Q
∆ Water Flow in Porous Media Porous in Flow Water
Q
gravity
water pressure and and pressure water
a combination of of combination a water flows due to to due flows water
∆
Q
gravity
water pressure and and pressure water
a combination of of combination a
water flows due to to due flows water water pressure “pushes” pressure water
∆
Q
gravity gravity
gravity “pulls” gravity water pressure and and pressure water
a combination of of combination a
water flows due to to due flows water water pressure “pushes” pressure water
∆ Water pressure “pushes” and gravity “pulls”
The combination of these two quantities is called the hydraulic head
Water moves due to a difference in hydraulic head between two locations.
The change in hydraulic head over some distance is called the hydraulic gradient.
Q
z p + h + h = h = h
The total head at the surface the at head total The of the sand is sand the of
z h
z elevation head or h or head elevation
the bottom of the sand due to gravity. This is called called is This gravity. to due sand the of bottom the
A water molecule at the surface wants to “fall” to to “fall” to wants surface the at molecule water A
p
the sand. It is called the pressure head or h or head pressure the called is It sand. the
p h water pressure due to the height of the water above above water the of height the to due pressure water
A water molecule at the surface of the sand senses a a senses sand the of surface the at molecule water A ∆
The total head at the surface the at head total The of the sand the of
Q
h = 0 = h
The total head at the bottom the at head total The of the sand is sand the of
z = 0 = Therefore, h Therefore,
distance because it is already at the bottom! bottom! the at already is it because distance
A water molecule at the bottom doesn’t fall any any fall doesn’t bottom the at molecule water A
p p = 0 = to the atmosphere, therefore h therefore atmosphere, the to water pressure because the valve opening is exposed exposed is opening valve the because pressure water
A water molecule at the bottom of the sand senses no no senses sand the of bottom the at molecule water A ∆
The total head at the bottom the at head total The of the sand the of
Q
z h
z p ∆ + h + h = h – h = h = h = 0
∆ h = head at the top “minus” the head at the bottom the at head the “minus” top the at head = h
p h
∆
∆ The change in total head ( head total in change The h)
Q
∆ L
∆ The length of the sand is defined as as defined is sand the of length The L
∆
Q
z ∆ L h
∆ ∆ The hydraulic gradient is is gradient hydraulic The L h/
p h
∆ The hydraulic gradient hydraulic The
Q
water flow water
surfaces will resist resist will surfaces friction along the grain grain the along friction
∆ Stream-Flow Analogy
highest stream velocity
lowest stream velocity
energy lost due to friction along the stream channel Stream-Flow Analogy
Equivalent stream-channel volumes.
Which one has the lower velocity? Why? Water Flow in Porous Media
Pore space between grains
friction along grain grain grain
higher water velocity lower water velocity The amount of friction along grain boundaries depends on the surface area of the sediment Assuming spherical sediments, the surface area per volume is given as
av = 6/d
where d = grain diameter
Q
v
Surface area, a area, Surface per cm per cm 15 =
3 2
diameters of 4.0 mm mm 4.0 of diameters gravel having grain grain having gravel
∆
Q
v
Surface area, a area, Surface per cm per cm 150 =
3 2
diameters of 0.4 mm 0.4 of diameters sand having grain grain having sand
∆
Q
v
Surface area, a area, Surface per cm per cm 1500 =
3 2
diameters of 0.04 mm 0.04 of diameters silt having grain grain having silt
∆ 1 gram of smectite clay has 8,000,000 cm2 of surface area
or
5 grams of smectite clay has the surface area of a football field!
smectite is a common name for montmorillonite clay, the clay that attracts water and “swells” Water flow in porous media is measured with a permeameter Permeameter
Sand filled cylinder (saturated)
Cylinder has an area = A Permeameter
water flows through the sand and out the valve
water pressure in the vessel “pushes” water into the sand Permeameter
∆h ∆L
The volume of water that flows out is controlled by the hydraulic gradient and the amount of energy loss due to friction along the grains First Experiment
the water height in the vessel remains constant
∆h ∆L
The volume of water that flows out in some length of time is the discharge = Q Plot the results of the 1st experiment
Q/A
∆h/∆L Second Experiment
increased water height
∆h ∆L
larger discharge Q Plot the results of the 2nd experiment
Q/A
∆h/∆L Third Experiment
in all experiments the ∆h is kept constant
increased water height
∆h ∆L
larger discharge Q Plot the results of the 3rd experiment
Q/A
∆h/∆L Darcy’s Law
Q/A = -K(∆h/∆L)
Q/A slope = K = hydraulic conductivity = permeability
∆h/∆L The hydraulic conductivity is a measure of the sediments ability to transmit fluid.
