Fluorite Solubility

1
Fluorite Solubility

• Define the following two solutions by typing in
  PhreeqcI or PFW and run
• SOLUTION 1
• -units mg/L
• Ca 1 Fluorite
• F 1.5
• SOLUTION 2
• -units mmol/L
• Ca 1 Fluorite
• F 0.3
• Fill in results in exercises.doc.

2
Geochemical Calculations Using PHREEQC

• David Parkhurst
• U.S. Geological Survey
• dlpark_at_usgs.gov
• http//wwwbrr.cr.usgs.gov/projects/GWC_coupled/ind
  ex.html

3
Overview

• SOLUTION and SOLUTION _SPREAD
• Units
• Concentrations
• pH
• pe
• Other options
• Speciation calculations
• Exercise
• Ion association
• Pitzer
• Saturation indices
• Uncertainties
• Useful minerals
• Identify potential reactants
• Exercise

4
Solution Definition and Speciation Calculations
Speciation calculation
5
Seawater Units are ppm
6
Initial Solution 1. Questions

• What is the approximate molality of Ca?
• What is the approximate alkalinity in eq/kgw?
• What effect does density have on the calculated
  molality?

PHREEQC results are always moles or molality
7
Periodic_table.bmp
8
Default Gram Formula Weights
Default GFW is defined in 4th field of
SOLUTION_MASTER_SPECIES in database file.
9
Databases

• Ion association approach
• Phreeqc.datsimplest
• Wateq4f.datmore trace elements
• Minteq.dattranslated from minteq v 2
• Minteq.v4.dattranslated from minteq v 4
• Llnl.datmost complete set of elements and
  temperature dependence
• Iso.dat(in development) thermodynamics of
  isotopes
• Phreeqd.datmulticomponent diffusion
• Pitzer specific interaction approach
• Pitzer.datSpecific interaction model

10
Database Data Blocks

• SOLUTION_MASTER_SPECIESRedox states and gram
  formula weight
• SOLUTION_SPECIESReaction and log K
• PHASESReaction and log K
• PITZERPitzer parameters (pitzer.dat)
• (Data related to Exchangers and Surfaces)

11
What is a speciation calculation?

• Input
• pH
• pe
• Concentrations
• Equations
• Mass-balancesum of the calcium species total
  calcium
• Mass-actionactivities of products divided by
  reactants constant
• Activity coefficientsfunction of ionic strength
  or Pitzer
• Output
• Molalities, activities of aqueous species
• Saturation indices

12
Mass-Balance Equations

• Analyzed concentration of sulfate (SO4-2)
  (MgSO40) (NaSO4-) (CaSO40) (KSO4-)
  (HSO4-) (CaHSO4) (FeSO4) (FeSO4)
  (Fe(SO4)2-) (FeHSO4) (FeHSO42)
• () indicates molality
• These species are from an ion-association model.

13
Mass-Action Equations

• Ca2 SO4-2 CaSO40

indicates activity
14
Activity Coefficients
Ionic strength
WATEQ activity coefficient
Davies activity coefficient
15
Pitzer Activity Coefficients
ma concentration of anion mc concentration of
cation functions of ion
specific parameters
F funtion of ionic strength, molalities of
cations and anions
16
Aqueous Models

• Ion association
• Pros
• Data for most elements (Al, Si)
• Redox
• Cons
• Ionic strength lt 1
• Best only in Na, Cl medium
• Inconsistent thermodynamic data
• Temperature dependence

• Pitzer specific interaction
• Pros
• High ionic strength
• Thermodynamic consistency for mixtures of
  electrolytes
• Cons
• Limited elements
• Little if any redox
• Difficult to add elements
• Temperature dependence

17
PhreeqcI SOLUTION Data Block
18
pH, pe, Temperature
19
Solution Composition

• Set units!
• Default is mmol/kgw

Select elements
Set concentrations As, special units
Click when done
20
Run Speciation Calculation

• Run

Select files
21
Results of Speciation Calculation
Cascade
22
Initial Solution 2. Exercise
Units are ppm

• Run a speciation calculation for seawater using
  phreeqc.dat
• Use pitzer.dat Copy input to a new buffer (cntl
  a cntl c File-gtnew or cntl-n cntl v)

23
Initial Solution 2. Questions

• Write the mass-balance equation for calcium in
  seawater for each database.
• What fraction of the total is Ca2 ion for each
  database?
• What fraction of the total is Fe3 ion for each
  database?
• What are the log activity and log activity
  coefficient of CO3-2 for each database?
• What is the saturation index of calcite for each
  database?

24
More on Solution Definition

• pH, Carbon, Alkalinity, pe

25
What is pH?
pH 6.3 log(HCO3-)/(CO2)
pH 10.3 log(CO3-2)/(HCO3-)

• Questions
• 1. How does the pH change when CO2 degasses
  during an alkalinity titration?
• 2. How does pH change when plankton respire CO2?
• 3. How does pH change when calcite dissolves?

