PPT PowerPoint Presentation

Review Of

Basic

Hydrogeology

Principles

Types of Terrestrial Water Types of Terrestrial Water

Groundwater Groundwater

SoilSoil Moisture Moisture Surface

Water

Unsaturated Zone – Zone of Aeration

Pores Full of Combination of Air and Water

Zone of Saturation Pores Full Completely with Water

Porosity Porosity

Primary Porosity

Primary Porosity Secondary Porosity Secondary Porosity

Sediments Sediments

Sedimentary Rocks Sedimentary Rocks

Igneous Rocks Igneous Rocks Metamorphic Rocks Metamorphic Rocks

Porosity Porosity

n = 100 (Vv / V) n = 100 (Vv / V)

n = porosity (expressed as a percentage) n = porosity (expressed as a percentage) Vv = volume of the void space

Vv = volume of the void space

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

= =

Porosity Porosity

Permeability Permeability

VS VS

Ability to hold water Ability to transmit water Size, Shape, Interconnectedness Porosity

Porosity



PermeabilityPermeability

Some rocks have high porosity, but low permeability!!

Some rocks have high porosity, but low permeability!!

Vesicular Basalt Vesicular Basalt

Porous Porous

But Not Permeable But Not Permeable

ClayClay

Porous Porous

But Not Permeable But Not Permeable

High Porosity,

High Porosity, but Low Permeability but Low Permeability

Interconnectedness

Interconnectedness Small PoresSmall Pores

SandSand

The Smaller the Pore Size The Smaller the Pore Size The Larger the Surface Area The Larger the Surface Area

The Higher the Frictional Resistance The Higher the Frictional Resistance

The Lower the Permeability The Lower the Permeability

HighHigh

LowLow

Darcy’s Experiment Darcy’s Experiment

He investigated the flow of water in a column of sand He investigated the flow of water in a column of sand He varied:

He varied: Length and diameter of the columnLength and diameter of the column Porous material in the column

Porous material in the column

Water levels in inlet and outlet reservoirs Water levels in inlet and outlet reservoirs Measured the rate of flow (Q): volume / time

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

K = constant of proportionality

Q = -KA (

Q = -KA (   h / L) h / L) Darcy’s Law Darcy’s Law

Empirical Law – Derived from Observation, not from Theory 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)

LL³³ x L x L T x L

T x L²² x L x L

What is K?

What is K?

K = Hydraulic Conductivity = coefficient of permeability K = Hydraulic Conductivity = coefficient of permeability

K = QL / A (-

K = QL / A (-   h) h) / /

/ / / /

LL TT

What are the units of K?

What are the units of K?

= =

The larger the K, the greater the flow rate (Q) The larger the K, the greater the flow rate (Q) KK is a function of both: is a function of both:

Porous medium Porous medium

The Fluid

The Fluid

ClayClay 1010^-9-9 – 10 – 10^-6-6 SiltSilt 1010^-6-6 – 10 – 10^-4-4

Silty Sand

Silty Sand 1010^-5-5 – 10 – 10^-3-3 Sands

Sands 1010^-3-3 – 10 – 10^-1-1 Gravel

Gravel 1010^-2-2 – 1 – 1

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

Clay Clay Silt Silt

Sand Sand Gravel Gravel

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

Q = -KA (

Q = -KA (   h / L) h / L)

Rearrange Rearrange

Q Q A A

q = q = = -K = -K ( (   h / L) h / L)

q = specific discharge (Darcian velocity) q = specific discharge (Darcian velocity)

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

if it were an open conduitif it were an open conduit

Average linear velocity = v = Average linear velocity = v =

True Velocity – Average Mean Linear Velocity?

True Velocity – Average Mean Linear Velocity?

Q Q A A

q = q = = -K = -K ( (   h / L) h / L)

Only account for area through which flow is occurring Only account for area through which flow is occurring

Flow area = porosity x area Flow area = porosity x area

Water can only flow through the pores Water can only flow through the pores

Q Q nA nA q q

n n = =

Aquifers

Aquifer – geologic unit that can store and transmit water at rates fast enough to

supply reasonable amounts to wells

Confining Layer – geologic unit of little to no permeability

Aquitard, Aquiclude

Gravels

Clays / Silts

Sands

Water table aquifer

Confined aquifer

Types of Aquifers

Unconfined Aquifer

high permeability layers to the surface

overlain by

confining layer

Homogeneity – same properties in all locations

Homogeneous vs Heterogenous

Variation as a function of Space

Heterogeneity

hydraulic properties change spatially

Anisotropic

changes with direction

Isotropy vs Anisotropy

Variation as a function of direction Isotropic

same in direction

In Arid Areas: Water table flatter

In Humid Areas: Water Table Subdued Replica of Topography

Regional Flow

Subdued replica of topography

Discharge occurs in topographically low spots

Water Table Mimics the Topography

Need gradient for flow

If water table flat – no flow occurring Sloping Water Table – Flowing Water

Flow typically flows from high to low areas

Q = -KA (

Q = -KA (   h / L h / L ) )

