Transcript Hydrogeologyx

Hydrogeology
Groundwater flow and Darcy’s law
– Experiment by Henry Dracy:
– Principles of groundwater flow
•
(steady state flow)
Set up principle of Darcy’s experiment
(Bear &Verruijt’in (1987).
Page 2
Conclusions of Darcy
 Indicated that steady state flow is a function of hydraulic head and
coefficient of hydraulic conductivity (characteristic of the soil)
• Flow is maintained by differences in hydraulic head, not (only) pressure
differences.
• Differences of hydraulic head can be used to assess the tendency water
to flow from one point to the other in soil
 Potential energy of water can be described in terms of hydraulic head or
fluid potential
 Hydraulic head : potential energy/unit weight (physical dimension L
length)
 Potential = potential energy/unit mass (dimension L2/T2, L= length, T=
time)
Page 3
Darcy’s law
• Darcy’s law expresses the relation between hydraulic head differences and
hydraulic conductivity
• Can be expressed as :
•
•
•
•
•
h
l
h
l
Where Q=discharge (volumetric flow rate) [L3/T], h hydraulic head, l distance, A
cross-sectional area
n= porosity
q=Q/A= “specific discharge”= flow per unit rate
Flow is therefore driven by the negative gradient of hydraulic head
Average linear flow rate V
Q   KA
q  K
V  q
n

K h
n l
Q has been called also Darcy velocity which has been also a subject of
confusion. It is not flow rate but unit discharge !
Page 4
Darcy’s law
– can be used to produce rough estimates and working hypotheses
– In modelling:
– Differential equations are formulated by assuming that equation
determines flow in each point in an aquifer (infinitesimally small unit
volume)
– How long it takes when maximum impacts of groundwater pollution
emerge around tailing ponds without sealing bottom structures.
Page 5
Example
–
An tailing pond has radius of 100 m, tailing are saturated to the surface (90 m asl).
Gw-level is at level 80 m asl (perennial level of discharge in drainage ditches).
Subsurface is till with K=10-7 m/s. Calculate average linear velocity of groundwater
underneath the pond if porosity of till is 15 %
– How long would it take for contaminated water leaked into the till at the center of the
pond to leave the area of the tailing pond area (horizontal travel time).
+90 m
+80 m
Page 6
• Hydraulic head is a sum of
elevation head and pressure head
– One should not say “groundwater
is moving from high pressure to
low pressure”
– See the examples.
• Ingebritsen, Sanford & Neuzil,
1999. Groundwater in Geologic
Processes, 2nd ed.
Hydraulic conductivity of soil/ porous
media
• Hydraulic conductivity in Darcy’s law
– Physical dimension: L/T
• Hydraulic conductivity K
– Properties of porous media
– Properties of the fluid (g specific weight, m viscosity)
 g 
g 


K  ki 
 ki  

 m 
m
•
• ki is intrinsic permeability”/permeability [dimension L2]
– “basic parameter” in oil geology/engineering
Page 8
•
•
Hydraulic conductivity in subsurface
Unsaturated zone
Pores contain water and gas
Darcy’s law is valid but
– Conductivity is a function of water
content
– Kunsat< Ksat
– Water pressure is influenced by
capillary suction (pressure of soil
moisture is less than air pressure)
•
Hydraulic conductivity can be
can be applied for fractured
rock mass (although should be
done with care)
–
–
•
Equivalent porous media
Flow follows Darcy’s law
K is not “strongly dependent “ on
porosity
Note in next slices range of K values in nature!
Compare to porosity range!
Coarse gravel or sand can have similar porosity
but K-values are quite different
Fractured rocks can have porosity of few
percent but high K-values
Page 9
Hydraulic conductivity values
• Freeze and Cherry (1979)
• Note the range of K-values
from 10-11 to 1 m/s
• Eurocode requirements:
– K must be measured in situ
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Porosity
•
Effective porosity:
Interconnected pores
0-35%vol
Total porosity:
In unconsolidated clays up to 70%
More typically see the table
In clays extremely high porosity but extremely
low K
Page 11
Soil moisture
• Unsaturate zone
– Seasonal variation of moisture
content
– In Nordic conditions recharge
takes mostly place after snow
melt
• (in some humid areas also
recharge in autum)
– Heavy raining rarely induces
recharge by infiltration
• horisontal: water content (relative)
vertical: z
Governing equations of groundwater
flow
Under steady state mass balance of in an
infinitesimal volume is




