Analytical hydrogeochemistry
1. Water on Earth
Spring 2022
Outline
• The Hydrologic Cycle
• Precipitation
• Groundwater
– Hydrogeological zonation (vertical)
• Groundwater table
• Piezometric levels
– Groundwater flow
• Unsaturated zone
• Saturated zone
• Darcy‘s Law
• Diffusion
• Dispersion
• Retardation
• Sorption and cation exchange
THE HYDROLOGIC CYCLE
The Hydrologic Cycle
• Draw a scheme of the hydrologic cycle
– Highlight the main reservoirs
– Highlight the main flows
– Compare the relativ sizes of individual fluxes
The Hydrologic Cycle
Main flows and reservoirs:
Hydrological cycle
• Try to build a hydrological cycle
– Main streams and reservoirs
Oki and Kanae 2006
Retention times
Ocean 39,000 years Groundwater (underground runoff) 9,500 years
Atmosphere 10 days Groundwater (river runoff) 270 years
Hydrosphere
• Water on (and near) the Earth's surface – liquid,
gaseous and frozen
• Reservoirs:
• ocean 97.5%
• fresh water 2.5%
– 1.85% (74% of fresh water) permanently frozen polar
cover
– 0.64% (98.5% of residue) groundwater
• atmosphere, surface water (streams, lakes)
0.01%
The Hydrologic Cycle
1. How does The Hydrologic Cycle influence the
chemical properties of Groundwater?
– How different would be properties of water in
individual reservoirs?
The Hydrologic Cycle
1. How does The Hydrologic Cycle influence the
chemical properties of Groundwater?
– How different would be properties of water in
individual reservoirs?
2. What forces cause movement of water in the
hydrologic cycle?
The Hydrologic Cycle
1. How does The Hydrologic Cycle influence the
chemical properties of Groundwater?
– How different would be properties of water in
individual reservoirs?
2. What forces cause movement of water in the
hydrologic cycle?
3. Which water contains the least solubles?
Total dissolved solids in different waters
Clark 2015
ATMOSPHERIC PRECIPITATION
Rain and snow
Net precipitation distribution
What are the consequences of this distribution?
Appelo&Postma2005
Composition of precipitation
• The composition of the rain is very variable
• Natural and anthropogenic sources
• In a clean environment
– N2, O2, CO2 + SO3, NOx and Na-Cl
• Above the oceans the composition of dilute
sea water
• Solid aerosols
• Washing dust from vegetation
Fractionation
• It expresses the ratio in the content of
elements
– Enrichment / depletion (eg. against Na)
Appelo & Postma 2005
Composition of precipitation –
chlorides
Appelo&Postma2005
Composition of precipitation – calcium
Appelo&Postma2005
Maps
• Compare maps
• What differences do you see?
• What can be the cause?
– You can use online maps.
• Can you deduce any laws?
Drever 1997
Compare the
relative proportions
of ions in different
rainfall sources
What can be the
cause of
deviations?
Can you deduce any
rules?
Appelo&Postma2005
Appelo&Postma2005
Water analysis
• Compare c,d and e,f analyzes
– What is the difference?
– What can be the cause?
– Can you deduce any rules?
• Table 2-3 shows the enrichment / depletion of
precipitation compared to seawater.
– Where are the biggest deviations?
– What can be the cause?
– Can you deduce any rules?
GROUNDWATER
Groundwater
Aquifer
Groundwater
• Formed by infiltrated
precipitation
• Immediate interaction with
the environment
– Soil water is different from
both surface- and ground-
water
• Surface flow hydrology –
basal outflow + other
sources
• Important medium
properties
– Porosity
– Permeability
Drever 1997
• How are the
pictures
different?
• How does the
propagation of
elements differ?
• What can be the
cause?
1. Ion adsorption
2. Dispersion
3. Diffusion
4. Different ion
sizes
5. Different ion
charges
6. Something else
Appelo & Postma 2005
Flow in the unsaturated zone
• Under normal conditions, the water percollates
vertically downward along the maximal gradient of the
soil moisture
• The rate is derived from a mass balance
𝑣 𝐻2 𝑂 = ൗ𝑃
𝜀 𝐻2 𝑂
v … velocity of water (m/year)
P… precipitation surplus (m/year)
𝜀… effective (water filled) porosity (m3/m3)
• Water velocity in pores
• Piston flow
Flow in the unsaturated zone
Appelo & Postma 2005
Question 1
A. What is the water velocity if P = 0.3 m/yr
and εH2O = 0.1?
