Hydrologic Cycle

1
Hydrologic Cycle
Source US Geological Survey, http//ga.water.usgs
.gov/edu/watercycleinfiltration.html
2
Facts and Figures

• While estimates vary, 70-75 of the Earth is
  covered by water

3
Facts and Figures

• 97.2 Saline water in oceans
• 2.14 Ice caps and glaciers
• 0.61 Groundwater
• 0.009 Surface water (lakes, etc.)
• 0.005 Soil moisture (vadose zone)
• 0.001 Atmosphere

4
Facts and Figures

• 98 of the available water is groundwater
• In the North Carolina, and in the U.S.A., about
  50 of the drinking water is derived from
  groundwater

5
Subsurface Characteristics
Source US Geological Survey, http//ga.water.usgs
.gov/edu/watercycleinfiltration.html
6
Aquifer Characteristics
Source US Geological Survey, http//ga.water.usgs
.gov/edu/watercycleinfiltration.html
7
Basic Definitions
Porosity Vv/VT Void Ratio Vv/Vs Degree of
Saturation Vw/VV Moisture Content Mw/Ms
8
Q K (h1-h2)/l A K i A Q V A V K i
Source LaGrega et al. 2001, Hazardous Waste
Management, 2nd Edition, McGraw Hill
9
Saturated Zone

• Darcys Law
• Q vA kiA
• Where Q the rate of flow, v velocity, k a
  constant known as Darcy's coefficient of
  permeability,
• i hydraulic gradient, and A cross-sectional
  area for which flow can pass through. The
  equation can be rewritten as
• v ki Q/A
• Flow Velocity and Seepage Velocity If the
  hydraulic gradient, i, is unity, then the
  velocity, v, is equal to k. Also, v is called
  approach velocity or superficial velocity. The
  average effective velocity, vs, also known as
  seepage velocity of flow through the soil can be
  computed as
• vs v/n
  
• Where vs seepage velocity and n porosity

10
Source LaGrega et al. 2001, Hazardous Waste
Management, 2nd Edition, McGraw Hill
FIGURE 4-12 Flow lines and equipotentials.
11
4-4.
The groundwater contours are spaced at intervals
of about 50 m.
12
EXAMPLE 4-7. FLOW NET FOR A WATER TABLE AQUIFER.
13
FIGURE 4-13 Flow net for steady-state flow
through a homogeneous embankment.
14
Hydraulic Conductivity Measurement

• Laboratory
• Constant and Variable Head tests
• Rigid wall vs. flexible wall tests
• Consolidometers
• Field
• Groundwater
• Pump tests-one well vs. time, several wells vs.
  distance
• Slug tests
• Compacted or Surface Soils
• Lysimeters
• Infiltrometers

15
Constant and Falling Head MethodsSee class
notes
16
Triaxial-Flexible Wall System
17
Saturated Zone

• Darcys Law
• Q vA KiA
• Where
• Q the rate of flow,
• v discharge velocity,
• K a constant known as Darcy's coefficient of
  permeability or hydraulic conductivity
• i hydraulic gradient, and
• A cross-sectional area for which flow can pass
  through. The equation can be rewritten as
• v Ki Q/A

18
Constant Head Setup
Q K (h1-h2)/l A K i A Q V A v K i
Source LaGrega et al. 2001, Hazardous Waste
Management, 2nd Edition, McGraw Hill
19
Seepage Velocity

• Seepage Velocity, vs v/n
  
• Where
• vs seepage velocity and
• n porosity

20
Pipe Flow Example
21
Seepage Velocity Example

• Given K 70 ft/day ( 2.5 x 10-2 cm/s)
• n0.45
• How long for a conservative tracer to travel from
  MW-1 to MW-2?

22
Seepage Velocity Example

• How long for the center of mass of a conservative
  tracer to travel from MW-1 to MW-2?

