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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Pores Full of Combination of Air and Water
Unsaturated Zone – Zone of Aeration
Zone of Saturation
Pores Full Completely with Water
Secondary Porosity
Primary Porosity
Sediments
Sedimentary Rocks
Igneous Rocks
Metamorphic Rocks
n = 100 (Vv / V)
n = porosity (expressed as a percentage)
Vv = volume of the void space
V = total volume of the material (void + rock)
Permeability
VS
Ability to hold water
Ability to transmit water
Size, Shape, Interconnectedness
=
Porosity
Permeability
Some rocks have high porosity, but low permeability!!
Clay
Small Pores
Interconnectedness
Porous
Porous
But Not Permeable
But Not Permeable
High Porosity, but Low Permeability
Sand
Porous andPermeable
The Larger the Surface Area
The Higher the Frictional Resistance
The Lower the Permeability
High
Low
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
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
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)
Clay
Sediments have wide range of values for K (cm/s)
Clay 109 – 106
Silt 106 – 104
Silty Sand 105 – 103
Sands 103 – 101
Gravel 102 – 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
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 =
=
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
Unconfined Aquifer
Water table aquifer
high permeability layers
to the surface
overlain by
confining layer
Confined aquifer
Variation as a function of Space
Homogeneity – same properties in all locations
Heterogeneity
hydraulic properties
change spatially
Variation as a function of direction
Isotropic
same in direction
Anisotropic
changes with direction
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
Recharge
Topographically High Areas
Topographically Low Areas
Deeper Unsaturated Zone
Shallow Unsaturated Zone
Flow Lines Converge
Flow Lines Diverge
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
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
w
t
[(w)(n)]
After Differentiation and Many Substitutions
h
t
(wg + nwg)
= aquifer compressibility
= compressibility of water
h
t
x
h
x
y
h
y
(
(
)
z
h
z
)
(
Kx
)
(wg + nwg)
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
Pumping causes a
decline in the water table
Water is derived from
storage by vertical drainage
Sy
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
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