26
Alkalinity, Total Carbon

• Total inorganic carbon CO2 HCO3- CO3-2
• Alkalinity HCO3- 2CO3-2 OH- - H

SOLUTION Data Block

• pH AlkalinityCalculate total C(4)
• pH C(4)Calculate total alkalinity
• C(4) AlkalinityCalculate pH

27
What is pe?
Fe2 Fe3 e- pe log( Fe3/Fe2 )
13 HS- 4H2O SO4-2 9H 8e- pe log(
SO4-2/HS- ) 9/8pH 4.21 N2 6H2O
2NO3- 12H 10e- pe 0.1log( NO3-2/N2 )
1.2pH 20.7
28
More on pe

• Aqueous electrons do not exist
• Redox reactions are frequently not in equilibrium
• Multiple pes from multiple redox couples
• However, we do not expect to see major
  inconsistenciese.g. both D.O. and HS-in a
  single environment

29
Redox Elements
30
Redox and pe in SOLUTION Data Blocks

• When do you need pe for SOLUTION?
• To distribute total concentration of a redox
  element among redox states e.g. As to As(5) and
  As(3)
• A few saturation indices with e- in dissociation
  reactions
• Pyrite
• Native sulfur
• Manganese oxides
• Can use a redox couple Fe(2)/Fe(3) in place of pe
• Rarely, pe 16.9Eh. (25 C and Eh in Volts).
• Redox choices only apply to speciation
  calculations

31
Seawater Initial Solution

• Fe total was entered. How were Fe(3) and Fe(2)
  concentrations calculated?

For initial solutions For reactions
32
Charge Balance Options

• For most analyses, just leave it
• Adjust the major anionmissing major analyte
• Adjust pHpH of 1 molal HCl solution

33
Adjustments to Phase Equilibrium

• For most analyses, dont do it
• The following are reasonable
• Adjust concentrations to equilibrium with
  atmosphere (O2, CO2)
• Adjust pH to calcite equilibrium
• Estimate aluminum concentration by equilibrium
  with gibbsite
• Calculate fluoride concentration in equilibrium
  with fluorite

34
SOLUTION_SPREAD
35
SATURATION INDEXThermodynamic state of a
solution relative to a mineral

• SI lt 0, Mineral should dissolve
• SI gt 0, Mineral should precipitate
• SI 0, Mineral reacts fast enough to maintain
  equilibrium
• Maybe
• Kinetics
• Uncertainties

36
Rules for Saturation Indices

• Mineral can not dissolve if it is not present
• If SI lt 0 and mineral is presentthe mineral
  could dissolve, but not precipitate
• If SI gt 0the mineral could precipitate, but not
  dissolve
• If SI 0the mineral could dissolve or
  precipitate to maintain equilibrium

37
Uncertainties in SI Analytical data

• 5 uncertainty in element concentration is .02
  units in SI.
• 0.5 pH unit uncertainty is 0.5 units in SI of
  calcite, 1.0 units in dolomite
• 1 pe or pH unit uncertainty is 8 units in SI of
  FeS for the following equation
• SI(FeS) logFelogSO4-2-8pH-8pe-log
  K(FeS)

38
Uncertainties in SI Equation

• Much smaller uncertainty for SI(FeS) with the
  following equation
• SI(FeS) logFelogHS-pH-log K(FeS)
• For minerals with redox elements, uncertainties
  are smaller if the valence states of the elements
  in solution are measured.

39
Uncertainties in SI Log K

• Apatite from Stumm and Morgan
• Ca5(PO4)3(OH) 5Ca2 3PO4-3 OH-
• Apatite from Wateq log K -55.4
• Log Ks especially uncertain for aluminosilicates

40
Useful Mineral ListMinerals that may react to
equilibrium relatively quickly
41
IS 3. Speciate and interpret Saturation Indices
Units are mmol/kg water
Use SOLUTION_SPREAD or SOLUTION to enter the
data. Run with phreeqc.dat database. Examine
concentrations and saturation indices. What can
you say about reactions affecting this water?
42
Summary

• Aqueous speciation model
• Mole-balance equationsSum of species containing
  Ca equals total analyzed Ca
• Aqueous mass-action equationsActivity of
  products over reactants equal a constant
• Activity coefficient equations
• SIlog(IAP/K)

43
Summary

• SOLUTION and SOLUTION _SPREAD
• Units
• pHratio of HCO3-/CO2
• peratio of oxidized/reduced valence states
• Charge balance
• Phase boundaries
• Saturation indices
• Uncertainties
• Useful minerals
• Identify potential reactants
• Starting place for all other PHREEQC capabilities

44
Reaction Calculations

EQUILIBRATION REACTOR
45
EQUILIBRIUM REACTANTS

• SURFACE
• EXCHANGE
• SOLID_SOLUTIONS
• EQUILIBRIUM_PHASES
• GAS_PHASE

46
NON-EQUILIBRIUM REACTIONS

• MIX
• REACTION
• REACTION_TEMPERATURE
• KINETICS

47
PHREEQCReactions

• From the shelf

To the beakerUSE
Kinetics 10
React and SAVE
48
CONCEPTUAL MODEL

• Initial conditionSOLUTION or MIX
• Add irreversible reactants
• REACTION
• KINETICS
• REACTION_TEMPERATURE
• Add reversible reactants
• EQUILIBRIUM_PHASES
• SURFACE
• EXCHANGE
• SOLID_SOLUTION
• GAS_PHASE
• Calculate new composition
• SAVE compositions if needed

49
Geochemical Reactions

• Carbonates
• Oxidation of organic carbon
• Oxidation of pyrite
• Aluminosilicate reactions
• (Bubbles)

50
Reactions

• Implicit redox reactions

51
MIX One or more SOLUTIONS

• Solution number
• Mixing fraction

52
REACTION 1. Exercise Implicit Redox
Reactionsmg/L

• Define rainwater as SOLUTION 1 with log partial
  pressure of O2 -0.7 and CO2 -3.5.
• Define END.
• Define MIX by using solution 1 and mixing
  fraction 1.
• Define END.
• Run.