Discharge vs Recharge Areas

Recharge Downward Vertical Gradient Discharge

Upward

Vertical Gradient

Discharge Topographically High Areas

Deeper Unsaturated Zone Flow Lines Diverge

Recharge

Topographically Low Areas Shallow Unsaturated Zone

Flow Lines Converge

Equations of Groundwater Flow

Fluid flow is governed by laws of physics

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 Law of Mass Conservation

Continuity Equation

Matter is Neither Created or Destroyed Darcy’s Law

Balancing your checkbook

$

My Account

Let’s consider a control volume

dx

dy

dz

Confined, Fully Saturated Aquifer

dx

dy

dz

q_x

q_y

q_z

q = specific discharge = Q / A

dx

dy

dz

q_x

q_y

q_z

_w = fluid density (mass per unit volume)

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

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.

dx

dy dz

- (_wq_x) dxdydz

-

(

_^_x^{wqx +} _^_y^{wqy +}_^_z ^wqz

)

^dxdydz

x

- ( _wq_y) dxdydz

y

- ( _wq_z) dxdydz

z (_wq_x) dydz

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)

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

dx

dy

n dz

[(_w)(n)(dx)(dy)(dz)]

M

t 

t

=

[(_w)(n)(dx)(dy)(dz)]

t =

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

-

(

_^_x^{wqx +} _^_y^{wqy +}_^_z ^wqz

)

^dxdydz

Divide both sides by the volume [(_w)(n)]

t = -

(

_^_x^{wqx +}_^_y^{wqy +}_^_z ^wqz

)

If the fluid density does not vary spatially [(_w)(n)]

t = -

(

_^_x^qx+_^_y^qy+_^_z^qz

)

1

_w

q

_x

= - K

_x

(  h/  x) q

_y

= - K

_y

(  h/  y) q

_z

= - K

_z

(  h/  z)

xq_x+ 

yq_y+ 

zq_z

Remember Darcy’s Law

x

( K

_x^_^h_x

)

_^_y

( K

_y^_^h_y

)

^

z

( K

_z ^_^h_z

)

+ +

dx

dy dz

x

( K

_x^_^h_x

)

_^_y

( K

_y^_^h_y

)

^

z

( K

_z ^_^h_z

)

+ +

[(_w)(n)]

t 1

 =

(

-

)

[(_w)(n)]

t 1

_w

After Differentiation and Many Substitutions (wg + nwg) h

t

 = aquifer compressibility

 = compressibility of water

x

( K

_x^_^h_x

)

_^_y

( K

_y^_^h_y

)

^

z

( K

_z ^_^h_z

)

+ +

(_wg + n_wg) h =

t

S_s = _wg ( + n)

But remember specific storage

x

( K

_x^_^h_x

)

_^_y

( K

_y^_^h_y

)

^

z

( K

_z ^_^h_z

)

+ + =

S

_s^h

t

3D groundwater flow equation for a confined aquifer

If we assume a homogeneous system

K S

_s^h

t

²h

x² + ²h +

y² ²h

z² =

( )

transient anisotropic

heterogeneous

x

(

K

_x ^_^h_x

) K

_y^_y

(

^_^h_y

)

^

z

(

K

_z ^_^h_z

)

+ + =

S

_s^h

t If we assume a homogeneous, isotropic system

Transient – head changes with time

Steady State – head doesn’t change with time Homogeneous – K doesn’t vary with space

Isotropic – K doesn’t vary with direction: K_x = K_y = K_z = K

Let’s Assume Steady State System

Laplace Equation

Conservation of mass for steady flow in an Isotropic Homogenous aquifer

²h

x² + ²h +

y² ²h

z² = 0

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

Kb S

_s

b

^h

t

²h

x² + ²h

y² =

( )

S T

^^ht

²h

x² + ²h

y² =

K S

_s^h

t

²h

x² + ²h +

y² ²h

z² =

( )

x

( K

_x^_^h_x

)

_^_y

( K

_y^_^h_y

)

^

z

( K

_z ^_^h_z

)

+ + = 0

Heterogeneous Anisotropic Steady State

K S

_s^h

t

²h

x² + ²h +

y² ²h

z² =

( )

Homogeneous Isotropic Transient

²h

x² + ²h +

y² ²h

z² = 0

Homogeneous Isotropic Steady State

Unconfined Systems

Water is derived from storage by vertical drainage

Sy

Pumping causes a

decline in the 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

Water Table

x

( K

_x^_^h_x

)

_^_y

( K

_y^_^h_y

)

^

z

( K

_z ^_^h_z

)

+ + =

S

_s^h

t Remember the Confined System

x

( hK

_x^_^h_x

)

⁺ _^_y

( hK

_y ^_^h_y

)

⁼

S

_y^h

t Let’s look at Unconfined Equivalent

Assume Isotropic and Homogeneous

x

( h

^_^h_x

)

⁺ _^_y

( h

^_^h_y

)

⁼

S

^y

K

h

t

Boussinesq Equation

Nonlinear Equation

K R y

h x

h 2

2 2 2 2

2 2



 

 





K R y

v x

v 2

2 2 2

2



 

 





Let v = h²

For the case of

Island Recharge and steady State