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Monday-Tuesday• Solutions
– Thermodynamics of aqueous solutions– Saturation indices
• Mineral equilibria• Cation exchange• Surface complexation• Advective transport• Diffusive transport• Acid mine drainage
1
Processes that Control Major Element Chemistry1. Carbonate reactions2. Ion exchange3. Organic carbon oxidation
O2/Nitrate reductionIron oxyhydroxide reductionSulfate reductionMethanogenesis
4. Gypsum dissolution5. Pyrite oxidation6. Seawater evaporation7. Silicate weathering
Processes that Control Minor Element Chemistry
1. Redox OxyanionsTrace metalsNitrate
2. Surface complexation Phosphate OxyanionsTrace metals
3. Cation exchange4. Solid solutions5. Minerals
PHREEQC Programs• PHREEQC Version 3
– PHREEQC: Batch with Charting – PhreeqcI: GUI with Charting– IPhreeqc: Module for programming and scripting
• PHAST– Serial—soon to be Multithreaded– Parallel—MPI for transport and chemistry– TVD (not done)– 4Windows—GUI just accepted
• WEBMOD-Watershed reactive transport
4
Solution Definition and Speciation Calculations
Ca NaSO4 MgFeCl HCO3
ReactionsSaturation
IndicesSpeciation calculation
Inverse Modeling
Transport5
Constituent ValuepH
pe
Temperature
Ca
Mg
Na
K
Fe
Alkalinity as HCO3
Cl
SO4
8.22
8.45
10
412.3
1291.8
10768
399.1
.002
141.682
19353
2712
SOLUTION: Seawater, ppm
6
Periodic_table.bmp
7
Initial Solution 1. Questions1. What is the approximate molality of Ca?
2. What is the approximate alkalinity in meq/kgw?
3. What is the alkalinity concentration in mg/kgs as CaCO3?
4. What effect does density have on the calculated molality?
PHREEQC results are always moles or molality
8
Initial Solution 1.
For most waters, we can assume most of the mass in solution is water. Mass of water in 1 kg seawater ~ 1 kg.
1. 412/40 ~ 10 mmol/kgw ~ 0.01 molal
2. 142/61 ~ 2.3 meq/kgw ~ 0.0023 molal
3. 2.3*50 ~ 116 mg/kgw as CaCO3
4. None, density will only be used when concentration is specified as per liter.
9
Default Gram Formula Mass
Element/Redox State Default “as” phreeqc.dat/wateq4f.dat
Alkalinity CaCO3
C, C(4) HCO3
CH4 CH4
NO3- N
NH4+ N
PO4 P
Si SiO2
SO4 SO4
Default GFW is defined in 4th field of SOLUTION_MASTER_SPECIES in database file.
10
Databases
• Ion association approach– Phreeqc.dat—simplest (subset of Wateq4f.dat)– Amm.dat—same as phreeqc.dat, NH3 is separated from N– Wateq4f.dat—more trace elements– Minteq.dat—translated from minteq v 2– Minteq.v4.dat—translated from minteq v 4– Llnl.dat—most complete set of elements, temperature dependence– Iso.dat—(in development) thermodynamics of isotopes
• Pitzer specific interaction approach– Pitzer.dat—Specific interaction model (many parameters)
• SIT specific interaction theory– Sit.dat—Simplified specific interaction model (1 parameter)
11
PHREEQC Databases
Other data blocks related to speciation
SOLUTION_MASTER_SPECIES—Redox states and gram formula mass
SOLUTION_SPECIES—Reaction and log K
PHASES—Reaction and log K
12
Solutions• Required for all PHREEQC calculations• SOLUTION and SOLUTION _SPREAD
– Units– pH– pe– Charge balance– Phase boundaries
• Saturation indices– Useful minerals– Identify potential reactants
13
What is a speciation calculation?
• Input: – pH– pe– Concentrations
• Equations:– Mass-balance—sum of the calcium species = total calcium– Mass-action—activities of products divided by reactants =
constant– Activity coefficients—function of ionic strength
• Output– Molalities, activities– Saturation indices
14
Mass-Balance Equations
Analyzed concentration of sulfate = (SO4-2)
+ (MgSO40) + (NaSO4
-) + (CaSO40) +
(KSO4-) + (HSO4
-) + (CaHSO4+) + (FeSO4)
+ (FeSO4+) + (Fe(SO4)2
-) + (FeHSO4+) +
(FeHSO4+2)
() indicates molality
15
Mass-Action Equations
Ca+2 + SO4-2 = CaSO4
0
]][[
][2
42
4
SOCa
CaSOK
[] indicates activity
]log[]log[]log[log 24
204
SOCaCaSOK
16
Activityiii ma
i
i
ii b
Ba
Az
0
2
1log
0
0.2
0.4
0.6
0.8
1
1.2
0 0.5 1 1.5
IONIC STRENGTH
AC
TIV
ITY
CO
EF
FIC
IEN
T
gamma_Na+
gamma_Z-2
gamma_SO4-2
WATEQ activity coefficient
iii Az 3.01
log 2
Davies activity coefficient
ii
i mz 2
2
1
17
Uncharged Species
18
ii blog
bi, called the Setschenow coefficient
Value of 0.1 used in phreeqc.dat, wateq4f.dat.
