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Review Of Basic Hydrogeology Principles. Types of Terrestrial Water. Surface Water. Soil Moisture. Groundwater. Pores Full of Combination of Air and Water. Unsaturated Zone – Zone of Aeration. Zone of Saturation. Pores Full Completely with Water. Porosity. Secondary Porosity.

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Review

Of

Basic

Hydrogeology

Principles


Types of Terrestrial Water

Surface

Water

Soil

Moisture

Groundwater


Pores Full of Combination of Air and Water

Unsaturated Zone – Zone of Aeration

Zone of Saturation

Pores Full Completely with Water


Porosity

Secondary Porosity

Primary Porosity

Sediments

Sedimentary Rocks

Igneous Rocks

Metamorphic Rocks


Porosity

n = 100 (Vv / V)

n = porosity (expressed as a percentage)

Vv = volume of the void space

V = total volume of the material (void + rock)


Porosity

Permeability

VS

Ability to hold water

Ability to transmit water

Size, Shape, Interconnectedness

=

Porosity

Permeability

Some rocks have high porosity, but low permeability!!


Vesicular Basalt

Clay

Small Pores

Interconnectedness

Porous

Porous

But Not Permeable

But Not Permeable

High Porosity, but Low Permeability

Sand

Porous andPermeable


The Smaller the Pore Size

The Larger the Surface Area

The Higher the Frictional Resistance

The Lower the Permeability

High

Low


Darcy’s Experiment

He investigated the flow of water in a column of sand

He varied:

Length and diameter of the column

Porous material in the column

Water levels in inlet and outlet reservoirs

Measured the rate of flow (Q): volume / time


Darcy’s Law

Q = -KA (Dh / L)

Empirical Law – Derived from Observation, not from Theory

Q = flow rate; volume per time (L3/T)

A = cross sectional area (L2)

h = change in head (L)

L = length of column (L)

K = constant of proportionality


What is K?

K = Hydraulic Conductivity = coefficient of permeability

Porous medium

K is a function of both:

The Fluid

What are the units of K?

/

L3 x L

T x L2 x L

L

T

K = QL / A (-Dh)

=

/

/

The larger the K, the greater the flow rate (Q)


Silt

Clay

Sediments have wide range of values for K (cm/s)

Clay 10-9 – 10-6

Silt 10-6 – 10-4

Silty Sand 10-5 – 10-3

Sands 10-3 – 10-1

Gravel 10-2 – 1

Gravel

Sand


Q = -KA (h / L)

Rearrange

Q

A

q =

= -K (h / L)

q = specific discharge (Darcian velocity)

“apparent velocity” –velocity water would move through an aquifer

if it were an open conduit

Not a true velocity as part of the column is filled with sediment


Q

A

q =

= -K (h / L)

True Velocity – Average Mean Linear Velocity?

Only account for area through which flow is occurring

Water can only flow through the pores

Flow area = porosity x area

q

n

Q

nA

Average linear velocity = v =

=


Aquifers

Gravels

Aquifer – geologic unit that can store and

transmit water at rates fast enough to

supply reasonable amounts to wells

Sands

Confining Layer – geologic unit of little

to no permeability

Clays / Silts

Aquitard, Aquiclude


Types of Aquifers

Unconfined Aquifer

Water table aquifer

high permeability layers

to the surface

overlain by

confining layer

Confined aquifer


Homogeneous vs Heterogenous

Variation as a function of Space

Homogeneity – same properties in all locations

Heterogeneity

hydraulic properties

change spatially


Isotropy vs Anisotropy

Variation as a function of direction

Isotropic

same in direction

Anisotropic

changes with direction


Regional Flow

In Humid Areas: Water Table Subdued Replica of Topography

In Arid Areas: Water table flatter


Water Table Mimics the Topography

Subdued replica of topography

Q = -KA (Dh / L)

Need gradient for flow

If water table flat – no flow occurring

Sloping Water Table – Flowing Water

Flow typically flows from high to low areas

Discharge occurs in topographically low spots


Discharge vs Recharge Areas

Discharge

Upward

Vertical Gradient

Recharge

Downward

Vertical Gradient


Discharge

Recharge

Topographically High Areas

Topographically Low Areas

Deeper Unsaturated Zone

Shallow Unsaturated Zone

Flow Lines Converge

Flow Lines Diverge


Equations of Groundwater Flow

Fluid flow is governed by laws of physics

Darcy’s Law

Law of Mass Conservation

Continuity Equation

Matter is Neither Created or Destroyed

Any change in mass flowing into the small volume of the

aquifer must be balanced by the corresponding change

in mass flux out of the volume or a change in the mass

stored in the volume or both



Let’s consider a control volume

Confined, Fully Saturated Aquifer

dz

dy

dx

Area of a face: dxdz


dz

qx

qy

dy

dx

qz

q = specific discharge = Q / A


dz

qx

qy

dy

dx

qz

w = fluid density (mass per unit volume)

Apply the conservation of mass equation


Conservation of Mass

The conservation of mass requires that the change in mass

stored in a control volume over time (t) equal the difference

between the mass that enters the control volume and that

which exits the control volume over this same time increment.

