aquifer nomenclature aquifer - a geologic unit that can store and transmit water at rates sufficient...
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Aquifer Nomenclature• Aquifer - a geologic unit that can
store and transmit water at rates sufficient enough to supply exploitable quantities of water
• Confining Layer - a geologic unit having little or no intrinsic permeability– Don’t Use
• Aquifuge - no water transmission• Aquitard - stores water, little
transmission• Aquiclude - aquifuge that forms upper boundary
to aquifer
• Leaky Confining Layer - a confining layer that leaks
Types of Aquifers
Rock
Clay
Sand
K>>K’
K’<10-7
Confined
• K = Horizontal Hydraulic Conductivity• K’ = Vertical Hydraulic Conductivity
Unconfined
Sand
ClayK’<<K
K
Leaky ConfiningLayer - Storage Ignored
Semi-Confined
Sand
ClayK’<K
K
Real Leaky ConfiningLayer - Storage cannotbe ignored
Semi-Unconfined
Sand
Perched Water Table
Unconfined Confined
Water Table
PotentiometricSurface
Water Table Well
ArtesianWell Flowing
Well
The same aquifer can be both confined and unconfined.
Basic Hydraulic Parameters
Soil
Solid
Water
Air
Vs = Vol of Solids
Vw = Vol. of Water
Va = Vol of Air
TotalVol.(Vt)
Va + Vw = Vv = Vol of Voids = Pore Space
Variable No. 1
Porosity (n) = (Vv/Vt)x100
Expressed as %
Known Volume of Dry Soil
Saturate
Determining Porosity
Volume of Water Added = Vol of Voids
Example: 100 cm3 soil, add 42 cm3 water= 42% porosity
Example: 1 m2
10 m column
Add 3 m of water to saturate soilWhat is porosity?
Variable No. 2 - Specific Yield
Known Volume of Dry Soil
Saturate
Drain
Volume Water Drained
Total Volume Samplex 100
= Specific Yield (Sy)
by Gravity
Volume Remaining on Soil Particles
Total Volume
= Specific Retention (Sr)
Note:
Specific Yield Dictates water bearing properties not porosity
n = Sy + Sr
Variable No. 3 – Specific Retention
Typical Values of n and Sy
Unconsolidated n % Sy % Deposits
Gravel 25 - 40 22 - 25
Sand 25 - 50 20 - 27
Silt 35 - 50 18
Clay 40 - 70 2
Rocks Primary n % Secondary n %
sandstone 5 - 30
shale 0 - 10
crystalline < 5
Fractures increase overalln 2 to 5 % or more if weathered
Key Points
• Specific Yield is the Important Property for Flow
• Smaller the grain size – lower the Specific Yield
• n = Sy + specific retention
• Values usually estimated
• Porosity varies only over two orders of magnitude
Distribution of Water in EarthMaterials
Fluid Pressure:
a. closed tube w/ sandb. saturated & sealedc. under pressured. no flow - static
Water in pore space exerts pressure on grainsaround pore space
Define fluid pressure - P kg m/sec2
P Force/Unit Area = m2 = N/m2 = Pa
Place Piezometer into tube to measure pressure
A
hp
“Water will rise in tube a height hp until Force produced by the weight of water in piezometer balances P being exerted in the pore space”
hpP = ghp
= density of water
g = accel. of gravity
hp= ht. of water in well
Unit Weight
Define - g as unit weight - Force exerted by one unit volume of water
= g
w = 9820 N/m3 (metric) = 62.4 pcf (English)
For water:
Typical Application
clay
A
hp
P@A = whp
Note: taking measurements of water levels in in a well provides more than P
Unit Weight can be determined for anything -
d = dry unit weight - solids
b = bulk unit weight - solids + moisture
s = saturated unit weight - solids + waterat saturation
Typical ValuesPierre shale - 90-100 pcfSandy Gravel 8% moisture - 125-135 pcfLimestone - 165 pcf
surface
