REACTION KINETICSPresented by Ray Johnson with notes from Pierre Glynn and Alex Blum, March 2011

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OutlineWhy look at kinetics?Things that control kineticsVarious reaction rate lawsClass examplesOptional examples (good reference, have digital copy of example K1)*

Thermodynamics vs. KineticsThermodynamics predicts equilibrium dissolution/precipitation concentrationsProbably OK for reactive minerals (Mondays useful minerals list) and groundwaterNeed kinetics for slow reactions and/or fast moving water*

Kinetics is Concentration versus TimeAppelo and Postma, 2005Dissolution half-life*

Half-life (pH 5 dissolution of the solid phase)Gypsum hoursCalcite daysDolomite yearsBiotite, kaolinite, quartz millions of yearsIf half-life is > residence time then kinetics will need to be considered*

Factors that affect kineticsConcentrationpHLightTemperatureOrganicsCatalystsSurface areaDiffusionBiogeochemistryAnd more

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General Concepts Transport vs. Reaction Control

Elementary vs. Overall Reactions Detailed Balancing Microscopic Reversibility

Temperature Dependence

Surface Area

Silicate mineral dissolution kinetics & weathering

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Transport vs. Reaction Controla) Transport controlb) Surface reaction controlc) Mixed Transport and surface-reaction control*

Transport limitations: diffusion in solution solid-state diffusionReaction limitations: surface reaction control surface characteristicscrystal defectsimpuritiescrystal morphology *

Elementary vs. overall reactionsReactions 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. *

Example of fast reactions (only 1 elementary step): Example of a two step reaction:The reaction rate requires knowledge of the rate-limiting elementary reaction (usually only one). Overall reaction:*

Principle of Detailed Balancing:The net rate of a reaction is the difference between the forward and the backward microscopic rates (eg. microscopic dissolution vs. precipitation). Principle of Microscopic Reversibility:The forward and the backward reactions have the same molecular mechanism. *

Activation Energies and Temperature DependenceReaction rates are often exponentially dependent on temperature, and are also highly depend on the activation energy EA required for a molecular reaction. The pre-exponential factor A may depend on pH, solution chemistry, surface characteristics, and many other factors including temperature. *

from http://www.ucdsb.on.ca/tiss/stretton/chem2/rate03Exothermic reactionEndothermic reactionEAActivation 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)*

Note log scale for rates*

Surface AreaCritical to rate calculations and predictionsGeometric area estimation (often requires averaging or stochastic theory)BET measurements, usually w/ N2 (4 compared to 3 for H2O) Surface roughness (BET/Geometric): SR = 5 - 12 for fresh ground silicate SR = 300 - 2000 for deeply weathered natural silicates*

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Silicate dissolution kinetics and pH*

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Silicate weathering reaction rates*

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What model to use?*

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Solute accumulation*

Conclusions: silicate weatheringNatural weathering rates in soils are 102 to 105 slower than experimental ratesWeathering rates in aquifers depend on (water chemistry)/(residence time)/(extent of reaction)??Accumulation of solutes retards dissolution rates??Discrepancies between natural and experimental rates are consistent w/ models of solute accumulation in pores *

Putting kinetics into a geochemical modelUse rate lawsHopefully have some experimental and/or real world data referencesGive it a try, dont let the equations and mathematics make you sweatFirst, understand the rate law and then convert into PHREEQC command lines

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Rate LawsMathematically 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-linearRemember that experimental data may not represent real world conditions

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Appelo and Postma, 2005*

Oxidation of Fe2+Look at example on p. 156 of Appelo and Postma, 2005With multiple species (iron, pH, and oxygen), we can have different rate ordersNote pH to OH- calculation and second order rate dependence

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Appelo and Postma, 2005*

PHREEQC can simulate irreversible reactions with either the:

REACTION keyword for specified amounts of stoichiometric reactions.

KINETICS keyword, where the reaction rate is determined by a mathematical expression taking into account the composition and other pertinent information for the reacting phases.