  w q x 
 w q y   w q z dxdydz  0
y
z
 x

In practice, the mathematical formulation the
governing equation proceeds by assuming that
the volume of water leaving or entering a
macroscopic elementary volume follows
Darcy's law.
•Mass-flux entering in x-direction
• Mass flux leaving:
wqx dydz
 w q x dydz 

  q  dxdydz
x w x
_________________________________________
•
difference
In y-direction:
In z-direction
•Assuming no-net change in
storage and summing up the
components gives
Which can be fulfilled only if



  q  dxdydz
x w x


 q dydxdz
y w y



  q  dzdxdy
z w z




  w q x 
 w q y   w q z dxdydz  0
y
z
 x



 
 q x  q y  q z   0
y
z 
 x
•Q is given by Darcy’s law
 
h   
h   
h 

   K x    K y     K z   0
x  y 
y  z 
z 
 x 
•If homogeneous
K x K y K z


0
x
y
z
•And isotropic (Kx=Ky=Kz)
  2h
 2h
 2h 
 K x 2  K y 2  K z 2   0
y
z 
 x
•We need only Laplace’s equation for solving flow
2 h 2 h 2 h

 2 0
x 2 y 2
z
Unsteady flow
• Changes in water storage
• During unsteady flow, changes of the volume of water in
a macroscopic elementary volume of an aquifer can be
expressed in terms of the specific storage coefficient Ss.
• The volume of fluid that is released or retained by a unit
volume of an aquifer per a unit change in hydraulic head
1  V 
is:


