Transcript Unit 01 : Advanced Hydrogeology Review of Groundwater Flow

Unit 01 : Advanced Hydrogeology
Review of Groundwater Flow
What is hydrogeology?
• Hydrogeology is the study of the laws
governing the movement of subsurface
water,
• the mechanical, chemical and thermal
interaction of this water with the porous
solid,
• and the transport of energy, chemical
constituents and particulates by the flow.
Domenico and Schwartz, 1997
Laws governing movement
Darcy’s Law
• Q = -A.K dh/dx
Q is the flow,
K is the hydraulic conductivity,
dh/dx is the head gradient and
A is the cross sectional area normal to x.
• Q/A = q = -K dh/dx
q is called the specific discharge
• v = q/n = -(K/n) dh/dx
v is the advective (flow) velocity
n is the porosity
Mechanical, Thermal and Chemical Interactions
• Mixing caused by
– Hydraulic (mechanical) gradients (dh/dx)
– Thermal gradients (dT/dx)
– Chemical gradients (dC/dx)
• Interactions of fluids with the porous
medium
Groundwater Transport
• Groundwater transports fluids. The
process is called advection.
• Advection of fluid also carries:
– Solutes (metals, organics, nutrient, etc)
– Particulates (colloids, bacteria, etc)
– Energy (mainly heat)
Hydrologic Cycle
Elements of the Hydrologic Cycle
•
•
•
•
•
•
•
•
Condensation
Precipitation
Evaporation
Transpiration
Interception
Infiltration
Percolation
Runoff
Soil Water
Intermediate Vadose Water
Capillary Water
Groundwater
Water in Unconnected Pores
Bound Water in Minerals
Interstitial Zone
Saturated
Unsaturated
Water Profile
Subsurface Flow
• Infiltration
• flow entering at the ground surface
• Percolation
• vertical downward unsaturated flow
• Interflow
• sub-horizontal unsaturated and perched saturated flow
• Groundwater flow
• sub-horizontal saturated flow
Millimetres of Water
Soil Moisture
Adjusted
Precipitation
Potential
Evaporation
Soil Moisture
Depletion
Spring
Recharge
J
F
M
A
Fall
Recharge
M
J
J
A
S
O
N
D
Infiltration Capacity
• Water supplied to the soil surface at an
increasing rate will eventually runoff.
• Water supplied to the soil surface at a
constant rate infiltrates at a rate that
decreases with time to a limiting rate.
• This limiting rate (when the soil is
saturated) is called the infiltration
capacity of the soil surface.
Field Capacity
• Flow of water in an unsaturated soil
cannot take place until a limiting
moisture content is reached.
• This limiting moisture content is called
the field capacity of the soil in soil
science and the residual water
saturation in hydrogeology.
0%
Infiltration Capacity [ LT-1 ]
Field Capacity
[ % ]
Field
Capacity
Infiltration Rate
Infiltration
Infiltration
Capacity
Moisture Content
100%
Hydrograph Components
• Steamflow hydrographs can be broken
down into three components:
– Runoff (overland flow)
– Interflow (unsaturated sub-horizontal flow)
– Baseflow (groundwater flow)
• Each component has a characteristic
recession (decay) rate.
Baseflow
• The decline of the flow in a stream in the
absence of input is called recession
• Empirically, recession curves are exponential
decay functions Q = Qoe-kt.
• After long periods without precipitation, the
recession rate is called baseflow and is
characteristic of the goundwater system
feeding the stream.
• The groundwater recession constant is given
by the equation k = ln(Qo/Q)/t
Hydrograph Analysis
• Point A is minimum Q
gradient is determined
from recession rate
• Point B is maximum Q
• Point C is Q at time T*
after the peak:
Discharge
T*
C
A
B
T* = An
where A is the drainage area and n
is an empirical power.
Time
If A is in km2, n = 0.14
If A is in mile2, n = 0.20
Global Hydrological Equation
Input – Output = Change in Storage
P – E –T – Ro = DS
P
E
T
Ro
DS
precipitation
evaporation
transpiration
runoff
change in groundwater storage
Elements of the Basin Cycle
P
E
For the groundwater sub-system
Rs + Qi – Ta – Qa = DS
Qo
Surface
F
Qs
Soil
Rs
Ta
Qa
Aquifer
Qi
Stream Channels
Ts
Ro
Aquifer Types
• Unconfined - storage LARGE depends on specific yield
• Confined - storage SMALL depends on compressibilities
Porosity
Material
Porosity
(%)
well-sorted sand or gravel
25-50
sand and gravel, mixed
20-35
glacial till
10-20
silt
35-50
clay
33-60
Specifics of Aquifer Storage
Unconfined
Sy = n - Sr
Confined
S = b.Ss
n porosity
Sy specific yield (gravity
drainage)
Sr specific retention (like
field capacity)
b thickness
Ss specific storage
Ss = g.(a + n. b )
g specific weight
a matrix compressibility
b water compressibility
Specific Yield
Material
coarse gravel
medium gravel
fine gravel
gravelly sand
coarse sand
medium sand
fine sand
silt
sandy clay
clay
Specific Yield
(%)
Max
Min
Mean
25
12
22
26
13
23
30
21
25
35
20
25
35
20
27
32
15
26
28
10
21
19
4
18
12
3
7
5
0
2
Hydraulic Conductivity
Material
well-sorted gravel
well-sorted sand
silty sands, fine sands
silt, clayey sand, till
clay
Hydraulic
Conductivity
(m/s)
-4
-2
10 to 10
-5
-3
10 to 10
-7
-5
10 to 10
-8
-6
10 to 10
-11
-8
10 to 10
Steady-State Flow
• q = -K dh/dx
K is hydraulic conductivity
h is hydraulic head
[ LT-1 ]
[L]
• q = -(kg/m) dh/dx
k is intrinsic permeability
m is absolute viscosity
g is specific weight
[ L2 ]
[ FL-2T ]
[ FL-3 ]
For horizontal flow gdh/dx = dp/dx
• q = -(k/m) dp/dx
p is fluid pressure
[ FL-2 ]
Vertical Flow
• For vertical flow
q = -K dh/dz
h = p/g + z
dh/dz = (1/g) dp/dz
q = -(kg/m) dh/dz
q = -(k/m)(dp/dz + 1)
Steady-State Flow Systems
Density-Dependent Flow
• For density-dependent flow
q = K dh/dz
h = p/g + z
dh/dz = (1/g)(dp/dz – (p/g)dg/dz + 1)
q = -(kg/m) dh/dz
q = -(k/m)(dp/dz + 1 – (p/g)dg/dz)
Unsaturated Flow
For unsaturated flow
q = -K(y) dh/dz
h=y+z
y is the pressure head
z is the elevation head
h is the total hydraulic head
The pressure head, y, depends on saturation.
At full saturation, y increases with depth. In
the unsaturated zone, y is negative and is
called suction pressure.
Pressure
Water
Table
+
Water
Table
-
Pressure
+
0%
Saturation
Hydraulic Conductivity
Depth
-
Soil Water Characteristic Curve
100%
Steady-State and Transient Flow
Steady-State
Inflow = Outflow
dq/dx = d(K dh/dx)/dx = 0
Transient
Inflow - Outflow = Change in Storage
dq/dx = d(K dh/dx)/dx = S.dh/dt
K is hydraulic conductivity [ LT-1 ]
S is storage coefficient
[]
h is hydraulic head
[L]