Using the KINETICS keyword also means that at least one RATE keyword must be entered to define the rate law for a particular reaction. Multiple RATE definitions can be entered for a given KINETICS keyword.

Reaction Kinetics in PHREEQC*

Explore in PHREEQCFind the rate icon (d/dt) and openWhat does this screen do for us?Open the help on RATESExplore this page together*

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Explore in PHREEQCFind the kinetics icon (K) and openWhat do these three screens do for us?Note Runge-Kutta (faster) and CVODE (more robust for multiple interacting rates) for ordinary differential equationsSelect pyrite as a defined rate and hit OK. What happened?Find pyrite in the RATES block in phreeqc.dat database*

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########Pyrite######### Williamson, M.A. and Rimstidt, J.D., 1994,# Geochimica et Cosmochimica Acta, v. 58, p. 5443-5454.## Example of KINETICS data block for pyrite rate:# KINETICS 1# Pyrite# -tol 1e-8# -m0 5.e-4# -m 5.e-4# -parms 2.0 0.67 .5 -0.11Pyrite -start 1 remWilliamson and Rimstidt, 1994 2 remparm(1) = log10(A/V, 1/dm) parm(2) = exp for (m/m0) 3 remparm(3) = exp for O2 parm(4) = exp for H+

10 if (m = 0) then goto 200 25 rate = -10.19 + parm(1) + parm(3)*lm("O2") + parm(4)*lm("H+") + parm(2)*log10(m/m0) 30 moles = 10^rate * time 40 if (moles > m) then moles = m 200 save moles -endWould have to add parms*

Book ExampleWork through Example 4.15 together on page 164 in Appelo and Postma, 2005.Start with understanding the rate expression equation 4.66 and go from there.*

R = overall reaction rate (mol/L/s)k = specific rate (mol/m2/s)A0 = initial surface area of solid (m2)V = volume of solution (m3)m = moles of solid at a given timem0 = initial moles of solid(m/mo)n accounts for changes in reactive surface sites during dissolutiong(C) = function for things in the solution composition that can influence the rate (i.e., pH, distance from equilibrium, catalysis, etc.) General Rate Law*

Start with calculating surface volume factor (A0/V)porositydensitySurface area (A0) = 22.6 m2/kgVolume of water in contact with 1 kg of soil = 0.162 L (do unit conversion)*

m = calculatedm0 is given as 103 mol/LIAP/K = SR(Quartz) = calculated in PHREEQC*

Now use PHREEQCExample 4.15Appelo and Postma, 2005*

Exercise KAUsing the rate and kinetic blocks for pyrite dissolution in the phreeqc.dat file, write out and explain the rate laws and equations used.Simulate the reaction of pyrite (use 2% pyrite and the phreeqc.dat rate expression) with an oxygen-equilibrated water such as the Oklahoma recharge water (used in sorption exercise S3). How long does it take to react away the oxygen dissolved in one unit volume of water? Given the initial concentration of pyrite specified, how many volumes of recharge water would it take to consume all the pyrite?

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Enter the two Sierra Spring waters from Garrels & Christ into a PHREEQC input file. Assume a temperature of 25 C for both. Units are mmol/L. Exercise KBUsing the most dilute water, add the RATE laws and suggested KINETICS blocks that are present in the phreeqc.dat file to simulate the kinetic reaction of the water with albite and K-spar.

Ignoring other possible reactions, how long would it take to obtain a water with Si, Na and K concentrations similar to those in the Perennial Spring? *