Pitzer Activity Coefficients
a a c acaacmmaaaa
a c aMcaaMccMaMaaMM
Cmmzmm
MmZCBmFz
'''
2 )()2(ln
ma concentration of anionmc concentration of cation Ion specific parameters,,, BCF function of ionic strength, molalities of cations and anions
19
SIT Activity Coefficients
kk
ikii mB
Az
1ln 2
mk concentrations of ion
ik
20
Interaction parameter
A = 0.51, B = 1.5 at 25 C
Aqueous Models
Ion association – Pros
• Data for most elements (Al, Si)• Redox
– Cons• Ionic strength < 1• Best only in Na, Cl medium• Inconsistent thermodynamic data• Temperature dependence
21
Aqueous Models
22
• 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
Aqueous Models
23
• SIT– Pros
• Possibly better for higher ionic strength than ion association
• Many fewer parameters• Redox• Actinides
– Cons• Poor results for gypsum/NaCl in my limited testing• Temperature dependence• Consistency?
PhreeqcI: SOLUTION Data Block
24
Number, pH, pe, Temperature
25
Solution Composition
Set units!Default is mmol/kgw
Click when done
Set concentrations“As”, special units
Select elements
26
Run Speciation CalculationRun
Select files
27
Seawater Exercise
A. Use phreeqc.dat to run a speciation calculation for file seawater.pqi
B. Use file seawater-pitzer.pqi
or copy input to a new buffer
• Ctrl-a (select all) • Ctrl-c (copy)• File->new or ctrl-n
(new input file)• Ctrl-v (paste)
Constituent ValuepH
pE
Temperature
Ca
Mg
Na
K
Fe
Alkalinity as HCO3
Cl
SO4
8.22
8.45
10
412.3
1291.8
10768
399.1
.002
141.682
19353
2712
Units are ppm
28
Ion Association Model Results
29
Results of 2 Speciation Calculations
Tile
30
Ion Association
Pitzer
Questions
1. Write the mass-balance equation for calcium in seawater for each database.
2. What fraction of the total is Ca+2 ion for each database?
3. What fraction of the total is Fe+3 ion for each database?
4. What are the log activity and log activity coefficient of CO3
-2 for each database?
5. What is the saturation index of calcite for each database?
31
Initial Solution 2. Answers() indicates molality
1a. Ca(total)= 1.066e-2 = (Ca+2) + (CaSO4) + (CaHCO3+) + (CaCO3) + (CaOH+) + (CaHSO4+)
1b. Ca(total) = 1.066e-2 = (Ca+2) + (CaCO3)
2a. 9.5/10.7 ~ 0.952b. 1.063/1.066 ~ 1.0
3a. 3.509e-019 / 3.711e-008 ~ 1e-113b. No Fe+3 ion.
4a. log activity CO3-2 = -5.099; log gamma CO3-2 = -0.684b. log activity CO3-2 = -5.091; log gamma CO3-2 = -1.09
5a. SI(calcite) = 0.765b. SI(calcite) = 0.70
32
SATURATION INDEXThe thermodynamic state of a mineral relative to a solution
33
)/(10log KIAPSI
IAP is ion activity productK is equilibrium constant
)/]][([10log 23 CalciteCalcite KCOCaSI
)(10log])([10log])([10log 23 CalciteCalcite KCOCaSI
SATURATION INDEX
SI < 0, Mineral should dissolve
SI > 0, Mineral should precipitate
SI ~ 0, Mineral reacts fast enough to maintain equilibrium
Maybe– Kinetics– Uncertainties
34
Rules for Saturation Indices
• Mineral cannot dissolve if it is not present
• If SI < 0 and mineral is present—the mineral
could dissolve, but not precipitate
• If SI > 0—the mineral could precipitate, but not
dissolve
• If SI ~ 0—the mineral could dissolve or
precipitate to maintain equilibrium35
Saturation Indices
• SI(Calcite)
• SI(CO2(g))
= log(PCO2)
36
Useful Mineral ListMinerals that may react to equilibrium relatively quickly
Carbonates PhosphatesCO2(g) CO2 Hydroxyapatite Ca5(PO4)3OHCalcite CaCO3 Vivianite Fe3(PO4)2Dolomite CaMgCO3 OxyhydroxidesSiderite FeCO3 Fe(OH)3(a) Fe(OH)3Rhodochrosite MnCO3 Goethite FeOOH
