1 Ground Water Basics Porosity Head Hydraulic Conductivity

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