unit 08a advanced hydrogeology l.
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Unit 08a : Advanced Hydrogeology. Aqueous Geochemistry. Aqueous Systems. In addition to water, mass exists in the subsurface as: Separate gas phases (eg soil CO 2 ) Separate non-aqueous liquid phases (eg crude oil) Separate solid phases (eg minerals forming the pm)

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aqueous systems
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
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
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
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
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
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)
  • Na2SO4dissociates in water:

Na2SO4 = 2Na+ + SO42-

  • The molar concentrations of Na+ and SO42- are 0.2 M and 0.1 M respectively
seawater molarity
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
  • 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
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)
  • Na2SO4dissociates in water:

Na2SO4 = 2Na+ + SO42-

  • The molal concentrations of Na+ and SO42- are 0.202 m and 0.101 m respectively
seawater molality
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
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
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
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
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
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
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

+

-

105o

+

Structure of Water
  • Covalent bonds between H and O
  • 105o angle H-O-H
  • Water molecule is polar
  • Hydrogen bonds join molecules
    • tetrahedral structure
  • Polar molecules bind to charged species to “hydrate” ions in solution
chemical equilibrium
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
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 My

Reaction Rate Half-Life

Reaction Rates

After Langmuir and Mahoney, 1984

relative reaction rates
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
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
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
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 h ckel equation
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 h ckel equation
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
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
divalent ions

1

0.9

0.8

0.7

0.6

Activity Coefficient

0.5

Debye-Huckel

0.4

Extended

0.3

0.2

Davis

0.1

Pitzer

0

0.001

0.01

0.1

1

10

Ionic Strength

Divalent Ions
activity and ionic charge
Activity and Ionic Charge

Monovalent

Divalent

non equilibrium
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
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
  • 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
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+ + CO32-

IAP = [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
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
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
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
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
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.