53
Questions

• 1. Explain the differences between the initial
  solution composition and the reaction (mixed)
  solution composition, particularly pH, pe, N(5),
  N(0), and N(-3).

54
Redox Calculations

• Initial solution
• Allows redox disequilibria
• Total N(5), N(-3), O(0)
• Reaction calculations
• Complete aqueous redox equilibrium
• Can redefine elements for disequilibrium
• N, N(5), N(3), N(0), N(-3), Ngas, Amm

55
Reactions

• Sequential reactions
• USE, SAVE, REACTION, EQUILIBRIUM_PHASES, END

56
SAVE and USE

• Save results of reaction calculations
• Use previously defined SOLUTIONs,
  EQUILIBRIUM_PHASES, REACTIONs, etc
• Use previously SAVEd SOLUTIONS,
  EQUILBRIUM_PHASES, etc

57
SAVE results from a Reaction Calculation
Index numbers are used to keep track Index
numbers do not need to be sequential

• Note SOLUTION defines an initial solution
  calculation, which is automatically saved.

58
USE Previously defined or SAVEd

• USE includes KINETICS, MIX, REACTION, and
  REACTION_TEMPERATURE
• Can USE previously SAVEd EQUILIBRIUM_PHASES,
  EXCHANGE, SOLID_SOLUTION, SOLUTION, or SURFACE

59
REACTION Reactants and stoichiometry

• Choose phase or type formula
• Define relative stoichiometry
• Must be charge balanced

60
REACTION Reaction amounts

• Steps are a number of equal increments
• or
• Steps are a specified list
• Specify units

61
EQUILIBRIUM_PHASES

• Assembly of minerals/gases that react to
  equilibrium or zero moles
• Define
• Mineral/gas
• Target saturation index
• Moles present

62
Initial Solution and Reaction Calculations
63
Initial Solution and Reaction CalculationsThe
END statement

• ENDdefines a Simulation
• Within a simulation
• Every SOLUTION results in an initial solution
  calculation (unique index)
• Reaction calculationSOLUTION one of each
  reactant type before END
• Reactants can be keyword blocks
• Reactants be defined by USE
• END
• Run speciation calculations
• Run reaction calculations
• Run transport calculations
• SAVE results

64
REACTION 3. Exercise Sequential Reactions

• Make an unsaturated zone water. Build on previous
  exercise with rainwater. Add SAVE solution 2
  after MIX step and before END. After the END, add
  USE solution 2 and equilibrate (EQUILIBRIUM_PHASES
  ) with CO2, log partial pressure 2, and calcite
  (SI 0), save solution as solution 3.
• Use solution 3, add 1 mmol CO2 (REACTION),
  equilibrate with calcite (EQUILIBRIUM_PHASES),
  save as solution 4.

65
Questions

• What is the log pCO2 of the rainwater, rainwater,
  in redox equilibrium (the mixture), the mixture
  equilibrated with CO2 and calcite, and after
  reaction with CO2 and calcite?
• How many millimoles of calcite and CO2 reacted to
  make solution 3?
• How many millimoles of calcite reacted to make
  solution 4 from solution 3?

66
REACTION 5. Extra Credit Exercise

• Use MIX and REACTION to evaporate rainwater 20
  fold (at constant pCO2) before reaction with CO2
  and calcite. Hint You must remove water and
  water has 55.5 mol per kg.

67
Reaction Exercise

• Dedolomitization

68
Dedolomitization

• Anhydrite dissolution
• Calcite precipitation
• Dolomite dissolution

69
REACTION 6. Exercise

• Make a ground water with log pCO2 -2,
  equilibrium with calcite and dolomite.
• React 50 mmol of anhydrite (CaSO4) in increments
  of 10 mmol. Maintain equilibrium with calcite and
  dolomite, allow anhydrite to precipitate if it
  becomes saturated.
• You need to use these data blocks SOLUTION,
  EQUILIBRIUM_PHASES, REACTION, USE, SAVE in two
  simulations.

70
Questions

• What trends do you expect in water composition
  with anhydrite-driven dedolomitization?
• Why is the following reaction misleading?
• CaSO4 CaMg(CO3)2 2CaCO3 Mg2 SO4-2
• 3. How does the water composition change from
  step 4 to step 5?

71
Dedolomitization
72
SELECTED_OUTPUT
File name
1. Set file name (default selected.out)
2. Reset all to false
3. Set pH to true
4. Set Reaction true
73
Selected Output Total Molalities
74
Selected Output
75
Selected Output File

• Open with Excel
• Manipulate/plot data
• PFW has built-in plotting capability

76
Carbonate Reactions

• Carbonate ground water
• PCO2 -1 to -3.0
• Calcite, or calcite and dolomite
• CO2 supply in the UZ
• Dedolomitization
• Anhydrite dissolution
• Calcite precipitation
• Dolomite dissolution
• Other reactions
• Sulfate reduction
• Ion exchange

77
Reactions

• Organic decomposition

78
Organic Decomposition

• Sequential removal of electron acceptors, usually
  in the sequence
• O2
• NO3-
• MnO2
• Fe(OH)3
• SO4-2
• HCO3-

79
Redox Environments

• OxicDissolved O2 reduction
• CH2O O2 CO2 H2O
• Post-oxicNO3-, MnO2, Fe(OH)3 reduction
• CH2O 4Fe(OH)3 7CO2 4Fe2 8HCO3- 3H2O
• SulfidicSO4-2 reduction
• 2CH2O SO4-2 2HCO3- H2S
• MethanicCH4
• CH2O CO2 CH4

80
Redox Environments
81
Redox Sequence at pH 7
82
Organic decomposition REACTION
2CH2O SO4-2 2HCO3- H2S

• WRONG!
• REACTION
• CH2O -2
• SO4-2 -1
• HCO3- 2
• H2S 1
• 5 mmol

RIGHT! REACTION CH2O 1 10 mmol Or
perhaps, REACTION CH2O 1 Doc -1 10 mmol
83
REACTION 11. Exercise

• React seawater with 100 mmol of CH2O in 5 equal
  steps. Equilibrate with .1 moles of Fe(OH)3(a).
  Allow mackinawite (FeS) to precipitate.
• Use SELECTED_OUTPUT to print moles of reaction
  (-rxn) and total concentrations of C(4), C(-4),
  Fe(2), Fe(3), S(6), S(-2). Plot results.

