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Прикладная
Гидрогеология
Yoram Eckstein, Ph.D.
Fulbright Professor 2013/2014
Tomsk Polytechnic University
Tomsk, Russian Federation
Spring Semester 2014
Useful links
http://www.onlineconversion.com/
http://www.digitaldutch.com/unitconverter/
http://water.usgs.gov/ogw/basics.html
http://water.usgs.gov/ogw/pubs.html
http://ga.water.usgs.gov/edu/earthgwaquifer.html
http://water.usgs.gov/ogw/techniques.html
http://water.usgs.gov/ogw/CRT/
III. Physical Properties of
water-bearing formations
Porosity of Earth Materials
The porosity of earth materials is
V
v
defined as the part of rock or soil
n
that is void space, often expressed as
V
T
a percentage:
Porosity has the units
of
3
L voids
3
L R.E.V .
where n is the porosity
Vv is the void volume
VT is the total volume.
R.E.V. = representative
elementary volume
Representative elementary
volume
Representative elementary
volume
Representative elementary
volume
Representative elementary
volume
Types of porosity
Primary porosity – porosity that
ocurred syngeneticly with the
geologic formation
Types of porosity
Primary porosity – porosity that ocurred
syngeneticly with the geologic formation
well-sorted sedimentary deposit having
high porosity
poorly sorted sedimentary deposit
having low porosity
Types of porosity
Primary porosity – porosity
that ocurred syngeneticly
with the geologic formation
well-sorted sedimentary deposit consisting of
pebbles that are themselves porous, so that
the deposit as a whole has a very high porosity
well-sorted sedimentary deposit whose
porosity has been diminished by the
deposition of mineral matter in the
interstices
Types of porosity
Secondary porosity – porosity that formed
postgeneticly with the geologic formation
rock rendered porous by
solution, e.g., development
of karst solution channels
in limestone
Types of porosity
Secondary porosity
– porosity that
formed postgeneticly
with the geologic
formation
rock rendered
porous by fracturing
Determination of porosity
in the laboratory
Porosity can be determined in a couple of ways in laboratory.
One method is to take a known volume of sediment and dry it
in an oven at 105 °C until it reaches a constant weight. This
removes moisture in the sample, but not water in the mineral
structure. The dried sample is then added to a known volume
of water, and the resulting increase in volume as determined
by the increased water level represents the volume of the
solid part of the sample.
The bulk volume (solid + voids) are determined by geometric
measurements (e.g., of a core sample).
Determination of porosity
in the laboratory
Alternatively, if one determines the bulk density of the
sample, one can calculate its porosity. The bulk density (ρb)
represents the density of the sample including its voids.
Recall that density is mass over volume, and the volume used
in bulk density is the volume of solids plus voids, or R.E.V.:
Mb
b  3
L R.E.V .
while the density of the solid part of the
sample (ρs) does not include the voids:
For most rock and soil, the
particle density is 2.65 g⋅cm-3
Msolid
s  3
L solid.
Determination of porosity
in the laboratory
b
n 1 
s
ρs ≈ 2.65 g⋅cm-3
Porosity ranges in
unconsolidated sediments
Material
Gravel, coarse
Gravel, fine
Sand, coarse
Sand, fine
Silt
Clay
Porosity (%)
24-36
25-38
31-46
26-53
34-61
34-60
Porosity ranges in consolidated
sedimentary rocks
Rock
Sandstone
Siltstone
Limestone
dolomite
Karst limestone
Shale
Porosity (%)
5-30
21-41
0-40
0-40
0-40
Porosity ranges in igneous
(crystalline) rocks
Rock
Dense crystalline
rocks
Fractured crystalline
rocks
Basalt
Weathered granite
Weathered gabbro
Porosity (%)
0-5
0-10
3-35
34-57
42-40
Grain-size distribution
The grain-size distribution expresses the percent
of the sediment mass that is finer than a given
grain size
Grain-size distribution
The grain-size distribution expresses the percent
of the sediment mass that is finer than a given
grain size
Grain-size distribution
The grain-size distribution expresses the percent
of the sediment mass that is finer than a given
grain size
Grain-size distribution
The grain-size distribution expresses the percent
of the sediment mass that is finer than a given
grain size
Grain-size
distribution
curve of a
silty fine to
medium
sand.
Grain-size distribution
An important parameter used to describe the grain size
distribution is the uniformity coefficient, Cu, which is
the ratio of the grain size for which 60% of the
sediment is finer by weight, to the grain size for which
10% of the sediment is finer by weight.
d
60
Cu =
d 10
A sediment with Cu less than 4 is well sorted. If Cu is
more than 6, the sediment is poorly sorted.
Grain-size distribution
homogeneous
heterogeneous
WELL SORTED
Coarse (sand-gravel)
POORLY SORTED
Coarse - Fine
WELL SORTED
Fine (silt-clay)
Permeability and Hydraulic Conductivity
High
Low
Sorting of material affects groundwater movement.
Poorly sorted (well graded) material is less porous than
well-sorted material.
Porosity and Permeability
 Porosity - the percentage of rock or sediment that
consists of voids or openings
 Measurement of a rock’s ability to hold water
 Loose sand has ~30-50% porosity
 Compacted sandstone may have only 10-20% porosity
 Permeability - the capacity of a rock to transmit
fluid through pores and fractures
 Interconnectedness of pore spaces
 Most sandstones and conglomerates are porous
and permeable
 Granites, schists, unfractured limestones are
impermeable
Specific Yield
Specific yield (Sy) is the volume of water that
drains from a saturated rock or sediment by
gravity, relative to the total volume of the
rock:
3
L yield
Sy  3
L R.E.V .
The water retained by the rock or
sediment is called pendular water,
and volume to the total volume of
the rock is called the specific
retention (Sr).
Sr = n - Sy
Specific Yield
Types of Terrestrial
Water
Surface
Water
Soil
Moisture
Ground water
Pores Full of Combination of
Air and Water
Unsaturated Zone / Zone of Aeration / Vadose
(Soil Water)
Zone of Saturation (Ground water)
Pores Full Completely with Water
Subsurface
Water
Zone of Aeration or Vadose
Saturated
Zone


