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