Transcript Slide 1

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/
IV. Physical Properties of
water-bearing formations
ρs ≈ 2.65 g⋅cm-3
Porosity of Sedimentary Rocks
Primary Porosity:
- porosity between grains
- acquired syngenetically
with the rock or sediment
- sedimentary rocks usually have lower porosity than
unconsolidated sediment because of compaction, and
infilling of cementing material (e.g. calcite, dolomite,
silica), although dissolution can reverse the latter
effect
 Effective porosity is the fraction of the
porosity that is available for transporting
water (excludes fraction of pores too small
to hold water, or those that are not interconnected
 - can be measured in the lab directly by
saturating a dried sample of known volume
and measuring water uptake in a sealed
chamber over time
 - for unconsolidated coarse-grained
sediments there is no significant difference
Uniformity
coefficient
- measure of sorting
On a grain-size
vs %finer plot:
d60 is the grain size diameter that corresponds to
60% finer by weight
d10 is the grain size diameter that corresponds to 10%
finer by weight (i.e. d60 is coarser than d10)
 Cu < 4 is well sorted
 Cu > 6 is poorly sorted
Secondary Porosity:
- porosity acquired post-genetically
 Secondary pores (fractures) can be enlarged
through dissolution by the ground water flow
 sedimentary rock may have primary porosity from
deposition and secondary porosity from
fractures along bedding planes
 secondary porosity also possible in cohesive
sediments through wetting/drying, tectonic
activity, etc.
 limestones, dolomites, gypsum can all have
deposition reversed
 when in groundwater zone dissolution can occur
 flow starts initially through limited pore spaces,
fractures, and bedding planes, and porosity
enlarges over time
Porosity of Plutonic and
Metamorphic Rocks
 primary porosity extremely low,
but often not zero
 porosity increased over time by
weathering and fracturing
 fracturing increases porosity
of crystalline rocks 2 to 5%
Porosity of Plutonic and
Metamorphic Rocks
 chemical and physical weathering
increases with porosity
 highly weathered plutonic and
metamorphic rocks can have
porosities between 30 to 60%
 sheet-like structures
of weathering
minerals such as
micas can have very
high porosities
Porosity of Volcanic Rocks
 lava cools rapidly at surface, traps degassing
products
 holes in rock (vesicular) may or may not be
interconnected
 pumice (very high gas content) can have porosity
approaching 90% (but effective porosity if not this
high)
Porosity of Volcanic Rocks
 cracks form during cooling
 volcanic rocks vary in porosity but can be very high
 basalt has lower gas content with porosity between
1 and 12%
 weathering of volcanic deposits will also increase
porosity
Physical Properties
Density of Fluid - mass per unit volume
(e.g., kg/m3 or g/cm3).
Dynamic Viscosity of Fluid - resistance
to relative flow of a Newtonian
fluid (Pa-s or poise (g/s-cm))
Bulk Modulus - Proportionality constant
between density and pressure.
Inverse of compressibility (Pa or
kg/cm2)
Properties of Earth Materials
associated with porosity
Specific Yield (Sy) = ratio of the volume of
water that drains from a saturated rock owing
to the attraction of gravity to the total volume
of the rock.
Specific Retention (Sr) = ratio of the volume
of water a rock can retain against gravity
drainage to the total volume of the rock.
n = Sy + Sr
Maximum specific yield occurs in medium to
coarse sand size sediments.
http://techalive.mtu.edu/meec/module06/Percolation.html
Hydraulic Conductivity
of saturated media
and Darcy’s Law
- ability of the rock to transmit and hold water
are the most important hydrologic
properties
- only effective porosity is important with
regards to groundwater flow
- vesivcular basalt - lack of interconnectivity
- clays and shale – Sr to high in small pores t
Darcy’s experiment
Reality
For educational purposes
Darcy’s experiment
Henry Darcy in 1856 was playing around with
movement of water through sand filtration columns
for the City of Dijon, France.
Darcy found that the flow of water through a bed of
“a given nature” is:
 - proportional to the difference in the height of
the two ends,
 - inversely proportional to the length of the flow
path
 - proportional to the x-sectional area of the pipe
 - flow is further related to a coefficient dependent
on the nature of the media
Hydraulic conductivity
 Fluid density and viscosity depend on temperature,
salinity and pressure.