Zone or Unsaturated Zone:
Overlies Phreatic Zone.
Pore spaces partly filled
with water. Contains soil
moisture.
Zone of Saturation or Phreatic Zone:
saturated zone overlying impermeable bed
rock. Water fills all the available pore spaces
Water Table: top of the zone of saturation
where not confined by impermeable rock
Specific Yield
Specific yield (Sy) is the volume of water that
drains from a saturated rock or sediment by
gravity, relative to the total volume of the
rock:
3
L yield
Sy  3
L R.E.V .
The water retained by the rock or
sediment is called pendular water,
and volume to the total volume of
the rock is called the specific
retention (Sr).
Sr = n - Sy
Water table follows the topography but more gently
Intersection of water table and ground surface
produces lakes, streams, spring, wetlands…
Ground water flows from higher elevation to lower,
from areas of lower use to higher use, from wet areas
to dry areas.
Permeability and hydraulic
conductivity
Permeability is a physical
property of material, describing
the ability of the material to
transmit fluids or gases
 In 1856, Darcy investigated
the flow of water through
sand filters for water
purification.
 h1 and h2 – water levels above
a datum level are called
hydraulic heads
Permeability and hydraulic
conductivity
Q∞A
Q∞
A – cross-sectional
area of the tube
hydraulic
gradient
Darcy’s observations:
dh
Q=-KA
dl
K – hydraulic
conductivity
v=
Q
A
=-K
dh
dl
Hydraulic conductivity
dh
Q=-KA
dl
K=
K units:
K=
- (L 3/T)
(L2)(L/L)
= (L/T)
-Q
A dh
dl
Hydraulic conductivity
In 1956 Hubbert pointed out
that Darcy’s coefficient of
proportionality K is a function
of both the porous medium
and the physical properties of
the fluid passing through it
d2
Q∞ γ
1/μ
γ=ρg
K=
-Q
A dh
dl
g
K  ki

Hydraulic conductivity
intrinsic permeability
g
K  ki

ki = C d2
(L2)
1 darcy = 9.87×10-9cm2
ki
in hydrogeology: intrinsic permeability
in oil industry:
permeability
Intrinsic permeabilities and hydraulic
conductivities for unconsolidated sediments.
Material
Intrinsic
Hydraulic
permeability conductivity
(darcys)
(cm/sec)
Clay
10-6 – 10-3
10-9 – 10-6
Silt, sandy silts, clayey
sands, till
Silty sands, fine sands
10-3 – 10-1
10-6 – 10-4
10-2 – 100
10-5 – 10-3
Well-sorted sands, glacial
outwash
Well-sorted gravel
100 – 102
10-3 – 10-1
101 – 103
10-2 – 100
Confined (artesian) and
unconfined (phreatic)
aquifers
Aquifers and Aquitards
 Hydrogeologists distinguish between rocks that transmit
water easily and rocks that do not easily transmit water.
 Aquifer – A rock that easily transmits water
 Aquitard – A rock that does not transmit water easily (i.e.
retards water motion)
 Aquifuge – A rock that does not transmit water at all
• Unconfined Aquifer – An
aquifer that has direct access to
the surface of the Earth
– Can be quickly recharged
by meteoric water
• Confined Aquifer – An aquifer
that is trapped below an
aquitard or aquifuge
Confined and
Unconfined
Aquifer
Unconfined Aquifer: open to atmosphere e.g.,
overlain by permeable rocks and soils
Confined aquifer: sandwiched between
aquitards
Artesian System: Water rises above the level
in aquifer because of hydrostatic pressure
Potentiometric surface: Height to which water
pressure would raise the water.
Storativity or the storage coefficient is the
volume of water released from storage per
unit decline in hydraulic head in the aquifer,
per unit area of the aquifer
Storage coefficient
It's the volume of water that a
permeable unit will absorb or loss
from storage per unit surface area per
unit change in head.
S = b Ss
S = Sy +h Ss
(Confined aquifer)
(Unconfined aquifer)
Confined (artesian) and
unconfined (phreatic)
aquifers
Groundwater Terms
artesian aquifer
aquifer
cone of depression
confined aquifer
Darcy's Law (all terms)
discharge
effluent stream
flow lines
flow net
groundwater
hydraulic conductivity
hydraulic gradient
hydraulic head
infiltration
influent stream
overdraft
overland flow
perched aquifer
permeability
pores
porosity
recharge
residence time
soil water
specific retention
specific yield
spring
unconfined aquifer
vadose zone
water table
water table contour lines
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