Solutions

SeawaterSOLUTION_SPREAD

-units ppm

DescriptionNumberTemppHpeCaMgNaKAlkalinityClS(6)Fe

as HCO3

Seawater8.228.45412.31291.810768399.1141.6821935327120.002

Ok ground WaterSOLUTION_SPREAD

-units mg/L

DescriptionNumberTemppHO(0)CaMgNaKAlkalinityClS(6)N(5)N(-3)BaSrP

as CaCO3as Nas N

Rainwater254.50.3840.0430.1410.0360.2361.30.2370.2080.0003

City of Jones 13N-01W-34 CAB17.57.44.14221121.5196128.10.490.330.23

City of Wellston

CharlestonSOLUTION_SPREAD

-units mg/L

DescriptionNumberTemppHO(0)CaMgNaKAlkalinityClS(6)SiBSr

as CaCO3ug/lug/l

Recovered water617.4610.312.63.5330122912807519

Background1122.556.992126160041747180028040

Treated injection water22227.8202.3182.43223337.6

Florida, Flowpath IISOLUTION_SPREAD

-units mg/L

DescriptionNumberTemppHO(0)CaMgNaKAlkalinityClS(6)SiSrS(-2)

as H2S

1.1124.77.760388.140.8143.96.912130.0810

2.4431.57.45010052122.9176.11434021241.92

2.6627.27.4801147926517177.54121801915.32.6

Potomac EstuarySOLUTION_SPREAD

-units mmol/L

DescriptionNumberTemppHO(0)CaMgNaKAlkalinityClS(6)FeS(-2)N(-3)DOC

meq/L

V6, 1 cm1207.2304.725.32165.96.4257100.00910.3510

V6, 5 cm5207.4504.422.21905.3242230.50.0053.42.2711

V26D, 1 cm1156.9901.80.70.50.15.40.50.620.0050.36

V26D, 3 cm3157.0602.40.80.60.28.30.50.040.481.47

V28, 1 cm7.021.80.80.80.26.80.60.0330.7

V28, 36 cm7.143.11.410.524.90.80.4317.8

Cape CodSOLUTION_SPREAD

-units umol/L

DescriptionNumberTemppHO(0)CaMgNaKC(4)ClS(6)FeMnP

Background145.625029312001028140860.642.3

343 6/18/966.4804832352202272125915932965719.4105

Sierra SpringSOLUTION_SPREAD

-units mmol/L

DescriptionNumberTemppHO(0)CaMgNaKAlk.ClS(6)Si

Ephemeral Spring6.20.0780.0290.1340.0280.3280.0140.010.273

Perennial Spring6.80.260.0710.2590.040.8950.030.0250.41

Norman, OKSOLUTION_SPREAD

-units mg/L

DescriptiontemppHO(0)CaMgNaKAlkalinityClS(6)BrSiFe(2)MnSrBaN(5)N(-3)DOC

as HCO3as NO3as NH4

MLSNPD -616.67.010.0416652.691.82.5626180.98113.60.79318.600.131.941.060.140.052.12.9

MLS38-6ND6.780.1151423260614.426421026.60.17.53635.9019.300.909.877.123.4815.0158.7

MadisonSOLUTION_SPREAD

-units mmol/kgw

DescriptiontemppHO(0)CaMgNaKC(4)ClS(6)S(-2)Fe(2)Carbon-13SO4-Sulfur-34H2S-Sulfur-34Carbon-14

Recharge9.97.51.21.010.020.024.30.020.1600.001-79.7-52.3

Mysse flowing well636.6111.284.5431.892.546.8717.8519.860.260.0004-2.316.3-22.10.8

