02 by liwenting

VIEWS: 7 PAGES: 29

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




                               1
            Porosity Basics
• Porosity n (or f)

• Volume of pores is
  also the total volume
  – the solids volume




                              2
              Porosity Basics
• Can re-write that as:

• Then incorporate:
• Solid density: rs
  = Msolids/Vsolids
• Bulk density: rb
  = Msolids/Vtotal
• rb/rs = Vsolids/Vtotal
                                3
Cubic Packings and Porosity




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




                                                                       4
             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
  beads: n ≈ 0.4
          Smith et al. 1929, PR 34:1271-1274        5
Effective
Porosity



            6
Effective
Porosity



            7
            Porosity Basics

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




                              8
Sand and Beads




                                         9
Courtesey C.L. Lin, University of Utah
Aquifer Material
 (Miami Oolite)




                   10
           Ground Water Flow
•   Pressure and pressure head
•   Elevation head
•   Total head
•   Head gradient
•   Discharge
•   Darcy’s Law (hydraulic conductivity)
•   Kozeny-Carman Equation

                                           11
          Multiple Choice:
          Water flows…?
• Uphill
• Downhill
• Something else




                             12
                 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)


                                       13
  Pressure and Pressure Head
• Pressure relative to atmospheric, so P = 0
  at water table
• P = rghp
  – r density
  – g gravity
  – hp depth




                                           14
                        Elevation




     Head
                                                   P = 0 (= Patm)




                       Pressure Head
            (increases with depth below surface)
15
            Elevation Head
• Water wants to fall
• Potential energy




                             16
                              Elevation




     Head
            Elevation datum




                      Elevation Head
            (increases with height above datum)
17
              Total Head
• For our purposes:
• Total head = Pressure head + Elevation
  head
• Water flows down a total head gradient




                                           18
                              Elevation




     Head
            Elevation datum
                                                      P = 0 (= Patm)




                            Total Head
                (constant: hydrostatic equilibrium)
19
           Head Gradient
• Change in head divided by distance in
  porous medium over which head change
  occurs
• dh/dx [unitless]




                                          20
               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

                                      21
              Darcy’s Law
• Q = -K dh/dx A
  where K is the hydraulic
  conductivity and A is the
  cross-sectional flow area




                                           1803 - 1858

                                                               22
                              www.ngwa.org/ ngwef/darcy.html
               Darcy’s Law
• Q = K dh/dl A

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

• Mean pore water velocity:
  v = q/ne
                                            23
Intrinsic Permeability




L   T-1   L2
                         24
Kozeny-Carman Equation




                         25
Apparent K as a function of hydraulic gradient




                   t=1




                            Darcy-Forchheimer Equation




   • Gradients could be higher locally
                                                         26
   • 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




                            28
     • 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,
                                                                                                                            29
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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