B. Estimate the age of
water at 3 m depth
if P = 0.1 mm/yr
and εH2O = 0.0022?
Appelo&Postma2005
Water table
• Above – vadose zone
• Under – phreatic zone
• Capillary fringe
Cross-section of permable rock
Drever 1997
Groundwater
• In simplest conditions is a
subdued version of
topography –
intersections with surface
form springs, wetlands
etc.
• Water flows towards
lower level of water table
– Isolants, perched
collectors
Drever 1997
Hydraulic potential
• Water flows from place with higher water
table level towards the lower water table level
– From place with higher to place with lower
hydraulic potential
• Energy state of water
𝛷 = 𝑔 ℎ
g … gravitational acceleration
h … water table level (hydraulic height)
Appelo&Postma2005
Pilát 2013
Müllerová 2015
Darcy‘s Law
• Formulated in the 19th century
• Calculates flow (not flow rate)
• Homogenous porous medium (rock)
𝑄 = −𝑘 𝐴
ℎ 𝐴 − ℎ 𝐵
𝐿
= −𝑘 𝐴
𝑑ℎ
𝑑𝑙
• Specific flow
𝑞 = −𝑘
𝑑ℎ
𝑑𝑙
𝑑ℎ
𝑑𝑙
… hydraulic gradient
k … coefficient of permeability (hydraulic conductivity)
Darcy‘s Law – flow rate
• How far the water flows
• Only saturated parts of the rock should be
considered
𝑣 𝐻2 𝑂 = Τ𝑞 𝜀 𝐻2 𝑂
𝑣 𝐻2 𝑂 =
𝑄
𝐴 𝜀 𝐻2 𝑂
Question 2
• What is the water flow rate through
sandstone?
𝜀 𝐻2 𝑂 = 0,3
k = 5,79 × 10−4 m.s−1
Gradient = 0,001
Question 3
• The figure shows an unconfined aquifer. Water takes
1.91 yr to move from well A to well B. The hydraulic
conductivity for the aquifer rock is 135 m/d.
A. What is the effective porosity of the aquifer?
B. 8.42 × 105 m3
of water
flows through
cross section
of the aquifer
in 2 weeks.
Find the
width of the
aquifer.
Flow in the saturated zone
• Homogeneous aquifer with even infiltration
– Horizontal isochrons (ie. water at a given depth is
the same age)
Appelo&Postma2005
Effects of inhomogeneity
• Aquifers are usually inhomogeneous –
different hydraulic conductivities across the
body
Appelo&Postma2005
Aquifer chemistry
• The well passes through all "layers" of water
• Stabilization of chemistry – exponential
function
• Corresponds to a stirred reactor
Aquifer as a stirred reactor
• Great simplification
– Water mixing only in the well
– Different chemistry associated with development
along stream-lines in the rock
• Suitable for the first estimate of the spread of
contaminants
– We are not interested in the interaction of water
with the environment but in dilution of the input
concentration
Reaction-transport modeling
• Water reacts with the environment as it
percolates
• Basic description by advection-diffusion equation
– Simple one-dimensional form
• The sum of changes by diffusion, advection and
chemical reactions
𝜕𝐶𝑖
𝜕𝑡
= 𝐷𝑖
𝜕2 𝐶𝑖
𝜕𝑥2
− 𝑣
𝜕𝐶𝑖
𝜕𝑥
± (reaction members)
Diffusion
Advection
Unit volume
The overall change is a matter of mass balance in observed volumeDrever1997
Diffusion
• The difference in concentration between 2
points in solution balances naturally over time
• Brownian motion
• Described by Fick's 1st law (steady state)
F … flow (Flux)
D… diffusion coefficient
c… concentration
x… distance
𝐹 = −𝐷
𝛿𝑐
𝛿𝑥
Effects on diffusion
• Influence of flow through the porous medium
– Diffusion defined on free solution
1. Flow only via pores (porosity effect)
2. Different pore flow rate (pore edges vs.
center; tortuosity ϕ)
– Φ = dl/dx
– The ratio of distance traveled to absolute
distance
Hydrodynamic dispersion
• The mixing process associated with
movement through a porous
medium
• Longitudinal – different water
velocity in pores (large, small)
• Transverse – given by the available
flow paths
• Description analogous to diffusion
(derivatives of Fick's law); D =
dispersion coefficient
Appelo&Postma2005
ION EXCHANGE AND ADSORPTION
Crystal surfaces
• Crystal surfaces contain
numerous
imperfections and
defects.