Tar CreekSOLUTION_SPREAD

-units mg/L

DescriptiontemppHpeCaMgNaKAlkalinityClSAlCdCuFePbMnZn

Admiralty16155.73.4490250896.52602832001.40.013000.045.3150

SW site 81730311.1420110463.60821003.70.0020.008540.145.2100

Carbon

pHm_CO2m_HCO3-m_CO3-2

49.96E-044.47E-062.15E-12

59.57E-044.28E-052.04E-10

66.89E-043.11E-041.52E-08

71.80E-048.20E-044.12E-07

82.13E-059.74E-044.92E-06

92.08E-069.50E-044.83E-05

101.42E-076.57E-043.43E-04

113.29E-091.54E-048.46E-04

123.31E-111.61E-059.84E-04

pHCm_CO2m_HCO3-m_CO3-2

66.34E-034.34E-032.00E-031.04E-07

72.43E-034.34E-042.00E-031.04E-06

82.03E-034.29E-051.98E-031.03E-05

91.90E-033.90E-061.80E-039.43E-05

101.41E-031.98E-079.18E-044.89E-04

115.19E-041.77E-098.22E-054.37E-04

Carbon

000

000

000

000

000

000

000

000

000

m_CO2

m_HCO3-

m_CO3-2

peRedox

0000

0000

0000

0000

0000

0000

C

m_CO2

m_HCO3-

m_CO3-2

UsefulMin

Data in mmmo/kgw

SolutionFe(2)Fe(3)S(6)S(-2)PyriteGoethite

10.740.2611.00E-64-929.7

21NA11.00E-64-92NA

3NA111.00E-64NA10.3

40.740.261NANA9.7

50.840.16NA1.00E+00-289.5

61111.00E-68-9810.3

SWMix

Useful Minerals

CarbonatesPhosphates

CO2(g)CO2HydroxyapatiteCa5(PO4)3OH

CalciteCaCO3VivianiteFe3(PO4)2

DolomiteCaMgCO3Oxyhydroxides

SideriteFeCO3Fe(OH)3(a)Fe(OH)3

RhodochrositeMnCO3GoethiteFeOOH

SulfatesGibbsiteAl(OH)3

GypsumCaSO4BirnessiteMnO2

CelestiteSrSO4ManganiteMn(OH)3

BariteBaSO4Aluminosilicates

SulfidesSilica gelSiO2-2H2O

FeS(a)FeSSilica glassSiO2-H2O

MackinawiteFeSChalcedonySiO2

KaoliniteAl2Si2O5(OH)

