groundwater is the water in the saturated zone (Fig)
recharge is the water entering the saturated zone
30% of freshwater on Earth trapped below the surface
in many parts of the world, groundwater is the only source of
fresh
water
in the US about 10% of the rainfall becomes groundwater
eventually.
This
amount equals the annual use of water in the US, about 3 inch
per year
residence time = reservoir/flux = ~1000 m / 3 inch/year =
10,000
y!
This
is a very rough estimate.
water may stay in the groundwater reservoir between several
days
and
thousands
of years. We will discuss tracer techniques that may be used to
derive
residence times later in the class
management of catchment areas requires understanding of
groundwater
flow
underground repository built for certain radioactive wastes
not high-level, but they contain isotopes that remain
radioactive for
very
long periods of time (tens of thousands of years)
storage of waste in salt formations
quantitative description of groundwater flow necessary to
evaluate risk
Conceptual model of groundwater flow
the flow of water through a porous medium (Fig
6.1)
water flows tortuous paths
geometry of channels is very complex
frictionles flow is totally meaningless!
conceptual model of flow through a porous medium is flow
through
a
bundle
of very small (capillary) tubes of different diameters (Fig
6.2)
the flow (Q) through a horizontal tube can be described as: Q
= -
π
*D^{4}/(128*
µ
)*dp/dx
(Poiseuille's
law)
=> size of the capillary tubes is important!
Darcy's law
what drives groundwater flow?
water flows from high elevation to low elevation and from
high
pressure
to low pressure, gradients in potential energy drive
groundwater flow
Bernoulli equation said: u^{2}/(2*g)
+
z
+p/(ρ*g) = constant,
means: velocity head +
elevation head + pressure head = total head
in groundwater flow, we cannot make
the
assumption
that there is no friction, therefore the head is not
constant
also u is so small that that term
can
be
typically
neglected (example!)
groundwater flows from high to
low
head
how do you measure the head or potential? => drill an
observation
well,
the elevation of the water level in the well is a measure of
the
potential
energy at the opening of the well
in 1856, a French hydraulic engineer named Henry Darcy
published
an
equation
for flow through a porous medium that today bears his name (Fig.
6.3)
Q = KA (h_{1}-h_{2})/L or q = Q/A = -K dh/dl,
h: hydraulic
head, h = p/(ρg)
+ z
thought experiment: hydraulic head
distribution in
a lake
q = Q/A is the specific discharge [L/T], dh/dl
is
the hydraulic
gradient
K is the hydraulic conductivity
[L/T]
the law is very similar to Ohm's law for electrical
curcuits I =
1/R * U (current = voltage divided by resistance)
the original Darcy experiment yielded
these
data (Fig
6.4)
the analogy between Darcy's law and
Poiseulle's law
suggests that K = (const*d^{2})*ρg/m
the first term (const*d^{2}) is
k,
the
intrinsic permeability [L^{2}], summarized the
properties
of the porous medium, while rg/m describe
the
fluid
hydraulic conductivities and permeabilities vary over many
orders
of
magnitude
(Fig 6.5)
Example: calculation of a typical hydraulic gradient of 1/100 in a
salt formation with a hydraulic conductivity of 10^{-10 }m
s^{-1}
will produce a specific discharge of 10^{-12} m s^{-1},
or less than 1 mm per 30 years!
specific discharge has the dimension of a velocity, but it is
not
the velocity
at which the water flows in the porous medium, the water has to
squeeze
through the pores
tagged parcels that are averaged together, will appear
to
move
through
a porous medium at a rate that is faster than the specific
discharge
porosity n is the fraction of a porous material which
is
void
space n =
V_{void}/V_{total}
the mean pore water velocity is then: v = q/n (Fig)
(experiment)
Darcy's law has been found to be invalid for high values of
Reynolds
number
and at very low values of hydraulic gradient in some very
low-permeability
materials, such as clays.