84
Questions

• What sequence of electron acceptors is used?
• Where is Fe(3) important?
• Use Excel to plot the concentrations in the
  selected-output file (rxn is the x variable, set
  first line rxn from 99 to 0, omit
  d_mackinawite).
• 4. Why is C(4) not a straight line?
• 5. Why does Fe(2) increase after 30 mmol of CH2O
  is reacted.
• Should a gas bubble form?
• What trends are observed for sulfate reduction?

85
Organic Decomposition
86
GAS_PHASE

• PV nRT Ideal gas law
• Henrys law
• Log K CO2/P(CO2)
• Fixed pressureVolume varies
• Fixed volumePressure varies

87
GAS_PHASE

• Fixed volumeSpecify Vtotal
• Always present
• Specified gases distribute between water and gas
  phase
• Equilibrium Pgas Paq
• Ptotal varies
• Fixed pressureSpecify Ptotal
• Forms only when sum of partial pressure of
  specified gases exceeds Ptotal
• Equilibrium Pgas Paq
• Sum of partial pressures of specified gases
  Ptotal
• Volume varies

88
GAS_PHASE
89
Gases

• Fixed partial pressureuse EQUILIBRIUM_PHASES
• Fixed volume head spaceuse fixed volume
  GAS_PHASE
• Expanding Bubbleuse fixed pressure GAS_PHASE

90
REACTION 12.

• Redo the organic decomposition reaction with a
  gas phase.
• Include CO2, CH4, and H2S in gas phase
• Include CO2, CH4, and H2S in SELECTED_OUTPUT
  (-gases).
• Fix total pressure at 5 atm.

91
Organic decomposition with GAS_PHASE
92
Organic Decomposition

• Electron donors
• O2Atmosphere, DO negligible
• NO3Atmosphere, ag chemicals
• Fe(3)Iron oxyhydroxides
• SO4Seawater, atmosphere, gypsum
• Organic carbonCH4 and CO2
• PHREEQC
• Typically react CH2O or just C
• Let thermodynamics decide the rest

93
Reactions

• Sulfide oxidation

94
Sulfide Oxidation

• Pyrite/Marcasite are most important reactants
• Need Pyrite, Oxygen, Water, and bugs
• Oxidation of pyrite and formation of ferric
  hydroxide complexes and minerals generates acidic
  conditions

95
REACTION 18. Exercise

• React pure water with 10 mmol of pyrite,
  maintaining equilibrium with atmosphreric oxygen.
• React pure water with 10 mmol of mackinawite,
  maintaining equilibrium with atmosphreric oxygen.
• React pure water with 10 mmol of sphalerite,
  maintaining equilibrium with atmosphreric oxygen.

96
Questions

• Write qualitative reactions that explain the pH
  of the 3 solutions.
• What pH buffer starts to operate at pHs below 3?
• Run the input file with wateq4f.dat database.
  What minerals may precipitate during pyrite
  oxidation?

97
REACTION 20. Extra Credit Exercise

• React pure water with 20 mmol of pyrite,
  maintaining equilibrium with atmospheric oxygen
  and goethite.
• Acid mine drainage is usually treated with
  limestone. Use the results of exercise 1 and
  equilibrate with O2, Fe(OH)3(a), and calcite.

98
Questions

• Write a net reaction for the PHREEQC results for
  the low-pH simulation.
• Looking at the results of the calcite-equilibrated
  simulation, what additional reactions should be
  considered?

99
Picher Oklahoma Abandoned Pb/Zn Minemg/L

• Mines are suboxic
• Carbonates are present
• Iron oxidizes in stream

100
Pyrite Oxidation

• Requires
• Pyrite/Marcasite
• O2
• H2O
• Bacteria
• Produces
• Ferrihydrite/Goethite, jarosite, alunite
• Gypsum if calcite is available
• Evaporites
• Possibly siderite
• Acid generation
• Pyrite gt FeS gt ZnS

101
Reactions

• Aluminosilicate reactions

102
Aluminosilicate Reactions

• Disseminated calcite important in silicate
  terranes

• Bowen (Goldich) reaction series

Ca-Feldspar Plagioclase Na-Feldspar K-Feldspar Mus
covite Quartz

• Olivine
• Pyroxene (augite)
• Amphibole (hornblende)
• Biotite mica

103
Aluminosilicates

• Primary minerals react to form gibbsite,
  kaolinite, smectite, zeolites, SiO2
• Thermodynamic data is not reliable
• Compositional uncertainties
• Range of stabilities
• Difficulty of measurement
• Kinetics are slow

104
Add Reactant to Phase Boundary

• KAlSiO8 is added (or removed) until gibbsite
  equilibrium is reached
• Amount is amount of KAlSiO8, not gibbsite

105
Add Reactant to Phase Boundary
106
REACTION 22. Exercise Use phreeqc.dat

• Dissolve just enough K-feldspar (KAlSi3O8) to
  come to equilibrium with gibbsite.
• Dissolve just enough K-feldspar to come to
  equilibrium with kaolinite.
• Dissolve just enough K-feldspar to come to
  equilibrium with K-mica.