RedoxEnv

frac_swCalcite_dis_mmolDolomite_dis_mmol

0.00E+000.00E+000.00E+00

2.00E-01-4.74E-011.68E-01

4.00E-01-6.43E-012.54E-01

6.00E-01-5.98E-012.49E-01

8.00E-01-3.77E-011.62E-01

1.00E+000.00E+000.00E+00

RedoxEnv

00

00

00

00

00

00

CALCITE

DOLOMITE

FRACTION OF SEAWATER

MMOL DISSOLVED

SO4Reduce

pHH2MethanicSulfidicPost-oxicOxic

00.00E+003.30E+005.05E+002.03E+012.08E+01

1-1.00E+002.30E+003.93E+001.93E+011.98E+01

2-2.00E+001.30E+002.77E+001.83E+011.88E+01

3-3.00E+002.99E-011.56E+001.73E+011.78E+01

4-4.00E+00-7.01E-013.13E-011.63E+011.68E+01

5-5.00E+00-1.70E+00-9.36E-011.53E+011.58E+01

6-6.00E+00-2.72E+00-2.18E+001.43E+011.48E+01

7-7.00E+00-3.79E+00-3.39E+001.33E+011.38E+01

8-8.00E+00-4.91E+00-4.55E+001.23E+011.28E+01

9-9.00E+00-6.04E+00-5.68E+001.13E+011.18E+01

10-1.00E+01-7.18E+00-6.80E+001.03E+011.08E+01

11-1.10E+01-8.39E+00-7.93E+009.28E+009.78E+00

12-1.20E+01-9.64E+00-9.05E+008.28E+008.78E+00

13-1.30E+01-1.09E+01-1.01E+017.28E+007.78E+00

14-1.40E+01-1.22E+01-1.12E+016.29E+006.79E+00

00.00E+00

1-1.00E+00

2-2.00E+00

3-3.00E+00

4-4.00E+00

5-5.00E+00

6-6.00E+00

7-7.00E+00

8-8.00E+00

9-9.00E+00

10-1.00E+01

11-1.10E+01

12-1.20E+01

13-1.30E+01

14-1.40E+01

03.30E+00

12.30E+00

21.30E+00

32.99E-01

4-7.01E-01

5-1.70E+00

6-2.72E+00

7-3.79E+00

8-4.91E+00

9-6.04E+00

10-7.18E+00

11-8.39E+00

12-9.64E+00

13-1.09E+01

14-1.22E+01

05.05E+00

13.93E+00

22.77E+00

31.56E+00

43.13E-01

5-9.36E-01

6-2.18E+00

7-3.39E+00

8-4.55E+00

9-5.68E+00

10-6.80E+00

11-7.93E+00

12-9.05E+00

13-1.01E+01

14-1.12E+01

02.03E+01

11.93E+01

21.83E+01

31.73E+01

41.63E+01

51.53E+01

61.43E+01

71.33E+01

81.23E+01

91.13E+01

101.03E+01

119.28E+00

128.28E+00

137.28E+00

146.29E+00

02.08E+01

11.98E+01

21.88E+01

31.78E+01

41.68E+01

51.58E+01

61.48E+01

71.38E+01

81.28E+01

91.18E+01

101.08E+01

119.78E+00

128.78E+00

137.78E+00

146.79E+00

SO4Reduce

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

H2

Methanic

Sulfidic

Post-oxic

Oxic

pH

pe

Sheet1

reactionO(0)C(4)C(-4)Fe(3)Fe(2)S(6)S(-2)mackinawited_mackinawite

04.05E-041.09E-030.00E+000.00E+000.00E+001.46E-020.00E+000.00E+000.00E+00

1.00E-041.65E-041.19E-030.00E+002.57E-084.45E-181.46E-020.00E+000.00E+000.00E+00

2.00E-040.00E+001.29E-032.42E-392.52E-085.09E-051.46E-029.39E-360.00E+000.00E+00

1.00E-020.00E+001.11E-025.97E-133.58E-082.02E-031.02E-022.31E-104.46E-034.46E-03

2.00E-020.00E+002.11E-021.75E-123.38E-083.63E-035.56E-031.93E-109.06E-039.06E-03

3.00E-020.00E+003.11E-021.16E-113.38E-085.52E-039.98E-041.60E-101.36E-021.36E-02

4.00E-020.00E+003.83E-022.72E-035.82E-081.44E-026.76E-133.41E-111.46E-021.46E-02

5.00E-020.00E+004.37E-027.34E-035.60E-081.86E-022.34E-132.89E-111.46E-021.46E-02

Sheet1

00000000

00000000

00000000

00000000

00000000

00000000

00000000

00000000

O(0)

C(4)

C(-4)

Fe(3)

Fe(2)

S(6)

S(-2)

mackinawite

CH2O REACTED, IN MOLES

MOLES

Exercise KB (part 2) Using the rate and kinetic blocks for K-spar and albite dissolution. Write out and explain the rate laws and equations used.

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Enter the 2 waters from the Norman, OK, landfill into a PHREEQC input file. Assume a temperature of 16.6 C for both. Units are mg/L. Do not enter DOC. Which water is contaminated? How did you specify redox conditions?Exercise K1 (optional if time)(Ulrich et al., 2003) used field and lab techniques to identify the biogeochemical factors affecting the rate of sulfate reduction in the leachate contaminated water. They obtained a Michaelis-Menten type relationship with KM & Vmax values of 80 mM SO4 and 0.83 mM SO4/day, resp.*

Solutions

SeawaterSOLUTION_SPREAD

-units ppm

DescriptionNumberTemppHpeCaMgNaKAlkalinityClS(6)Fe

as HCO3

Seawater8.228.45412.31291.810768399.1141.6821935327120.002

Ok ground WaterSOLUTION_SPREAD

-units mg/L

DescriptionNumberTemppHO(0)CaMgNaKAlkalinityClS(6)N(5)N(-3)BaSrP

as CaCO3as Nas N

Rainwater254.50.3840.0430.1410.0360.2361.30.2370.2080.0003

City of Jones 13N-01W-34 CAB17.57.44.14221121.5196128.10.490.330.23

City of Wellston

CharlestonSOLUTION_SPREAD

-units mg/L

DescriptionNumberTemppHO(0)CaMgNaKAlkalinityClS(6)SiBSr

as CaCO3ug/lug/l

Recovered water617.4610.312.63.5330122912807519

Background1122.556.992126160041747180028040

Treated injection water22227.8202.3182.43223337.6

Florida, Flowpath IISOLUTION_SPREAD

-units mg/L

DescriptionNumberTemppHO(0)CaMgNaKAlkalinityClS(6)SiSrS(-2)

