ground water basics
DESCRIPTION
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 PresentationTRANSCRIPT
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Ground Water BasicsPorosityHeadHydraulic Conductivity
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Porosity BasicsPorosity n (or f)
Volume of pores is also the total volume the solids volume
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Porosity BasicsCan re-write that as:
Then incorporate:Solid density: rs = Msolids/VsolidsBulk density: rb= Msolids/Vtotal rb/rs = Vsolids/Vtotal
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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
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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
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EffectivePorosity
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EffectivePorosity
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Porosity Basics
Volumetric water content (q)Equals porosity for saturated system
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Sand and BeadsCourtesey C.L. Lin, University of Utah
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Aquifer Material (Miami Oolite)
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Aquifer MaterialTucson recharge site
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Aquifer MaterialX-Ray Tomography
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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
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Borehole Televiewer DataNew USGS ProjectImage provided courtesy of A. Manda, Florida International University and the United States Geological Survey.
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Thresholding
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3-D Coordinate ExtractionColumns map to x,yRows map to z
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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
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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)
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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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Use ImageJ for raw volume creation from slice dataVisualize with 3dView
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(Unconditioned) Rock Simulation
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Aquifer Material (Keys limestone)
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Aquifer Material (Keys limestone)
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Bioturbated Aquifer Material
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Aquifer Materialhttp://www.uta.edu/geology/geol1425earth_system/images/gaia_chapter_5/sedimentary_structures.htm
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Aquifer Material (CA Coast)
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Aquifer Material (CA Coast)
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Aquifer Material (CA Coast)
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Aquifer Material (CA Coast)
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(CA Coast)
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Karst (MN)http://course1.winona.edu/tdogwiler/websitestufftake2/SE%20Minnesota%20Karst%20Hydro%202003-11-22%2013-23-14%20014.JPG
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Karsthttp://www.fiu.edu/~whitmand/Research_Projects/tm-karst.gif
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Ground Water FlowPressure and pressure headElevation headTotal headHead gradientDischargeDarcys Law (hydraulic conductivity)Kozeny-Carman Equation
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Multiple Choice:Water flows?UphillDownhillSomething else
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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)
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Pressure and Pressure HeadPressure relative to atmospheric, so P = 0 at water tableP = rghp r densityg gravityhp depth
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P = 0 (= Patm)Pressure Head(increases with depth below surface)Pressure HeadElevationHead
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Elevation HeadWater wants to fallPotential energy
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Elevation Head(increases with height above datum)Elevation HeadElevationHeadElevation datum
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Total HeadFor our purposes:Total head = Pressure head + Elevation headWater flows down a total head gradient
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P = 0 (= Patm)Total Head(constant: hydrostatic equilibrium)Pressure HeadElevation HeadElevationHeadElevation datum
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Head GradientChange in head divided by distance in porous medium over which head change occursdh/dx [unitless]
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DischargeQ (volume per time)
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Darcys LawPlot gradient (x-axis) vs. discharge (y-axis) for several imposed gradientsTry different materials
www.ngwa.org/ ngwef/darcy.html 1803 - 1858
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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
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Intrinsic PermeabilityL T-1L2
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Kozeny-Carman Equation
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Beads80 -120 mesh= 224 -149 mmAverage size: 186.5 mm
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Observations/ComputationsIntrinsic permeability?Hydraulic conductivity?
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Darcys LawQ = -KA dh/dl
Darcy velocity:qx = -Kx h/x
Mean pore water velocity:v = q/ne
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More on gradients
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More on gradientsThree point problems:
hhh400 m412 m100 m
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More on gradientsThree point problems:(2 equal heads)
h = 10mh = 10mh = 9m400 m412 m100 mCDGradient = (10m-9m)/CD CD?Scale from mapCompute
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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