107
Questions

• Given the thermodynamic data, which mineral
  should precipitate first?
• Does quartz need to be included in this
  calculation?

108
Sierra Nevada Springsmmol/kgw

• Increase in Ca, Alkalinity, pH
• Increase in SiO2
• Slight increase in Mg, K, Cl, SO4

109
Reaction Summary

• MIX
• EQUILIBRIUM_PHASES
• REACTION
• GAS_PHASE
• USE
• SAVE
• SELECTED_OUTPUT

110
Summary

• Carbonate minerals and CO2
• Dedolomitization
• Organic decomposition
• Sulfate reduction
• Other electron acceptors O2, NO3, FeOOH, CH2O
• Sulfide oxidation
• Aluminosilicate reactions

111
REACTION 24. TEST

• Make a soil zone, carbonate ground water, log
  PCO2 -2.0
• Titrate the water with by addition of HCl (use
  REACTION)
• Plot pH vs acid added, assuming equilibrium with
  atmospheric CO2
• Plot pH vs acid added, assuming no CO2 escapes
  from the sample

112
REACTION 25. TEST

• React this water with 50 mmol of CH2O(NH3)0.1 in
  freshwater sediment
• How is the reacted carbon distributed in the
  solution?
• How would you classify the water in terms of
  cations and anions?
• What other processes should we consider?

113
Still to Study

• SURFACE
• EXCHANGE
• KINETICS
• SOLID_SOLUTION

114
Sorption Reactions

• Pierre Glynn, USGS, March 2005

115
Sorption Processes

• Depend on
• Surface area amount of sorption sites
• Relative attraction of aqueous species to
  sorption sites on mineral/water interfaces
• Mineral surfaces can have
• Permanent structural charge
• Variable charge

116
EXCHANGE and SURFACE

• Sorption on permanent charge surfaces
• Ion exchange
• Occurs in clays (smectites), zeolites
• Sorption on variable charge surfaces
• Surface complexation
• Occurs on Fe, Mn, Al, Ti, Si oxides hydroxides,
  carbonates, sulfides, clay edges.

117
Semi-empirical models

• Assumptions
• Infinite supply of surface sites
• Adsorption is linear with total element aqueous
  conc.
• Ignores speciation, pH, competing ions, redox
  states
• Often based on sorbent mass, rather than surface
  area

118
The Langmuir adsorption model
At the limits Kc gtgt 1 ? q b Kc ltlt 1 ? q b Kc
where b and Kc are adjustable parameters.
Advantages Provides better fits, still simple,
accounts for sorption max.

• Assumptions
• Fixed number of sorption sites of equal affinity
• Ignores speciation, pH, competing ions, redox
  states

119
The Van Bemmelen-Freundlich adsorption model
where A and b are adjustable parameters with 0 lt
b lt 1 (usually).
Advantages Provides good fits because of 2
adjustable params. Still simple.

• Assumptions
• Assumes a log-normal distribution of Langmuir K
  parameters (I.e. affinities)
• Ignores speciation, pH, competing ions, redox
  states

120
pH edges for cation sorption
121
pH edges for anion sorption
122
Surface Complexation

• Important for trace elementsAs, P, other
  oxyanions and trace metals
• May be an important pH buffer
• Accounts for sorption as a function of pH and
  solution composition
• Considers variable charge surfaces. Number of
  sorption of sites is constant but site charge and
  surface charge vary as a function of solution
  composition
• Similar to aqueous complexation/speciation
• A mix of anions, cations neutral species can
  sorb
• Accounts for electrostatic work required to
  transport ions to a charged surface (similar to
  an activity coefficient correction) ?
  Gouy-Chapman theory

123
Surface charge depends on the sorption/surface
binding of potential determining ions, such as
H. Formation of surface complexes also affects
surface charge.
124
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125
Examples of Surface Complexation Reactions
outer-sphere complex
inner-sphere complex
bidentate inner-sphere complex
126
Gouy-Chapman Double-Layer Theory
The distribution of charge near a surface seeks
to minimize energy (charge separation) and
maximize entropy. A charged surface attracts a
diffuse cloud of ions, preferentially enriched in
counterions. The cation/anion imbalance in the
cloud gradually decreasses away from the surface.
127
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128
Diffuse Double-Layer Model Dzombak and Morel
129
CD-MUSIC

• Hiemstra and Van Rimsdijk
• Charge Distribution MUltiSIte Complexation model
• Inner sphere complexes have charge on central
  ion, say P, distributed between the 0 and 1
  planes
• Recently, tend not to have charge at the 2 plane.
• EXAFS, Molecular dynamics, and crystallography
  for bonding characteristics

130
Optional Explicit Diffuse Layer Calculation
Electroneutrality requires that
Borkovec and WestallCalculate the excess/deficit
of ions in the diffuse layer. PHREEQC has
capability for the Dzombak and Morell formulation.
Donnan assumption PHREEQC has capability for
Dzomak and Morell and CD-MUSIC
131
Surface complexation equations
1st deprotonation reaction
2nd deprotonation reaction
divalent cation complexation
132
For all surface reactions
where DZ is the net change in the charge number
of the surface species
is variable and represents the
electrostatic work needed to transport species
through the interfacial potential gradient. The
exponential factor basically is equivalent to an
activity coefficient correction. Kint strictly
represents the chemical bonding reaction.
133
Successful application of a DDLSC model
134
Surface Complexation

• 3 keywords to define surface complexation
• SURFACE_MASTER_SPECIES (component data)
• SURFACE_SPECIES (species thermo. data)
• SURFACE
• First 2 are found in phreeqc.dat and wateq4f.dat
  (for hydrous ferrous oxide, HFO, with both weak
  and strong sorption sites data from Dzombak
  Morel, 1990). Data can be modified in
  user-created input files.
• Last is user-specified to define amount and
  composition of a surface.

