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Ground Water Basics. Porosity Head Hydraulic Conductivity. Porosity Basics. Porosity n (or f ) Volume of pores is also the total volume – the solids volume. Porosity Basics. Can re-write that as: Then incorporate: Solid density: r s = M solids /V solids Bulk density: r b - PowerPoint PPT Presentation
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Ground Water BasicsPorosityHeadHydraulic Conductivity
Porosity BasicsPorosity n (or f)
Volume of pores is also the total volume the solids volume
Porosity BasicsCan re-write that as:
Then incorporate:Solid density: rs = Msolids/VsolidsBulk density: rb= Msolids/Vtotal rb/rs = Vsolids/Vtotal
Cubic Packings and Porosityhttp://members.tripod.com/~EppE/images.htm Simple Cubic Body-Centered Cubic Face-Centered Cubic n = 0.48 n = 0. 26 n = 0.26
FCC and BCC have same porosityBottom line for randomly packed beads: n 0.4http://uwp.edu/~li/geol200-01/cryschem/Smith et al. 1929, PR 34:1271-1274
EffectivePorosity
EffectivePorosity
Porosity Basics
Volumetric water content (q)Equals porosity for saturated system
Sand and BeadsCourtesey C.L. Lin, University of Utah
Aquifer Material (Miami Oolite)
Aquifer MaterialTucson recharge site
Aquifer MaterialX-Ray Tomography
Data SetData 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
Borehole Televiewer DataNew USGS ProjectImage provided courtesy of A. Manda, Florida International University and the United States Geological Survey.
Thresholding
3-D Coordinate ExtractionColumns map to x,yRows map to z
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 diameterNumber of pairsCommand file
Approximate Simple Variogram Model
gstat 2.4.1 (12 March 2003), BH1.cmd
enter/modify datachoose variable : BH1calculate what : semivariogramcutoff, width : 7.5, 0.1direction : totalvariogram model : 0.0639973 Nug(0) + 0.178246 Exp(0.622207)fit method : OLS (unwweighted)
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
Use ImageJ for raw volume creation from slice dataVisualize with 3dView
(Unconditioned) Rock Simulation
Aquifer Material (Keys limestone)
Aquifer Material (Keys limestone)
Bioturbated Aquifer Material
Aquifer Materialhttp://www.uta.edu/geology/geol1425earth_system/images/gaia_chapter_5/sedimentary_structures.htm
Aquifer Material (CA Coast)
Aquifer Material (CA Coast)
Aquifer Material (CA Coast)
Aquifer Material (CA Coast)
(CA Coast)
Karst (MN)http://course1.winona.edu/tdogwiler/websitestufftake2/SE%20Minnesota%20Karst%20Hydro%202003-11-22%2013-23-14%20014.JPG
Karsthttp://www.fiu.edu/~whitmand/Research_Projects/tm-karst.gif
Ground Water FlowPressure and pressure headElevation headTotal headHead gradientDischargeDarcys Law (hydraulic conductivity)Kozeny-Carman Equation
Multiple Choice:Water flows?UphillDownhillSomething else
PressurePressure is force per unit areaNewton: F = maF force (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)
Pressure and Pressure HeadPressure relative to atmospheric, so P = 0 at water tableP = rghp r densityg gravityhp depth
P = 0 (= Patm)Pressure Head(increases with depth below surface)Pressure HeadElevationHead
Elevation HeadWater wants to fallPotential energy
Elevation Head(increases with height above datum)Elevation HeadElevationHeadElevation datum
Total HeadFor our purposes:Total head = Pressure head + Elevation headWater flows down a total head gradient
P = 0 (= Patm)Total Head(constant: hydrostatic equilibrium)Pressure HeadElevation HeadElevationHeadElevation datum
Head GradientChange in head divided by distance in porous medium over which head change occursdh/dx [unitless]
DischargeQ (volume per time)
Darcys LawPlot gradient (x-axis) vs. discharge (y-axis) for several imposed gradientsTry different materials
www.ngwa.org/ ngwef/darcy.html 1803 - 1858
Darcys LawShould be linear:Q = K dh/dx Awhere K is the hydraulic conductivity and A is the cross-sectional flow areaSlope is K A, so K is slope/A
Intrinsic PermeabilityL T-1L2
Kozeny-Carman Equation
Beads80 -120 mesh= 224 -149 mmAverage size: 186.5 mm
Observations/ComputationsIntrinsic permeability?Hydraulic conductivity?
Darcys LawQ = -KA dh/dl
Darcy velocity:qx = -Kx h/x
Mean pore water velocity:v = q/ne
More on gradients
More on gradientsThree point problems:
hhh400 m412 m100 m
More on gradientsThree point problems:(2 equal heads)
h = 10mh = 10mh = 9m400 m412 m100 mCDGradient = (10m-9m)/CD CD?Scale from mapCompute
More on gradientsThree point problems:(3 unequal heads)
h = 10mh = 11mh = 9m400 m412 m100 mCDGradient = (10m-9m)/CD CD?Scale from mapCompute
Best guess for h = 10m
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