 Intrinsic Permeability is representative of the
porous medium alone. It depends on size of
openings, degree of interconnection, and amount of
open space. Thus, permeability depends on grain
size and sorting. Coarse grained and well-sorted
sediments have higher permeabilities.
Measuring Hydraulic
Conductivity
Constant Head Permeameter
Constant head test
Recommended for
coarse-grained soils.
Steady total head drop Dh is
measured across gauge length
L, as water flows through a
sample of cross-section area A.
Measuring Hydraulic
Conductivity
Falling Head Permeameter
Recommended for
fine-grained soils.
Total head h in standpipe of area
a is allowed to fall; heads h1 and
h2 are measured at times t1 and t2.
Hydraulic gradient Dh/L varies
with time.
Range of
values of
hydraulic
conductivity
and
permeability
for various
rocks and
sediments
Storativity (storage coefficient)
Water is released from storage via:
1. decrease in fluid pressure
2. increase in pressure from
overburden
Storativity (storage coefficient)
S
the volume of water that a permeable
unit will absorb or expel from storage
under unit surface area per unit change
in hydraulic head
Storativity (storage coefficient)
S = 0.02 to 0.3
S ~ Sy
S > 0.005
Storativity (storage coefficient)
Example Problem: An unconfined aquifer
with a storativity of 0.13 has an area
of 123 km2. The water table drops 0.9 m
during a drought.
How much water was lost from storage?
Specific Storage (elastic
storage coefficient)
Ss
The volume of water that a unit
volume of aquifer releases from
storage under a unit decline in
hydraulic head.
S = Ss × b
Compressibility and
Effective Stress
A.
Compressibility (general)
When pressure is applied to the aquifer,
a reduction of volume can occur in three
primary ways:
 compaction of water
 compression of
individual sand grains
 rearrangement of sand
grains into more closelypacked configuration
Compressibility and
Effective Stress
A.
Compressibility (general)
Compressibility and
Effective Stress
A.
Compressibility (general)
Compressibility and
Effective Stress

Compressibility of the Aquifer (α)
and Effective Stress
C.
Compressibility of Porous Medium
1. “In general”….Terzaghi (1925)
Stress Total
Fluid Pressure + Effective Stress
σt = P + σe
dσt = dP + dσe and
dP = -dσe
Stress Total
Fluid Pressure + Effective Stress
σt = P + σe
dσt = dP + dσe
dP = -dσe
dP = ρwgdh
Compressibility of the Aquifer (α)
and Effective Stress
C.
Compressibility of Porous Medium
α = dVt/Vt
dP
α = db/b
dP
Linking the Parameters of α, β, Ss
A.
Water produced by the compaction of
the aquifer
dVwater = ρgα
B. Water produced from expansion of
water
dVwater = ρgnβ
Linking the Parameters of α, β, Ss
Water produced by the compaction of
the aquifer
B. Water produced from expansion of
water
C. The Link
A.
dVwater = ρgα
dVwater = ρgnβ
dVwater from α + dVwater from β = Ss
ρgα + ρgnβ = Ss and ρg(α + nβ) = Ss
Linking the Parameters of α, β, Ss
“ a problem to work….”
A confined aquifer with initial thickness of
45 m compacts by 0.20 m when
hydraulic head is lowered by 25m.
a) what is the compressibility of the
aquifer?
b) If the porosity of the aquifer is 12%
after compaction, what is the
storativity of the aquifer?
Near Las Vegas
Earth Fissures
Approximate maximum subsidence amounts as of
1997 for selected locations in the Southwest
Arizona
Nevada
Las
Vegas
California
Texas
El
1
6 ft
Paso ft
Eloy
15
ft
West of
Phoenix
18
ft
New Mexico
Southwest of 29
Mendota
ft
Tucson
<1
ft
Albuquer <1
que
ft
Davis
6 ft Lancaster
Mimbres
Santa Clara
2 ft
Basin
Valley
Ventura
4 ft
12ft
2 ft
Hous 9
ton
ft
Now we can use
interferometric
processing of
Synthetic
Aperture Radar
(SAR) data.