Hydro Ch 3 – Aquifer Properties
3.1 - Start with matter and energy review
Get comfortable w/ English system (feet, etc) vs SI (metric) system
Energy – capacity to do work
Work is “equal to product of net force exerted times distance through
which the force moves”.
W=FxD
Note units:
D in L
F in ML/T2
F = mass x accel ; Wt = mass x gravity
Note units
Mass in M
Accel in L/T2
Force in SI is in Newtons
Force in English is pounds
Recognize that there is much confusion in units –
best example: we erroneously link
weight with mass by converting from
pounds to kilograms
This is not appropriate, as can be seen from the above equation.
Density = mass / unit volume (e.g., grams/cm3)
Similarly,
Specific weight = weight / unit volume (e.g., lbs/ft3)
Another important relationship:
Pressure = Force / unit area (e.g., lbs/in2)
Example - atmospheric pressure pressing on the Earth’s surface
Fetter Ch 3 p.2
Also need to be aware of dynamic viscosity, which is property that
resists fluid movement (e.g., oil and water have greatly different
viscosities).
Other info: water compressible (somewhat); under pressure, the same
mass can be squeezed into a smaller volume, which increases its density
As an elastic material, water will also re-expand if pressure that contains it
is released.
VERY GOOD TABLE on p. 69
3.2 – Porosity of Earth Materials
porosity (for “porous”) of materials is a quantitative measurement of the
opening or pore space between grains
3.2.1 - definition
Effective porosity (porosity available for fluid flow):
ne (%) = 100 x Vv
V
Total porosity: slightly different formula for slightly different conditions
3.2.2 – porosity and classification of seds
packing arrangement (Fig 3.1) causes big change in n, typical range for
spherical grains is 26% to 48%
however, reality often has a mix of grain sizes (poor sorting), which leads
to low porosity (Fig 3.2B)
Classification of grain size – (Fig 3.3) absolutely critical that the geology
student is comfortable and knowlegeable about this scheme
ASTM classification important (Table 3.3) important for practicing
professionals, but very complex.
Grain-size distrib curves (Fig 3.4) are an important tool for
visualizing/quantifying diffs
Plot “% finer by weight” on arithmetic y-axis, and diameter on logarithmic
x-axis…you use sieves to separate sizes down to 200 mesh, then you use
hydrometer for the finer-than-200 mesh fraction.
Hydro Ch 3 p.3
Can we do a sieve analysis here??
Compare Fig 3.4 and 3.5..one is well-sorted, one is poorly sorted…which
is which?
Uniformity coefficient helps you determine sorting
Cu = d60 / d10
(mm / mm)
Where d60 is the grain size value (in mm) at the point where 60% of the
sample (by weight) is finer than this size
Ditto for d10, the grain size value at the point where 10% of the sample (by
weight) is finer than this size
Let’s work up the Cu for both fig 3.4 and 3.5…
3.2.3 – porosity of Sed Rx
rx form from seds through diagenesis:
compaction
removal of material
addition of material
transformation of minerals
compaction usually reduces pore volume, as does precip of cement like
calcite, dolomite, silica…although later dissolution can improve porosity
Fetter mentions primary and secondary porosity – his def’ns may not
exactly square with others we see. His mention of fracture porosity as
secondary is consistent with other terminology
Special consideration made for limestone and dolomite. Why? Because
they are essentially chemical precipitates, or collections of marine
invertebrate shells that themselves are chem precipitates. They are
particularly responsive to cementation and dissolution. Calcite cement
ubiquitous, found every where, a major cementing agent in ALL sed rx, not
just limestone.
Fetter makes point that precip process is reversible – it’s all dependent
upon factors in that particular environment….this is what
hydrogeochemistry is all about … prediction of when you get precipitation,
when you get dissolution.
Fetter Ch 3 p.4
Fig 3.6 shows sequence of cementation – lousy graphics.
Bottom line – sed rx typically range from 1% to 30% porosity
3.2.4 – porosity of plutonic and m-m rx
because of structure of interlocking xls, these rx have very low porosity –
just a few % at best.
In these rx, wthrg and fracturing are the two processes most likely to
improve porosity. Example: heavily wthrd rx can have porosity as high as
30% - 60%
3.2.5 – porosity of volcanic rx
these rx include many diff types, but they tend to have some porosity
because they are extrusive, not intrusive
basalts can be 1% to 12%
pumice can be as high as 87%
tuff can be 14% to 40%
On to more terms, but they will start to make more sense as you see the
subject more in depth
3.3 – Specific Yield
Sy is ratio:
vol of drained wtr due to gravity
Total rock volume
Note that water will drip due to gravity until all that is left in the porosity is
described as specific retention, Sr. (Fig 3.9) This is a ratio too, like Sy.