as H2S

1.1124.77.760388.140.8143.96.912130.0810

2.4431.57.45010052122.9176.11434021241.92

2.6627.27.4801147926517177.54121801915.32.6

Potomac EstuarySOLUTION_SPREAD

-units mmol/L

DescriptionNumberTemppHO(0)CaMgNaKAlkalinityClS(6)FeS(-2)N(-3)DOC

meq/L

V6, 1 cm1207.2304.725.32165.96.4257100.00910.3510

V6, 5 cm5207.4504.422.21905.3242230.50.0053.42.2711

V26D, 1 cm1156.9901.80.70.50.15.40.50.620.0050.36

V26D, 3 cm3157.0602.40.80.60.28.30.50.040.481.47

V28, 1 cm7.021.80.80.80.26.80.60.0330.7

V28, 36 cm7.143.11.410.524.90.80.4317.8

Cape CodSOLUTION_SPREAD

-units umol/L

DescriptionNumberTemppHO(0)CaMgNaKC(4)ClS(6)FeMnP

Background145.625029312001028140860.642.3

343 6/18/966.4804832352202272125915932965719.4105

Sierra SpringSOLUTION_SPREAD

-units mmol/L

DescriptionNumberTemppHO(0)CaMgNaKAlkalinityClS(6)Si

Ephemeral Spring6.20.0780.0290.1340.0280.3280.0140.010.273

Perennial Spring6.80.260.0710.2590.040.8950.030.0250.41

Norman, OKSOLUTION_SPREAD

-units mg/L

DescriptiontemppHO(0)CaMgNaKAlk.ClS(6)BrSiFe(2)MnSrBaN(5)N(-3)DOC

as HCO3as NO3as NH4

MLSNPD -616.67.010.0416652.691.82.5626180.98113.60.79318.600.131.941.060.140.052.12.9

MLS38-6ND6.780.1151423260614.426421026.60.17.53635.9019.300.909.877.123.4815.0158.7

MadisonSOLUTION_SPREAD

-units mmol/kgw

DescriptiontemppHO(0)CaMgNaKC(4)ClS(6)S(-2)Fe(2)Carbon-13SO4-Sulfur-34H2S-Sulfur-34Carbon-14

Recharge9.97.51.21.010.020.024.30.020.1600.001-79.7-52.3

Mysse flowing well636.6111.284.5431.892.546.8717.8519.860.260.0004-2.316.3-22.10.8

