Title: Fluorite Solubility
1Fluorite 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.
2Geochemical Calculations Using PHREEQC
- David Parkhurst
- U.S. Geological Survey
- dlpark_at_usgs.gov
- http//wwwbrr.cr.usgs.gov/projects/GWC_coupled/ind
ex.html
3Overview
- 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
4Solution Definition and Speciation Calculations
Speciation calculation
5Seawater Units are ppm
6Initial 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
7Periodic_table.bmp
8Default Gram Formula Weights
Default GFW is defined in 4th field of
SOLUTION_MASTER_SPECIES in database file.
9Databases
- 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
10Database 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)
11What 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
12Mass-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.
13Mass-Action Equations
indicates activity
14Activity Coefficients
Ionic strength
WATEQ activity coefficient
Davies activity coefficient
15Pitzer 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
16Aqueous 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
17PhreeqcI SOLUTION Data Block
18pH, pe, Temperature
19Solution Composition
- Set units!
- Default is mmol/kgw
Select elements
Set concentrations As, special units
Click when done
20Run Speciation Calculation
Select files
21Results of Speciation Calculation
Cascade
22Initial 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)
23Initial 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?
24More on Solution Definition
- pH, Carbon, Alkalinity, pe
25What 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?
26Alkalinity, 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
27What 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
28More 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
29Redox Elements
30Redox 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
31Seawater Initial Solution
- Fe total was entered. How were Fe(3) and Fe(2)
concentrations calculated?
For initial solutions For reactions
32Charge Balance Options
- For most analyses, just leave it
- Adjust the major anionmissing major analyte
- Adjust pHpH of 1 molal HCl solution
33Adjustments 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
34SOLUTION_SPREAD
35SATURATION 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
36Rules 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
37Uncertainties 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)
38Uncertainties 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.
39Uncertainties 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
40Useful Mineral ListMinerals that may react to
equilibrium relatively quickly
41IS 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?
42Summary
- 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)
43Summary
- 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
44Reaction Calculations
EQUILIBRATION REACTOR
45EQUILIBRIUM REACTANTS
- SURFACE
- EXCHANGE
- SOLID_SOLUTIONS
- EQUILIBRIUM_PHASES
- GAS_PHASE
46NON-EQUILIBRIUM REACTIONS
- MIX
- REACTION
- REACTION_TEMPERATURE
- KINETICS
47PHREEQCReactions
To the beakerUSE
Kinetics 10
React and SAVE
48CONCEPTUAL 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
49Geochemical Reactions
- Carbonates
- Oxidation of organic carbon
- Oxidation of pyrite
- Aluminosilicate reactions
- (Bubbles)
50Reactions
51MIX One or more SOLUTIONS
- Solution number
- Mixing fraction
52REACTION 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.
53Questions
- 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).
54Redox 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
55Reactions
- Sequential reactions
- USE, SAVE, REACTION, EQUILIBRIUM_PHASES, END
56SAVE and USE
- Save results of reaction calculations
- Use previously defined SOLUTIONs,
EQUILIBRIUM_PHASES, REACTIONs, etc - Use previously SAVEd SOLUTIONS,
EQUILBRIUM_PHASES, etc
57SAVE 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.
58USE Previously defined or SAVEd
- USE includes KINETICS, MIX, REACTION, and
REACTION_TEMPERATURE - Can USE previously SAVEd EQUILIBRIUM_PHASES,
EXCHANGE, SOLID_SOLUTION, SOLUTION, or SURFACE
59REACTION Reactants and stoichiometry
- Choose phase or type formula
- Define relative stoichiometry
- Must be charge balanced
60REACTION Reaction amounts
- Steps are a number of equal increments
- or
- Steps are a specified list
- Specify units
61EQUILIBRIUM_PHASES
- Assembly of minerals/gases that react to
equilibrium or zero moles - Define
- Mineral/gas
- Target saturation index
- Moles present
62Initial Solution and Reaction Calculations
63Initial 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
64REACTION 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.
65Questions
- 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?
66REACTION 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.
67Reaction Exercise
68Dedolomitization
- Anhydrite dissolution
- Calcite precipitation
- Dolomite dissolution
69REACTION 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.
70Questions
- 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?
71Dedolomitization
72SELECTED_OUTPUT
File name
1. Set file name (default selected.out)
2. Reset all to false
3. Set pH to true
4. Set Reaction true
73Selected Output Total Molalities
74Selected Output
75Selected Output File
- Open with Excel
- Manipulate/plot data
- PFW has built-in plotting capability
76Carbonate 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
77Reactions
78Organic Decomposition
- Sequential removal of electron acceptors, usually
in the sequence - O2
- NO3-
- MnO2
- Fe(OH)3
- SO4-2
- HCO3-
79Redox 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
80Redox Environments
81Redox Sequence at pH 7
82Organic 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
83REACTION 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.
84Questions
- 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?
85Organic Decomposition
86GAS_PHASE
- PV nRT Ideal gas law
- Henrys law
- Log K CO2/P(CO2)
- Fixed pressureVolume varies
- Fixed volumePressure varies
87GAS_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
88GAS_PHASE
89Gases
- Fixed partial pressureuse EQUILIBRIUM_PHASES
- Fixed volume head spaceuse fixed volume
GAS_PHASE - Expanding Bubbleuse fixed pressure GAS_PHASE
90REACTION 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.
91Organic decomposition with GAS_PHASE
92Organic 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
93Reactions
94Sulfide 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
95REACTION 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.
96Questions
- 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?
97REACTION 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.
98Questions
- 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?
