Transcript Unit 08a : Advanced Hydrogeology Aqueous Geochemistry Aqueous Systems • In addition to water, mass exists in the subsurface as: – Separate gas phases.

Unit 08a : Advanced Hydrogeology
Aqueous Geochemistry
Aqueous Systems
• In addition to water, mass exists in the
subsurface as:
– Separate gas phases (eg soil CO2)
– Separate non-aqueous liquid phases (eg
crude oil)
– Separate solid phases (eg minerals
forming the pm)
– Mass dissolved in water (solutes eg Na+,
Cl-)
Chemical System in Groundwater
• Ions, molecules and solid particles in water
are not only transported.
• Reactions can occur that redistribute mass
among various ion species or between the
solid, liquid and gas phases.
• The chemical system in groundwater
comprises a gas phase, an aqueous phase
and a (large) number of solid phases
Solutions
• A solution is a homogeneous mixture where
all particles exist as individual molecules or
ions. This is the definition of a solution.
• There are homogeneous mixtures where the
particle size is much larger than individual
molecules and the particle size is so small
that the mixture never settles out.
• Terms such as colloid, sol, and gel are used
to identify these mixtures.
Concentration Scales
• Mass per unit volume (g/L, mg/L, mg/L)
is the most commonly used scale for
concentration
• Mass per unit mass (ppm, ppb, mg/kg,
mg/kg) is also widely used
• For dilute solutions, the numbers are
the same but in general:
mg/kg = mg/L / solution density (kg/L)
Molarity
• Molar concentration (M) defines the
number of moles of a species per litre of
solution (mol.L-1)
• One mole is the formula weight of a
substance expressed in grams.
Molarity Example
• Na2SO4 has a formula weight of 142 g
• A one litre solution containing 14.2 g of
Na2SO4 has a molarity of 0.1 M (mol.L-1)
• Na2SO4 dissociates in water:
Na2SO4 = 2Na+ + SO42• The molar concentrations of Na+ and
SO42- are 0.2 M and 0.1 M respectively
Seawater Molarity
• Seawater contains roughly 31,000 ppm of NaCl
and has a density of 1028 kg.m-3. What is the
molarity of sodium chloride in sea water?
• M = (mc/FW) * r
where mc is mass concentration in g/kg;
r is in kg/m3; and
FW is in g.
• Formula weight of NaCl is 58.45
• 31 g is about 0.530 moles
• Seawater molarity = 0.530 * 1.028 = 0.545 M
(mol.L-1)
Molality
• Molality (m) defines the number of
moles of solute in a kilogram of solvent
(mol.kg-1)
• For dilute aqueous solutions at
temperatures from around 0 to 40oC,
molarity and molality are similar
because one litre of water has a mass
of approximately one kilogram.
Molality Example
• Na2SO4 has a formula weight of 142 g
• One kilogram of solution containing 0.0142 kg
of Na2SO4 contains 0.9858 kg of water.
• The solution has a molality of 0.101 m
(mol.kg-1)
• Na2SO4 dissociates in water:
Na2SO4 = 2Na+ + SO42• The molal concentrations of Na+ and SO42are 0.202 m and 0.101 m respectively
Seawater Molality
• Seawater contains roughly 3.1% of NaCl. What
is the molality of sodium chloride in sea water?
m = (mc/FW)/(1 – TDS)
where mc is mass concentration in g/kg;
TDS is in kg/kg and
FW is in g.
•
•
•
•
Formula weight of NaCl is 58.45
31 g is about 0.530 moles
Average seawater TDS is 35,500 mg/kg (ppm)
m = (31/58.45)/ (1- 0.0355) = 0.550 mol.kg-1
Molar and Molal
• The molarity definition is based on the
volume of the solution. This makes molarity a
temperature-dependent definition.
• The molality definition does not have a
volume in it and so is independent of any
temperature changes.
• The difference is IMPORTANT for
concentrated solutions such as brines.
Brine Example
• Saturated brine has a TDS of about 319 g/L
• Saturated brine has an average density of
1.203 at 15oC
• The concentration of saturated brine is
therefore 265 g/kg or 319 g/L
• The molality m = (265/58.45)/(1-0.319)) is
about 6.7 m (mol.kg-1)
• The molarity M = (265/58.45)*1.203 is about
5.5 M (mol.L-1)
Equivalents
• Concentrations can be expressed in
equivalent units to incorporate ionic
charge
meq/L = mg/L / (FW / charge)
• Expressed in equivalent units, the
number of cations and anions in dilute
aqueous solutions should approximately
balance
Partial Pressures
• Concentrations of gases are expressed
as partial pressures.
• The partial pressure of a gas in a
mixture is the pressure that would be
exerted by the gas if it occupied the
volume alone.
