Introduction Hydrogeology is the science of water inside the earth. The name was introduced by J.-B. Lamarck (pictured) in 1802. Jean-Baptiste Lamarck (1744-1829) From Greek: = hydros = water = geo = earth = logos = science Table 1. Relation of hydrogeology to other disciplines. Geomorphology Stratigraphy Tectonics Topography macroscopic geological properties of materials through which ground water flows Soil science Mineralogy and petrology Chemistry Biology physical, chemical and biological properties of the environment and processes Hydrology Climatology outside forcing Physics Fluid mechanics Mathematics Statistics fluid flow fluid and media properties
Transcript
Introduction
Hydrogeology is the science of water inside the earth. The name was introduced by J.-B. Lamarck (pictured) in 1802.
Jean-Baptiste Lamarck (1744-1829)
From Greek: = hydros = water
= geo = earth
= logos = science
Table 1. Relation of hydrogeology to other disciplines.
GeomorphologyStratigraphyTectonicsTopography
macroscopic geological properties of materials through which ground water flows
Soil scienceMineralogy and petrologyChemistryBiology
physical, chemical and biological properties of the environment and processes
HydrologyClimatology
outside forcing
PhysicsFluid mechanicsMathematicsStatistics
fluid flowfluid and media properties
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Water below the land surface
Subsurface water is all water beneath the ground surface.
Ground water is the water in the zone of saturation (below water table). In agronomy, the term ground water is used to denote the sub-surface water below and above the water table.
Almost all ground water is meteoric water (i.e., water that is circulating in the water cycle). A small part of ground water may be from other sources, such as magmatic. Isotopic studies of O and H indicate that the magmatic component is less or much less than 1% of total circulating water.
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Clouds
Precipitation(on land)
Ocean
Sea water
Groundwater table
SR
Evaporation
Freshwater - salt waterinterface
LeakageUnsaturated flow
Spring
SR
ET
SR
Snow and ice
Sublimation
I
N I
Groundwater flow(saturated flow)
SRE
Lake
Evapotranspiration(from vegetation)
RF
River
E
Transpiration
Precipitation(on the ocean)
Clouds
Movement of moist
air masses
I
Returnflow from
septic tanks
Abbreviations: ET = evapotranspiration; E = evaporation; I = infiltration; SR = surface runoff; RF = return flow from irrigation; N = natural replenishment
Fig. 1. Schematic representation of water cycle (Bear and Verruijt, 1987, Modeling groundwater flow and pollution, Reidel, 414 p).
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Infiltration
Precipitation: - wetting and infiltration- surface runoff- evaporation
Temperate climates: infiltration is ca. 300 mm/yr (good as a first guess).Arid climates: infiltration is close to 0, except along rivers and mountain fronts.Recharge occurs mostly in winter time.
Properties of water
Chemical form:H2O
Physical states:gas (vapor)
liquid (water)solid (ice, snow)
Molecular structure:
One oxygen atom and two hydrogen atoms are arranged (figure). The molecule is polar (it has dipole moment). It has a positive charge on the side of the two hydrogen atoms and negative charge on the opposite side. Water is a good solvent because ot the polarity of water molecule.
Physical properties:
Table 2. Physical properties of water.
Temperature(C)
Density(kg m-3)
Viscosity(10-3 Pa s)
Compressibility(10-10 Pa-1)
0 999.8 1.781 5.098
5 1000.0 1.518 4.928
10 999.7 1.307 4.789
15 999.1 1.139 4.678
20 998.2 1.002 4.591
25 997.0 0.890 4.524
30 995.7 0.798 4.475
Range (%) 0.43 55.2 12.22
Data from de Marsily, 1986, Quantitative Hydrogeology, Academic Press, 440 p.
-
+120˚
10-10 m = 1 Å
Isotopic composition:
Three stable isotopes of oxygen:16O - common (abundance 99.76%)18O - rare (0.20%)17O - very, very, very rare (0.04%)
Two stable isotopes of hydrogen:1H - common (99.984%)2H = D = deuterium - rare (0.016%)
Combination H2O may result in:1H16O - "normal water"
HD16O - heavy water
H218O - heavy water
Radioactive isotope of hydrogen:3H = T = tritiumhalf-life of 12.3 y
decay to helium-3: T -> 3He + -
Beta decay of 3H to 3He occurs by emitting - (or e-), neutron becomes proton.