• These places allow
growth/dissolution
because they have
different energy.
Silicon surface with visible edges,
kinks and other surface defects
ByGescott14(talk)(Uploads)-Ownwork,GFDL,
https://en.wikipedia.org/w/index.php?curid=14546580
Mineral surfaces
The energy of all particles (and positions) on the surface is not the same –
their stability differs.
Schematic representation of the crystal surface at the level of atomic dimensions:
a – atom in smooth surface area (most stable position), b – adatom (solo atom on
surface – least stable), c – free space on surface, d – corner, e – niche in step, f –
corner, g – atom in stairs
Ion exchange and sorption
• In terms of surface processes in aquifers:
• Cation exchange – change of the main cations
in solution by contact with the mineral surface
• Adsorption – binding of trace metals and
organics to mineral surfaces (contaminants)
• They are usually summarized under the term
sorption
Sorption on mineral surfaces
• Enormous importance in environmental geology.
– Groundwater composition, transport of contaminants,
availability of nutrients for plants.
• Very fast ion bonding/releasing processes.
• Even very soluble substances can be in low
concentration, thanks to sorption on surfaces:
– The total content is then lower than the estimate based on
solubility/precipitation.
– Simple surface process – an order of magnitude faster than
dissolution.
– Reversible process – complicates measurement of rates.
• Sorption
– Adsorption – binding to the surface.
– Absorption – entry into the structure of the absorbent.
Appelo&Postma(2005)
Phyllosilicates
• If all SiO4 tetrahedra share three oxygens with another
tetrahedra, a continuous planar structure is formed.
– They form sheets (infinite planes).
• Anions can enter the „meshes“ in the network.
• General formula Si4O10 or Si2O5.
– Al replaces up to 50% of Si in tetrahedra, although usually
less than 25%.
• Different types of phyllosilicates (chlorites, clay
minerals) differ in "fillers" between silicate layers.
• Silicate layers are much more cohesive than the filler that's
why they are fissile (typically mica).
Phyllosilicates
• Significant absorption capacity (especially
cations).
• Relatively reactive – significantly affect the
properties of water, soil and sediments.
• 2 main building elements
– Tetrahedral layers
– Octahedral layers
2: 1 Phyllosilicates
• "Sandwich" tetrahedral
layer – octahedral –
tetrahedral
• Between the "sandwiches"
are cations – they fit into
the hexagonal "mesh" of
the tetrahedral layer
• Without an interlayer –
held together by van der
Waals forces
Trioctahedral : 3 Mg2+ in octahedral
layer per building unit (talc)
Dioctahedral : 2 Al3+ in octahedral
layer per building unit (pyrophyllite)
TakenfromRyan(2014)
1: 1 Phyllosilicates
• One octahedral and tetrahedral plate is
repeated
• Trioctahedral: 3 Mg2+ in octahedral layer per
building unit (serpentines)
• Dioctahedral: 2 Al3+ in octahedral layer per
building unit (kaolins)
Clay minerals
• Phyllosilicates with grains below 2 µm
• Large surface area by weight – high reactivity
• The most common reactive phase in low
temperature conditions
• They differ from each other by substitutions and
thus by the charge on the interlayer
– Kaolinite group – no positions in the interlayer (low
CEC)
– Smectite group – Na and Ca easily washed from the
interlayer, replaced by water => swelling (+ high CEC)
– Illite Group – tightly bound K in the interlayer (lower
CEC)
Humic substances
• An important component of the soil
• Product of vegetation biodegradation
• Heterogeneous group, large molecules of COH- (N, S)
– Three-dimensional networks of aromatic cycles lined with
functional groups
– (-COOH) and (-OH) can dissociate and form sorption binding
sites
• Dark brown color of soil and water
• Humic acids soluble in pH > 2
• Humins – refractory component, strongly adsorbs on
mineral surfaces
Clark 2015
Fe (and Mn) Oxohydroxides
• Amorphous, hydrated iron oxide – coatings on
grains
• Crystalline form – goethite, limonite…
• Insoluble in neutral pH and oxidizing
conditions
• Oxygen has a negative surface charge
Colloids
• Small (10 µm), non-crystalline particles
• Hydroxides of Si, Fe, Mn, Al or organic comp.