Sulfates Gibbsite Al(OH)3Gypsum CaSO4 Birnessite MnO2Celestite SrSO4 Manganite Mn(OH)3Barite BaSO4 Aluminosilicates
Sulfides Silica gel SiO2-2H2OFeS(a) FeS Silica glass SiO2-H2OMackinawite FeS Chalcedony SiO2
Kaolinite Al2Si2O5(OH)37
Data Tree• Files
(double click to edit)– Simulation
(END)• Keywords
(double click to edit)
– Data
38
Edit Screen
• Text editor
39
Tree Selection
• Input
• Output
• Database
• Errors
• PfW
40
Keyword Data Blocks
41
Also right click in data tree—Insert keyword
PfW Style
42
Alkalinity
• Approximately HCO3
- + 2xCO3-2 + OH- - H+
• Alkalinity is independent of PCO2
Total Inorganic Carbon• Number of moles of carbon of valence 4
43
SOLUTION_SPREAD
44
Carbon and Alkalinity
solution_spread.pqi
SOLUTION_SPREAD
SELECTED_OUTPUT
USER_GRAPH
45
Carbon Speciation and Alkalinity
46
pH and pe
Keywords
SOLUTION—Solution composition
END—End of a simulation
USE—Reactant to add to beaker
REACTION—Specified moles of a reaction
USER_GRAPH—Charting
47
Constituent ValuepH
pe
Temperature
Alkalinity
Na
7
4
25
1
1 charge
SOLUTION, mmol/kgw
48
END
USE
49
Solution 1
REACTIONCO2 1.0
1, 10, 100, 1000 mmol
USER_GRAPH -axis_titles "CO2 Added, mmol" "pH" "Alkalinity"
-axis_scale x_axis auto auto auto auto log
-axis_scale sy_axis 0 0.002
-start
10 GRAPH_X rxn
20 GRAPH_Y -LA("H+")
30 GRAPH_SY ALK
-end
Input filepH.pqi
SOLUTION 1
temp 25
pH 7
pe 4
redox pe
units mmol/kgw
density 1
Alkalinity 1
Na 1 charge
-water 1 # kg
END
USE solution 1
REACTION 1
CO2 1
1 10 100 1000 millimoles
USER_GRAPH 1
-axis_titles "CO2 Added, mmol" "pH" "Alkalinity"
-axis_scale x_axis auto auto auto auto log
-axis_scale sy_axis 0 0.002
-start
10 GRAPH_X rxn
20 GRAPH_Y -LA("H+")
30 GRAPH_SY ALK
-end
END 50
pH is the ratio of HCO3- to CO2(aq)
51Alkalinity is independent of PCO2
What is pH?
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?
pH = 6.3 + log[(HCO3-)/(CO2)]
pH = 10.3 + log[(CO3-2)/(HCO3
-)]
52
pH = logK + log[(PO4-3)/(HPO4
-2)]
Constituent ValuepH
pe
Temperature
Fe(3)
Cl
2
4
25
1
1 charge
SOLUTION, mmol/kgw
53
END
USE
54
Solution 1
REACTIONFeCl2 1.0
1, 10, 100, 1000 mmol
USER_GRAPH -axis_titles "FeCl2 Added, mmol" "pe" ""
-axis_scale x_axis auto auto auto auto log
-start
10 GRAPH_X rxn
20 GRAPH_Y -LA("e-")
-end
Input file
SOLUTION 1
temp 25
pH 3
pe 4
redox pe
units mmol/kgw
density 1
Cl 1 charge
Fe(3) 1
-water 1 # kg
END
USE solution 1
REACTION 1
FeCl2 1
1 10 100 1000 millimoles
USER_GRAPH 1
-axis_titles "FeCl2 Added, mmol" "pe" ""
-axis_scale x_axis auto auto auto auto log
-start
10 GRAPH_X rxn
20 GRAPH_Y -LA("e-")
-end
END55
pe
56
What is pe?Fe+2 = Fe+3 + e-
pe = log( [Fe+3]/[Fe+2] ) + 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
pe = 16.9Eh, Eh in volts (platinum electrode measurement) 57
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. Fe to Fe(2) and Fe(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).• pe options can only be applied to speciation
calculations; thermodynamic pe is used for all other calculations
58
Iron Speciation with PhreePlot
59
Redox ElementsElement Redox
stateSpecies
Carbon C(4) CO2
C(-4) CH4
Sulfur S(6) SO4-2
S(-2) HS-
Nitrogen N(5) NO3-
N(3) NO2-
N(0) N2
N(-3) NH4+
Oxygen O(0) O2
O(-2) H2O
Hydrogen H(1) H2O
H(0) H2
Element Redox state
Species
Iron Fe(3) Fe+3
Fe(2) Fe+2
Manganese Mn(2) Mn+2
Arsenic As(5) AsO4-3
As(3) AsO3-3
Uranium U(6) UO2+2
U(4) U+4
Chromium Cr(6) CrO4-2
Cr(3) Cr+3
Selenium Se(6) SeO4-2
Se(4) SeO3-2
Se(-2) HSe-60
Seawater Initial Solution
Fe total was entered. How were Fe(3) and Fe(2) concentrations calculated?