Ss 
V  h 
•
where Va is the unit volume of
the aquifer, and Vp is the volume of water in pores.
p
a
Storage and compressibility
•
•
•
Specific storage is actually a lumped parameter resulting from the analogy
between heat and groundwater flow (Theis, 1935).
In well testing of oil reservoirs and sedimentary rock aquifers, it is
commonly represented simply as:
where  is the porosity and ct is
the total compressibility. Ss  gc t
–
•
However, different formulas representing specific storage as a function of the compressibility
of rock and water have been developed based on the vertical compaction of an aquifer (e.g.
in Freeze and Cherry, 1979; Bear and Verruijt, 1994, ).
Storativity is a dimensionless parameter that determines the volume of
water that is released or retained by aquifer per unit surface area per unit
change of head perpendicular to that surface. As transmissivity, storativity
was initially developed for the analysis of confined porous aquifers.
S  Ssb
Where b is the thickness
of an aquifer
Specific yield
• Storativity in an unconfined aquifer is determined by
specific yield
– the volume of water which a unit volume of a saturated aquifer,
will yield by gravity;
– Approximately same as effective porosity
– Compression of/changes in porous media or compression of
water are substantially smaller:
•
•
S  Sy  Ssh  Sy
where h’ is the thickness of saturated aquifer
– In sand and gravel Sy a magnitude to decade higher than Ssh’
• S typically 0,02-0.3
Measurement of hydraulic conductivity
1) Laboratory test
• Representativity of the sample is a problem: small volume and
disturbance during sampling
2) Empirically based on grain-size distribution
Hazen method ( K in cm/s)
•
•
•
•
K  Cd
Where d10 is defined from cumulative grain-size distribution (from sieve results)
C is a cofficient
fine sands, sandy loams C=40-80
medium coarse, sorted sands and
coarse poorly sorted sands, C= 80-120
sorted coarse sand and gravels C= 120-150
3) In situ –measurements i.e. hydraulic tests
Page 19
2
10
Hydraulic tests
In situ –measurements by
Hydraulic tests
Several methods: choice depends on
investigation objectives and
hydrogeology (soil, rock fracturing etc.)
Most important
•Test pumping by constant rate or
pressure
•Spinner-tests
•Slug- ja bail-tests
For poorly conductive soils and rocks
Page 20
Slug-tests
– Slug- ja bail-tests
– An instantaneous change in hydraulic head and
measurement of recovery
• Either increase of head (slug) or reduction (bail)
– Nowadays slug-test is used as a general term
• Interpretation similar
– Several interpretation methods
• Cooper-Papanpodoulus confined aquifer, fully penetrative well
• Hvroslev-method unconfined aquifer, partial penetration
• Bouwer-Rice
Tekijä ja päiväys
21
Hydraulic conductivities
•
•
•
Zero pressure at the underground
mine (at depth of about 600 m)
Under extremely high gradient flow
can be significant
We must be able to measure
extremely low hydraulic
conductivites in situ!!!
Page 22
Freeze and Cherry (1979)
Slug tests
• Sudden change in
head+ monitoring of
the change (recovery)
• Recovery period can
be slow, overall
testing can be very
slow
• + in fractured rocks
could be used also an
interference test
(USA)
Hinkkanen, 2011, Posiva Working report 2011-40
• Difference flow
method
• Flow rates that are
slower than the
growth of your hair!
Posiva working report WR2006-47
Thiem equation
• h is hydraulic head
• hs is hydraulic head at the
radius of influence
• r0 radius at the well bore
• Ts transmissivity of the test
section (typically 0,5- 2 m)
• Qs0 and Qs1 flows out of the
borehole in natural and pumped
conditions
• h0 an h1 are the measured
heads
Example: Slug test
– Hvroslev-method
– unconfined system, partial
penetration (well or
piezometer penetrates only a
part of a groundwater
formation)
– Semilogarithmic plot h/h0 (log)
L
vs. t
r 2 ln  e 
 R
K
– Straigline fitting
2 Let0
– Define t0 when h/h0 = 0.37=
1/e
Le screen legths
R screen radius: (assumption Le/R >8, if <8
another forms of Hvroslev-equation must be used)
Tekijä ja päiväys
27
Water injection tests
• Empirical injection test a.k.a.
Lugeon-test,
• Pressure is maintained in a bore
hole and the injection rate is
measured
– Repeated using several
pressure levels during the test
Lugeon-tests are widely used because
• As a result an estimate of
estimates for
hydraulic conductivity expressed they provide pragmatic
grouting
in therms of a Lugeon unit
For environmental studies not
(litre/minute*length of testes
sensitive enough!
http://www.google.fi/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=0CA
section* 100 kPa),
cQjRw&url=http%3A%2F%2Fwww.geotechdata.info%2Fgeotest%2FLugeon_test.html&ei=Hd56
VNfxFur4ywPRkYCQAw&bvm=bv.80642063,d.bGQ&psig=AFQjCNH8MvIfSbgaLG4j5HNAK7mm
-7
• Lugeon is about 1-2 x 10 m/s
GwPUSg&ust=1417424796483853
(de Marsily, 1986),
Tekijä ja päiväys
28
Objectives of test pumping
– 1. in situ- estimates of (large scale) hydraulic properties of soils
and rock
– 2. assessment of long term impacts (over 1 month)
– In the context of mining: planning of dewatering
– Assuring water quality and yield for (drinking water/fresh water
supply)
– 3. Calibration/verification of numerical flow models
Tekijä ja päiväys
29
– Measurements during test pumping
•
Mostly by pressure transducers and automatic systems
– Q (constant), drawdown vs time