• High negative surface charge
• In water with low ionic strength in suspension
• Adsorption of contaminants to the surface
– The total content can greatly exceed the solubility
(eg Pb2+)
– Transport of contaminants
Zeolites
• Low temperature tectosilicates
• Open crystal structure – holds large amounts
of water
• Substitution of Al3+ for Si4+ is compensated by
the incorporation of cations
– Surface charges may occur
Ions in solution
Cation exchange
• Adsorption given by the attraction of cations to mineral
surfaces.
• Driven by several factors:
1. Chemical attraction
2. Electrostatic attraction
3. Physical attraction (van der Waals forces)
– All due to the properties of the mineral, sorbed
substance and solution.
• Large exchange = high exchange capacity
• Especially clay minerals, oxohydroxides and organic
matter.
• At low pH, oxohydroxides also have an anion exchange
layer.
Factors affecting the attraction of
cations from solution to the surface
1. Particle charge – smectite and other clay
minerals have a negative charge of interlayer.
2. Particle size – large surface area to the volume
of the mineral has a greater binding potential.
3. Additional binding sites – interlayers, channels in
zeolites, etc.
4. Bonding sites on surface – various surface
shapes (dimples and edges), suitable bonding
sites because they usually contain free bonds
(the metal in the octahedral position is in
contact with less than 6 oxygens).
Isoelectric point
• In acidic solutions, the surfaces are coated
with H+ and attract anions.
• In alkaline solutions they attract cations (esp.
oxides, hydroxides, silicates).
• Isoelectric point (IEP) – the pH value at which
the surface charge in solution with only H+
and OH− ions is equal to zero.
• In natural waters with more ions: point of
zero charge (PZC).
• pH < PZC – the surface charge is positive and
attracts anions.
• pH > PZC – the surface charge is negative and
attracts cations.
• Clay minerals adsorb cations even at very low
pH due to the charge of the interlayer.
– In the natural environment (soils, river
sediments) the sorption of cations over anions
dominates.
• PZC of iron oxides and hydroxides is in the
range of pH ~ 5-9.
surface charge
Transient pH
pH acidic
Alkaline pH
Taken from Ryan (2014)
Electrical double layer
• The exchangeable ions
are on the surface of
the particle in the
electrical double layer:
– Complexes in the
inner layer – directly
on the surface,
compact (fixed).
– Complexes in the
outer layer – farther
from the surface,
diffuse.
– Uneven distribution of
cations and anions at
the surface.
electrical double layer sorption
Selectivity coefficient
• The activities of cations in solution are easily determined by
analysis.
• Note that the coefficient is based on activities – it will depend on the ionic
strength. Solutions with a high value of ionic strength will show a greater
tendency for monovalent ions to bind.
• The cation exchange process can be characterized by the
equation:
• Special type of equilibrium constant (selectivity coefficient):
General Example
Selectivity coefficient
• The activities of cations on the surface of clays are best
expressed as a molar fraction of the total surface:
• The coefficient is determinable for all cation exchange processes,
yet due to complicated circumstances, it is more an empirical
value rather than a constant describing a specific environment
(reservoir).
• It includes surface heterogeneity, ionic strength of the solution
and other phenomena affecting the final values.
Sorption nature
• Each cation has a different tendency to bind to
the charged surface
• Ability of electrostatic interactions
– Surface charge of the cation
– Stability of the solvation envelope
• Divalent ions and smaller ions bind more
• In general:
>
Cation exchange capacity
• Number of absorption positions per dry weight
(meq/100 g)
• Conventional inert substances (Q, crushed
crystalline rocks, sand…) can have a significantly
increased sorption capacity by the presence of
coatings.
• Important in pedology – the nature of clays
affects permeability, fertility, etc.
• Environmental geology – spread of contaminants,
development of geochemical properties of
waters.