)2(/)6()3(/)5(/)0( 2 SSNNOHO pepepe
)2(/)6()3(/)5(/)0( 2 SSNNOHO pepepe
For initial solutions
For “reactions”
61
Final thoughts on pe• pe sets ratio of redox states• Some redox states are measured directly:
– NO3-, NO2-, NH3, N2(aq)– SO4-2, HS-– O2(aq)– Sometimes Fe, As
• Others can be assumed: – Fe, always Fe(2) except at low pH– Mn, always Mn(2)– As, consider other redox elements– Se, consider other redox elements– U, probably U(6)– V, probably V(5)
62
Berner’s Redox Environments
• Oxic
• Suboxic
• Sulfidic
• Methanic
Thorstenson (1984)
63
-15
-10
-5
0
5
10
15
20
25
0 2 4 6 8 10 12 14
pH
pe
H2
Methanic
Sulfidic
Post-oxic
Oxic
64
Parkhurst and others (1996)
65
SummarySOLUTION and SOLUTION _SPREAD
– Units– pH—ratio of HCO3/CO2
– pe—ratio of oxidized/reduced valence states– Charge balance– Phase boundaries
• Saturation indices– Uncertainties– Useful minerals
• Identify potential reactants
66
Summary
Aqueous speciation model– Mole-balance equations—Sum of species
containing Ca equals total analyzed Ca
– Aqueous mass-action equations—Activity of products over reactants equal a constant
– Activity coefficient model • Ion association with individual activity coefficients• Pitzer specific interaction approach
– SI=log(IAP/K)
67
PHREEQC: Reactions in a Beaker
SOLUTION EQUILIBRIUM_PHASES
EXCHANGE SURFACE KINETICSMIX REACTION
REACTION BEAKER
+
SOLUTIONEQUILIBRIUM_
PHASESEXCHANGE SURFACE
GAS_PHASE
GAS_PHASE
68
REACTION_TEMPERATURE REACTION_PRESSURE
Reaction Simulations• SOLUTION, SOLUTION_SPREAD, MIX, USE solution, or USE mix
Equilibrium
Nonequilibrium
69
EQUILIBRIUM_PHASES
EXCHANGE
SURFACE
SOLID_SOLUTION
GAS_PHASE
REACTION_TEMPERATURE
REACTION_PRESSURE
• END
KINETICS
REACTION
Calculate the SI of Calcite in Seawater at Pressures from
100 to 1000 atm
70
Keywords
SOLUTION 1
END
USE solution 1
REACTION_PRESSURE
USER_GRAPH
END71
USE—Item on shelf
Item number on shelf To the beaker
72
USEAll of these Reactants are Numbered
• SOLUTION• EQUILIBRIUM_PHASES• EXCHANGE• GAS_PHASE• KINETICS• SOLID_SOLUTIONS• SURFACE
• REACTION• REACTION_PRESSURE• REACTION_TEMPERATURE
73
REACTION_PRESSURE
• List of pressures100 200 300 400 500 600 700 800 900 1000
Or
• Range of pressure divided equally100 1000 in 10 steps
74
USER_GRAPH
10 GRAPH_X PRESSURE
20 GRAPH_Y SI(“Calcite”)
30 GRAPH_SY expr
• Expressions are defined with Basic functions
• Basic—+-*/, SIN, COS, EXP,…
• PHREEQC—PRESSURE, SI(“Calcite”), MOL(“Cl-”), TOT(“Cl-”), -LA(“H+”),…
75
Plot the SI of Calcite with TemperatureSeawater-p.pqi
76
SI Calcite for Seawater with P
77
Arsenic in the Central Oklahoma
Aquifer• Arsenic mostly in confined part of
aquifer• Arsenic associated with high pH• Flow:
– Unconfined
– Confined
– Unconfined
78
Geochemical Reactions • Brine initially fills the aquifer
• Calcite and dolomite equilibrium
• Cation exchange – 2NaX + Ca+2 = CaX2 + 2Na+
– 2NaX + Mg+2 = MgX2 + 2Na+
• Surface complexationHfo-HAsO4- + OH- = HfoOH + HAsO4-2
79
More Reactions and Keywords
EQUILIBRIUM_PHASES
SAVE
EXCHANGE
SURFACE
80
EQUILIBRIUM_PHASESMinerals and gases that react to equilibrium
Calcite reaction
CaCO3 = Ca+2 + CO3-2
Equilibrium
K = [Ca+2][CO3-2]
EQUILIBRIUM_PHASES Data Block
• Mineral or gas
• Saturation state• Amount
Example EQUILIBRIUM_PHASES 5:CO2 Log PCO2 = -2, 10 moles
Calcite equilibrium 1 moles
Dolomite equilibrium 1 moles
Fe(OH)3 equilibrium 0 moles
Let’s Make a Carbonate Groundwater
• SOLUTION—Pure water or rain
• EQUILIBRIUM_PHASES– CO2(g), SI -1.5, moles 10– Calcite, SI 0, moles 0.1– Dolomite, SI 0, moles 1.6
• SAVE solution 0
83
Oklahoma Rainwater x 20Ignoring NO3- and NH4+
SOLUTION 0 20 x precipitation
pH 4.6
pe 4.0 O2(g) -0.7
temp 25.
units mmol/kgw
Ca 0.191625
Mg 0.035797
Na 0.122668
Cl 0.133704
C 0.01096
S 0.235153 charge
84
Limestone Groundwater
85
Brine
• Oil field brine
86
SOLUTION Data Block
• SOLUTION 1: Oklahoma Brine units mol/kgw
pH 5.713temp 25.Ca 0.4655
Mg 0.1609 Na 5.402 Cl 6.642 C 0.00396 S 0.004725 As 0.03 (ug/kgw)
•PHREEQC “speciates” the “exchanged species” on the exchange sites either:
– Initial Exchange Calculation: adjusting sorbed concentrations in response to a fixed aqueous composition
– Reaction Calculation: adjusting both sorbed and aqueous compositions.
