Physical Properties of Aquifers
Groundwater Hydraulics
Daene C. McKinney
Outline
• Porous Medium
–
–
–
–
–
–
–
Porosity
Moisture Content
Particle Size
Distribution of water in subsurface
Capillary Pressure
Soil Moisture Characteristic Curves
Specific Yield and Retention
• Piezometric head in aquifers
• Aquifer Types
– Aquifer Storage
Porous Medium
•
•
•
•
Groundwater
– All waters found beneath the
ground surface
– Occupies pores (void space space
not occupied by solid matter)
Porous media
– Numerous pores of small size
– Pores contain fluids (e.g., water
and air)
– Pores act as conduits for flow of
fluids
Type of rocks and their
– Number, size, and arrangement
of pores
– Affect the storage and flow
through a formation.
Pores shapes are irregular
– Differences in the minerals
making up the rocks
– Geologic processes experienced
by them.
Continuum Approach to Porous
Media
• Pressure, density etc. apply to fluid elements that are
large relative to molecular dimensions, but small
relative to the size of the flow problem
• We adopt a Representative Elementary Volume (REV)
approach
• REV must be large enough to contain enough pores to
define the average value of the variable in the fluid
phase and to ensure that the pore-to-pore fluctuations
are smoothed out
• REV must be small enough that larger scale
heterogeneities do not get averaged out (layering, etc.)
Porosity
Soil volume V
(Saturated)
Pore
with
water
solid
Porosity
• Property of the voids of
the porous medium
• % of total volume
occupied by voids
Cubic
Packing
Soil volume V
(Saturated)
Pore
with
water
solid
Rhombo
Packing
Porosity
Porosity: total volume of soil
that can be filled with water
V
f= i
V
f=
Soil volume V
(Saturated)
V - Vs
V
V = Total volume of element
Vi = Volume of Pores
Vs = Volume of solids
Pore
with
water
solid
r - rd
r
f= m
= 1- d
rm
rm
rm = particles density (grain density) Void Ratio:
Vi
f
e
=
=
rd = bulk density
Vs 1- f
Typical Values of Porosity
Material
Porosity (%)
Peat Soil
60-80
Soils
50-60
Clay
45-55
Silt
40-50
Med. to Coarse Sand
35-40
Uniform Sand
30-40
Fine to Med Sand
30-35
Gravel
30-40
Gravel and Sand
30-35
Sandstone
10-20
Shale
1-10
Limestone
1-10
8
Volumetric Water Content
Soil volume V
(Unsaturated)
Saturation
Soil volume V
(Unsaturated)
Particle Size of Some Soils
11
Particle Size Distribution
Poorly sorted
silty fine to
medium sand
Well sorted fine sand
• Particle size distribution curves
– Relative % of grain sizes
• Soil classification standards
• Soil texture
12
Particle Size Distribution
Sand
49%
Clay
40%
Soil Characteristics
of Cyprus Soil
Sample
13
Occurrence of Groundwater
• Ground water occurs when
water recharges the subsurface
through cracks and pores in soil
and rock
• Shallow water level is called
the water table
14
Distribution of Water in Subsurface
Moisture Profile
•
Different zones
–
•
Unsaturated Zone
–
•
Water moves down
(up) during infiltration
(evaporation)
Capillary fringe
–
–
•
Water held by capillary
forces, water content
near field capacity
except during
infiltration
Soil zone
–
•
depend on % of pore
space filled with water
Saturated ar base
Field capacity at top
Saturated Zone
–
Fully saturated pores
Field capacity - Water remaining after gravity drainage
Wilting point - Water remaining after gravity drainage &
evapotranspiration
Soil Profile
Description
Saturation
• Saturation
• Water Content
• Water Saturation
Soil volume V
(Unsaturated)
Surface Tension
• Below interface
– Forces act equally in all directions
• At interface
– Some forces are missing
– Pulls molecules down and together
– Like membrane exerting tension on
the surface
• Curved interface
Interface
water
air
Net force
inward
– Higher pressure on concave side
• Pressure increase is balanced by
surface tension
–
s = 0.073 N/m (@
20oC)
• Capillary pressure
– Relates pressure on both sides of interface
No net force
Surface Tension
sgl
gas
ssg
b < 90o - liquid is wetting the solid
b > 90o - liquid is non-wetting the solid
b
solid
air
air
solid
solid
b
Hg
b
water
Mercury nonwetting solid
Water wetting solid
liquid
ssl
Capillary Pressure
• Two immiscible fluids in contact exhibit a
discontinuity in pressure across the interface
separating them.
