1 Ground Water Basics Porosity Head Hydraulic Conductivity Transmissivity

2 Porosity Basics Porosity n (or  ) Volume of pores is also the total volume – the solids volume

3 Porosity Basics Can re-write that as: Then incorporate: Solid density:  s = M solids /V solids Bulk density:  b = M solids /V total  b  s = V solids /V total

4 Cubic Packings and Porosity Simple Cubic Body-Centered Cubic Face-Centered Cubic n = 0.48 n = n = 0.26

5 FCC and BCC have same porosity Bottom line for randomly packed beads: n ≈ Smith et al. 1929, PR 34:

6 Effective Porosity

7

8 Porosity Basics Volumetric water content (  ) –Equals porosity for saturated system

9 Sand and Beads Courtesey C.L. Lin, University of Utah

10 Aquifer Material (Miami Oolite)

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

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

13 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 -2 m -2 = kg s -2 m -1 = Pa)

14 Pressure and Pressure Head Pressure relative to atmospheric, so P = 0 at water table P =  gh p –  density –g gravity –h p depth

15 P = 0 (= P atm ) Pressure Head (increases with depth below surface) Pressure Head Elevation Head

16 Elevation Head Water wants to fall Potential energy

17 Elevation Head (increases with height above datum) Elevation Head Elevation Head Elevation datum

18 Total Head For our purposes: Total head = Pressure head + Elevation head Water flows down a total head gradient

19 P = 0 (= P atm ) Total Head (constant: hydrostatic equilibrium) Pressure Head Elevation Head Elevation Head Elevation datum

20 Head Gradient Change in head divided by distance in porous medium over which head change occurs dh/dx [unitless]

21 Discharge Q (volume per time) Specific Discharge/Flux/Darcy Velocity q (volume per time per unit area) L 3 T -1 L -2 → L T -1

22 Darcy’s Law Q = -K dh/dx A where K is the hydraulic conductivity and A is the cross-sectional flow area ngwef/darcy.html

23 Darcy’s Law Q = K dh/dl A Specific discharge or Darcy ‘velocity’: q x = -K x ∂h/∂x … q = -K grad h Mean pore water velocity: v = q/n e

24 Intrinsic Permeability L T -1 L2L2

25 Kozeny-Carman Equation

26 Apparent K as a function of hydraulic gradient Gradients could be higher locally Expect leveling at higher gradient? Darcy-Forchheimer Equation  = 1

27 Streamlines at different Reynolds Numbers Streamlines traced forward and backwards from eddy locations and hence begin and end at different locations Re = 152 K = 20 m/s Re = 0.31 K = 34 m/s

28 Transmissivity T = Kb

29 T > 1,600,000 ft2 d-1 7,000 gpm wells Renken, R.A., Dixon, J., Koehmstedt, J., Lietz, A.C., Ishman, S., Marella, R.L., Telis, P., Rogers, J., and Memberg, S., 2005, Impact of Anthropogenic Development on Coastal Ground-Water Hydrology in Southeastern Florida, : Reston, Va., U.S. Geological Survey Circular 1275, 77 p. T>10 5 m 2 d -1 (K ~ 0.04 ms -1 ) 4-7 m 3 s -1