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1
Ground Water Basics
• Porosity
• Head
• Hydraulic Conductivity
2
Porosity Basics
• Porosity n (or )
• Volume of pores is also the total volume – the solids volume
total
pores
V
Vn
total
solidstotal
V
VVn
3
Porosity Basics
• Can re-write that as:
• Then incorporate:• Solid density: s
= Msolids/Vsolids
• Bulk density: b
= Msolids/Vtotal • bs = Vsolids/Vtotal
total
solidstotal
V
VVn
total
solids
V
Vn 1
s
bn
1
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
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
6
Effective
Porosity
7
Effective
Porosity
8
Porosity Basics
• Volumetric water content ()– Equals porosity for
saturated system total
water
V
V
9
Sand and Beads
Courtesey C.L. Lin, University of Utah
10
Aquifer Material Aquifer Material (Miami Oolite)(Miami Oolite)
11
Aquifer MaterialAquifer MaterialTucson recharge siteTucson recharge site
12
Aquifer MaterialAquifer Material
• X-Ray Tomography
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
Borehole Televiewer Data
• New USGS Project
Image provided courtesy of A. Manda, Florida International University and the United States Geological Survey.
15
Thresholding
16
3-D Coordinate Extraction
• Columns map to x,y
• Rows map to z
sinrx cosry
17
Omnidirectional Sample Variogram
0
0.05
0.1
0.15
0.2
0.25
0 1 2 3 4 5 6 7
sem
iva
rian
ce
distance
5661166
16938663
28780654
39918522
48828731
6355468072936724
8569633895861073106363138118762364128892085139929608155357118163361233175380856190054284201109314213315963222894000237246324251821115266048328275098166292559477307462204321399484341996256354799851371674464395962224411647215436106202458820894491644811527426130566204562614891956702184847902810370910845656708908389644702534599093810568090621547591632523372192509864474491170841481657708470199590458817905453116174443307984433175701430640602419882764410727884410520789402346728400397900392321195387234344383705616376623821375675454367845128366827160364425285355071850356956628347715921347989628344737596335893999
BH1
# # 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
Approximate Simple Variogram Model
0
0.05
0.1
0.15
0.2
0.25
0 1 2 3 4 5 6 7
sem
iva
rian
ce
distance
5661166
16938663
28780654
39918522
48828731
6355468072936724
8569633895861073106363138118762364128892085139929608155357118163361233175380856190054284201109314213315963222894000237246324251821115266048328275098166292559477307462204321399484341996256354799851371674464395962224411647215436106202458820894491644811527426130566204562614891956702184847902810370910845656708908389644702534599093810568090621547591632523372192509864474491170841481657708470199590458817905453116174443307984433175701430640602419882764410727884410520789402346728400397900392321195387234344383705616376623821375675454367845128366827160364425285355071850356956628347715921347989628344737596335893999
BH1
0.0639973 Nug(0) + 0.178246 Exp(0.622207)
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)
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
20
• Use ImageJ for raw volume creation from slice data
• Visualize with 3dView
21
(Unconditioned) Rock Simulation
22
Aquifer Material Aquifer Material (Keys limestone)(Keys limestone)
23
Aquifer Material Aquifer Material (Keys limestone)(Keys limestone)
24
Bioturbated Aquifer Material
25
Aquifer MaterialAquifer Material
http://www.uta.edu/geology/geol1425earth_system/images/gaia_chapter_5/sedimentary_structures.htm
26
Aquifer Material (CA Coast)Aquifer Material (CA Coast)
27
Aquifer Material (CA Coast)Aquifer Material (CA Coast)
28
Aquifer Material (CA Coast)Aquifer Material (CA Coast)
29
Aquifer Material (CA Coast)Aquifer Material (CA Coast)
30
(CA Coast)(CA Coast)
31
Karst (MN)
http://course1.winona.edu/tdogwiler/websitestufftake2/SE%20Minnesota%20Karst%20Hydro%202003-11-22%2013-23-14%20014.JPG
32
Karst
http://www.fiu.edu/~whitmand/Research_Projects/tm-karst.gif
33
Ground Water Flow
• Pressure and pressure head
• Elevation head
• Total head
• Head gradient
• Discharge
• Darcy’s Law (hydraulic conductivity)
• Kozeny-Carman Equation
34
Multiple Choice:Water flows…?