example :
K= 10^{-5} m/s, h_{2}-h_{1}
= 100m, L = 10km, A = 1m^{2} > Q = 3.15 m^{3}/y;
the
K
value above is typical for a sandstone aquifer
the actual flow velocity v may be
calculated with
the following formula: v=Q/(A*f)=q/n, n
is the porosity, and q the specific discharge
if the porosity n is 30%, the flow
velocity
in the
example above is 10.5 m/y
Water in natural formations
an aquifer is a saturated geological formation that
contains
and
transmits "significant" quantities of water under normal field
conditions
(=> gravel, sand, volcanic and igneous rocks, limestone) (Fig
6.6)
an aquitard is a formation with relatively low
permeability
an aquiclude is a formation that may contain water but
does not
transmit significant quantities (clays and shales)
an aquifuge is a
foamtion that does not contain or transmit significant amounts
of water
formation
contains
water
permeability
aquifer
Y
high
aquitard
Y
low
aquiclude
Y
very low
aquifuge
N
negligible
confined and unconfined (water-table) aquifers
an unconfined aquifer has a water table (water table
aquifer)
a confined aquifer does not have a water table. If you drill
a
well,
water
will rise (in the well) above the top of the aquifer
perched groundwater is groundwater sitting on top of a
poorly
permeable
layer with an unconfined aquifer underneath
the height to which water rises in a well defines the piezometric
or potentiometric surface
geology of aquifers (show examples)
unconsolidated sediments: loose granular deposit, particles
are
not
cemented
together (e.g.: Long Island)
consolidated sediments, most important: sandstone, porosity
varies
depending
on the degree of compaction (e.g. Zion, Bryce, and Grand
Canyon
National
Parks)
limestone: composed mainly of calcium carbonate, CO2 rich
water
dissolves
limestone, e.g.: limestone caves, karst (e.g. Floridan
aquifer)
volcanic rock
basalt lava, fractures (e.g.: Hawaii, Palisades)
crystalline rocks: igneous and metamorphic rocks, e.g.
Granite,
have
often
very low porosity, flow through fractures
porosities and hydraulic conductivities of different aquifer
rocks (Fig
6.5)
lines of equal hydraulic head are called equipotentials
flow occurs perpendicularly to those, lines indicating those
are
called flowlines
together, the equipotentials and the streamlines constitute a
flow
net (Fig
6.8)
generally, groundwater flow follows topography, in detail the
situation
can be more complicated though
groundwater flow not only occurs near the water table, but
does
penetrate
deep into the aquifer (Fig
6.9)
flownets provide a lot of information about groundwater flow,
they are
generated by computer models these days
Quantifying groundwater
flow using flownets
T = Kb [L^{2 }T^{-1}] is called the
transmissivity
of the aquifer, this term is often the more useful parameter for
estimating
the yield of an aquifer, it is relevant when we want to estimate
the
discharge
per unit length of stream, for example
the area between a pair of streamlines is referred to as a streamtube
in more complicated flow nets, these squares might become
"curvilinear
squares," as can be seen in (Fig
6.9)
if we isolate one of these squares (ds=dm) (Fig
6.10) and make use of Darcy's law, we can calculate the
discharge
through
the streamtube: Q = K*b*dh
you can imagine each streamtube as a "pipe," because water
cannot
cross
a streamline
the specific discharge will be greatest where the streamtube
is
narrowest,
analogue to the laminar flow table
the total discharge through the streamtube must be the same at
any
cross
section
by counting the number of stream tubes, we can determine the
total flow
another example is steady flow under a dam (Fig
6.11)
the dam is 100m wide (direction into the page), and the
hydraulic
conductivity
beneath the dam is 10^{-10} m s^{-1}
we use the length of the dam (100 m) in place of the aquifer
thickness
(b)
Heterogeneity and anisotropy
so far we have considered only homogeneous aquifer (the same K
everywhere)
virtually all natural materials through which groundwater
flows
display
variations in intrinsic permeability from point to point, this
is
referred
to as heterogeneity (Example: Fig)
permeable zones tend to focus groundwater flow, while,
conversely, flow
tends to avoid less permeable zones
in anisotropic media the permeability depends on the direction
of
measurement,
in isotropic media, it does not
Resources
Manning, J.C. (1997) Applied Principles
of
Hydrology.
Prentice Hall, third edition, 276p.
Freeze, R.A. and Cherry, J.A. (1979)
Groundwater.
Prentice Hall, 604p.