Ground Water Basics

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

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

Porosity Basics • Can re-write that as: • Then incorporate: • Solid density: rs = Msolids/Vsolids • Bulk density: rb = Msolids/Vtotal • rb/rs = Vsolids/Vtotal

Cubic Packings and Porosity Simple Cubic Body-Centered Cubic Face-Centered Cubic n = 0.48 n = 0. 26 n = 0.26 http://members.tripod.com/~EppE/images.htm

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

EffectivePorosity

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

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

Aquifer Material (Miami Oolite)

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

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

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)

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

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

Elevation Head • Water wants to fall • Potential energy

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

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

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

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

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

Darcy’s Law • Q = -K dh/dx A where K is the hydraulic conductivity and A is the cross-sectional flow area 1803 - 1858 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 gradh • Mean pore water velocity: v = q/ne

Intrinsic Permeability L2 L T-1

Kozeny-Carman Equation

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

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

Transmissivity • T = Kb

T > 1,600,000 ft2 d-1 • 7,000 gpm wells 4-7 m3s-1 T>105 m2d-1 (K ~ 0.04 ms-1) 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, 1900-2000: Reston, Va., U.S. Geological Survey Circular 1275, 77 p.

Ground Water Basics