MW-2
MW-1
166
180
23
Seepage Velocity Example

• Vs Ki / n v / n distance / time
• Distance is the actual flow path, not straight
  line distance

Right angle
24
Seepage Velocity Example

• Assume measured distance along flow path is 6,
  or 600 feet in the field
• i?H/L 180-166 / 600 14 / 600 0.023
• Vs Ki / n (70 ft/day)(0.023) / 0.45 3.58
  ft/day
• Vs distance / time Time distance / Vs
• Time 600 ft / 3.58 ft/day 167.7 days

25
Determining Groundwater Direction and Hydraulic
Gradient

• Simple three well system
• Process
• Identify groundwater elevation at three
  locations, in triangular fashion
• Draw a line between the highest and lowest
  elevation
• Identify point on the newly drawn line that
  corresponds to the elevation of the intermediate
  well

26
Determining Groundwater Direction and Hydraulic
Gradient
A
Well GW Elevation A 78.75 B 78.20 C 77.27
469 feet
B
533 feet
368 feet
C
Scale 1 100
27
Determining Groundwater Direction and Hydraulic
Gradient
A
GW Elev. 78.20
x
B
533 feet
Connecting point B to the point on the line AC
where the distance x is located creates an
equipotential line
C
Scale 1 100
28
Determining Groundwater Direction and Hydraulic
Gradient
Direction is computed as normal to equipotential
line If drawing is scaled, then distance can be
measured from equipotential line to Point C Lets
say that distance was measured at 200 feet Then
the hydraulic gradient, i?h/L(78.20-77.27) /
200 i0.0047
A
GW Elev. 78.20
B
C
Scale 1 100
29
Slug Test
Step 1 Identify monitoring well
Step 1 Insert slug (or bail out water)
Step 3 Record change in water versus time
30
Slug test Data
Assume Well screen (R) and well casing (r)
radius 2 in. 0.17 ft Assume length of well
(Le) screen 10 ft Hvorslev (1951) Method
31
Plot data
32
Plot semi-log
33
Use Equation
34
Chemical transport

• Transport in coarse soils advection
• Transport in fine-grained soils diffusion
• Molecular diffusion
• Net transport of molecules in a liquid or gas as
  a result of intermolecular collisions rather than
  turbulence or bulk transport, i.e., convection or
  mixing does not control it
• Rate of diffusion controlled by nature of
  diffusing substance and properties of medium

35
Chemical TransportDiffusion in Soils

• Reduced cross-sectional area (solids)
• Tortuosity (Le/L)
• Influence of electrical force fields
• Retardation as a result of chemical reactions in
  fluid and media
• Biodegradation (organics)
• Effective Diffusion Coefficient
• D ?aD0
• ?a 0.01 to 0.5, accounts for porosity and
  tortuosity
• Values for D0 typically on the order of 10-5
  cm2/s (in water)

36
Ficks First and Second Laws

• First Law, JD D (?C/ ?L)A
• Steady state conditions

100 Solute Concentration
Contaminant Free Flush
?L
?C
Concentration
Distance from source
37
Ficks First and Second Laws

• Second Law
• Unsteady state conditions

100 Solute Concentration
Contaminant Free Flush
?L
?C
Concentration
t1
t2
t3
Distance from source
38
Unsteady Diffusion Mass Transport
39
Sample Problem-Diffusion
Backfill Material
Ground Surface
Direction of Contaminant Plume
Clean Soil
C Co
C 0
Bedrock
40
Sample Problem Diffusion

• Determine the time required for 25 of the source
  concentration to reach the other side of the
  slurry wall
• Given
• D 5 x 10-10 m2/s
• x 90 cm

41
Sample Problem Diffusion

• C/C0 0.25
• erfc(B) 0.25
• From table, B ? 0.80

42
Organization

• Contaminant Barriers
• Diffusion
• Advection/Dispersion
• Retardation/Distribution Coefficients

43
Advection-Dispersion

• Dispersion includes the effects of molecular
  diffusion as well as velocity-induced mixing

44
Advection-Dispersion
Ogata and Banks (1961)
Short Form
C(x ? ?, t) 0
C(0, t) Co
C(x, 0) 0
45
Advection-Dispersion

• Transport in compacted clay dominated by
  diffusion

46
Organization

• Contaminant Barriers
• Chemical Compatibility
• Diffusion
• Advection/Dispersion
• Retardation/Distribution Coefficients

47
Advection-Dispersion

• Include a new term
• R Retardation coefficient
• Mass transport across liners

48
Advection Dispersion

• Retardation coefficient
• Increase dry density or distribution coefficient
  to improve attenuation

49
Advection Dispersion
50
Advection-Dispersion
Ogata and Banks (1961)
Short Form
C(x ? ?, t) 0
C(0, t) Co
C(x, 0) 0
51
Laboratory Measurements
52
Traditional and Low-Cost Additives
53
Contaminant Transport