• Atmospheric CO2 has a partial pressure
of 10-3.5atm or about 32 Pa.
Mole Fractions
• In solutions, the fundamental concentration
unit in is the mole fraction Xi; in which for j
components, the ith mole fraction is
•
Xi = ni/(n1 + n2 + ...nj),
•
where the number of moles n of a component
is equal to the mass of the component
divided by its molecular weight.
Mole Fractions of Unity
• In an aqueous solution, the mole fraction of
water, the solvent, is always near unity.
• In solids that are nearly pure phases, e.g.,
limestone, the mole fraction of the dominant
component, e.g., calcite, will be near unity.
• In general, only the solutes in a liquid solution
and gas components in a gas phase will have
mole fractions that are significantly different
from unity.
Structure of Water
•
•
•
•
Covalent bonds between H and O
105o angle H-O-H
+
Water molecule is polar
105o
Hydrogen bonds join molecules
– tetrahedral structure
• Polar molecules bind to charged
species to “hydrate” ions in solution
+
Chemical Equilibrium
• The state of chemical equilibrium for a closed
system is that of maximum thermodynamic
stability
• No chemical energy is available to
redistribute mass between reactants and
products
• Away from equilibrium, chemical energy
drives the system towards equilibrium
through reactions
Kinetic Concepts
• Compositions of solutions in equilibrium with
solid phase minerals and gases are readily
calculated.
• Equilibrium calculations provide no
information about either the time to reach
equilibrium or the reaction pathway.
• Kinetic concepts introduce rates and reaction
paths into the analysis of aqueous solutions.
Reaction Rates
Solute-Solute
Solute-Water
Gas-Water
Hydrolysis of multivalent ions (polymerization)
Adsorption-Desorption
Mineral-Water Equilibria
Mineral Recrystallization
Secs
Mins
Hrs
Days Months Years Centuries
Reaction Rate Half-Life
My
After Langmuir and Mahoney, 1984
Relative Reaction Rates
• An equilibrium reaction is “fast” if it takes
place at a significantly greater rate than the
transport processes that redistribute mass.
• An equilibrium reaction is “slow” if it takes
place at a significantly smaller rate than the
transport processes that redistribute mass.
• “Slow” reactions in groundwater require a
kinetic description because the flow system
can remove products and reactants before
reactions can proceed to equilibrium.
Partial Equilibrium
• Reaction rates for most important reactions
are relatively fast. Redox reactions are often
relatively slow because they are mediated by
micro-organisms. Radioactive decay
reactions and isotopic fractionation are
extremely variable.
• This explains the success of equilibrium
methods in modelling many aspects of
groundwater chemistry.
• Groundwater is best thought of as a partial
equilibrium system with only a few reactions
requiring a kinetic approach.
Equilibrium Model
• Consider a reaction where reactants A and B react to
produce products C and D with a,b,c and d being the
respective number of moles involved.
aA + bB = cC + dD
• For dilute solutions the law of mass action describes
the equilibrium mass distribution
K = (C)c(D)d
(A)a(B)b
where K is the equilibrium constant and (A),(B),(C), and
(D) are the molal (or molar) concentrations
Activity
• In non-dilute solutions, ions interact electrostatically
with each other. These interactions are modelled by
using activity coefficients (g) to adjust molal (or molar)
concentrations to effective concentrations
[A] = ga(A)
• Activities are usually smaller for multivalent ions than
for those with a single charge
• The law of mass action can now be written:
K = gc(C)c gd(D)d = [C]c[D]d
ga(A)a gb(B)b [A]a[B]b
Debye-Hückel Equation
• The simplest model to predict ion ion activity
coefficients is the Debye-Hückel equation:
log gi = - Azi2(I)0.5
where A is a constant, zi is the ion charge, and I is the
ionic strength of the solution given by:
I = 0.5 SMizi2
where (Mi) is the molar concentration of the ith species
• The equation is valid and useful for dilute solutions
where I < 0.005 M (TDS < 250 mg/L)
Extended Debye-Hückel Equation
• The extended Debye-Hückel equation is used
to increase the solution strength for which
estimates of g can be made:
log gi = - Azi2(I)0.5
1 + Bai(I)0.5
where B is a further constant, ai is the ionic
radius
• This equation extends the estimates to
solutions where I < 0.1 M (or TDS of about
5000 mg/L)
More Activity Coefficient Models
• The Davis equation further extends the
ionic strength range to about 1 M
(roughly 50,000 mg/L) using empirical
curve fitting techniques
• The Pitzer equation is a much more
sophisticated ion interaction model that
has been used in very high strength
solutions up to 20 M
Monovalent Ions
1
0.9
Activity Coefficient
0.8
0.7
0.6
0.5
0.4
Debye-Huckel
0.3
Extended
0.2
Davis
0.1
Pitzer
0
0.001
0.01
0.1
Ionic Strength
1
10
Divalent Ions
1
0.9
Activity Coefficient
0.8
0.7
0.6
0.5
0.4
Debye-Huckel
0.3
Extended
0.2
Davis
0.1
Pitzer
0
0.001
0.01
0.1
Ionic Strength
1
10
Activity and Ionic Charge
1
Monovalent
0.9
Activity Coefficient
0.8
0.7
0.6
Divalent
0.5
0.4
Debye-Huckel
0.3
Extended
0.2
Davis
0.1
Pitzer
0
0.001
0.01
0.1
Ionic Strength
1
10
Non-Equilibrium
• Viewing groundwater as a partial equilibrium
system implies that some reactions may not
be equilibrated.