Tar CreekSOLUTION_SPREAD

-units mg/L

DescriptiontemppHpeCaMgNaKAlkalinityClSAlCdCuFePbMnZn

Admiralty16155.73.4490250896.52602832001.40.013000.045.3150

SW site 81730311.1420110463.60821003.70.0020.008540.145.2100

Carbon

pHm_CO2m_HCO3-m_CO3-2

49.96E-044.47E-062.15E-12

59.57E-044.28E-052.04E-10

66.89E-043.11E-041.52E-08

71.80E-048.20E-044.12E-07

82.13E-059.74E-044.92E-06

92.08E-069.50E-044.83E-05

101.42E-076.57E-043.43E-04

113.29E-091.54E-048.46E-04

123.31E-111.61E-059.84E-04

pHCm_CO2m_HCO3-m_CO3-2

66.34E-034.34E-032.00E-031.04E-07

72.43E-034.34E-042.00E-031.04E-06

82.03E-034.29E-051.98E-031.03E-05

91.90E-033.90E-061.80E-039.43E-05

101.41E-031.98E-079.18E-044.89E-04

115.19E-041.77E-098.22E-054.37E-04

Carbon

000

000

000

000

000

000

000

000

000

m_CO2

m_HCO3-

m_CO3-2

peRedox

0000

0000

0000

0000

0000

0000

C

m_CO2

m_HCO3-

m_CO3-2

UsefulMin

Data in mmmo/kgw

SolutionFe(2)Fe(3)S(6)S(-2)PyriteGoethite

10.740.2611.00E-64-929.7

21NA11.00E-64-92NA

3NA111.00E-64NA10.3

40.740.261NANA9.7

50.840.16NA1.00E+00-289.5

61111.00E-68-9810.3

SWMix

Useful Minerals

CarbonatesPhosphates

CO2(g)CO2HydroxyapatiteCa5(PO4)3OH

CalciteCaCO3VivianiteFe3(PO4)2

DolomiteCaMgCO3Oxyhydroxides

SideriteFeCO3Fe(OH)3(a)Fe(OH)3

RhodochrositeMnCO3GoethiteFeOOH

SulfatesGibbsiteAl(OH)3

GypsumCaSO4BirnessiteMnO2

CelestiteSrSO4ManganiteMn(OH)3

BariteBaSO4Aluminosilicates

SulfidesSilica gelSiO2-2H2O

FeS(a)FeSSilica glassSiO2-H2O

MackinawiteFeSChalcedonySiO2

KaoliniteAl2Si2O5(OH)

