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Unit 08a Advanced Hydrogeology-Aqueous Geochemistry

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Unit 08a  Advanced Hydrogeology-Aqueous Geochemistry Powered By Docstoc
					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 SO42-
  are 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              My
                      Reaction Rate Half-Life
                                    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

                       0.8
Activity Coefficient




                       0.7

                       0.6

                       0.5
                                 Debye-Huckel
                       0.4

                       0.3       Extended

                       0.2       Davis
                       0.1
                                 Pitzer
                        0
                         0.001                  0.01        0.1         1   10

                                                       Ionic Strength
                                         Divalent Ions
                        1

                       0.9

                       0.8
Activity Coefficient




                       0.7

                       0.6

                       0.5
                                Debye-Huckel
                       0.4

                       0.3      Extended

                       0.2      Davis
                       0.1
                                Pitzer
                        0
                        0.001              0.01       0.1          1   10

                                                  Ionic Strength
                       Activity and Ionic Charge
                        1
                                                         Monovalent
                       0.9

                       0.8
Activity Coefficient




                       0.7

                       0.6
                                 Divalent
                       0.5
                                   Debye-Huckel
                       0.4

                       0.3         Extended

                       0.2         Davis
                       0.1
                                   Pitzer
                        0
                         0.001                    0.01                0.1        1   10

                                                                Ionic Strength
           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+ + 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
• 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.

				
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Lingjuan Ma Lingjuan Ma MS
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