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1 Ground Water Basics Porosity Head Hydraulic Conductivity

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

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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

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

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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

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6 Effective Porosity

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

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

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10 Aquifer Material (Miami Oolite)

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11 Aquifer Material Tucson recharge site

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12 Aquifer Material X-Ray Tomography

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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

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

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15 Thresholding

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

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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

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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)

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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

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

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21 (Unconditioned) Rock Simulation

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22 Aquifer Material (Keys limestone)

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23 Aquifer Material (Keys limestone)

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24 Bioturbated Aquifer Material

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

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26 Aquifer Material (CA Coast)

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27 Aquifer Material (CA Coast)

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28 Aquifer Material (CA Coast)

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29 Aquifer Material (CA Coast)

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30 (CA Coast)

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

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

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

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

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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)

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

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

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38 Elevation Head Water wants to fall Potential energy

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

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

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

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

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43 Discharge Q (volume per time)

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

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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

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46 Intrinsic Permeability L T -1 L2L2

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47 Kozeny-Carman Equation

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48 Beads 80 -120 mesh = 224 -149 m Average size: 186.5 m

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49 Observations/Computations Intrinsic permeability? Hydraulic conductivity?

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

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51 More on gradients

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

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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

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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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