Hydraulic Conductvity
D
constant headreservoir
Measure Q
LSand
datum
h1
h2
Darcy’s Experiment (1857)
h
Q h
Q L
Q A
Pulling Terms Together
Q (h/L) A
Hydraulic Gradient
(Slope of the fluid pressure term)
h
L
Slope = Hydraulic Gradient
h/L = I = dh/dL = i ft/ft or unitless
Q/A
gradient
slope = K =
Hydraulic Conductivity
Rewrite,
Q = Darcy’s Law
sometimes see it written withnegative sign b/c flow is in the direction of decreasing fluidpressure
-
Units - m/sec, cm/sec, m/day, ft/daygpd/ft2
1UnitVolume
1
1
Conceptually,
Gradient = 1
1
1
KIA
K = Flow in gpd per unit area under unit hydraulicgradient @ 25 C°
Typical Values
sandy gravel 10-2 to 102 cm/secsilty clay 10-6 to 10-9 cm/sec
Important Points to Remember:
K varies over 12 to 14 orders of magnitude
Major control on rate at which contaminants move in subsurface
Main parameter needed in modeling
Varies spatially in response to geology
K1
K2
K3
K2 > K3 > K1
contaminant
Need to know how depositional/tectonicprocesses might influence spatial heterogeneity of K
Intrinsic Permeability
Add Non-aqueous phase liquid
D
Measure Q
LSand
datum
h1
h2
h
Darcy’s ExperimentRepeat
Hold h, L and A constant
Q for water Q for NAPL
Q = KIA
K must vary with fluid properties -
K unit weight ()
unit wt. = Force/unit volume = g
K (density)
K (viscosity of fluid)
Pulling terms together:
K g/ or
K = ki g/
Property of fluidProperty of medium
ki = intrinsic permeability - property of just the medium
K = hydraulic conductivity - property of the medium and of fluid
Units for Intrinsic Permeability -cm2, m2, ft2, etc
Typical Values
Material ki (cm2) K (cm/sec)Clay 10-12 to 10-15 10-6 to 10-9
Silt or Till 10-10 to 10-12 10-4 to 10-6
Fine Sand 10-9 to 10-11 10-3 to 10-5
Well Sorted Sand 10-7 to 10-9 10-1 to 10-3
Well Sorted Gravel 10-6 to 10-8 100 to 10-2
Define intrinsic permeability with lower case k with subscript i
Hydraulic conductivity defined with a capital K
Darcy’s Law
Q = ki(g/ ) (h/L) A
K
Key Points
ki property of the medium only
K a property of the medium and fluid
K through identical material will vary with density, viscosity and temperature of fluid
Define Specific Storage
Ss = wg ( n)
w = initial density of water
g = acceleration due to gravity
n = porosity
= fluid compressibility
= aquifer compressibility
The volume of water either released from ortaken into storage per unit volume ofconfined aquifer per unit change in fluid pressure
Ss = Specific Storage
clay
aquifer
Conceptual meaning of Ss
surface
1 unitvol
Vol Out or In
Ss = Volume of water released or taken intostorage per unit volume of confined aq.
1 unit
per unit head change in fluid pressure
Units - m3/m3/m = 1/m so units of 1/L
clay
aquifer
surface
1 unitvol
Vol Out or In
1 unit
b
b = aquifer thickness
1 unit area of aquifer
Ss
x
b
S = Ss x b
Volume of water released or taken into storage from a vertical column of aquifer of height b, and unit basal areawhen subjected to a unit change influid pressure
Storage Coefficient
S is dimensionless
Transmissivity (T)
surface
clay
aquiferb
1 unitvol
I = 1
K
K = volumetric flow per unit time per unitarea of aquifer under a hydraulicgradient of one at 25 °C
I = 1
K
T
T = volumetric flow per unit time per one unitwidth of the aquifer extended over theentire thickness of the aquifer at 25 °C
K x b = T
Units are: gpd/ft or m3/sec/m or m2/sec
Pumping a Confined Aquifer
clay
aquifer
Q
drop
Aquifer is still saturated - how can this be?