As you might expect, assuming you start with a saturated rock, the
following is also true:
N = Sy + Sr
As expected, due to surface tension, Sr incr
as
n decr
Pump tests in the field, as well as lab analysis, can give you specific yield.
Hydro Ch 3 p. 5
3.4 – Hydraulic conductivity
NOW we start getting to the meat of hydro…..
It is not enough for rocks to hold water….they must be able to TRANSMIT
water..
A variety of rocks have trouble with transmission. Some have pores, but
the pores are not interconnected.
Some sediments and rocks have high porosity, like clays and shale, but
the pores are so small that they effectively block water transmission.
Henry Darcy started the discipline with studies in Paris in 1850s. He used
pipes filled with sand, found a couple interesting things:
 Rate of flow is proportional to difference in height between ends
of pipe (more steep, faster the flow)
hA
L
hB

Rate of flow inversely proportional to length of flow path through
the sample (more length, the slower the flow)

Rate of flow also proportional to K, which is the hydraulic
conductivity , and to cross-sectional area
Q = -KA (hA – hB)
L
(Fig 3-12)
Recall that Q = discharge = L3/sec in units
Q = -KA (hA – hB)
L
can also be written as
Q = -K (hA – hB)
A
L
where units of Q
A
are L/sec
This leads to a rewrite of the equation:
q = -K dh where q is called specific discharge or Darcy velocity.
dl
Hydro Ch 3 p.6
Dimensionally, q and K both have velocity dimensions, because dh and dl
have the same units, length, which cancel out in the equation.
Fig 3.13 shows how Darcy’s lines can be draw on an x-y coord system
that show this equation as one of a straight line:
Y = m X + b, where b is the y-intercept and m is the slope of the line
q = K dh + 0, where y-intercept is zero, and K is the slope of the line
dl
many people use the terms “hydraulic conductivity” and “permeability”
interchangeably, which is not quite right
3.4.3 – Permeability of Sediments
extremes exist in permeability – coarse grained sand is prolific producer
of water, and fine-grained clay is a routinely used water-blocker (e.g.,
landfill liners)
table 3.7 shows relation between perm and hyd cond. – difference is 3
orders of magnitude (1 darcy = 10-3 cm/sec = 3 feet/day)
several factors relate perm to grain size:
 As grain size increases, so do pore spaces, so does perm
 For a given grain size, as sorting becomes poorer, perm drops
 Coarser seds decr in perm faster than fine gr seds when sorting
becomes poorer
3.4.4 - Permeability of rocks
“intrinsic perm. is due to primary openings formed at the same time rock
was formed, and due to secondary openings created after the rock was
formed”
key factors to perm are:
 Size of openings
 Interconnection of openings
 Number of openings (amt of open space)
Clastic sed rx often undergo diagenesis that preserves amt of primary
porosity, but decreases perm by blocking or restricting pore throats.
Conversely, primary perm can remain along sedimentary structures, such
as bedding planes, cross-beds, ripples, etc.
Hydro Ch 3 p.7
Crystalline rx tend to have both low perm and low porosity. Diagenetic
fluids have difficulty running through these rx.
Secondary perm can develop through fractures. Fractures and bedding
planes in rx such as limestone, dolomite (chem-precipitated) can often be
enlarged through solution….
From this
To this
3.5 - Permeameters
These are devices that measure hydraulic conductivity. Couple diff types
mentioned….
Constant head permeameter – for non-cohesive high-perm sediments like
sand. Water moves through the sample, from bottom to top, at a constant
rate fed by a source like a faucet (giving a constant head, Fig 3-16).
K= VL
Ath
describes the equation
Some caveats for this method:
Keep h less than ½ the sample length
Falling head permeameter – for cohesive, low-perm seds Fig 3-17 .
Water level in feeder tube starts off at a certain head, you keep track of its
fall.
K = dt2 L ln (ho)
dc2 t
(h)
let’s do the problems on p.93
Hydro Ch 3 p.8
3.6 Water Table
Note Fig 3.18 – observe how WT is defined as the point at which
atmospheric press is equal to pore water pressure.