Ion Exchange Calculations (#1)
• Layers of clays have a net negative charge• Exchanger has a fixed CEC, cation exchange capacity, based on charge deficit• Small cations (Ca+2, Na+, NH4
+, Sr+2, Al+3) fit in the interlayers
• PHREEQC uses 3 keywords to define exchange processes
– EXCHANGE_MASTER_SPECIES (component data)– EXCHANGE_SPECIES (species thermo. data)– EXCHANGE
• First 2 are found in phreeqc.dat and wateq4f.dat (for component X- and exchange species from Appelo) but can be modified in user-created input files.
• Last is user-specified to define amount and composition of an “exchanger” phase.
Ion Exchange (#2)
• “SAVE” and “USE” keywords can be applied to “EXCHANGE” phase compositions.
• Amount of exchanger (eg. moles of X-) can be calculated from CEC (cation exchange capacity, usually expressed in meq/100g of soil) where:
where sw is the specific dry weight of soil (kg/L of soil), is the porosity and B is the bulk density of the soil in kg/L. (If sw = 2.65 & = 0.3, then X- = CEC/16.2)
• CEC estimation technique (Breeuwsma, 1986): CEC (meq/100g) = 0.7 (%clay) + 3.5 (%organic carbon) (cf. Glynn & Brown, 1996; Appelo & Postma, 2005, p. 247)
Ion Exchange (#3)
100 / / 1 100 / B
CEC CECX
sw
EXCHANGECation exchange composition
Reaction:
Ca+2 + 2NaX = CaX2 + 2Na+
Equilibrium:
][][
]][[22
22
CaNaX
NaCaXK
EXCHANGE Data Block
• Exchanger name
• Number of exchange sites
• Chemical composition of exchanger
Example EXCHANGE 15:CaX2 0.05 moles (X is defined in databases)
NaX 0.05 moles
Often
X 0.15 moles, Equilibrium with solution 1
EXCHANGE
• Calculate the composition of an exchanger in equilibrium with the brine
• Assume 1 mol of exchange sites
93
Input File
94
Exchange Composition
-------------------------------------------------------
Beginning of initial exchange-composition calculations.
-------------------------------------------------------
Exchange 1.
X 1.000e+000 mol
Equiv- Equivalent Log
Species Moles alents Fraction Gamma
NaX 9.011e-001 9.011e-001 9.011e-001 0.242
CaX2 4.067e-002 8.134e-002 8.134e-002 0.186
MgX2 8.795e-003 1.759e-002 1.759e-002 0.517
95
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
• Sorption can occur even when a surface is neutrally charged.
Some Simple Models
Linear Adsorption (constant Kd):
d
qK
c 1 b
dR K
where q is amount sorbed per weight of solid, c is amount in solution per unit volume of solution; R is the retardation factor (dimensionless), is porosity, b is bulk density. Kd is usually expressed in ml/g and measured in batch tests or column experiments.
Assumptions:1) Infinite supply of surface sites2) Adsorption is linear with total element aqueous conc.3) Ignores speciation, pH, competing ions, redox states…4) Often based on sorbent mass, rather than surface area
Thermodynamic Speciation-based Sorption Models
• Sorption on variable charge surfaces:–“Surface complexation”–Occurs on Fe, Mn, Al, Ti, Si oxides & hydroxides, carbonates, sulfides, clay edges.
Surface charge depends on the sorption/surface binding of potential determining ions, such as H+. Formation of surface complexes also affects surface charge.
Examples of Surface Complexation Reactions
2+ 2+
2+ + +
2+ 0 +2
SOH + (M ) SOH(M )
SOH + (M ) SOM H
2 SOH + (M ) ( SO) M 2H
aq aq
aq
aq
outer-sphere complex
inner-sphere complex
bidentate inner-sphere complex
pH “edges” for cation sorption
• PHREEQC uses 3 keywords to define exchange processes
– SURFACE_MASTER_SPECIES (component data)– SURFACE_SPECIES (species thermo. data)– SURFACE
• First 2 are found in phreeqc.dat and wateq4f.dat (for component Hfo and exchange species from Dzombak and Morel) but can be modified in user-created input files.
• Last is user-specified to define amount and composition of a surface.