• This pressure difference is capillary pressure pc
• It depends on the curvature of the interface.
pnw is the pressure in the nonwetting fluid (air, say)
pw is the pressure in the wetting fluid (water, say)
Capillary Pressure
Air
pair
z
pair
y
p
Solid
pw
Solid
Water
pc
r
Rise of water in a capillary tube. Capillary forces must balance the weight of water
Capillary pressure head
Capillary Pressure
Air
pair
z
B
Negative
pressure
y
Solid
A pw
p
Positive
pressure
pair
Water
pc
r
(A) Below the water level
(B) Above the water level
Difference in pressure across the interface is
Solid
Drainage
• Drainage occurs when the water pressure in
the pores becomes less than the air pressure
• Interfacial tension prevents displacement of
water in the left pore
solid
Pore water
press. = -p
r
Pore air
press. = 0
solid
If pc increases, radius must decrease, or water occupies smaller pores.
Water recedes into pores small enough to support the interface with a radius required
to balance the capillary force. Water drains from the large pores first.
Energy in Flow Systems
Velocity head
p/g Pressure head
z Elevation head
v2/(2g)
v2/(2g)
EGL
HGL
p/g
v2/(2g)
z
Hydraulic grade line (HGL)
– height of water in
piezometer tube
datum
Energy grade line (EGL) –
Height of water in pitot tube
Piezometric Head
• Confined aquifer
h
p
g
z
• Unconfined aquifer
h
p
g
z
Pressure
p  0 head = 0
p
g
hz
z
Piezometric Head in Unsaturated
Flow
Soil volume V
(Unsaturated)
Saturated Zone
Water Table
Unsaturated Zone
qf
<0
=0
q<f
>0
pw > 0
pw = 0
pw < 0
Subsurface Pressure Distribution
z
 Capillary pressure head
in zone above water
table
y = y(q )
 Hydrostatic pressure
distribution exists below
the water table (p = 0).
¶p
= -g
¶z
Ground surface
Pressure is
negative above
water table
Unsaturated zone
y
Water table
Pressure is
positive below
water table
Saturated zone
p<0
z  0; p  0
d1
P  gd1  0
p0
p0
Soil Water Characteristic Curves

Vadose
Zone
Porosity
y = y(q )
Capillary
Zone
b
Critacal
Head
(Bubbling
Press.)
• Capillary pressure head
• Function of:
– Pore size distribution
– Moisture content
qo
Irreducible
Water content
y = y(q )
f
Porosity
Capillary Rise in Soils
Aquifer Types
•
Confined aquifer
–
–
•
Phreatic or water table
Bounded by a water table
Aquifer
– Store & transmit water
– Unconsolidated deposits sand and gravel,
sandstones etc.
Under pressure
Bounded by impervious layers
Unconfined aquifer
–
–
•
•
Aquitard
– Transmit don’t store water
– Shales and clay
Aquifer Storage
• Storativity (S) - ability of
an aquifer to store water
• Change in volume of
stored water due to
change in piezometric
head.
• Volume of water released
(taken up) from aquifer
per unit decline (rise) in
piezometric head.
Unit area
Unit decline
in head
Released
water
Aquifer Storage
• Fluid Compressibility (b)
• Aquifer Compressibility (a)
• Confined Aquifer
– Water produced by 2
mechanisms
1. Aquifer compaction due to
increasing effective stress
2. Water expansion due to
decreasing pressure
• Unconfined aquifer
– Water produced by draining
pores
V  arg
S = r g(a + fb )
S = Sy Unconfined Aquifer Storage
• Storativity of an
unconfined aquifer (Sy,
specific yield) depends
on pore space drainage.
• Some water will remain
in the pores - specific
retention, Sr
• Sy = f – Sr
Unit area
Unit decline
in head
Released
water
Porosity, Specific Yield, & Specific Retention
Sr  f  S y
Confined Aquifer Storage
• Storativity of a confined
aquifer (Ss) depends on
both the compressibility
of the water (b) and the
compressibility of the
porous medium itself
(a).
Unit area
Unit decline
in head
Released
water
Example
•
•
•
•
•
•
Storage in a sandstone aqufier
f = 0.1, a = 4x10-7 ft2/lb, b = 2.8x10-8 ft2/lb, g = 62.4 lb/ft3
ga  2.5x10-5 ft-1 and gbf  1.4x10-7 ft-1
Solid 
Fluid
2 orders of magnitude more storage in solid
b = 100 ft, A = 10 mi2 = 279,000,000 ft2
S = Ss*b = 2.51x10-3
• If head in the aquifer is lowered 3 ft, what volume is released?
V = SAh = 2.1x10-6 ft3
Summary
• Porous Medium
–
–
–
–
–
–
–
Porosity
Moisture Content
Particle Size
Distribution of water in subsurface
Capillary Pressure
Soil Moisture Characteristic Curves
Specific Yield and Retention
• Piezometric head in aquifers
• Aquifer Types
– Aquifer Storage