Transcript No Slide Title
Ground Water Hydrology Introduction - 2005
Philip B. Bedient Civil & Environmental Engineering Rice University
GW Resources - Quantity
• Aquifer system parameters • Rate and direction of GW flow • Darcy’s Law - governing flow relation • Dupuit Eqn for unconfined flow • Recharge and discharge zones • Well mechanics- pumping for water supply, hydraulic control, or injection of wastes
GW Resources - Quality
• Contamination sources • Contaminant transport mechanims • Rate and direction of GW migration • Fate processes-chemical, biological • Remediation Systems for cleanup
Trends in Ground Water Use
Ground Water: A Valuable Resource • Ground water supplies 95% of the drinking water needs in rural areas.
• 75% of public water systems rely on groundwater.
• In the United States, ground water provides drinking water to approximately 140 million people.
• Supplies about 40% of Houston area
Regional Aquifer Issues
Typical Hydrocarbon Spill
Aquifer Characteristics
1.
2.
3.
4.
5.
6.
7.
8.
Matrix type Porosity (n) Confined or unconfined Vertical distribution (stratigraphy or layering) Hydraulic conductivity (K) Intrinsic permeability (k) Transmissivity (T) Storage coefficient or Storativity (S)
Vertical Distribution of Ground Water
Vertical Zones of Subsurface Water
• Soil water zone: extends from the ground surface down through the major root zone, varies with soil type and vegetation but is usually a few feet in thickness • Vadose zone (unsaturated zone): extends from the surface to the water table through the root zone, intermediate zone, and the capillary zone • Capillary zone: extends from the water table up to the limit of capillary rise, which varies inversely with the pore size of the soil and directly with the surface tension
Typical Soil-Moisture Relationship
Soil-Moisture Relationship
• The amount of moisture in the vadose zone generally decreases with vertical distance above the water table • Soil moisture curves vary with soil type and with the wetting cycle
Vertical Zones of Subsurface Water Continued
• Water table: the level to which water will rise in a well drilled into the saturated zone • Saturated zone: occurs beneath the water table where porosity is a direct measure of the water contained per unit volume
Porosity
– Porosity averages about 25% to 35% for most aquifer systems – Expressed as the ratio of the volume of voids V v the total volume V: n = V v /V = 1 b / m to where: b m is the bulk density, and is the density of grains
Water
Porosity
Arrangement of Particles in a Subsurface Matrix Porosity depends on: • particle size • particle packing • Cubic packing of spheres with a theoretical porosity of 47.65%
• Rhombohedral packing of spheres with a theoretical porosity of 25.95%
Soil Classification Based on Particle Size (after Morris and Johnson)
Material
Clay Silt Very fine sand Fine sand Medium sand Coarse sand
Particle Size, mm
<0.004
0.004 - 0.062
0.062 - 0.125
0.125 - 0.25
0.25 - 0.5
0.5 - 1.0
Soil Classification…cont.
Material
Very coarse sand Very fine gravel Fine gravel Medium gravel Coarse gravel Very coarse gravel
Particle Size, mm
1.0 - 2.0
2.0 - 4.0
4.0 - 8.0
8.0 - 16.0
16.0 - 32.0
32.0 - 64.0
Particle Size Distribution Graph
Particle Size Distribution and Uniformity
• The uniformity coefficient U indicates the relative sorting of the material and is defined as D 60 /D 10 U is a low value for fine sand compared to alluvium which is made up of a range of particle sizes
Cross Section of Unconfined and Confined Aquifers
Unconfined Aquifer Systems
• Unconfined aquifer: an aquifer where the water table exists under atmospheric pressure as defined by levels in shallow wells • Water table: the level to which water will rise in a well drilled into the saturated zone
Confined Aquifer Systems
• Confined aquifer: an aquifer that is overlain by a relatively impermeable unit such that the aquifer is under pressure and the water level rises above the confined unit • Potentiometric surface: in a confined aquifer, the hydrostatic pressure level of water in the aquifer, defined by the water level that occurs in a lined penetrating well
Special Aquifer Systems
• Leaky confined aquifer: represents a stratum that allows water to flow from above through a leaky confining zone into the underlying aquifer • Perched aquifer: occurs when an unconfined water zone sits on top of a clay lens, separated from the main aquifer below
Ground Water Flow
Darcy’s Law Continuity Equation Dupuit Equation
Darcy’s Law
• Darcy investigated the flow of water through beds of permeable sand and found that the flow rate through porous media is proportional to the head loss and inversely proportional to the length of the flow path • Darcy derived equation of governing ground water flow and defined hydraulic conductivity K: V = Q/A where: A is the cross-sectional area V -∆h, and V 1/∆L
Darcy’s Law
V= - K dh/dl Q = - KA dh/dl
Example of Darcy ’ s Law
• • • • •
A confined aquifer has a source of recharge. K for the aquifer is 50 m/day, and n is 0.2.
The piezometric head in two wells 1000 m apart is 55 m and 50 m respectively, from a common datum. The average thickness of the aquifer is 30 m, The average width of flow is 5 km.