Databases do not have CD-MUSIC species!
135
SURFACE

• Initial surface calculation
• Sites units (moles or sites/nm2)
• Model
• Explicit diffuse layer
• Type, sites, area, mass

1
2
3
4
5
136
Sorption Parameters for HFO(from Dzombak
Morel, 1990)
Specific surface area 600m2/g (range
200-840) Site density for weak sites 0.2
mol/mol Fe (range 0.1-0.3) 3.5
sites/nm2 (-sites density) Weak sites apply to
sorption of protons, cations and anions Site
density for strong sites 0.005 mol/mol Fe
(range 0.001-0.01) 0.1 sites/nm2 Strong sites
are a smaller set of high-affinity cation binding
sites. Dzombak Morel assume HFO to be
Fe2O3.H2O, i.e. 89g HFO/mol Fe Note HFO ages to
goethite (a-FeOOH), a crystalline oxide with
lower and less reactive surface area. 2-10
goethite appears after 12-15 days of aging.
137
Initial Surface Calculation

• Calculates the composition of a surface in
  equilibrium with a solution
• Solution composition does not change
• Not a reaction, think of it as a shortcut
• Simplest, most reasonable way to define a surface
  composition
• Alternative to initial solution composition is
  HfoOHUncharged OH form of surface

138
SURFACE Sites Related to an EQUILIBRIUM_PHASE

• Sites and area are proportional to moles of
  mineral
• Index numbers of SURFACE and EQUILIBRIUM_PHASES
  must match
• Other SURFACE options are the same
• Can also relate surface to a KINETIC reactant
  (last tab)

139
SURFACE Exercise R27

• Calculate the composition of a Hydrous Ferric
  Oxide (Hfo) surface in equilibrium with seawater.
• Use Dzombak and Morel DDL model, with each
  explicit diffuse-layer option (default
  thickness). Note, one option fails.
• Assume only weak sites, site density 3.5
  sites/nm2, mass of sorbent is 10 grams, and
  specific area is 600 m2/g.

140
SURFACE Caveats

• Competition, especially cation vs anion, may be
  inaccurate
• DM is only for Hfo, the real world is some
  combination of Fe, Al, Si, and organic matter
• Site-specific data are needed
• Explicit diffuse layer calculation is at best an
  approximation
• Thickness
• Negative concentrations
• Theory lacking for finite pore spaces
• Borkovec requires charge balance
• Still developing New data, EXAFS, Molecular
  Dynamics, CD-MUSIC

141
SURFACE Exercise R30

• Define a 100 umol/kgw NaHPO4 solution
• Define surface in equilibrium with the solution
• 1 mmol Hfo_w sites
• 5000 g of solid
• 0.3 m2/g solid
• Add 3 mmol of NaOH in 30 steps
• Plot dissolved P and major sorbed phosphate
  species versus pH

142
Questions

• How much phosphate is on the surface at pH 6?
• What are the sorbed species?
• Which species is predominant?
• What happens to surface charge as the pH
  increases?

143
REACTION KINETICS
Pierre Glynn, March 2005 (w/ notes from Alex Blum)
144
General Concepts

• Transport vs. Reaction Control
• Elementary vs. Overall Reactions
• Detailed Balancing
• Microscopic Reversability
• Temperature Dependance
• Transition State Theory
• Michaelis-Menten/Monod Kinetics
• Surface Area
• Silicate mineral dissolution kinetics
  weathering

145
Transport vs. Reaction Control
a) Transport control b) Surface reaction
control c) Mixed Transport and surface-reaction
control
146

• Transport limitations
• diffusion in solution
• solid-state diffusion

• Reaction limitations
• surface reaction control
• surface characteristics
• crystal defects
• impurities
• crystal morphology

147
Surface Area

• Critical to rate calculations and predictions
• Geometric area estimation (often requires
  averaging or stochastic theory)
• BET measurements, usually w/ N2 (4Å compared to
  3Å for H2O)
• Surface roughness (BET/Geometric)
• SR 5 - 12 for fresh ground silicate
• SR 300 - 2000 for deeply weathered natural
  silicates
• Rate correction factor (m/m0)n, n lt 1.