Change in Mass in Control Volume = Mass Flux In – Mass Flux Out

x

- (wqx) dxdydz

dz

y

- (wqy) dxdydz

(wqx) dydz

dy

z

- (wqz) dxdydz

dx

x

y

z

)

(

wqx

wqy

wqz

dxdydz

-

+

+


Change in Mass in Control Volume = Mass Flux In – Mass Flux Out

dz

n

dy

dx

Volume of control volume = (dx)(dy)(dz)

Volume of water in control volume = (n)(dx)(dy)(dz)

Mass of Water in Control Volume = (w)(n)(dx)(dy)(dz)

M

t

t

=

[(w)(n)(dx)(dy)(dz)]


Change in Mass in Control Volume = Mass Flux In – Mass Flux Out

x

y

z

)

t

(

wqx

wqy

wqz

dxdydz

-

+

+

[(w)(n)(dx)(dy)(dz)]

=

Divide both sides by the volume

x

y

z

)

t

(

wqx

wqy

wqz

[(w)(n)]

-

+

+

=

If the fluid density does not vary spatially

1

w

x

y

z

t

(

)

[(w)(n)]

-

qx

+

qy

+

qz

=


x

y

z

(

)

-

qx

+

qy

+

qz

Remember Darcy’s Law

qx = - Kx(h/x)

dz

qy = - Ky(h/y)

dy

dx

qz = - Kz(h/z)

x

h

x

y

h

y

(

(

)

z

h

z

)

(

Kx

)

Ky

+

+

Kz

1

w

t

x

h

x

y

h

y

(

(

)

z

h

z

)

(

[(w)(n)]

Kx

)

Ky

=

+

+

Kz


1

w

t

[(w)(n)]

After Differentiation and Many Substitutions

h

t

(wg + nwg)

 = aquifer compressibility

 = compressibility of water

h

t

x

h

x

y

h

y

(

(

)

z

h

z

)

(

Kx

)

(wg + nwg)

Ky

=

+

+

Kz

But remember specific storage

Ss = wg ( + n)


x

h

x

y

h

y

(

(

)

z

h

z

)

(

h

t

Kx

)

Ky

+

+

Kz

Ss

=

3D groundwater flow equation for a confined aquifer

heterogeneous

anisotropic

transient

Transient – head changes with time

Steady State – head doesn’t change with time

If we assume a homogeneous system

Homogeneous – K doesn’t vary with space

x

h

x

y

h

y

(

(

)

z

h

z

)

(

h

t

Kx

)

Ky

+

+

Kz

Ss

=

If we assume a homogeneous, isotropic system

Isotropic – K doesn’t vary with direction: Kx = Ky = Kz = K

2h

x2

2h

y2

2h

z2

h

t

)

(

Ss

K

=

+

+


Let’s Assume Steady State System

2h

x2

2h

y2

2h

z2

+

+

= 0

Laplace Equation

Conservation of mass for steady flow in an Isotropic

Homogenous aquifer


2h

x2

2h

y2

2h

z2

h

t

)

(

Ss

K

=

+

+

If we assume there are no vertical flow components (2D)

2h

x2

2h

y2

h

t

)

(

Ssb

Kb

=

+

S

T

2h

x2

2h

y2

h

t

=

+


x

h

x

y

h

y

(

(

)

z

h

z

)

(

Kx

)

Ky

+

+

Kz

= 0

Heterogeneous

Anisotropic

Steady State

2h

x2

2h

y2

2h

z2

h

t

)

(

Ss

K

=

+

+

Homogeneous

Isotropic

Transient

2h

x2

2h

y2

2h

z2

+

+

= 0

Homogeneous

Isotropic

Steady State


Unconfined Systems

Pumping causes a

decline in the water table

Water is derived from

storage by vertical drainage

Sy


Water Table

In a confined system, although potentiometric surface

declines, saturated thickness (b) remains constant

In an unconfined system,

saturated thickness (h) changes

And thus the transmissivity changes


Remember the Confined System

x

h

x

y

h

y

(

(

)

z

h

z

)

(

h

t

Kx

)

Ky

+

+

Kz

Ss

=

Let’s look at Unconfined Equivalent

x

h

x

y

h

y

(

(

)

)

h

t

hKx

hKy

Sy

+

=

Assume Isotropic and Homogeneous

x

h

x

Sy

K

y

h

y

(

(

)

)

h

t

h

h

+

=

Boussinesq Equation

Nonlinear Equation


For the case of Island Recharge and steady State

Let v = h2


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