Decay of tritium is used for dating of young ground water (up to few tens of years).
Isotopes - lead to fractionation. Useful in studies of environmental processes: evaporation, recharge, mixing.
pnn ppn
e
ee
1H 2H 3H
3He 4He
N = 0 1 2
Z = 1
Z = 2
16O 17O 18O
N = 8 9 10
Z = 8
Types of water on contact with solid
Hygroscopic immobile water (adsorbed in figure):
High binding energy. 1-3 molecules, attached to surface of grain due to molecular attraction. Can remove by heating to 150C
Hygroscopic mobile water (adsorbed in figure):
Lower binding energy. 10-20 molecules, it is maximum degree of hygroscopicity. Can remove by heating to 90C. Consti-tute 15-20% of all water in clays, but less than 5% in coarser materials.
Also varies according to mineralogy, e.g.: 0.9% in quartz, 8-17% in feldspars, 36-48% in micas.
Pellicular water (or pendular or funicular; adhesive in figure):
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1012
Bon
d en
ergy
(P
a)
Distance (10-6 m)0.1 0.5
freewater
adhesive
adsorbed
Fig. 2. Binding energy for water molecules (G. de Marsily, 1986, Quantitative hydrogeology, Academic Press, San Diego).
Low binding energy. It is a film over hygroscopic water. It is mobile. Maintained by molecular forces.
Free water
• in capillaries (small pores)• gravitational (moving)
Chemically bound water:
In minerals as H2O (e.g., gypsum, CaSO4·2H2O), HO-, (e.g., gibbsite, Al(OH)3), H+ and H3O+
Origin of ground water
Juvenile water
From the interior of the earth. Has never been in surficial water cycle. It is first water created from O and H.
• Mantle: largest source, 2·1022 kg
• Crust: from 2·1021 to 4·1021 kg (from mantle)
Example: mineral muscovite (KAl2(OH)2Si4O10) has 8.5% OH and 4.5% H2O
Connate water (or formation water or fossil water)
It was once a part of surficial water cycle and then it was trapped in sediments. Has composition dependent on rock through which it flows (dissolution and precipitation are important factors controlling chemical composition of water).
Meteoric water (or precipitation water)
Water presently circulating between the atmosphere and the hydrosphere. Enters groundwater systems by infiltration. It has composi-tion similar to rain water, but evolves towards equilibrium with rock formation.
Meteoric water is of interest to us because of its occurrence in the shallow subsurface.
Darcy’s law
Introduction
Imagine a parcel of water (A) in a column of water (figure); the parcel has the following characteristics:
A
, v, p
h
datum, z=0, p=p0 (p0 = atmospheric)
z
(1) elevation z(2) pressure p(3) velocity v(4) density
Parcel A has total energy that is the sum of potential, kinetic and elastic ener-gies.
Define: hydraulic head (h) - a measure of total energy of water
Hydraulic head has two components:
pressure head () - due to pressure of water above A
elevation head (z) - due to elevation of A above the datum
h = z +
Darcy’s experiment
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dL
Q
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z1, p1
h1
h2
A = cross-sectional area
z2, p2
Henry Darcy (1803-1858)
Darcy (1856) observed that flow Q is:
(1) proportional to head difference dh(2) inversely proportional to column length dL(3) proportional to cross-sectional area A
Add a proportionality constant (K), which depends on properties of fluid and properties of soil (porous medium), to get Darcy’s law:
Q KA dhdL-------–=
h = hydraulic head [L]A = column cross-sectional area [L2]L = column length [L]K = hydraulic conductivity [LT-1]Q = flow rate [L3T-1]dh = h2-h1 = change of hydraulic head along the flow line [L]h2 = is head down the flow line; h1 is head up the flow line-dh/dL= hydraulic gradient [-]
Darcy’s law per unit area:
q QA---- K– dh
dL-------= =
Flow velocities are faster than the specific discharge because flow occurs in pores only. Therefore, we have seepage (linear) velocity, v:
v qn--- K
n----– dh
dL-------= =
where n is the porosity (fraction of volume of aquifer that is taken by pores). This is average macroscopic velocity of water that is used for calculations of travel time.