148
Elementary vs. overall reactions
Reactions are the result of molecular collisions
almost invariably depend on the collision of no
more than 2 molecular species at a time.
Overall reactions, such as
do not reveal the sequential, and possibly
parallel, sets of molecular interactions, i.e.
elementary reactions, that are actually involved.
149
Example of fast reactions (only 1 elementary
step)
Example of a two step reaction
Overall reaction
Determining a rate law requires knowledge of the
rate-limiting elementary reaction (usually only
one). Allows accounting for the stoichiometry and
the reaction order. If this is not possible (eg.
for an overall reaction), rate laws are
determined experimentally.
150
Temperature Dependence
151
Activation Energy (EA)

• Reaction rates are exponentially dependent on EA
• EA depends on the direction of a reaction
• Catalysis lowers the EA required for a reaction
  (note activated complex)

Exothermic reaction
Endothermic reaction
EA
from http//www.ucdsb.on.ca/tiss/stretton/chem2/ra
te03

152
Transition State Theory

• Applies statistical mechanics to individual
  elementary reactions. Meaningless for overall
  reactions.
• Focuses on the activated complex, the molecular
  configuration present at the top of the energy
  barrier between reactants and products in an
  elementary reaction.
• Assumes this complex is a true chemical species
  and assumes that the initial reactants are always
  at equilibrium with the complex.
• Predicts that the rate is proportional to the
  number of activated complexes and to their rate
  of decomposition.

153
Transition State Theory

• Applies statistical mechanics to individual
  elementary reactions. Meaningless for overall
  reactions.
• Focuses on the activated complex, the molecular
  configuration present at the top of the energy
  barrier between reactants and products in an
  elementary reaction.
• Assumes this complex is a true chemical species
  and assumes that the initial reactants are always
  at equilibrium with the complex.
• Predicts that the rate is proportional to the
  number of activated complexes and to their rate
  of decomposition.
• Applies near equilibrium.

154
Transition State Theory
Rate is related to the degree of supersaturation
or undersaturation
Alternatively,
Often,
155
(From Burch et al., 1993) DG -8 kcal/mol gt
log Q/K -3.7 gt Sat 0.02
156
Surface Speciation Kinetic Model

• Fast reversible adsorption reaction to form a
  surface species
• Irreversible dissolution reaction at that surface
  species

157
Surface complexation theory allows guessing the
form of the activated complex. In this case
(dissolution of Amelia albite Blum, 1994, GCA),
the dissolution rate is proportional to the
degree of protonation, or deprotonation of the
surface
Log Rate (mol/m2/s)
-4.0
Log (DSurface charge) (mol/m2)
-6.5
158
Calcite Dissolution, Plummer and others, 1978
But, k4 is not really a constant, but a function
of equilibrium at the surface
159
Pyrite dissolution
Williamson and Rimstidt, 1994, phreeqc.dat
Iron oxidation
Stumm and Lee, 1961 abiotic
Williamson and others, 1992 biotic
Note No Back-Reaction
160
Michaelis-Menten/Monod Kinetics

• Based on enzyme kinetics
• Similar to TST theory based on the idea of an
  activated complex, or an enzyme-substrate
  (ES) compound, whose concentration controls the
  rate of reaction
• The Michaelis-Menten equation is

161
Variations on Monod

• Sum several Monod rates
• Inhibitor factors

(BIOMOC, Essaid and others)
162
PHREEQC Strategy

• Wide variety of literature rate expressions
• PHREEQC has an imbedded Basic language
  interpreter
• Define rate expressions with Basic programs
• Use Basic functions to obtain activities,
  concentrations, saturation ratios of the solution

163
RATES Linear decay example

• Define an element DocSOLUTION_MASTER_SPECIES
• Define master species for DocSOLUTION_SPECIES
• Define initial solutionSOLUTION
• Define a first order rate expression for Doc
  decayRATES
• Define reaction stoichiometryKINETICS
• Run

164
(No Transcript)
165
1. Define DocSOLUTION_MASTER_SPECIES
166
2. Define aqueous species of DocSOLUTION_MASTER_S
PECIES
167
3. Define seawater initial solution DocSOLUTION
168
4. Define rate expressionRATES

• Can define multiple rate expressions
• RATES expressions are used in KINETICS
• A few RATES definitions in phreeqc.dat
• PhreeqcI gives help with functions and arguments
• PhreecI tries to check Basic statements

169
RATES (continued)

• Rate name is DOC_decomposition
• -start/-end mark Basic program (optional)
• TOT returns molality of element
• PARM(1) is defined in KINETICS, meaning is
  defined by user, day-1 in this case
• K is converted to sec-1
• Rate is first order with Doc
• TIME is internally generated time step (seconds)
• SAVE is used to save the moles of reaction over
  the time step
• If mass of water not 1 kg water, be careful of
  units
• PRINT statements can be used to debug

RATES DOC_decomposition -start 10 doc
TOT("Doc") 20 k PARM(1) / (360024) 30 rate
kdoc 40 molality rate TIME 50 moles
molalityTOT("water") 60 SAVE moles 70 PRINT
doc, k, rate, TIME -end
170
Define kinetic reactantsKINETICS

• Define rate name(s)
• Tab for each rate name
• Moles of reactant
• Tolerance (moles)
• Parameters
• Reactant formula

171
KINETICS and RATESMoles of Reactant

• M increases and/or decreases depending on the
  sign of moles in the rate expression (RATES)
• If moles is positive, M decreases
• If moles is negative, M increases.
• If M 0 no reaction occurs if moles is
  positive.
• M0 is constant, intended for surface area
  adjustment

172
KINETICS and RATES Signs

• moles has positive sign in our example
• Formula has signsDoc -1, CH2O 1
• Doc moles(-1) is negative, Doc is removed from
  solution
• CH2O moles(1) is positive, Doc is added to
  solution

173
KINETICSODE Method

• KINETICS integrates Ordinary Differential
  Equations
• Explicit Runge-Kutta is default and will be
  faster if it works
• May need the implicit method CVODE
• 1-SR rate equations
• Multiple interacting rates
• Fast rate to simulate equilibrium
• Stiff equations
• Both methods use a tolerance to control automatic
  time stepping