Two Ways Water is Removed from Storage in a Confined Aquifer
, water expands as itis released
1. Pumping decreases fluid pressure, so …...
P w Vw
Water Compressibility Component
, water expelledby compressionof aquifer
2. Pumping decreases fluid pressure, so ……
P e Vt n storage
Aquifer Compressibility
Summary - In a confined aquifer, water is released from storage by:
1. Expansion of water
2. Compression of the Aquifer
S is unitless
Typical Values of S are 10-3 to 10-6
Removal of Water From Storage in an Unconfined Aquifer
Surface
P = 0
drop
When you pump water out from an unconfinedaquifer - you literally dewater the porespaces
Water drains by gravity - in accordance w/ Sy
Typical Values for Sy = 10-1 to 10-3
Storage actually = Sy + (Ss x b)
Note:
Usually neglect any aquifercompression or water expansionb/c Sy is so much larger
S = Sy for an Unconfined Aquiferso,
Key Points About Storage
1. Water released from storage in a confinedaquifer by a) expansion of water and b) consolidation of aquifer material and is governed by S
2. Water is released from storage in anunconfined aquifer by dewatering the aquifer pores and is governed dominantlyby Sy
clay
aquifer
Q
drop
Specific Capacity (SC)
• Pump well until steady drawdown in well is achieved
• Pumping Rate, Q / drawdown = Specific Capactiy
• Units are L3/T/L, eg., gal/day/ft,
General Relationship Between Specific Capacityand Transmissivity
Transmissivity can be estimated by two empirical relationships and making some assumptions
For a confined aquifer
T = SC x 2000Where,
well radius = 0.5 feetpumping period = 1 dayInitial T estimate = 30,000 gpd.ftStorage estimate = 10-3
For an unconfined aquifer
T = SC x 1500Where,
same as above except storage is7.5 x 10-2
Note: the effect of assuming a T value to estimate a TValue using this formula is not really a problem because It is derived from the Jacob modified non-equilibrium Equation and appears in a log term. So large variationsIn the assumed T has very little affect on the result.
Bedrock Aquifers
Hydraulic Conductivity and Transmissivity of bedrock wells can also be determined through pumping tests
• Average K values can be determined for entire borehole
• T is determined by multiplying the average K value by the length of saturated uncased borehole
length
• You can also set up packers and isolate individualwater-bearing fractures to determine the K for an individual fracture
Example Problem:
Pump Well at10 m3/min for 1 day
Water Level drops7 m over 1 ha
What is the specific yield?
Example Problem:
Pump Well at10 m3/min for 1 day
Water Level drops7 m over 1 ha
What is the specific yield?
1. 10 m3/min x 60 min/hr x 24 hr/day x 1 day= 14400 m3
2. 14400 m3/10000 m2 = 1.44 m3/m2 = 1.44 m= Volume of water extracted
3. Change in water level was 7 m or 7 m3/m2 which is the total over which the change occurred
4. Therefore, 1.44/7 = 21 %
Tectonic
Alluvial Valley
Alternating layers of Sand, Silt, Clay
General Sequence
polished bedrock
Till veneer (lodgement or ablation or both
Sand and Gravel
Lacustrine Deposits
Recent Deposits
surface
P>0Saturated
Zone
Ground-water
P<0
UnsaturatedZone
(Aeration orVadoseZone)
P=0 Water TablePhreatic Surface
Capillary Zone
Capillary Zone - combination of molecular attraction and surface tension betweenwater and air capillarity
Capillary zone can be saturated or nearlysaturated but fluid pressure is negative
soil-water (root) zone
intermediate zone
Typical Water Profile in Soil
0 100%
Saturation
Dep
th (m
)
Water TableP=0Saturated
Zone
CapillaryZone
Tension SaturatedZone
root zone
intermediatezone
Field Capacity
(Specific Retention)PWP
AWC
SoilMoisture
Recharge Happens
Importance of K and ki Distinction
1. Different fluids will travel at different rates
Water and Non-Aqueous phase liquidswill move at different rates due todifferences in density and viscosity
2. Brines and highly saline solutions will moveat different rates due to higher densityof saline waters over fresh water.