Travel time calculation:
Given the distance (d) and the velocity (v), the travel time (t) is computed as:
t dv---=
�y
Example
A factory has been dumping chemical waste into an abandoned well (figure). Calculate the specific discharge (q) through the system. If the chemical travels with the water velocity, estimate how long it will take to contaminate the lake.
K=8.25 m/dn=0.15
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h=122 m
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500 m
LAKE
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Specific discharge:
q = -K·(dh/dL) = -8.25·(122-124)/500 = 0.033 m/d
Travel time:
t = d/v = d/(q/n) = 500/(0.033/0.15) = 2728 d = 7.47 y
Hydraulic conductivity
In Darcy’s law, the proportionality constant K is called hydraulic conductivity (units: L T-1). Graphically, it is the slope of the line in Darcy’s law:
K-dh/dL
q
q = - K(dh/dL)
What does the hydraulic conductivity depend on?
K kg
------=
where k is the intrinsic permeability, is water density, g is the acceleration due to gravity, and is the viscosity.
Dimension of K:
L2ML
3–L
2T
2–
ML2T
2–L
2–T
----------------------------------- LT1– K has units of velocity=
Intrinsic permeability (k) is a function of the porous medium alone. In general, it is considered proportional to some characteristic length, e.g., grain size: k = cd2, where c is a dimensionless proportionality constant that may be found experimentally, and d is median grain size.
Dimension of k: L2
Common unit: darcy = 10-8 cm2 = 10-12 m2
Typical values of hydraulic conductivity (m/s):
gravel 10-3 - 101
sand 10-7 - 10-2
sandstone 10-10 - 10-5
silt 10-9 - 10-5
clay 10-12 - 10-5
karst limestone 10-5 - 10-1
crystalline rock 10-13 - 10-10
Methods of determining hydraulic conductivity
From grain-size analysis
K kg
------= C d102 g
------=
where K is hydraulic conductivity, k is intrinsic permeability (equal to C·d102) , C is an empirical constant (with value close to 1), d10 is
the tenth percentile grain diameter of the porous medium, is water density, g is acceleration due to gravity, and is water viscosity.
Note: K is proportional to square of grain size!
Measurements
Laboratory columns (see Class Experiment)
Field tests (pumping tests)
Modeling
With known (measured) flux Q and gradient dh/dx, compute hydraulic conductivity K.
Porosity
Definitions: n = Vvoid/Vtotal
Primary porosity - between grains
Secondary porosity - fracture or solution porosity
Fractures - similar definition of porosity: Vvoid/Vtotal
Total porosity - defined earlier; total pore space in a porous medium; total water content
n pore volumetotal volume------------------------------=
Effective porosity - interconnected pore space. Some water is in dead-end pores or otherwise
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captured and excluded from circulation.
neinterconnected pore volume
total volume-------------------------------------------------------------------=
Total porosity and effective porosity are related as in the figure below.
0.5
0.4
0.3
0.2
0.1
00.0001 0.001 0.01 0.1 1 10 100
Mean graindiameter (mm)
Fin
e cl
ay
Cla
y
Silt
Fim
e sa
nd
Coa
rse
sand
Fin
e gr
avel
Coa
rse
grav
el
Blo
cks
Total porosityEffective porosityP
oros
ity
Fig. 3. Porosity and effective porosity for different grain sizes (G. de Marsily, 1986, Quantitative hydrogeology, Academic Press, San Diego).
Aquifers and aquitards
Aquifer - geological formation which contains and yields water.
- saturated, permeable geologic unit which can transmit significant quantities of water.
Aquitard - saturated, permeable geologic unit which cannot transmit significant quantities of water (but can transmit small quanti-ties). Also called a semi-pervious formation or leaky formation.
Types of aquifers
(1) Unconfined aquifer is one whose upper boundary is the water table, i.e., where pressure is zero (p=0).
Look ate the total head h: h = z + p/
At the top of the aquifer, htop = ztop + ptop/
but because ptop = 0, we have:
htop = ztop
which means that if the head (h) increases, groundwater table rises.
Surface recharge is negligible because of high evapotranspiration rates. Only in valleys, rivers may carry water from mountains and recharge the aquifer.
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floodedwadi
divide
VALLEY AQUIFER (IN ARID ZONES)
Here, contrary to valley aquifers (in humid, temperate climatic zones), water table is highest beneath rivers.