174
KINETICSSteps

• Time is seconds
• Only applies to reaction calculations
• INCREMENTAL_REACTIONS more efficient for multiple
  time steps. Default, every step starts at zero
  time.
• TRANSPORT time step supersedes KINETICS time step

175
First Order Kinetics

• k is 1 per day
• Doc0 is 12 mg/kgs, which is 1.035 mmol/kgw
• After 1 day, concentration should be 0.3808 mmol
  Doc

176

• R28
• SOLUTION_MASTER_SPECIES
• Doc Doc 0 C
  12
• SOLUTION_SPECIES
• Doc Doc
• log_k 0
• SOLUTION 1 Seawater
• temp 25
• pH 8.22
• pe 8.45
• redox pe
• units ppm
• density 1
• Ca 412.3
• Mg 1291.8
• Na 10768
• K 399.1
• Fe 0.002
• Alkalinity 141.682 as HCO3

RATES DOC_decomposition -start 10 doc
TOT("Doc") 20 k PARM(1) / (360024) 30 rate
kdoc 40 molality rate TIME 50 moles
molalityTOT("water") 60 SAVE moles -end KINETICS
1 DOC_decomposition -formula Doc -1 CH2O
1 -m 1 -m0 1 -parms
1 -tol 1e-08 -steps 86400 in 1
steps seconds -step_divide 1 -runge_kutta 3
177
RUN
178
KNOBS

• Convergence
• Parameter changes
• Step_size 10
• Pe_step_size 5
• Iterations 200
• Redox problems
• SOLUTION_SPECIES
• H2O .01e- H2O-0.01
• Log_k -9
• Higher precision
• Convergence_tol 1e-12

179
USER_PUNCH

• Must define include SELECTED_OUTPUT data block
• Basic program
• PUNCH command prints to selected-output file
• Also USER_PRINT data block
• PRINT command prints to output file

180
R29 Denitrification

• Assume
• Agricultural infiltration has 1 mmol/kgw NO3-
• Aquifer contains abundant organic carbon
• Rate of organic carbon oxidation follows Monod
  kinetics
• Vmax 1e-11 sec-1
• Half saturation 1e-4 mol/kgw
• Calculate solution composition every quarter for
  3 years
• Make a spreadsheet file with
• Time in years
• Millimoles of nitrate and dissolved N2
• Amount of organic carbon consumed
• Plot results

181
Questions

• Why did the reaction slow down with time?
• Why is the final dissolved nitrogen not equal to
  the initial nitrate concentration?
• How do you account for the stoichiometry of
  organic carbon and dissolved nitrogen?
• How much denitrification is needed to form a
  bubble at 10 m hydrostatic pressure?

182
SOLID_SOLUTIONS

• No solids are really pure phases
• Activity of components in solids are not equal to
  1
• Need definition of activity

183
Ideal Solid Solution

• Activity is equal to mole fraction
• Mass-action equation for CaCO3

184
Non-Ideal Binary Solid Solution

• Activity is equal to mole fraction times activity
  coefficient
• Activity coefficients
• Mass-action

185
Non-Ideal Binary Solid Solution Activity
Coefficient Parameters

• -Gugg_nondimensional 5.08 1.90  
• -Gugg_kj 12.593 4.70
• -activity_coefficients 24.05 1075. 0.0001
  0.9999
• -distribution_coefficients 0.0483 1248. .0001
  .9999
• -miscibility_gap 0.0428 0.9991
• -spinodal_gap 0.2746 0.9483
• -critical_point 0.6761
  925.51
• -alyotropic_point 0.5768 -8.363
• -Thompson 17.303 7.883
• -Margules -0.62 7.6

186
USER_PRINT

• USER_PRINT
• 10 PRINT "Ca mg/L ", TOT("Ca")401000
• 20 PRINT "Zn mg/L ", TOT("Zn")65.41000
• 30 PRINT "Cd mg/L ", TOT("Cd")112.41000
• 40 PRINT "Pb mg/L ", TOT("Pb")207.21000

187
R31 Trace metal sequestration

• Waste water composition in mg/L
• Ca 40
• Zn 10
• Pb 0.1
• Cd 0.5
• Simulate the percolation of this water into a
  soil zone and reaction with calcite
• Use USER_PRINT to calculate mg/L of each metal

188
Questions

• How do concentrations compare to standards 5,
  0.01, and 0.01 mg/L for Zn, Cd, Pb?
• What are the important factors in this
  calculation?

189
Summary

• SOLUTION, SOLUTION_SPREAD
• Irreversible reactions
• MIX
• REACTION
• KINETICS (RATES)
• REACTION_TEMPERATURE
• Reversible reactions
• EQUILIBRIUM_PHASES
• EXCHANGE
• SURFACE
• SOLID_SOLUTIONS
• GAS_PHASE
• SAVE, USE, ENDDefinition of simulation

190
Summary

• INCREMENTAL_REACTIONSEfficiency
• KINETICS
• REACTION
• Printing
• TITLE
• PRINT
• USER_PRINT
• SELECTED_OUTPUT
• USER_PUNCH
• KNOBSConvergence parameters

191
Summary

• 1D transport
• ADVECTION
• TRANSPORT
• Inverse modeling
• INVERSE_MODELING

192
Summary

• Reactions and Thermodynamics
• PITZER
• SOLUTION_MASTER_SPECIES
• SOLUTON_SPECIES
• SURFACE_MASTER_SPECIES
• SURFACE_SPECIES
• EXCHANGE_MASTER_SPECIES
• EXCHANGE_SPECIES
• PHASES