99Picher Oklahoma Abandoned Pb/Zn Minemg/L
- Mines are suboxic
- Carbonates are present
- Iron oxidizes in stream
100Pyrite 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
101Reactions
- Aluminosilicate reactions
102Aluminosilicate 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
103Aluminosilicates
- 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
104Add Reactant to Phase Boundary
- KAlSiO8 is added (or removed) until gibbsite
equilibrium is reached - Amount is amount of KAlSiO8, not gibbsite
105Add Reactant to Phase Boundary
106REACTION 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.
107Questions
- Given the thermodynamic data, which mineral
should precipitate first? - Does quartz need to be included in this
calculation?
108Sierra Nevada Springsmmol/kgw
- Increase in Ca, Alkalinity, pH
- Increase in SiO2
- Slight increase in Mg, K, Cl, SO4
109Reaction Summary
- MIX
- EQUILIBRIUM_PHASES
- REACTION
- GAS_PHASE
- USE
- SAVE
- SELECTED_OUTPUT
110Summary
- Carbonate minerals and CO2
- Dedolomitization
- Organic decomposition
- Sulfate reduction
- Other electron acceptors O2, NO3, FeOOH, CH2O
- Sulfide oxidation
- Aluminosilicate reactions
111REACTION 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
112REACTION 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?
113Still to Study
- SURFACE
- EXCHANGE
- KINETICS
- SOLID_SOLUTION
114Sorption Reactions
- Pierre Glynn, USGS, March 2005
115Sorption 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
116EXCHANGE 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.
117Semi-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
118The 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
119The 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
120pH edges for cation sorption
121pH edges for anion sorption
122Surface 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
123Surface charge depends on the sorption/surface
binding of potential determining ions, such as
H. Formation of surface complexes also affects
surface charge.
124(No Transcript)
125Examples of Surface Complexation Reactions
outer-sphere complex
inner-sphere complex
bidentate inner-sphere complex
126Gouy-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(No Transcript)
128 Diffuse Double-Layer Model Dzombak and Morel
129CD-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
130Optional 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
131Surface complexation equations
1st deprotonation reaction
2nd deprotonation reaction
divalent cation complexation
132For 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.
133Successful application of a DDLSC model
134Surface 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!
135SURFACE
- Initial surface calculation
- Sites units (moles or sites/nm2)
- Model
- Explicit diffuse layer
- Type, sites, area, mass
1
2
3
4
5
136Sorption 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.
137Initial 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
138SURFACE 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)
139SURFACE 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.
140SURFACE 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
141SURFACE 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
142Questions
- 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?
143REACTION KINETICS
Pierre Glynn, March 2005 (w/ notes from Alex Blum)
144General 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
145Transport 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
147Surface Area
- Critical to rate calculations and predictions
- Geometric area estimation (often requires
averaging or stochastic theory) - BET measurements, usually w/ N2 (4Ã… compared to
3Ã… 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.
148Elementary 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.
149Example 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.
150Temperature Dependence
151Activation 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
152Transition 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.
153Transition 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.
154Transition 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
156Surface Speciation Kinetic Model
- Fast reversible adsorption reaction to form a
surface species - Irreversible dissolution reaction at that surface
species
157Surface 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
158Calcite Dissolution, Plummer and others, 1978
But, k4 is not really a constant, but a function
of equilibrium at the surface
159Pyrite dissolution
Williamson and Rimstidt, 1994, phreeqc.dat
Iron oxidation
Stumm and Lee, 1961 abiotic
Williamson and others, 1992 biotic
Note No Back-Reaction
160Michaelis-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
161Variations on Monod
- Sum several Monod rates
- Inhibitor factors
(BIOMOC, Essaid and others)
162PHREEQC 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
163RATES 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)
1651. Define DocSOLUTION_MASTER_SPECIES
1662. Define aqueous species of DocSOLUTION_MASTER_S
PECIES
1673. Define seawater initial solution DocSOLUTION
1684. 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
169RATES (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
170Define kinetic reactantsKINETICS
- Define rate name(s)
- Tab for each rate name
- Moles of reactant
- Tolerance (moles)
- Parameters
- Reactant formula
171KINETICS 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
172KINETICS 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
173KINETICSODE 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
174KINETICSSteps
- 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
175First 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
177RUN
178KNOBS
- 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
179USER_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
180R29 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
181Questions
- 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?
182SOLID_SOLUTIONS
- No solids are really pure phases
- Activity of components in solids are not equal to
1 - Need definition of activity
183Ideal Solid Solution
- Activity is equal to mole fraction
- Mass-action equation for CaCO3
184Non-Ideal Binary Solid Solution
- Activity is equal to mole fraction times activity
coefficient - Activity coefficients
- Mass-action
185Non-Ideal Binary Solid Solution Activity
Coefficient Parameters
- -Gugg_nondimensional 5.08 1.90 Â
- -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
186USER_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
187R31 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
188Questions
- 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?
189Summary
- 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
190Summary
- INCREMENTAL_REACTIONSEfficiency
- KINETICS
- REACTION
- Printing
- TITLE
- PRINT
- USER_PRINT
- SELECTED_OUTPUT
- USER_PUNCH
- KNOBSConvergence parameters
191Summary
- 1D transport
- ADVECTION
- TRANSPORT
- Inverse modeling
- INVERSE_MODELING
192Summary
- Reactions and Thermodynamics
- PITZER
- SOLUTION_MASTER_SPECIES
- SOLUTON_SPECIES
- SURFACE_MASTER_SPECIES
- SURFACE_SPECIES
- EXCHANGE_MASTER_SPECIES
- EXCHANGE_SPECIES
- PHASES