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1 Ground Water Basics Porosity Head Hydraulic Conductivity.

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1 1 Ground Water Basics Porosity Head Hydraulic Conductivity

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

3 3 Porosity Basics Can re-write that as: Then incorporate: Solid density:  s = M solids /V solids Bulk density:  b = M solids /V total  b  s = V solids /V total

4 4 Cubic Packings and Porosity Simple Cubic Body-Centered Cubic Face-Centered Cubic n = 0.48 n = n = 0.26

5 5 FCC and BCC have same porosity Bottom line for randomly packed beads: n ≈ 0.4 Smith et al. 1929, PR 34:

6 6 Effective Porosity

7 7

8 8 Porosity Basics Volumetric water content (  ) –Equals porosity for saturated system

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

10 10 Aquifer Material (Miami Oolite)

11 11 Aquifer Material Tucson recharge site

12 12 Aquifer Material X-Ray Tomography

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

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

15 15 Thresholding

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

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

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

19 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): Nug(0) Exp( ); 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 20 Use ImageJ for raw volume creation from slice data Visualize with 3dView

21 21 (Unconditioned) Rock Simulation

22 22 Aquifer Material (Keys limestone)

23 23 Aquifer Material (Keys limestone)

24 24 Bioturbated Aquifer Material

25 25 Aquifer Material

26 26 Aquifer Material (CA Coast)

27 27 Aquifer Material (CA Coast)

28 28 Aquifer Material (CA Coast)

29 29 Aquifer Material (CA Coast)

30 30 (CA Coast)

31 31 Karst (MN) SE%20Minnesota%20Karst%20Hydro% % %20014.JPG

32 32 Karst

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

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

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

36 36 Pressure and Pressure Head Pressure relative to atmospheric, so P = 0 at water table P =  gh p –  density –g gravity –h p depth

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

38 38 Elevation Head Water wants to fall Potential energy

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

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

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

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

43 43 Discharge Q (volume per time)

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

45 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 46 Intrinsic Permeability L T -1 L2L2

47 47 Kozeny-Carman Equation

48 48 Beads mesh =  m Average size:  m

49 49 Observations/Computations Intrinsic permeability? Hydraulic conductivity?

50 50 Darcy’s Law Q = -KA dh/dl Darcy ‘velocity’: q x = -K x ∂h/∂x Mean pore water velocity: v = q/n e

51 51 More on gradients

52 52 More on gradients Three point problems: h h h 400 m 412 m 100 m

53 53 More on gradients Three point problems: –(2 equal heads) h = 10m h = 9m 400 m 412 m 100 m CD Gradient = (10m- 9m)/CD CD? –Scale from map –Compute

54 54 More on gradients Three point problems: –(3 unequal heads) h = 10m h = 11m h = 9m 400 m 412 m 100 m CD Gradient = (10m- 9m)/CD CD? –Scale from map –Compute Best guess for h = 10m


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