– Or Q vs time, in h constant
– (derivative for log time)
Linear flow
Spherical flow
Radial flow
– Interpretation using graphic and curve
fitting methods
Log-log plot characteristic
1/2-log-log-slope
1
1
10
0
10
-1
Theis-curve
1
10
0
10
-1
10
100
2
10
log drawdown
• Solutions of differential equations
2
10
log drawdown
– Utilizing analytical models
log drawdown
• Developed particularly for oil and gas testing,
1
2
10
3
10
4
100
10
0
10
2
10
1
10
2
10
3
10
4
100
10
log time
log time
1
10
-1
10
10
2
10
1
10
2
10
log time
time
Page 30
drawdow
drawdow
drawdow
Specialized plot characteristics
log time
1/ time
3
10
4
10
Groundwater, effective stress and total
stress
• Terzaghi (1928)
• Compaction of soil takes
place as a response to a
change in effective stress
• Shear strength depends
effective stress
• 𝜎 ′ = 𝜎 − 𝛼𝑝𝑣
• Where 𝜎 is external load or
total vertical stress, 𝛼 is a
coefficient ranging from 0-1
• Equation is valid for changes
of stresses and pressure as
well
s’ effective stress
pv fluid pressure
Apparent cohesion
•
•
•
•
•
•
In unsaturated zone air and water
Pore water pressure less than air pressure
Capillary forces squeeze grains to each
others
Effective stress increases compared to
saturated situation
Soil is apparently more stable (excavations
will not collide as easily etc.)
Apparent cohesion disappears when
saturation is reached
𝜎 ′ = 𝜎 − 𝛼𝑝𝑣
s’ grain pressure
pv pore water pressure
Effective stress and hydraulic failure
𝜎 = 𝜎 ′ + 𝛼𝑝𝑣
𝜎 ′ = 𝜎 − 𝛼𝑝𝑣
•
•
If effective stress is 0, no friction
between grains (at least at that point)
sediment liquefies/looses its
consistency
–
–
–
–
Piping under tailing dams
Erosion
Slope failures
Debris flow
Pressure change
s's  P
• Increasing water pressure may change
the stress state to conditions where
shear failure takes place
– In soil
– Existing fracture
– Fracturing
Dewatering of mines can induce
compaction similar to underground
construction and civil engineering
projects
the extent can be huge!
Example of changes if groundwater
pressure to rock stability
• Vajont dam catastrophy
• Huokosveden paineen nousun aiheuttama maanvyöry ja
hyökyaalto
• http://www.landslideblog.org/2008/12/vaiont-vajontlandslide-of-1963.html
Some aspects of
HARD ROCK HYDROGEOLOGY
Characteristics of hard rocks
• Hydraulic conductivity of large open fractures and
fracture zones can be high (>1e-5 m/s)
– same as in sand or gravel
• Flow takes place in interconnected open fractures
– Comprise only a small fraction of the fracture network!
• Tracer test, NWM studies, models, theoretical studies of
percolation theory
• Fracture porosity is typically 1-2 %
– Evidence NWM-studies, models, applied geophysics
• Compressibility of rocks extremely small
• Storage-properties extremely low!
• Impacts of dewatering or pumping spread fast and
extensively
• In sedimentary rocks faults
commonly act as seams
– Gouge and differential stress
• In hard rocks the situation is
opposite!
– Multiple tectonic events
– Brittle deformation but less
gouge
– Fracture zones that may be
highly conductive
Fracture mechanisms and Fracture
zones
Caine and Forster, 1999, Fault zone
architecture and Fluid Flow.
• In Finland, bedrock comprises almost entirely of
Precambrian igneous and metamorphic rocks.
• The surface topography of bedrock is strongly controlled
by rock fracturing.
• Long and narrow valleys commonly trace faults, shear
zones and lithological boundaries along which bedrock
is commonly more intensively fractured than in the
surrounding outcropping areas.
Rock fracturing
• Precambrian bedrock
– Caledonian orogeny and youger tectonic
phenomena,ice ages
• Bedrock has mostly low hydraulic
conductivity , relatively solid and
unbroken
• Mosaic-like block structure
• Poorly fractured bedrock blocks split
by fracture zones
GTK’s image database
– Commonly follown old zones of
ductile deformation and bedrock
contacts
– Can be distiguished as linear
structures on topographic and
aerogeophysical maps
•
lineament
• Directions of lineaments and
fractures from outcrops are
statistically similar
Maanmittauslaitoksen numeerinen korkeusmalli: © National
Survey lupanro 13/MML/09 ja Logica Suomi Oy
Fracture zones
• Intensively fractured planar
zones of intensive fracturing
• Commonly products of multiple
deformations
Processes reducing conductivity
•
•
•
•
Fault gouge
Ductile deformation
Alteration
Weathering
Strong weathering
along fractures to clay
in test tunnel of
Otaniemi
Ultramylonitic fault
Conceptualization of fracture flow
•
•
•
Fractured rocks can be considered as “porousmedia” only
over very large dimensions
– Block sizes exceeding 500 m in dimensions
Single fractures can be considered as conduits with
transmissivity/conductivity determined by the (average)
aperture
gw3
Tf  K f w 
12m
Between these extreme cases flow in fractured rock volumes
must be considered as discrete networks comprising fracture
conduits and matrix blocks (possibly with K and storage).
Lähde: Posiva
Engineering geological investigations of fracture zones
Regional
interpretation
- aerogeophysics
- aerial photos
- satellite data
Electrical tomography
Detailed interpretation
- seismic refraction
- electrical tomography
- other methods
fracture zones
5 km
Aeromagnetic map
Fracturing
• Intensity of fracturing typically
reduced after 100 m in depth
• Conductive fracture zones
continue to much greater depths