Surface Complexation
SURFACE—Surface CompositionTrace elements Zn, Cd, Pb, As, P
Reaction:
Hfo_wOH + AsO4-3 = Hfo_wOHAsO4
-3
Equilibrium:
)/exp(]][_[
]_[3
4
34 RTzF
AsOwOHHfo
wOHAsOHfoK
SURFACE Data Block• Surface name—Hfo is Hydrous Ferric Oxide• Number of surface sites
• Chemical composition of surface
• Multiple sites per surface
Example SURFACE 21:Hfo_wOH 0.001 moles, 600 m2/g, 30 g
Hfo_sOH 0.00005 moles
Often
Hfo_w 0.001 moles, Equilibrium with solution 1
SURFACE
• Calculate the composition of a surface in equilibrium with the brine
• Assume 1 mol of exchange sites
• Use the equilibrium constants from the following slide
106
Dzombak and Morel’s Model
SURFACE_MASTER_SPECIES
Surf SurfOH
SURFACE_SPECIES
SurfOH = SurfOH
log_k 0.0
SurfOH + H+ = SurfOH2+
log_k 7.29
SurfOH = SurfO- + H+
log_k -8.93
SurfOH + AsO4-3 + 3H+ = SurfH2AsO4 + H2O
log_k 29.31
SurfOH + AsO4-3 + 2H+ = SurfHAsO4- + H2O
log_k 23.51
SurfOH + AsO4-3 = SurfOHAsO4-3
log_k 10.58
107
SOLUTION_MASTER_SPECIES
As H3AsO4 -1.0 74.9216 74.9216
SOLUTION_SPECIES
H3AsO4 = H3AsO4
log_k 0.0
H3AsO4 = AsO4-3 + 3H+
log_k -20.7
H+ + AsO4-3 = HAsO4-2
log_k 11.50
2H+ + AsO4-3 = H2AsO4-
log_k 18.46
Input File
108
Surface Composition------------------------------------------------------
Beginning of initial surface-composition calculations.
------------------------------------------------------
Surface 1.
Surf
5.648e-002 Surface charge, eq
3.028e-001 sigma, C/m**2
4.372e-002 psi, V
-1.702e+000 -F*psi/RT
1.824e-001 exp(-F*psi/RT)
6.000e+002 specific area, m**2/g
1.800e+004 m**2 for 3.000e+001 g
Surf
7.000e-002 moles
Mole Log
Species Moles Fraction Molality Molality
SurfOH2+ 5.950e-002 0.850 5.950e-002 -1.225
SurfOH 8.642e-003 0.123 8.642e-003 -2.063
SurfHAsO4- 9.304e-004 0.013 9.304e-004 -3.031
SurfOHAsO4-3 6.878e-004 0.010 6.878e-004 -3.163
SurfH2AsO4 2.073e-004 0.003 2.073e-004 -3.683
SurfO- 2.875e-005 0.000 2.875e-005 -4.541
109
Modeling the Geochemistry Central Oklahoma
• Reactants– Brine– Exchanger in equilibrium with brine– Surface in equilibrium with brine– Calcite and dolomite– Carbonate groundwater
• Process– Displace brine with carbonate groundwater– React with minerals, exchanger, and surface
110
Explicit Approach
• Repeat– USE carbonate groundwater– USE equilibrium_phases– USE exchange– USE surface– SAVE equilibrium_phases– SAVE exchange– SAVE surface
111
1D Solute Transport
Terms Concentration change with time Dispersion/diffusion Advection Reaction
Rx
cv
x
cD
t
c
2
2
PHREEQC Transport Calculations
1 2 3 4 5 6 nAdvection
Dispersion 1 2 3 4 5 6 n
Reaction 1 2 3 4 5 6 n
ADVECTION Data Block
1 2 3 4 5 6 nCarbonate groundwater
Reaction 1 2 3 4 5 6 n
Brine
Minerals, Exchange, Surface
ADVECTION
• Cells are numbered from 1 to N.• Index numbers (of SOLUTION,
EQUILIBRIUM_PHASES, etc) are used to define the solution and reactants in each cell
• SOLUTION 0 enters the column• Water is “shifted” from one cell to the next
ADVECTION
• Number of cells
• Number of shifts
• If kinetics—time step
ADVECTION
• Output file– Cells to print– Shifts to print
• Selected-output file– Cells to print– Shifts to print
Complete simulation1. Define As aqueous and surface model
2. Define brine (SOLUTION 1)
3. Define EXCHANGE 1 in equilibrium with brine
4. Define SURFACE 1 in equilibrium with brine
5. Define EQUILIBRIUM_PHASES 1 with 1.6 mol dolomite and 0.1 mol calcite
6. Define carbonate groundwater (SOLUTION 0) 1. Pure water
2. EQUILIBRIUM_PHASES calcite, dolomite, CO2(g) -1.5
3. SAVE solution 0
118
Complete simulation (continued)7. Define ADVECTION
8. Define USER_GRAPH
X—step or pore volume
Y—ppm As, and molality of Ca, Mg, and Na
SY—pHUSER_GRAPH Example 14
-headings PV As(ppb) Ca(M) Mg(M) Na(M) pH
-chart_title "Chemical Evolution of the Central Oklahoma Aquifer"
-axis_titles "PORE VOLUMES OR SHIFT NUMBER" "Log(CONCENTRATION, IN PPB OR MOLAL)" "pH"
-axis_scale x_axis 0 200
-axis_scale y_axis 1e-6 100 auto auto Log
10 GRAPH_X STEP_NO
20 GRAPH_Y TOT("As")*GFW("As")*1e6, TOT("Ca"), TOT("Mg"), TOT("Na")
30 GRAPH_SY -LA("H+")
119
Keywords in Input FileSURFACE_MASTER_SPECIES
SURFACE_SPECIES
SOLUTION_MASTER_SPECIES
SOLUTION_SPECIES
SOLUTION 1 Brine
END
EXCHANGE 1
END
SURFACE 1
END
EQUILIBRIUM_PHASES 1
END
SOLUTION 0
EQUILIBRIUM_PHASES 0
SAVE solution 0
END
ADVECTION
USER_GRAPH Example 14
END
120
Advection Results
121
Geochemical Reactions • Cation exchange
– 2NaX + Ca+2 = CaX2 + 2Na+
– 2NaX + Mg+2 = MgX2 + 2Na+
• Calcite and dolomite equilibrium– CaCO3 + CO2(aq) + H2O = Ca+2 + 2 HCO3
-
– CaMg(CO3)2 + 2CO2(aq) + 2H2O = Ca+2 + Mg+2 + 4 HCO3
-