Clark 2015
Cation exchange capacity
• Determined experimentally
• Indicator of sorption and exchange potential
Clark 2015
Cationic imbalance
• The evolution of the composition of water by cation
exchange is a response to the disturbance of the balance
between groundwater and the environment
• Anthropogenic disturbances
– eg winter treatment of roads
– Infiltrating Na-Cl type water replaces Ca2+ with Na+ in clays
– Change of water type at the outlet from Ca-HCO 3 to Ca-Cl
– Replenishing Ca-HCO3 type water outside the winter season,
desorption of Na+ on clays -> changing the output to Na-Cl
and gradually again to Ca-HCO3
• Natural disturbances
– Flow changes, erosion, sea level movements
Clark 2015
Distribution coefficient
• Adsorption
• Due to lower concentrations of sorbents, we express
the distribution coefficient
• The amount of sorbed substance proportional to
concentration
• Depends on concentration, but also on the medium
(CEC, organic, mineral composition…)
– Empirical determination in the laboratory = non-
transferable
– Series of measurements manifests itself as a sorption
isotherm of the given system
Sorption isotherm
𝑆 = 𝐾 𝑑 𝐶𝑒𝑞
The more reactive substance, the steeper the line
Slope = distribution coefficient
Clark 2015
Nonlinear sorption isotherm
• For highly reactive substances and high
concentrations, the linear isotherm is
inaccurate
Clark 2015
Freundlich sorption isotherm
𝑆 = 𝐾 𝑑 𝐶𝑒𝑞
𝑛
• n <1
• Less steep at higher concentrations
• Empirical or model of a gradual occupation of
adsorption positions on the surface
Goldbergetal.(2006)
Langmuir sorption isotherm
𝑣𝑎𝑐𝑎𝑛𝑡 𝑠𝑖𝑡𝑒 + 𝐴+
= [𝑜𝑐𝑐𝑢𝑝𝑖𝑒𝑑 𝑠𝑖𝑡𝑒]
• Process equilibrium constant:
𝐾𝐿𝑎𝑛𝑔 =
𝑆
𝐶𝑒𝑞 × [𝑣𝑎𝑐𝑎𝑛𝑡 𝑠𝑖𝑡𝑒𝑠]
• Substitution 𝑆 𝑚𝑎𝑥 = 𝑣𝑎𝑐𝑎𝑛𝑡 𝑠𝑖𝑡𝑒 + 𝑆
𝑆 = 𝑆 𝑚𝑎𝑥
𝐾𝐿𝑎𝑛𝑔 𝐴+
1 + 𝐾𝐿𝑎𝑛𝑔 𝐴+
Goldbergetal.(2006)
Sorption and retardation
• Retardation given by the available surface area of
the sorbent
• Retardation factor R
– Difference between water and contaminant velocity
What will be the value of the retardation factor for conservative ions?
And for the highly reactive?
Clark 2015
Retardation
Appelo&Postma2005
• What is the
difference?
• How does
element
transport differ?
• What is the
cause?
1. Ion adsorption
2. Dispersion
3. Diffusion
4. Ion size
5. Ion charge
6. Something else
Appelo & Postma 2005
References
• APPELO, C. A. J. a Dieke POSTMA. Geochemistry, groundwater and pollution :. 2nd
ed. Leiden: A. A. Balkema publishers, c2005. ISBN 0-415-36421-3.
• CLARK, I. (2015): Groundwater Geochemistry and Isotopes. BocaRaton, Florida:
CRC Press.
• DREVER, James I. The geochemistry of natural waters: surface and groundwater
environments. 3th ed. Upper Saddle River, NJ: Prentice Hall, c1997. ISBN 0-13-
272790-0
• Oki and Kanae 2006: dostupné z http://www.u-
tokyo.ac.jp/en/about/publications/tansei/14/science_1.html
• MÜLLEROVÁ, Sabina. Proudění podzemních vod v oblasti vodního zdroje Sajnšand,
Mongolsko. 2015. Dostupné také z: http://is.muni.cz/th/409069/prif_b/
• PILÁT, Patrik. Intenzifikace sanačního zásahu v areálu Fosfa Břeclav. 2016.
Dostupné také z: http://is.muni.cz/th/379545/prif_m/
• RYAN, Peter Crowley. Environmental and low temperature geochemistry.
Chichester, West Sussex, UK: Wiley Blackwell, 2014. ISBN 978-1-118-86735-8