Properties of Aquifers Part I - Porosity & Permeability - Myweb @ CW ...

GLY 15/518 - Groundwater Geology
Chapter 2: Sections 3.2 - 3.5
Material for week of 9/17/12
Properties of Aquifer Materials
There are two basic characteristics of an aquifer in terms of its potential as a water
resource.
I) First is various measures as to how much water is held in an aquifer including:
porosity (η), specific yield (Sy), and storage (Sr)
II) The other is measures of how easily the water flows through the aquifer:
permeability, hydraulic conductivity (k), transmissivity (T)
I) Quantity of Available Water in an Aquifer
porosity types: Most sediment and rock contains some amount of void space
intergrain spaces: ! a primary porosity in sediments and sedimentary rock
! ! (though cementation decreases this)
vessicles: !
a primary porosity in volcanic rocks
dissolution voids: ! a secondary porosity in limestone
fractures: !
a secondary porosity in all kinds of rock
porosity: Porous aquifer materials contain void spaces throughout the mass of
sediment and rock. The space available for water storage can be defined as
porosity in sediments: The amount of void space in sediments and sedimentary rocks
depends on the properties of the materials, including packing, grain size, grain
shape, sorting, the degree of cementation, etc.
packing: Uniform-size spheres stacked one on top of another (like balls in a box) have
a cubic packing structure. Cubic packing results in about 48% porosity (52% of
space taken up by the solid balls). If uniform spheres are stacked so the spheres of
every other row fit into the hollows between balls of the adjacent row, this
rhombohedral packing reduces porosity to its minimum (for uniform spheres) of
about 26%. Of course natural sediments are neither perfectly spherical, perfectly
uniform in size, nor packed in perfectly cubic or rhombohedral order but will fall
somewhere between those two end members.
sorting: Well-sorted (fairly uniformly sized) sediments (or spheres) maintain a relatively
high degree of porosity. But if sediments occur in a mixture of sizes, the smaller
particles will fill in the spaces between the larger particles, reducing the porosity.

sediment size:
geological classification:! gravel: particles > 2mm (boulders, cobbles, pebbles, granules)
! sand: particles between 2 mm and 1/16 mm
! silt: particles between 1/16 mm and 1/256 mm
! clay: particles smaller than 1/256 mm
Gravel and sand are all visible particles. Clay and all but the very coursest silt are
microscopic. Silt and clay are called mud.
sediment size gradation: The size distribution of a sediment is determined by passing
a sample through a stack of nested baskets with each lower basket having a finer wire
mesh. The size fractions caught in each basket are then weighed. The sediment size
distribution is then plotted on a semi-log grain-size distribution plot. A wide distribution
of particle sizes is a poorly sorted sediment. A tight distribution of grain sizes is a wellsorted
sediment.
uniformity coefficient, C u is a measure of the gradation of a sediment. It is
calculated as the following ratio:
C u = d 60 / d 10
d 60 = soil particle diameter at which 60% of the mass of a soil sample is finer
d 10 = the diameter at which 10% is finer
d 60 and d 10 can be read off a grain-size distribution plot
C u > 6 is well graded (poorly-sorted)
porosity ranges
well-sorted gravel or sand! 25-50% porosity
poorly-sorted gravel and sand! 20-35%
silt or clay! 33-60%
effective porosity
However, not all of the water in pore spaces is available (can drain out). Some water is
held by capillary forces (capillary water) and some by electrostatic forces
(hygroscopic water). The available water is called gravitational water because it is
able to drain out of the rock under the force of gravity.
The effective porosity is less than the total porosity because of these forces that retain
water in the pores spaces.

The term specific yield (Sy) is another term for effective porosity, but is commonly used
when referring to an aquifer rather than individual samples.
Specific retention (Sr) refers to the portion of the total porosity that is not available due
to capillary and electrostatic forces.
porosity = specific yield + specific retention
η = S y + S r
Fine sediments like clay and silt have a high porosity but also a high specific retention
and low specific yield. Capillary and electrostatic forces become very important in fine
sediments where the pores spaces are very small. Clay minerals have electrostatic
forces that attract large amounts of water (dipolar molecule).
Coarse sediments like sand and gravel have a lower porosity than fine sediments but
high specific yield and low specific retention because the void spaces are larger and
electrostatic attractions are much less. A much smaller proportion of water in voids is in
close contact to the grains. Coarse and medium sand generally has the greatest
specific yield because the void spaces are still relatively large, but they have greater
porosity than gravel (cobbles & boulders).
determination of effective porosity/specific yield
For a saturated sediment or rock sample, the effective porosity can be determined as:
which is
η e
=
void volume saturated weight − drained weight
×
total volume saturated weight − dried weight
η e
= porosity ×
gravitational water weight
total water weight
Then multiply by 100% to express as a percent.
Knowing the average specific yield in an aquifer and the volume of the aquifer, one can
calculate the total amount of water held in storage that could be extracted. Weʼll see
that later.