• Surface complexationHfo-HAsO4- + OH- = HfoOH + HAsO4-2
122
Diffusive TRANSPORT and Kinetics
• Potomac River Estuary data
• KINETICS– Non-equilibrium reactions– Biogeochemical– Annual cycle of sulfate reduction
• TRANSPORT capabilities
123
Thermodynamics vs. Kinetics
• Thermodynamics predicts equilibrium dissolution/precipitation concentrations
• Probably OK for “reactive” minerals (Monday’s useful minerals list) and groundwater
• Need kinetics for slow reactions and/or fast moving water
124
Kinetics is Concentration versus Time
Appelo and Postma, 2005
Dissolution “half-life”
125
Half-life (pH 5 dissolution of the solid phase)
• Gypsum – hours• Calcite – days• Dolomite – years• Biotite, kaolinite, quartz – millions of
years• If half-life is << residence time then
equilibrium conditions can be used• If half-life is >> residence time then
kinetics will need to be considered126
Appelo and Postma, 2005127
Rate Laws
• Mathematically describes the change in concentration with time (derivative)
• Simple if constant rate (zero order - linear)
• Complex if rate constant changes with time due to multiple factors (i.e., concentration, temperature, pH, etc.), thus higher order, non-linear
• Remember that experimental data may not represent real world conditions
128
Organic decomposition KINETICS
WRONG!
-formula
CH2O -2
SO4-2 -1
HCO3- +2
H2S +1
2CH2O + SO4-2 = 2HCO3- + H2S
RIGHT!
-formula
CH2O 1
Or perhaps,
-formula
CH2O 1
Doc -1
129
Organic Decomposition in PHREEQC
• Mole balance of C increases • H and O mole balances increase too, but
equivalent to adding H2O• If there are electron acceptors, C ends up as
CO3-2 species
• Electron acceptor effectively gives up O and assumes the more reduced state
• The choice of electron acceptor is thermodynamic
130
RATE EQUATION CH2ORATES
CH2O
-start
10 sec_per_yr = 365*24*3600
20 k = 1 / sec_per_yr
30 pi = 2*ARCTAN(1e20)
40 theta = (TOTAL_TIME/sec_per_yr)*2*pi
50 cycle = (1+COS(theta))/2
60 rate = k*TOT("S(6)") * cycle
70 moles = rate*TIME
80 SAVE moles
-end
END
131
(1+COS(theta))/2
132
KINETICS
KINETICS 1-4
CH2O
-formula (CH2O)8NH3
END
133
TRANSPORT
• 20 cells
• 100 shifts
• 0.1 y time step
134
TRANSPORT
• Diffusion only
• Diffusion coefficient
• Constant boundary (1/2 seawater)
• Closed boundary
135
TRANSPORT
• Cell lengths
0.025 m
• Dispersivities
TRANSPORT
• Output file
• Selected output and USER_GRAPH
TRANSPORT Options
• At end of exercise we will try multicomponent diffusion, where ions diffuse at different rates
• Capability for diffusion in surface interlayers
TRANSPORT Options
• Stagnant cells/dual porosity-One stagnant cell
-Multiple stagnant cells• Dump options
TRANSPORT—Charge-Balanced Diffusion
TRANSPORT
-multi_d true 1e-9 0.3 0.05 1.0
SOLUTION_SPECIES
H+ = H+
log_k 0.0
-gamma 9.0 0.0
-dw 9.31e-9
• Multicomponent diffusion—true
• Default tracer diffusion coefficient—1e-9 m2/s
• Porosity—0.3
• Minimum porosity—0.05(Diffusion stops when the porosity reaches the porosity limit)
• Exponent of porosity (n) –1.0. (Effective diffusion coefficient–De = Dw * porosity^n)
• -dw is tracer diffusion coefficient in
SOLUTION_SPECIES
V3.pqi
• Check periodic steady state
• Adjust parameters– More SO4
consumption– Greater depth
range
141
Options• Rate expression
– K controls rate of reaction– Cycle controls periodic function– Rate is overall rate of reaction (mol/s)
• TRANSPORT – Diffusion coefficient
• KINETICS– Cells with kinetics
142
One Choice
• Diffusion coefficient
• RATES k• RATES
cycle• Cells
143
SO4-2
Multicomponent diffusion 144
Fixed diffusion coefficient
NH4+
145
Multicomponent diffusion Fixed diffusion coefficient
H2S
146
Multicomponent diffusion Fixed diffusion coefficient
Acid Mine Drainage
147
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
Iron Mountain, California
• Sulfide deposits at the top of a mountain
• Lots of precipitation
• Unsaturated conditions
• Tunnels drain
Picher, Oklahoma
• Flat topography
• Mines 200 to 500 ft below land surface
• Saturated after dewatering ceased
• Cut off the supply of oxygen
Simplified Reactions
High pH
FeS2 + 15/4O2 + 4HCO3- = Fe(OH)3 + 2SO4-2 + 4CO2 + 1/2H2O
Or
FeS2 + 15/4O2 + 7/2H2O = Fe(OH)3 + 2SO4-2 + 4H+
Low pH FeS2 + 15/4O2 + 1/2H2O = Fe+3 + SO4-2 + HSO4-
Additional reactions
• Hydrous ferric oxides– Ferrihydrite– Goethite– Jarosite
• Aluminum hydroxides– Alunite
• Carbonates• Gypsum
Modeling Pyrite Oxidation
FeS2 + 15/4O2 + 7/2H2O = Fe(OH)3 + 2SO4-2 + 4H+
• Pick the irreversible reactant: O2 or FeS2– Oxygen rich environment of a tailings pile– We are going to react up to 50 mmol FeS2