• Uphill
• Downhill
• Something else
35
Pressure
• Pressure is force per unit area• Newton: F = ma
– Fforce (‘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)
36
Pressure and Pressure Head
• Pressure relative to atmospheric, so P = 0 at water table
• P = ghp
– density– g gravity
– hp depth
37
P = 0 (= Patm)
Pre
ssur
e H
ead
(incr
ease
s w
ith d
epth
bel
ow s
urfa
ce)
Pressure Head
Ele
vati
on
Head
38
Elevation Head
• Water wants to fall
• Potential energy
39
Ele
vatio
n H
ead
(incr
ease
s w
ith h
eigh
t ab
ove
datu
m)
Eleva
tion
Head
Ele
vati
on
Head
Elevation datum
40
Total Head
• For our purposes:
• Total head = Pressure head + Elevation head
• Water flows down a total head gradient
41
P = 0 (= Patm)
Tot
al H
ead
(con
stan
t: h
ydro
stat
ic e
quili
briu
m)
Pressure Head
Eleva
tion
Head
Ele
vati
on
Head
Elevation datum
42
Head Gradient
• Change in head divided by distance in porous medium over which head change occurs
• dh/dx [unitless]
43
Discharge
• Q (volume per time)
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
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
Intrinsic Permeability
gkK w
L T-1 L2
47
Kozeny-Carman Equation
1801
2
2
3md
n
nk
48
Beads
• 80 -120 mesh
• = 224 -149 m
• Average size: 186.5 m
49
Observations/Computations
• Intrinsic permeability?
• Hydraulic conductivity?
50
Darcy’s Law
• Q = -KA dh/dl
• Darcy ‘velocity’:qx = -Kx ∂h/∂x
• Mean pore water velocity:v = q/ne
51
More on gradients1 2 3 4 5 6 7 8 9 10 11
2.445659 2.445659 2.937225 3.61747 4.380528 5.182307 5.999944 6.817582 7.619361 8.382418 9.062663 9.554228 9.5542283.399753 3.399754 3.685772 4.152128 4.722335 5.348756 5.99989 6.651023 7.277444 7.847651 8.314006 8.600023 8.6000234.067833 4.067834 4.253985 4.582937 5.007931 5.490497 5.999838 6.509179 6.991744 7.416737 7.745689 7.931838 7.9318384.549766 4.549768 4.679399 4.917709 5.235958 5.605464 5.999789 6.394115 6.76362 7.081868 7.320177 7.449806 7.4498064.902074 4.902077 4.99614 5.172544 5.412733 5.695616 5.999745 6.303874 6.586756 6.826944 7.003347 7.097408 7.0974085.160327 5.160329 5.230543 5.363601 5.546819 5.764526 5.999705 6.234885 6.452591 6.635808 6.768864 6.839075 6.8390755.348374 5.348377 5.402107 5.504502 5.646422 5.815968 5.999672 6.183375 6.35292 6.494838 6.597232 6.650959 6.6509595.482701 5.482704 5.52501 5.605886 5.718404 5.853259 5.999644 6.146028 6.280883 6.393399 6.474273 6.516576 6.5165765.574732 5.574736 5.609349 5.675635 5.768053 5.879029 5.999623 6.120216 6.231191 6.323607 6.389891 6.424502 6.424502
5.63216 5.632163 5.662024 5.719259 5.799151 5.895187 5.999608 6.10403 6.200064 6.279955 6.337188 6.367045 6.3670455.659738 5.659741 5.68733 5.740232 5.814114 5.902965 5.999601 6.096237 6.185087 6.258968 6.311867 6.339453 6.339453
5.659741 5.68733 5.740232 5.814114 5.902965 5.999601 6.096237 6.185087 6.258968 6.311867 6.339453 6.339453
1 2 3 4 5 6 7 8 9 10 11
S1
S2
S3
S4
S5
S6
S7
S8
S9
S10
S11
S12
10.5-11
10-10.5
9.5-10
9-9.5
8.5-9
8-8.5
7.5-8
7-7.5
6.5-7
6-6.5
5.5-6
5-5.5
4.5-5
4-4.5
3.5-4
3-3.5
2.5-3
2-2.5
1.5-2
52
More on gradients
• Three point problems:
h
h
h
400 m
412 m
100 m
53
More on gradients
• Three point problems:– (2 equal heads)
h = 10m
h = 10m
h = 9m
400 m
412 m
100 m
CD • Gradient = (10m-9m)/CD
• CD?– Scale from map– Compute
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