II) Groundwater Ease of Flow (Permeability - Hydraulic Conductivity (k), etc.)
Darcy's Law
Darcy (1856) reported on experiments comparing the rate of flow of water through sand
(used for water filtration). He varied the slope (head loss over a certain length) of
various sizes of sand packed in a cylinder.
Darcy determined that in a permeable medium, the flow velocity is:
- directly proportional to the head loss
- inversely proportional to the length (distance)
V d
∝ H L
where Vd is the Darcy velocity, H is the head loss or difference in the height of the water
table or potentiometric surface, and L is the length or distance between observation
points. This is the "rise over the run" or the slope of the water table or potentiometric
surface. This slope is also known as the hydraulic gradient. So the groundwater flow
velocity is proportional to the slope of the water table or potentiometric surface.
The constant of proportionality is called the hydraulic conductivity (K), which is
analogous to the permeability.
V d
= K H L
Darcy Velocity = (hydraulic conductivity) (hydraulic gradient)
Note on groundwater velocity: Because not all of the groundwater is flowing (some is
held by capillary and electrostatic forces) the true velocity (Vt) or seepage velocity is
greater than the Darcy velocity (Vd). The true velocity is equal to the Darcy velocity
divided by the effective porosity
V t = V d / η e
Additionally, groundwater does not flow in straight paths but rather flows around grains
through connected void spaces. The velocity of the individual water molecules in their
sinuous paths is faster yet. A complete treatment of Vt would ideally include the
sinuosity, but the sinuosity is difficult to quantify.

The hydraulic conductivity has units of distance per time (like velocity). The hydraulic
gradient is a ratio and has no units (length divided by length cancels units).
Since the discharge (Q; volume of water flowing through a medium in a given amount
of time) is equal to the flow velocity times the cross sectional area through which it flows
(Q = VA), Darcy's Law becomes:
Q = KA H L
discharge = (hydraulic conductivity) (cross-sectional area) (hydraulic gradient)
fluid properties effect on discharge: The rate of flow depends not just on the
properties of the permeable media, but also the properties of the fluid. Flow depends
on the specific gravity (density) and viscosity (resistance to flow) of the fluid. The
density and the viscosity of water both increase with increasing temperature (aside
from the density peak for water at 4 °C).
Petroleum, another common fluid that flows through permeable media, is more viscous
than water.
intrinsic permeability: Since the hydraulic conductivity (K) in Darcyʼs Law depends
not only on the properties of the porous media but also of the viscous fluid, another
measure is needed to define the properties of the media alone.
Factoring out the characteristics of the fluid (specific gravity and viscosity) one can
define a property of the permeable media alone.
intrinsic permeability,
K i
= K µ γ
where μ (mu) is the fluidʼs viscosity; γ (gamma) is the fluidʼs specific gravity
It has been shown that for sandy sediments (d 10 between 0.1 and 3 mm)
intrinsic permeability, K i = Cd 2 10
where C and d 10 relate to the shape and size of the pore spaces
C is the shape coefficient; d 10 is the characteristic grain size
and more generally, K i = Cd j 50
where C is the shape coefficient; d 50 is the mean grain size;
j is an exponent

permeability increases as the size of sediments (size of void spaces) increases
permeability decreases as the degree of sorting decreases
(and smaller particles fill spaces between larger particles)
coarse sediments have lower porosity (less proportional void space)
but higher permeability (larger voids - easier flow)
fine sediments have higher porosity
but lower permeability
measuring permeability: permeameters
the rate that water will flow through porous materials (hydraulic conductivity) can be
determined by measuring the discharge of water through a sample of known
diameter with the water supply at a known hydraulic head (constant or decreasing)
constant head permeameters are used for high hydraulic conductivity samples
falling head permeameters are used for low hydraulic conductivity samples