Examples: North African aquifers (Nubian Aquifer), aquifers in the American Southwest (Arizona, New Mexico).
(c) alluvial aquifer
Along streams. Usually in equilibrium with the stream, i.e., alternately drains and recharges streams along their length and at different times.
Example: Rhine River
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Rhine River
Stream may be either gaining water from the aquifer or losing water to the aquifer.
Stream
losing part(upstream)
gaining part(downstream)
red = equipotentialsgreen = flow directions
(d) perched aquifer
Located on impermeable lenses or discontinuous layers.
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water table
clay lenssand
(2) Confined aquifer is one in which the top of the saturated zone is confined (bounded) by an aquitard, i.e., at the top of the aquifer, pressure is not zero (ptop 0).
htop = ztop + ptop/
thus,
htop ztop
which means that if the head (h) increases, the pressure (p) also increases.
In a confined aquifer, the piezometric head (or water level in an observation well, or a piezometer) is higher than the upper boundary of the aquifer.
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piezometricsurface
artesianwell
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rechargearea
dischargearea
If the head is higher than the surface elevation, the aquifer is artesian.
Piezometric surface - a conceptual, imaginary (!) surface joining the water levels in all piezometers in the aquifer. In a phreatic aquifer, it was the water table and it had a physi-cal meaning.
Examples of artesian aquifers: the Great Artesian Basin in Australia, Milk River aquifer in Alberta (Canada).
Example 1: layered aquifer system
Example 2: High Plains aquifer
Area: 450,000 km2
Elevation range: 355 m - 2400 m
Few streams = reliance on ground water (30% of all pumped ground water in the USA
25% of crops production in the USA
High Plains aquifer - formation
Composed of sands, gravels, silts, clays.
Fluvial and aeolian origin.
Age: Tertiary (65 My - 1.8 My) to Quaernary (1.8 My - now).
Thickness: ca. 1000 m
High Plains aquifer - withdrawals and flow patterns
High Plains aquifer - withdrawals and depth to water
High Plains aquifer - withdrawals and water level change
Storage of water
We will use the usual mass balance in a reservoir: Qin - Qout = storage
Look at a pumping well in a confined aquifer (Figure below). If the aquifer is unbounded on the sides (that is, if it is confined on top and bottom, but not on the sides), water comes from the sides. But in a system that is totally isolated on all sides, pumped water comes from storage ( storage < 0).
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Q
clay
sand
clay
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Q
isolatedlaterally
isolated only ontop and bottom
isolated on top and bottom,and on the sides
Where does the water come from?
(1) water expands (water is compressible);
(2) matrix consolidates (e.g., grains rearrange).
Define specific storage coefficient, Ss, as the volume of water released per unit volume of aquifer per unit decline of hydraulic head:
SS
dVw
VT dh– -------------------------=
It is computed using compressibility ( and ) and porosity (n) values as follows:
Ss n+ g n+ = =
Some values:
water: = 4.4E-10 m2/N
clay: = 10-6 to 10-8 m2/N
sand: = 10-7 to 10-9 m2/N
jointed rock: = 10-9 to 10-10 m2/N
solid rock: = 10-10 to 10-11 m2/N
Typical values of Ss: 3x10-6 m-1
Related (derivative) storage parameter:
Storativity = S = Ss · b
where b is the thickness of the aquifer.
Water-table aquifer:
More water released by unit volume per unit decline of water table. Why?
Pores are drained. In clean sand it may be 30-40% of the total volume that is drainable.
Define specific yield = Sy = volume of water drained per unit area of phreatic aquifer per unit decline of water table.
Sy < n
Sy = n - specific retention
Specific retention = SR = amount of water that remains in porous medium after gravity draining, i.e., due to chemistry etc. Specific retention is high in clays, low in sands.
Examples:
n (%) Sy (%) SR (%)
Clay 40 10 30
Sand 20 16 4
Gravel 25 24 1
Transport of miscible substances
Advection - transport with groundwater velocity (v)
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A
B
C
averagewater flowdirection
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v1
v2
Pore-scalemixing
Parabolicdistributionof velocitiesin pores
Velocitydifferencesbetweenpores
Mechanisms of dispersion
v2 < v1
Flux density = J = C·v [M L-2 T-1] (mass per unit area per unit time)
C = concentration [M L-3]
v = velocity [L T-1]
Dispersion - mixing due to water flowing around grains in porous medium
J = -D·(dC/dx) [M L-2 T-1] (mass per unit area per unit time)
where D is the mechanical dispersion coefficient (what are the units of D?)
