand/Research_Projects/tm-karst.gif

33. Ground Water Flow • Pressure and pressure head • Elevation head • Total head • Head gradient • Discharge • Darcy’s Law (hydraulic conductivity) • Kozeny-Carman Equation

34. Multiple Choice:Water flows…? • Uphill • Downhill • Something else

35. Pressure • Pressure is force per unit area • Newton: F = ma • Fforce (‘Newtons’ N or kg ms-2) • m mass (kg) • a acceleration (ms-2) • P = F/Area (Nm-2 or kg ms-2m-2 = kg s-2m-1 = Pa)

36. Pressure and Pressure Head • Pressure relative to atmospheric, so P = 0 at water table • P = rghp • r density • g gravity • hpdepth

37. P = 0 (= Patm) Pressure Head Pressure Head (increases with depth below surface) Elevation Head

38. Elevation Head • Water wants to fall • Potential energy

39. Elevation Head (increases with height above datum) Elevation Elevation Head Elevation datum Head

40. Total Head • For our purposes: • Total head = Pressure head + Elevation head • Water flows down a total head gradient

41. P = 0 (= Patm) Pressure Head Total Head (constant: hydrostatic equilibrium) Elevation Elevation Head Elevation datum Head

42. Head Gradient • Change in head divided by distance in porous medium over which head change occurs • dh/dx [unitless]

43. Discharge • Q (volume per time)

44. Darcy’s Law • Plot gradient (x-axis) vs. discharge (y-axis) for several imposed gradients • Try different materials 1803 - 1858 www.ngwa.org/ ngwef/darcy.html

45. Darcy’s Law • Should be linear: • Q = K dh/dx A where K is the hydraulic conductivity and A is the cross-sectional flow area • Slope is K A, so K is slope/A

46. Intrinsic Permeability L2 L T-1

47. Kozeny-Carman Equation

48. Beads • 80 -120 mesh • = 224 -149 mm • Average size: 186.5 mm

49. Observations/Computations • Intrinsic permeability? • Hydraulic conductivity?

50. Darcy’s Law • Q = -KA dh/dl • Darcy ‘velocity’: qx = -Kx∂h/∂x • Mean pore water velocity: v = q/ne