It’s magnitude is controlled by the grain size (or pore size) which determines the amount of frictional resistance Slope is K for sand
Q/A
Slope is K for silt
∆h/∆L Slope is K for sand
Q/A
Q/A
Slope is K for silt
Q/A ∆h/∆L ∆h/∆L Slope is K for sand
Q/A
Slope is K for silt
Q/A
∆h/∆L ∆h/∆L ∆h/∆L
Q Q
∆ ∆
1 x 10 x 1 ≈ K cm/s cm/s 10 x 1 ≈ K
-3 -6
Sand Silt To get the same amount of Q out of both cylinders in the same amount of time, the ∆h for the silt would have to be 1000 times that of the sand.
Slope is K for sand
Q/A
Slope is K for silt
Q/A
∆h/∆L ∆h/∆L ∆h/∆L Saturated Flow in Porous Media
water moves fastest in the center of the pore Saturated Flow in Porous Media
Smaller pores, more frictional resistance, lower hydraulic conductivity Unsaturated Flow in Porous Media
air pockets Unsaturated Flow in Porous Media
water is a wetting fluid, i.e., it likes to adhere to the grains surfaces
air pockets Unsaturated Flow in Porous Media
Water flows through a smaller available area—as such there is more frictional resistance and the rate at which water can flow decreases—i.e., the hydraulic conductivity decreases with water content. Unsaturated Flow in Porous Media
Ksat
K(θ)
0 Water Content (θ) θ = n = saturated Saturated Flow in Porous Media
Darcy Flux = q = Q/A = -K(∆h/∆L)
Darcy Flux is the average flux of water discharging through the entire cross sectional area of the conduit. Saturated Flow in Porous Media
average pore water velocity = v = q/n or v = q/n = -K/n(∆h/∆L)
In actuality, water is only flowing through the available pore space in the porous media. Therefore, the average velocity of the water is the Darcy Flux divided by the porosity of the sediment. Abbotsford-Sumas Aquifer
The aquifer covers approximately 200 km2 and serves as a water supply for approximately 110,000 people in BC and WA.
Ground Water Flow is from North-to-South
Glacial Marine Drift Marine Glacial
A W BC
25 m 25 - 15
10 m 10 - 1
∆ NS
Sumas Outwash Sumas
(Sumas Outwash) deposited about 10,000 years ago. years 10,000 about deposited Outwash) (Sumas
The aquifer is unconfined and comprised comprised and unconfined is aquifer The of glacial outwash sands outwash glacial of and gravels gravels and Abbotsford-Sumas Aquifer Abbotsford-Sumas Sumas Outwash
NS ∆ s s r e l e t e Mi .5 m 1 o l ES T Ki A .1
D 2
R DA
ST
K A
C
D I N
T E
S T
R CA I
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V
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A 4 .
H 1 V9 BC6 .5 0 V8 .7 0
V2
V3 V7 V10
V A U N B V6 E N
R R V4 D 25 35 0. 0. H8 V1 BC5 0 0 V5 2 e V1 k H7 a P2 L H6 dson P3 Ju s T1 e T2 t i H5 S H4 ing l p H2 e m k a a BC4 L H3 S s n r o b g eam eam
D
n D r r t t
R K1
R
Well Sampling Sites
Pa S S
N K H1
R
d
C I
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B S
G
e R
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A g V
P
L A
s H Le ell s l l W BC3 w We o l p e al h De S 26 wells Water-level measurements and sampling Depth to Water Table
shallow wells deep wells 60
40 Depth to Water (ft)
20 T1 T2 P1 P3 V5 V6 V7 V8 V9 V1 V2 V4 H2 H3 H4 H5 H6 V11 V12 s s r e l e t e Mi .5 m 1 o l ES T Ki A .1
D 2
R DA
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K A
C
D I N
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S T
R CA I
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V
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A 4 .