3. Low temperature fluids will move at different rate than high temperature fluids
Recall, viscosity and density are temperature dependent
Effective Stress & Storage
Spring
A
z
Spring = soil matrix
Block of cement
= Total Stress (psf)
Now let’s place the spring in a cell
cell
A
imaginarypiezometer
closedh
1. fill to base of block
2. water represents fluid in pore spaces
3. no load carried by fluid
Water rises in piezometer under its ownweight -
Hydrostatic Pressure
P@A = gh
A
h
Place additional load on spring
1. Load applied matrix wants to consolidate and realign
2. Sealed tube, fluid has no where to go so additional load is borne by the fluidspring does not compress
Excess fluid pressure
3. Additional load on fluid manifested in anincrease in fluid pressure > hydrostatic
z
Start a Test
h
Drain
z
1. As water drains, excess fluid pressuredissipates
2. Load slowly transferred from fluid to matrix
3. Matrix responds by compressing - systemconsolidates and porosity decreases
z’
h
Fluid pressure returns to hydrostatic
z’’
hAquifer is consolidated
Total Stress, t ( + ) on system will resolve into 2 parts:
P = Fluid Pressure load borne by the fluid
e = Effective Stress load borne by the solids
t = e + P
We write,
z’
h
Total Stress is balanced by load borne by the
solids (e) and the load borne by thefluid (P)
- At start of test, load borne by fluid
- At completion of test load borne by solids
- In between, load was shared by solids andfluid
Excess Fluid Pressure
During the Test
Behavior in Confined Aquifers
surface
clay
aquifer
Fluid Pressure
Time
rise +
0
fall -
static
Train
clay
surface
clay
aquifer
Fluid Pressure
Time
Train
Train Stops
rise +
0
fall -
static
clay
Train leaves
Real Aquifers
In real aquifers - t (total stress) is constant
Total stress never really changes so,if you increase P (fluid pressure)
then you must reduce e (effective stress)and vice versa
So P and e are the only parameters changing
P + e = constant
P e
so,
Two Processes
1. Aquifer Compression
place load on aquifer, matrix consolidates,reduces porosity, expells water
e , Vt
, n , Storage
e , Vt
, n , Storage
Aquifer Compressibility is:
= - (Vt / Vto) / e
2. Water Compressibility
increase pressure on water, volume willdecrease, water will contract,density increases, more water canbe stored
P Vw storage
P
Water Compressibility is:
= - (Vw / Vwo) / P
or since Mass is conserved,
M = wVw then = (w / wo) / P
Vw storage
Fluid Pressure
Time
1. Train approaches - total stress goes up - initiallyload carried by fluid - increase P
Train Stops
2. Train stops - fluid pressure declines by draining rapid transfer from fluid to solids support -aquifer compresses by reducing porosity
Train leaves
3. Train leaves - effective stress on solids releasedaquifer rebounds elastically and increasesporosity - increase in pore volume lowersfluid pressure
4. Water flows back to low P zone - static
rise +
0
fall -
static
Geotechnical Application
clay
A
surface
b = 100 pcf
sand
s = 125 pcf
10 ft
5 ft
Total Stress (Pressure) @ A =
(100 pcf x 10 ft) + (125 pcf x 5 ft)= 1625 psf
Distribution of Water in Earth Materials – Saturated vs.Unsaturated
surface
water table
1. Take spot at 10 ft below water table
Total P = Force/unit area from water + force/unit area atmosphere
By convention, pressure at earth’s surfaceset is zero
P = whp= 62.4 pcf x 10 ft
Formal definition of the saturated zone - P > 0
Void space 100% saturatedVw/Vv = 1
surface
water table
2. Take spot at 10 ft above water table
Install tensiometer - surface tension and molecular attraction creates vacuum
Soil Exerts tension which is negative
Formal definition of the unsaturated zone - P < 0
Vw/Vv < 1Voids do not have to be 100% saturated
surface
water table
3. Take spot on the water table
There is no column of water inside thepiezometer exerting a force at water table
Soil is saturated at the water table
Formal definition of the water table - P = 0
Uniquely defines the water table
clay
aquifer
surface
Storage Coefficient (S)
b
b = aquifer thickness
1 unitvol
1 unit area of aquiferVol Out or In
S = volume of water a confined aquiferreleases or takes into storage
per unit surface area of aquifer
1 unit
per unit change in fluid pressure normalto that surface
extended over the entire thickness ofof the aquifer