Review

1
Review Of Basic Hydrogeology Principles
2
Types of Terrestrial Water
Surface Water
Soil Moisture
Groundwater
3
Pores Full of Combination of Air and Water
Unsaturated Zone Zone of Aeration
Zone of Saturation
Pores Full Completely with Water
4
Porosity
Secondary Porosity
Primary Porosity
Sediments Sedimentary Rocks
Igneous Rocks Metamorphic Rocks
5
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)
6
Porosity
Permeability
VS
Ability to hold water
Ability to transmit water
Size, Shape, Interconnectedness

Porosity
Permeability
?
Some rocks have high porosity, but low
permeability!!
7
Vesicular Basalt
Clay
Small Pores
Interconnectedness
Porous
Porous
But Not Permeable
But Not Permeable
High Porosity, but Low Permeability
Sand
Porous and Permeable
8
The Smaller the Pore Size
The Larger the Surface Area
The Higher the Frictional Resistance
The Lower the Permeability
High
Low
9
Darcys 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
10
Darcys 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
11
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)
12
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
13
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
14
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 nA
q n
Average linear velocity v

15
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
16
Types of Aquifers
Unconfined Aquifer
Water table aquifer
high permeability layers to the surface
overlain by confining layer
Confined aquifer
17
Homogeneous vs Heterogenous
Variation as a function of Space
Homogeneity same properties in all locations
Heterogeneity hydraulic properties change
spatially
18
Isotropy vs Anisotropy
Variation as a function of direction
Isotropic same in direction
Anisotropic changes with direction
19
Regional Flow
In Humid Areas Water Table Subdued Replica of
Topography
In Arid Areas Water table flatter
20
Water Table Mimics the Topography
Subdued replica of topography
Need gradient for flow
Q -KA (Dh / L)
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
21
Discharge vs Recharge Areas
Recharge Downward Vertical Gradient
Discharge Upward Vertical Gradient
22
Discharge
Recharge
Topographically High Areas
Topographically Low Areas
Deeper Unsaturated Zone
Shallow Unsaturated Zone
Flow Lines Converge
Flow Lines Diverge
23
Equations of Groundwater Flow
Fluid flow is governed by laws of physics
Darcys 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
24
Balancing your checkbook

My Account
25
Lets consider a control volume
Confined, Fully Saturated Aquifer
dz
dy
dx
Area of a face dxdz
26
dz
qx
qy
dy
dx
qz
q specific discharge Q / A
27
dz
qx
qy
dy
dx
qz
?w fluid density (mass per unit volume)
Apply the conservation of mass equation
28
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
-


29
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)

30
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
? ?x
? ?y
? ?z
1 ?w
? ?t
(
)
(?w)(n)
-
qx

qy

qz

31
? ?x
? ?y
? ?z
(
)
-
qx

qy

qz
Remember Darcys 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
? ?x
?h ?x
? ?t
? ?y
?h ?y
(
(
)
? ?z
?h ?z
)
(
(?w)(n)
Kx
)
Ky

Kz


32
1 ?w
? ?t
(?w)(n)
After Differentiation and Many Substitutions
?h ?t
(??wg n??wg)
? aquifer compressibility
? compressibility of water
? ?x
?h ?x
?h ?t
? ?y
?h ?y
(
(
)
? ?z
?h ?z
)
(
Kx
)
(??wg n??wg)
Ky

Kz


But remember specific storage
Ss ?wg (? n?)
33
? ?x
?h ?x
? ?y
?h ?y
(
(
)
? ?z
?h ?z
)
(
?h ?t
Kx
)
Ky
Kz


Ss

3D groundwater flow equation for a confined
aquifer
transient
anisotropic
heterogeneous
Transient head changes with time
Steady State head doesnt change with time
If we assume a homogeneous system
Homogeneous K doesnt 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 doesnt vary with direction Kx
Ky Kz K
?h ?t
?2h ?x2
?2h ?y2
?2h ?z2
)
(
Ss
K



34
Lets Assume Steady State System
?2h ?x2
?2h ?y2
?2h ?z2


0
Laplace Equation
Conservation of mass for steady flow in an
Isotropic Homogenous aquifer
35
?h ?t
?2h ?x2
?2h ?y2
?2h ?z2
)
(
Ss
K



If we assume there are no vertical flow
components (2D)
?h ?t
?2h ?x2
?2h ?y2
)
(
Ssb
Kb


S T
?2h ?x2
?2h ?y2
?h ?t


36
? ?x
?h ?x
? ?y
?h ?y
(
(
)
? ?z
?h ?z
)
(
Kx
)
Ky
Kz


0
Heterogeneous
Anisotropic
Steady State
?h ?t
?2h ?x2
?2h ?y2
?2h ?z2
)
(
Ss
K



Homogeneous
Isotropic
Transient
?2h ?x2
?2h ?y2
?2h ?z2


0
Homogeneous
Isotropic
Steady State
37
Unconfined Systems
Pumping causes a decline in the water table
Water is derived from storage by vertical
drainage Sy
38
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
39
Remember the Confined System
? ?x
?h ?x
? ?y
?h ?y
(
(
)
? ?z
?h ?z
)
(
?h ?t
Kx
)
Ky
Kz


Ss

Lets 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
40
For the case of Island Recharge and steady State
Let v h2