Ground Water Basics

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

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)

Bioturbated Aquifer Material

Aquifer Materialhttp://www.uta.edu/geology/geol1425earth_system/images/gaia_chapter_5/sedimentary_structures.htm

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

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Ground Water Basics