Interesting ideas for building a sand model
3.7 – Aquifers
pretty specific definition by Fetter – “a geologic unit that can store and
transmit water at rates fast enough supply reasonable amounts to wells.”
He defines this as an intrinsic permeability level as 10-2 darcys and
greater.
“confining layer” is close to being impermeable, but somewhat arbitrary
cutoff of 10-2 darcy and lower is given. Note how Fetter says that it really
depends upon local conditions that dictates when a low-perm unit is an
aquifer and when it’s a confining unit.
Confining layer broken into 3 categories:
 Aquitard, aka “leaky confining layer”– retards flow significantly
 Aquifuge – totally impermeable to flow
 Aquiclude – not defined by Fetter, but more or less synonymous w/
aquifuge
Aquifer types –
 Unconfined – in vertical communication with the surface, thus there is
a water table Fig 3.20
 Confined – as name implies, not in direct vertical communication with
surface, but are overlain by a confining layer Fig 3.21. Rather than a
water table surface that defines the “top” of the water, this aquifer has
a potentiometric surface, which is the level to which water rises in a
cased well that has its base in that aquifer. Fig 3.22
 Perched –as name implies, this is an aquifer “perched” above a main
aquifer, usually held up by a confining layer at its base. Fig 3.23
Perched aqs common in glacial and volcanic terranes
Hydro Ch3 p.9
3.8 Water-Table and Potentiometric Surface Maps
Maps are "basic tools" of investigation - need to understand what these
represent.
Fetter cites typical definition - 2D representation of a 3D surface, using
contour maps of lines of equal elevation (in this case, instead of surface
topography or top of a subsurface formation, we map the top of the
saturated zone, which is the surface we call the "water table".
Is everyone OK with how to contour a map of this type? CRITICAL SKILL
Some considerations:
 Data comes from elevation of WT or potentiometric surface as
measured in wells (equivalent to the hydraulic head of the aquifer at
that point - recall that this is an elevation msrmt).
 Need to map one aquifer, not multiple aquifers. Multiple aquifers yield
results that may not reflect individual aquifer heads.
 Water level must be SWL - static water level - with no influence due to
pumping, etc.
 With unconfined aqs, surface water bodies must be taken into acct
too, because they are part of the system and their elevations are part
of the system
Other considerations :
 GW contours Can NOT be above Ground elevations when aq is
unconfined
 GW contours CAN be above surface when aq is confined (an artesian
system)
Basic concepts:
 Gw will flow from high head to low head,  to contour lines Fig 3-24
Hydro Ch 3 p.10
3.9 Aquifer Characteristics
Another measure of an aquifer's ability to transmit water is it
transmissivity. Simple idea once you grasp it…
T = b x K; where T is in units of L2/Time (e.g., ft2 / day)
b = saturated thickness of aquifer (units of L)
K = hydraulic conductivity
So you have an area, or sheet, of water transmitted past a point every day
for each infinitesimally small unit width of aquifer:
Aquifer
Area "coming out"
per day per unit
width
b
water flow
Storativity (S) and specific storage (Ss) are other measures, these for amt
of water absorbed or expelled as head either increases or decreases, due
to mineral skeleton either expanding or contracting.
Confined aquifer:
S = b x Ss
Hydro Ch 3 p.11
Unconfined aq:
S = Sy + bSs
Since Sy >>> bSs in unconf aqs, a rule of thumb is that S = Sy in unconf
aqs
Volume of water drained from an aquifer as head lowers is:
V = S x A x h
Where S = storativity
A = area over the draining aquifer
h = avg decline in head
good problem to do on p. 102
3.10 compressibility and effective stress
Important concepts for engineering geology:
t = e + P
total stress = effec stress + pressure
3.11 homogeneity and anisotropy
definitions important here:
homogeneous unit is one that has similar properties in all directions ( it is
isotropic)
a heterogeneous unit is one whose aquifer properties are very dependent
upon direction of flow (anisotropic).
Figs 3.27A & 3.27B
Note much stronger referred horiz direction in picture B
In general terms, there are two separate equations to calculate each type
of conductivity on average
Hydro Ch 3 p.12
Horizontally:
Kh avg =  Khmbm
btot
that is, calculate these for each unit, sum them up
Vertically:
Kv avg =
btot
 bm
Kvm
3.12 Gradient of water table or Potentiometric surface
when you don't have much well control, there are straight-line methods
you can use to to calculate the hydraulic gradient
use Fig 3-30 as the go-by