review of basic hydrogeology principles
DESCRIPTION
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. - PowerPoint PPT PresentationTRANSCRIPT
ReviewOf
Basic Hydrogeology
Principles
Types of Terrestrial WaterTypes of Terrestrial Water
GroundwaterGroundwater
SoilSoilMoistureMoisture
SurfaceWater
Unsaturated Zone – Zone of Aeration
Pores Full of Combination of Air and Water
Zone of Saturation
Pores Full Completely with Water
PorosityPorosity
Primary PorosityPrimary Porosity Secondary PorositySecondary Porosity
SedimentsSedimentsSedimentary RocksSedimentary Rocks
Igneous RocksIgneous RocksMetamorphic RocksMetamorphic Rocks
PorosityPorosity
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 spaceVv = volume of the void spaceV = total volume of the material (void + rock)V = total volume of the material (void + rock)
==
PorosityPorosityPermeabilityPermeability
VSVS
Ability to hold water Ability to transmit water
Size, Shape, Interconnectedness
PorosityPorosity PermeabilityPermeability
Some rocks have high porosity, but low permeability!!Some rocks have high porosity, but low permeability!!
Vesicular BasaltVesicular Basalt
PorousPorous
But Not PermeableBut Not Permeable
ClayClay
PorousPorous
But Not PermeableBut Not Permeable
High Porosity,High Porosity, but Low Permeability but Low Permeability
InterconnectednessInterconnectedness Small PoresSmall Pores
SandSand
Porous andPorous and PermeablePermeable
The Smaller the Pore SizeThe Smaller the Pore Size
The Larger the Surface AreaThe Larger the Surface Area
The Higher the Frictional ResistanceThe Higher the Frictional Resistance
The Lower the PermeabilityThe Lower the Permeability
HighHigh
LowLow
Darcy’s ExperimentDarcy’s Experiment
He investigated the flow of water in a column of sandHe 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 columnPorous material in the column
Water levels in inlet and outlet reservoirsWater levels in inlet and outlet reservoirs
Measured the rate of flow (Q): volume / timeMeasured the rate of flow (Q): volume / time
K = constant of proportionality
Q = -KA (Q = -KA (h / L)h / L)
Darcy’s LawDarcy’s Law
Empirical Law – Derived from Observation, not from TheoryEmpirical 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 LT x L22 x L x L
What is K?What is K?K = Hydraulic Conductivity = coefficient of permeabilityK = Hydraulic Conductivity = coefficient of permeability
K = QL / A (-K = QL / A (-h)h) //// //
LLTT
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 mediumPorous medium
The FluidThe Fluid
ClayClay 1010-9-9 – 10 – 10-6-6
SiltSilt 1010-6-6 – 10 – 10-4-4
Silty SandSilty Sand 1010-5-5 – 10 – 10-3-3
SandsSands1010-3-3 – 10 – 10-1-1
GravelGravel 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)
ClayClay SiltSilt
SandSand GravelGravel
Not a true velocity as part of the column is filled with sedimentNot a true velocity as part of the column is filled with sediment
Q = -KA (Q = -KA (h / L)h / L)
RearrangeRearrange
QQAA
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?
QQAA
q =q = = -K = -K ((h / L)h / L)
Only account for area through which flow is occurringOnly account for area through which flow is occurring
Flow area = porosity x areaFlow area = porosity x area
Water can only flow through the poresWater can only flow through the pores
QQnAnA
qqnn
==
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 AquifersUnconfined 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
Heterogeneityhydraulic properties
change spatially
Anisotropicchanges with direction
Isotropy vs Anisotropy
Variation as a function of direction
Isotropicsame 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 flowIf water table flat – no flow occurring
Sloping Water Table – Flowing Water
Flow typically flows from high to low areas
Q = -KA (Q = -KA (h / Lh / L))
Discharge vs Recharge Areas
RechargeDownward
Vertical Gradient
DischargeUpward
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
stored in the volume or both
Law of Mass ConservationContinuity Equation
Matter is Neither Created or Destroyed
Darcy’s Law
Balancing your checkbook
$
My Account
Let’s consider a control volume
dx
dy
dz
Area of a face: dxdz
Confined, Fully Saturated Aquifer
dx
dy
dz
qx
qy
qz
q = specific discharge = Q / A
dx
dy
dz
qx
qy
qz
w = fluid density (mass per unit volume)
Apply the conservation of mass equation
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
- (wqx) dxdydz
- ( x
wqx + y
wqy + z
wqz ) dxdydz
x
- (wqy) dxdydzy
- (wqz) dxdydzz
(wqx) 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
dzn
[(w)(n)(dx)(dy)(dz)]Mt
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 = - (
xwqx +
ywqy +
zwqz )
If the fluid density does not vary spatially
[(w)(n)]t = - (
xqx+
y
qy+ z
qz )1w
qx = - Kx(h/x)
qy = - Ky(h/y)
qz = - Kz(h/z)
x
qx+y
qy+ z
qz
Remember Darcy’s Law
x
(Kx
hx )
y(Ky
hy )
z(Kz
hz )+ +
dx
dy
dz
x
(Kx
hx )
y(Ky
hy )
z(Kz
hz )+ +[(w)(n)]
t1w
=
(- )
[(w)(n)]t
1w
After Differentiation and Many Substitutions
(wg + nwg) ht
= aquifer compressibility
= compressibility of water
x
(Kx
hx )
y(Ky
hy )
z(Kz
hz )+ +=(wg + nwg) h
t
Ss = wg ( + n)
But remember specific storage
x
(Kx
hx )
y(Ky
hy )
z(Kz
hz )+ + = Ss
ht
3D groundwater flow equation for a confined aquifer
If we assume a homogeneous system
K Ssht
2hx2
+ +2hy2
2hz2
=( )
transientanisotropicheterogeneous
x
(Kx
hx )
y(Ky
hy )
z(Kz
hz )+ + = Ss
ht
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: Kx = Ky = Kz = K
Let’s Assume Steady State System
Laplace Equation
Conservation of mass for steady flow in an IsotropicHomogenous aquifer
2hx2
+ +2hy2
2hz2
= 0
If we assume there are no vertical flow components (2D)
Kb Ssbht
2hx2
+ 2hy2
=( )
ST
ht
2hx2
+ 2hy2
=
K Ssht
2hx2
+ +2hy2
2hz2
=( )
x
(Kx
hx )
y(Ky
hy )
z(Kz
hz )+ + = 0
Heterogeneous Anisotropic Steady State
K Ssht
2hx2
+ +2hy2
2hz2
=( )
Homogeneous Isotropic Transient
2hx2
+ +2hy2
2hz2
= 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 surfacedeclines, saturated thickness (b) remains constant
In an unconfined system, saturated thickness (h) changes
And thus the transmissivity changes
Water Table
x
(Kx
hx )
y(Ky
hy )
z(Kz
hz )+ + = Ss
ht
Remember the Confined System
x
(hKx
hx )
y(hKy
hy )+ = Sy
ht
Let’s look at Unconfined Equivalent
Assume Isotropic and Homogeneous
x
(hhx )
y(h h
y )+ =Sy
Kht
Boussinesq Equation
Nonlinear Equation
K
R
y
h
x
h 22
22
2
22
K
R
y
v
x
v 22
2
2
2
Let v = h2
For the case of Island Recharge and steady State