Calculate:
• • •
the Darcy and seepage velocity in the aquifer the average time of travel from the head of the aquifer to a point 4 km downstream
assume no dispersion or diffusion
The solution
• Cross-Sectional area 30(5)(1000) = 15 x 10 4 m 2 • Hydraulic gradient (55-50)/1000 = 5 x 10 -3 • Rate of Flow through aquifer Q = (50 m/day) (75 x 10 1 m 2 ) = 37,500 m 3 /day • Darcy Velocity: V = Q/A = (37,500m 3 /day) / (15 x 10 4 m 2 ) = 0.25m/day
Therefore:
• Seepage Velocity: V s = V/n = 0.25 / 0.2 = 1.25 m/day (about 4.1 ft/day) • Time to travel 4 km downstream: T = 4(1000m) / (1.25m/day) = 3200 days or 8.77 years •
This example shows that water moves very slowly underground.
Ground Water Hydraulics
• Hydraulic conductivity, K, is an indication of an aquifer’s ability to transmit water – Typical values: 10 -2 to 10 -3 cm/sec for Sands 10 -4 to 10 -5 cm/sec for Silts 10 -7 to 10 -9 cm/sec for Clays
Ground Water Hydraulics
Transmissivity (T) of Confined Aquifer
The product of K and the saturated thickness of the aquifer T = Kb - Expressed in m 2 /day or ft 2 /day - Major parameter of concern - Measured thru a number of tests - pump, slug, tracer
Ground Water Hydraulics
Intrinsic permeability (k)
Property of the medium only, independent of fluid properties Can be related to K by: K = k( g/µ) where: µ = dynamic viscosity = fluid density g = gravitational constant
Storage Coefficient
Relates to the water-yielding capacity of an aquifer S = Vol/ (A s H) – It is defined as the volume of water that an aquifer releases from or takes into storage per unit surface area per unit change in piezometric head - used extensively in pump tests.
• For confined aquifers, S values range between 0.00005 to 0.005
• For unconfined aquifers, S values range between 0.07 and 0.25, roughly equal to the specific yield
Regional Aquifer Flows are Affected by Pump Centers
Streamlines and Equipotential lines
Derivation of the Dupuit Equation - Unconfined Flow
Dupuit Assumptions
For unconfined ground water flow Dupuit developed a theory that allows for a simple solution based off the following assumptions: 1) The water table or free surface is only slightly inclined 2) Streamlines may be considered horizontal and equipotential lines, vertical 3) Slopes of the free surface and hydraulic gradient are equal
Derivation of the Dupuit Equation
Darcy’s law gives one-dimensional flow per unit width as:
q = -Kh dh/dx
At steady state, the rate of change of q with distance is zero, or OR
d/dx(-Kh dh/dx) = 0 (-K/2) d 2 h 2 /dx 2 = 0
Which implies that,
d 2 h 2 /dx 2 = 0
Dupuit Equation
Integration of d 2 h 2 /dx 2 = 0 yields
h 2 = ax + b
Where a and b are constants. Setting the boundary condition h = h o at x = 0, we can solve for b
b = h o 2
Differentiation of h 2 = ax + b allows us to solve for a,
a = 2h dh/dx
And from Darcy’s law,
hdh/dx = -q/K
Dupuit Equation
So, by substitution Setting h = h L 2 = h 0 2 Rearrangement gives
h 2 = h 0 2
– 2qL/K
– 2qx/K
q = K/2L (h 0 2 - h L 2 )
Dupuit Equation Then the general equation for the shape of the parabola is
h 2 = h 0 2 – x/L(h 0 2 - h L 2 )
Dupuit Parabola However, this example does not consider recharge to the aquifer.
Cross Section of Flow
q
Adding Recharge W Causes a Mound to Form
Divide
Dupuit Example
Example: 2 rivers 1000 m apart K is 0.5 m/day average rainfall is 15 cm/yr evaporation is 10 cm/yr water elevation in river 1 is 20 m water elevation in river 2 is 18 m Determine the daily discharge per meter width into each River.
Example
Dupuit equation with recharge becomes
h 2 = h 0 2 + (h L 2 - h 0 2 ) + W(x - L/2)
If W = 0, this equation will reduce to the parabolic Equation found in the previous example, and
q = K/2L (h 0 2 - h L 2 ) + W(x-L/2)
Given: L = 1000 m K = 0.5 m/day h 0 = 20 m h L = 28 m W = 5 cm/yr = 1.369 x 10 -4 m/day
Example
For discharge into River 1, set x = 0 m q = K/2L (h 0 2 - h L 2 ) + W(0-L/2) = [(0.5 m/day)/(2)(1000 m)] (20 2 m 2 – 18 m 2 ) + (1.369 x 10 -4 m/day)(-1000 m / 2)
q = – 0.05 m 2 /day
The negative sign indicates that flow is in the opposite direction From the x direction. Therefore,
q = 0.05 m 2 /day into river 1
Example
For discharge into River 2, set x = L = 1000 m: q = K/2L (h 0 2 - h L 2 ) + W(L-L/2) = [(0.5 m/day)/(2)(1000 m)] (20 2 m 2 – 18 m 2 ) + (1.369 x 10 -4 m/day)(1000 m –(1000 m / 2))
q = 0.087 m 2 /day into River 2
By setting q = 0 at the divide and solving for x d , the water divide is located 361.2 m from the edge of River 1 and is 20.9 m high
Flow Nets - Graphical Flow Tool Q = KmH / n n = # head drops m= # streamtubes K = hyd cond H = total head drop
Flow Net in Isotropic Soil
Portion of a flow net is shown below Y F
Curvilinear Squares
Flow Net Theory
1. Streamlines Y 2. Streamlines Y boundaries.
and Equip. lines are
.
are parallel to no flow 3. Grids are curvilinear squares, where diagonals cross at right angles.
4. Each stream tube carries the same flow.