Diffusion - molecular (Brownian motion)
1-D: J = -D*·(dC/dx)
Adsorption and retardation
If solute reacts with the medium, the molecules can be sorbed (attached) to the medium, and the transport of these molecules is slowed (retarded). In that case the retardation factor R>1. Otherwise, if solutes do not react with the medium, R=1.
Solution to advection-dispersion equation for non-reactive solutes (R=1)
Pulse input, 1-D:
C x t M
n 4Dt-------------------- x vt– 2–
4Dt-----------------------exp=
where M is the total mass of chemical introduced into the system.
Continuous, 1-D:
C x t C0
2------ erfc
x vt–
2 Dt------------- =
where C0 is the initial (or input) concentration, erfc() is the complementary error function (it is tabulated, and the tables are googleable).
Examples of transport - pulse input
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Q
t0 t1
t2
Distance
Con
cent
ratio
n
Con
cent
ratio
n
Time
No retardation
With retardation (R=3)
With retardationand tailing
Aquifer pumping tests
Aquifer tests are performed to obtain aquifer hydraulic properties: hydraulic conductivity, K (throught its derivative, transmissivity, T), and specific storage coefficient (throught its derivative, storativity, S).
If aquifer is infinite and confined, supply of water is from storage transient flow.
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Q
For long pumping test (at least an hour), the solution for drawdown (s) is:
sQ
4T---------- 2.25Tt
r2S---------------- Jacob solutionln=
Q = pumping rate [L3 T-1]T = transmissivity (=K·b) [L2 T-1]t = time [T]r = distance from pumping well [L]S = storativity (=Ss·b) [-]
Computing T and S from pumping-test data using the Jacob method:
We measure drawdown (s) as a function of time (t). Plot these on semi-log graph.
log t
ss
Q4T---------- 2.25Tt
r2S----------------ln=
t0
Late-time data (long t) should form a straight line.
Change to decimal log
s2.3Q4T------------
t2
t1
---log=
For one log t cycle, we have log(t2/t1) = log 10 = 1, and the solution for T is
T 2.3Q4s-------------=
Because we know the intercept (at s = 0), we can also calculate the storativity S:
S2.25Tt0
r2
------------------=
Groundwater fluctuations
time (years)
waterlevel
time (months)
0 5
0 1
time
1 yr
J F M A M J J A S O N D
winterrecharge
summer ET
0
heavy pumping
long-term trend (due to mining of aquifer)plus
short-term fluctuations (due to variable pumping)
ET = A(dh)Sy
A = areadh = decline in water tableSy = specific yield
Main causes of groundwater fluctuations are: pumping and seasonal changes in inputs (e.g., snowmelt) and outputs (e.g., evapotranspiration).
Some other causes of groundwater fluctuations: baro-metric pressure changes, tides, earth tides, earth-quakes, explosions, passing trains.
Radioisotope dating of ground water
Assume that at time t=0 we have N0 atoms of a radioactive isotope.
N0
½ N0
0 t1/2
0
N
t
¼ N0
2 t1/2
The isotope decays at a constant rate (=ln2/t½). N changes with time according to:
Nd
td------ N–= linear, first order ODE
or
Nd
N------ td–=
Integrate to get:
Nln t– C+=
From the initial condition N = N0 @ t = 0, integration constant C = lnN0, and the solution is:
N N0e t–=
This can be solved for time:
t1–------ N
N0
-----ln=
After one half-life (t½) one half of the original N0 remains, after two half-lives (2 t½) one-fourth remains, etc.
We date ground water by measuring N and computing t. This is the time since recharge. Note that in this method we need to know the initial concentration N0 at time t=0, which may or may not be possible. However, methods exist to bypass this requirement.
Radioisotopes commonly used for groundwater dating:
- tritium, 3H, t½=12.3 y
- radiocarbon, 14C, t½=5730 y
- chlorine-36, 36Cl, t½=301000 y
Can also use 3He-3H system, where 3He is from radioactive decay of 3H (this method does not require the knowledge of N0).