• Equilibrium reactions
REACTION 18. Exercise
1. React the pure water with 10 mmol of pyrite, maintaining equilibrium with atmosphreric oxygen.
2. React the pure water with 10 mmol of mackinawite, maintaining equilibrium with atmosphreric oxygen.
3. React the pure water with 10 mmol of sphalerite, maintaining equilibrium with atmosphreric oxygen.
REACTION 18. Questions1. Write qualitative reactions that explain
the pH of the 3 solutions.
2. What pH buffer starts to operate at pHs below 3?
3. Run the input file with wateq4f.dat database. What minerals may precipitate during pyrite oxidation?
Reaction 18. Answers1. Question 1
Pyrite oxidation:FeS2 + xO2 + yH2O -> Fe+3 + 2SO4-2 + H+In addition, ferric iron hydrolizes to make additional H+:Fe+3 + H2O = FeOH+2 + H+With net acid production to give pH 2.
Mackinawite oxidation:FeS + 2.25O2 + H+ -> Fe+3 + SO4-2 + .5H2OBut ferric iron hydrolizesFe+3 + H2O = FeOH+2 + H+With a net acid production that give pH 4.
Sphalerite oxidation:ZnS + 2O2 -> Zn+2 + SO4-2 Zinc hydrolosis is minimalZn+2 + H2O = FeOH+ + H+Net result is pH 7.
2. HSO4-/SO4-2
3. Iron oxyhydroxides, goethite (and often Fe(OH)3(a)) and jarosite. There is also a potassium jarosite and other solid solutions of jarosites. Aluminum has analogous minerals named alunite.
REACTION 20. Extra Credit Exercise
1. React the pure water with 20 mmol of pyrite, maintaining equilibrium with atmospheric oxygen and goethite.
2. Acid mine drainage is usually treated with limestone. Use the results of part 1 and equilibrate with O2, goethite, and calcite.
REACTION 20. Questions1. Write a net reaction for the PHREEQC
results for the low-pH simulation.
2. What are the pH values with and without calcite equilibrium.
3. Looking at the results of the calcite-equilibrated simulation, what additional reactions should be considered?
Reaction 20. Answers
1. 20FeS2 + 75O2 = 19FeOOH + .8Fe(+3) + 27HSO4- + 12SO4
-2 + 50H+
2. pHs are 1.4 and 5.8 without and with calcite equilibrium
3. Gypsum is supersaturated, and probably would precipitate.
pCO2 is 1 atmosphere. If O2 reacts to equilibrium with the atmosphere, logically, CO2 would also.
Picher Oklahoma Abandoned Pb/Zn Mine
mg/L
• Mines are suboxic
• Carbonates are present
• Iron oxidizes in stream
temp pH O(0) Ca Mg Na K Alkalinity Cl S(6)Admiralty 15 5.7 490 250 89 6.5 260 28 3200SW site 8 30 3 420 110 46 3.6 0 8 2100
Al Cd Cu Fe Pb Mn ZnAdmiralty 1.4 0.01 300 0.04 5.3 150SW site 8 3.7 0.002 0.008 54 0.14 5.2 100
Pyrite OxidationRequires
Pyrite/MarcasiteO2
H2OBacteria
Produces Ferrihydrite/Goethite, jarosite, aluniteGypsum if calcite is availableEvaporitesPossibly siderite
Acid generation Pyrite > FeS > ZnS
SOLID_SOLUTIONS—Composition of one or more solid solutions
Trace elements and isotopes
• List of solid solutions• Components of each solid solution
Example SOLID_SOLUTION 21:Calcite solid solution
Ca[13C]O3
CaCO3163
GAS_PHASE—Finite gas phase in equilibrium with solution
• Gas bubbles that grow
• Gas bubbles that fill a finite volume
164
GAS_PHASE—Composition of the gas phase
Fixed volume or Fixed pressure
• Initial volume• Initial pressure• Temperature• Partial pressure of each gas
Example GAS_PHASE 1:Fixed pressure
CO2(g) 0.0
CH4(g) 0.0
165