• Dissolution-precipitation reactions are
certainly in the non-equilibrium category.
• Departures from equilibrium can be detected
by observing the ion activity product (IAP)
relative to the equilibrium constant (K) where
IAP = [C]c[D]d = products
[A]a[B]b reactants
Dissolution-Precipitation
aA + bB = cC + dD
• If IAP<K (IAP/K<1) then the reaction is
proceeding from left to right.
• If IAP>K (IAP/K>1) then the reaction is
proceeding from right to left.
• If the reaction is one of mineral dissolution
and precipitation
– IAP/K<1 the system in undersaturated and is
moving towards saturation by dissolution
– IAP/K>1 the system is supersaturated and is
moving towards saturation by precipitation
Saturation Index
• Saturation index is defined as:
SI = log(IAP/K)
• When a mineral is in equilibrium with
the aqueous solution SI = 0
• For undersaturation, SI < 0
• For supersaturation, SI > 0
Calcite
• The equilibrium constant for the calcite dissolution
reaction is K = 4.90 x 10-9 log(K) = -8.31
• Given the activity coefficients of 0.57 for Ca2+ and 0.56
for CO32- and molar concentrations of 3.74 x 10-4 and
5.50 x 10-5 respectively, calculate IAP/K.
• Reaction: CaCO3 = Ca2+ + CO32IAP = [Ca2+][CO32-] = 0.57x3.37x10-4x0.56x5.50x10-5
[CaCO3]
1.0
= 6.56 x 10-9 and log(IAP) = -8.18
{IAP/K}calcite = 6.56/4.90 = 1.34
log{IAP/K}calcite = 8.31 - 8.18 = 0.13
• The solution is slightly oversaturated wrt calcite.
Dolomite
• The equilibrium constant for the calcite dissolution reaction
is K = 2.70 x 10-17 and log(K) = -16.57
• Given activity coefficients of 0.57, 0.59 and 0.56 for Ca2+,
Mg2+ and CO32- and molar concentrations of 3.74 x 10-4,
8.11 x 10-5 and 5.50 x 10-5 respectively, calculate IAP/K.
• Reaction: CaMg(CO3)2 = Ca2+ + Mg2+ + 2 CO32• Assume the effective concentration of the solid dolomite
phase is unity
log[Ca2+] = -3.67 log[Mg2+] = -4.32 log[CO32-] = -4.51
log(IAP)=log([Ca2+][Mg2+][CO32-]2)= -3.67-4.32-9.02= -16.31
log{IAP/K}dolomite = 16.57 – 17.01 = -0.44
• The solution is undersaturated wrt dolomite.
Kinetic Reactions
• Reactions that are “slow” by comparison with
groundwater transport rates require a kinetic
model
k1
aA + bB = cC + dD
k2
where k1 and k2 are the rate constants for the forward (L to R)
and reverse (R to L) reactions
• Each constituent has a reaction rate:
rA = dA/dt; rB = dB/dt; rc = dC/dt; rD = dD/dt;
• Stoichiometry requires that:
-rA/a = -rB/b = rC/c = rD/d
Rate Laws
• Each consituent has a rate law of the
form:
rA = -k1(A)n1(B)n2 + k2(C)m1(D)m2
where n1, n2, m1 and m2 are empirical or
stoichiometric constants
• If the original reaction is a single step
(elementary) reaction then n1=a, n2=b,
m1=c and m2=d
Irreversible Decay
14C
= 14N + e
d(14C)/dt = -k1(14C) + k2(14N)(e)
• Here there is only a forward reaction
and k2 for the reverse reaction is
effectively zero
d(14C)/dt = -k1(14C)
• k1 is the decay constant for radiocarbon
Elementary Reactions
Fe3+ + SO42- = FeSO4+
d(Fe3+)/dt = -k1(Fe3+)(SO42-) + k2(FeSO4+)
• The reaction rate depends not only on
how fast ferric iron and sulphate are
being consumed in the forward reaction
but also on the rate of dissociation of
the FeSO4+ ion.