H 1 V9 BC6 .5 0 V8 .7 0
V2
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V A U N B V6 E N
R R V4 D 25 35 0. 0. H8 V1 BC5 0 0 V5 2 e V1 k H7 a P2 L H6 dson P3 Ju s T1 e T2 t i H5 S H4 ing l p H2 e m k a a BC4 L H3 S s n r o b g eam eam
D
n D r r t t
R K1
R
Well Sampling Sites
Pa S S
N K H1
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d
C I
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B S
G
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s H Le ell s l l W BC3 w We o l p e al h De S 26 wells Water Table Hydrographs 35 T1 H2 30 25 Depth to Water (ft) 20 15
2Jul2002 1Jan2003 2Jul2003 1Jan2004 1Jul2004
25 m 25 - 15
10 m 10 - 1
∆ NS AB
Datum is mean sea level sea mean is Datum
A = elevation head elevation = hz
25 m 25 - 15
10 m 10 - 1
∆ NS AB
Datum is mean sea level sea mean is Datum
A = elevation head elevation = hz
25 m 25 - 15
10 m 10 - 1
∆ NS
A = pressure head pressure = hp AB
Datum is mean sea level sea mean is Datum
A = elevation head elevation = hz
25 m 25 - 15
10 m 10 - 1
∆ NS
A hp = pressure head pressure =
AB
A h = total head = pressure = head total = head + elevation head elevation + head
Datum is mean sea level sea mean is Datum
B = elevation head elevation = hz
25 m 25 - 15
10 m 10 - 1
∆ NS
B
hp = pressure head pressure = AB
B = total head = pressure = head total = h head + elevation head elevation + head
Datum is mean sea level sea mean is Datum
25 m 25 - 15
10 m 10 - 1
∆ NS
AB B A ∆ -h h = h
and B is what causes water to flow. flow. to water causes what is B and
∆ The change in total head ( head total in change The h) between A A between h)
∆ L is wells between Distance
25 m 25 - 15
10 m 10 - 1
∆ NS AB The hydraulic gradient between wells A and B is equal to the magnitude of the change in total head divided the distance over which the change occurs.
hydraulic gradient = ∆h/∆L The hydraulic gradient (∆h/∆L) between wells A and B is what drives water through the pore spaces. The hydraulic conductivity (K) will resist the fluid flow because of friction along the grain surfaces. The average velocity (v) at which water flows in the media is quantified by:
v = -K/n(∆h/∆L)
where n = porosity The average hydraulic gradient in the Abbotsford-Sumas aquifer is
∆h/∆L = -0.0055
The average hydraulic conductivity of the glacial sediments is
K = 545 ft/day or K = 0.187 cm/sec
The average porosity of the glacial sediments is
n = 0.30 The average pore-water velocity can be determined using Darcy’s Law
velocity = v = -K/n (∆h/∆L)
Using the aquifer parameters in the equation above yields
velocity = v = -545/0.30(-0.0055) = 10 ft/day
which is very fast for groundwater
25 m 25 - 15
10 m 10 - 1
∆ NS
AB
If the distance from A to B is 1000 ft 1000 is B to A from distance the If
How long would it take water to travel from well well from travel to water take it would long How B B well to A The average groundwater velocity is 10 ft/day ft/day 10 is velocity groundwater average The
25 m 25 - 15
10 m 10 - 1
∆ NS
AB
Time = 100 days 100 = Time
Time = 1000 ft ft 1000 = Time 10 ft/day 10 ⁄
Time = distance distance = Time ⁄ velocity
25 m 25 - 15
10 m 10 - 1
∆ NS
AB
Time = 10,000 days or 27 years!! 27 or days 10,000 = Time
Time = 1000 ft ft 1000 = Time 0.10 ft/day 0.10 ⁄
ty = 0.10 ft/day 0.10 = ty i c o l Ve
5.45 ft/day……then the ft/day……then 5.45
If the aquifer were a fine sand sand fine a were aquifer the If wi th a hydraulic conductivity of conductivity hydraulic a th Why is this important?
25 m 25 - 15
10 m 10 - 1
∆ NS
AB Transport of Septic System Discharge System Septic of Transport Contaminant transport in an aquifer
NS ∆
∆
contaminate streams contaminate
groundwater contaminants can can contaminants groundwater Groundwater surface water interactions water surface Groundwater
∆
winter flow winter Groundwater surface water interactions water surface Groundwater
∆
summer flow summer
pumping rates (irrigation) rates pumping
lower recharge and/or higher higher and/or recharge lower
water table drops because of of because drops table water Groundwater surface water interactions interactions water surface Groundwater Well A Well B sand gravel QA = QB = pumping rate
Q A QB sand gravel
cone of depression Q A QB sand gravel
shallow slope high permeability low permeability steep slope
The slope of the cone of depression is determined by the permeability Q > Q QA B A QB sand sand
lowlow perm permeeabilityability low permeability
The depth of the cone of depression is determined by the pumping rate Q = Q QA B A QB sand sand
r r
low permeability
The radius of the cone of depression is determined by the pumping duration
∆
influence streamflow influence
A pumping well can can well pumping A Groundwater surface water interactions water surface Groundwater