# 02

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```					         Ground Water Basics
•   Porosity
•   Hydraulic Conductivity
•   Transmissivity

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Porosity Basics
• Porosity n (or f)              V pores
n
• Volume of pores is             Vtotal
also the total volume
– the solids volume
Vtotal  Vsolids
n
Vtotal
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Porosity Basics
Vtotal  Vsolids
•   Can re-write that as: n
Vtotal
• Then incorporate:
• Solid density: rs               Vsolids
= Msolids/Vsolids
n  1
Vtotal
• Bulk density: rb
= Msolids/Vtotal
rb
• rb/rs = Vsolids/Vtotal    n  1
rs       3
Cubic Packings and Porosity

Simple Cubic            Body-Centered Cubic      Face-Centered Cubic
n = 0.48                   n = 0. 26                    n = 0.26

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http://members.tripod.com/~EppE/images.htm
FCC and BCC have same porosity

http://uwp.edu/~li/geol200-01/cryschem/

• Bottom line for randomly packed
Smith et al. 1929, PR 34:1271-1274        5
Effective
Porosity

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Effective
Porosity

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Porosity Basics

• Volumetric water
Vwater
content (q)
– Equals porosity for
q
saturated system         Vtotal

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Courtesey C.L. Lin, University of Utah
Aquifer Material
(Miami Oolite)

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Ground Water Flow
•   Discharge
•   Darcy’s Law (hydraulic conductivity)
•   Kozeny-Carman Equation

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Multiple Choice:
Water flows…?
• Uphill
• Downhill
• Something else

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Pressure
• Pressure is force per unit area
• Newton: F = ma
– F 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 relative to atmospheric, so P = 0
at water table
• P = rghp
– r density
– g gravity
– hp depth

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Elevation

P = 0 (= Patm)

(increases with depth below surface)
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• Water wants to fall
• Potential energy

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Elevation

Elevation datum

(increases with height above datum)
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• For our purposes:

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Elevation

Elevation datum
P = 0 (= Patm)

(constant: hydrostatic equilibrium)
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• Change in head divided by distance in
porous medium over which head change
occurs
• dh/dx [unitless]

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Discharge
• Q (volume per time)

Specific Discharge/Flux/Darcy
Velocity
• q (volume per time per unit area)
• L3 T-1 L-2 → L T-1

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Darcy’s Law
• Q = -K dh/dx A
where K is the hydraulic
conductivity and A is the
cross-sectional flow area

1803 - 1858

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www.ngwa.org/ ngwef/darcy.html
Darcy’s Law
• Q = K dh/dl A

• Specific discharge or Darcy ‘velocity’:
qx = -Kx ∂h/∂x
…

• Mean pore water velocity:
v = q/ne
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Intrinsic Permeability

rwg
K k

L   T-1   L2
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Kozeny-Carman Equation

3      2
n      d
k               m

1  n  180
2

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Apparent K as a function of hydraulic gradient
Approximate Reynolds Number
0.001    0.01          0.1         1       10       100     1000
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Hydraulic Conductivity (m s-1)

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30
t=1
25

20

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10                            Darcy-Forchheimer Equation

5

0
1.E-09   1.E-08     1.E-07        1.E-06   1.E-05   1.E-04   1.E-03

• Gradients could be higher locally
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• Expect leveling at higher gradient?
Streamlines at different
Reynolds Numbers
Re = 0.31                               Re = 152
K = 34 m/s                              K = 20 m/s

•   Streamlines traced forward and backwards from eddy locations and hence
begin and end at different locations                                   27
Transmissivity
• T = Kb

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• T > 1,600,000 ft2 d-1
• 7,000 gpm wells

4-7 m3s-1

Renken, R.A., Dixon, J., Koehmstedt, J., Lietz, A.C., Ishman, S., Marella, R.L., Telis, P., Rogers, J., and Memberg, S., 2005,
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Impact of Anthropogenic Development on Coastal Ground-Water Hydrology in Southeastern Florida, 1900-2000: Reston, Va.,
U.S. Geological Survey Circular 1275, 77 p.

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