RedoxEnv

frac_swCalcite_dis_mmolDolomite_dis_mmol

0.00E+000.00E+000.00E+00

2.00E-01-4.74E-011.68E-01

4.00E-01-6.43E-012.54E-01

6.00E-01-5.98E-012.49E-01

8.00E-01-3.77E-011.62E-01

1.00E+000.00E+000.00E+00

RedoxEnv

00

00

00

00

00

00

CALCITE

DOLOMITE

FRACTION OF SEAWATER

MMOL DISSOLVED

SO4Reduce

pHH2MethanicSulfidicPost-oxicOxic

00.00E+003.30E+005.05E+002.03E+012.08E+01

1-1.00E+002.30E+003.93E+001.93E+011.98E+01

2-2.00E+001.30E+002.77E+001.83E+011.88E+01

3-3.00E+002.99E-011.56E+001.73E+011.78E+01

4-4.00E+00-7.01E-013.13E-011.63E+011.68E+01

5-5.00E+00-1.70E+00-9.36E-011.53E+011.58E+01

6-6.00E+00-2.72E+00-2.18E+001.43E+011.48E+01

7-7.00E+00-3.79E+00-3.39E+001.33E+011.38E+01

8-8.00E+00-4.91E+00-4.55E+001.23E+011.28E+01

9-9.00E+00-6.04E+00-5.68E+001.13E+011.18E+01

10-1.00E+01-7.18E+00-6.80E+001.03E+011.08E+01

11-1.10E+01-8.39E+00-7.93E+009.28E+009.78E+00

12-1.20E+01-9.64E+00-9.05E+008.28E+008.78E+00

13-1.30E+01-1.09E+01-1.01E+017.28E+007.78E+00

14-1.40E+01-1.22E+01-1.12E+016.29E+006.79E+00

00.00E+00

1-1.00E+00

2-2.00E+00

3-3.00E+00

4-4.00E+00

5-5.00E+00

6-6.00E+00

7-7.00E+00

8-8.00E+00

9-9.00E+00

10-1.00E+01

11-1.10E+01

12-1.20E+01

13-1.30E+01

14-1.40E+01

03.30E+00

12.30E+00

21.30E+00

32.99E-01

4-7.01E-01

5-1.70E+00

6-2.72E+00

7-3.79E+00

8-4.91E+00

9-6.04E+00

10-7.18E+00

11-8.39E+00

12-9.64E+00

13-1.09E+01

14-1.22E+01

05.05E+00

13.93E+00

22.77E+00

31.56E+00

43.13E-01

5-9.36E-01

6-2.18E+00

7-3.39E+00

8-4.55E+00

9-5.68E+00

10-6.80E+00

11-7.93E+00

12-9.05E+00

13-1.01E+01

14-1.12E+01

02.03E+01

11.93E+01

21.83E+01

31.73E+01

41.63E+01

51.53E+01

61.43E+01

71.33E+01

81.23E+01

91.13E+01

101.03E+01

119.28E+00

128.28E+00

137.28E+00

146.29E+00

02.08E+01

11.98E+01

21.88E+01

31.78E+01

41.68E+01

51.58E+01

61.48E+01

71.38E+01

81.28E+01

91.18E+01

101.08E+01

119.78E+00

128.78E+00

137.78E+00

146.79E+00

SO4Reduce

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

H2

Methanic

Sulfidic

Post-oxic

Oxic

pH

pe

Sheet1

reactionO(0)C(4)C(-4)Fe(3)Fe(2)S(6)S(-2)mackinawited_mackinawite

04.05E-041.09E-030.00E+000.00E+000.00E+001.46E-020.00E+000.00E+000.00E+00

1.00E-041.65E-041.19E-030.00E+002.57E-084.45E-181.46E-020.00E+000.00E+000.00E+00

2.00E-040.00E+001.29E-032.42E-392.52E-085.09E-051.46E-029.39E-360.00E+000.00E+00

1.00E-020.00E+001.11E-025.97E-133.58E-082.02E-031.02E-022.31E-104.46E-034.46E-03

2.00E-020.00E+002.11E-021.75E-123.38E-083.63E-035.56E-031.93E-109.06E-039.06E-03

3.00E-020.00E+003.11E-021.16E-113.38E-085.52E-039.98E-041.60E-101.36E-021.36E-02

4.00E-020.00E+003.83E-022.72E-035.82E-081.44E-026.76E-133.41E-111.46E-021.46E-02

5.00E-020.00E+004.37E-027.34E-035.60E-081.86E-022.34E-132.89E-111.46E-021.46E-02

Sheet1

00000000

00000000

00000000

00000000

00000000

00000000

00000000

00000000

O(0)

C(4)

C(-4)

Fe(3)

Fe(2)

S(6)

S(-2)

mackinawite

CH2O REACTED, IN MOLES

MOLES

Michaelis-Menten kinetics Based on enzyme kinetics

Similar to transition state theory; based on the idea of an activated complex, or an enzyme-substrate (ES) compound, whose concentration controls the rate of reaction

Assumes that the concentration of ES is at steady-state (d(ES)/dt = 0)*

Measurements needed are: the total amount of enzyme, ET = E + ESthe concentration of substrate, Sthe measured steady state velocity: V = k2 (ES)

The maximal velocity is measured, Vmax = k2 (ET), using the highest substrate concentration

The Michaelis-Menten constant, KM = (k-1 + k2)/k1, is simply the substrate concentration that gives a reaction velocity half of Vmax. Also, for a slow reaction, k2

*

Norman landfill*

Norman landfill*

Enter the RATES keyword in PHREEQC to describe the Michaelis-Menten type rate law for SO4 reduction using the constants determined by Ulrich et al. (2003). Note that PHREEQC uses seconds and moles and adjust the KM & Vmax constants accordingly. Call the rate law Sulfate_reduction.

Sulfate will be the limiting substrate. Notice that KM is high compared to the initial SO4 concentrations. Nevertheless, as a first step, assume a zero-order reaction where the rate is simply equal to VMAX.

Exercise K1 (cont)*

Your RATE block (for the 0-order case) should look something like this, where you have substituted the correct value for Vmax:

RATES Sulfate_reduction-start10 if (m m) then moles = m100 save moles-end

Exercise K1 (cont)*

The sulfate reduction is simulated as a kinetic reaction adding organic matter (formula is CH2O) to the solution. The reduction of sulfate takes place as a consequence of the addition of CH2O. The amount of CH2O is not a limiting factor. To properly define the kinetics block you will need to determine how many moles n of CH2O get oxidized per mole of SO4 reduced. The number of moles of CH2O available (i.e. the DOC value) will define the current concentration available m. Your kinetics block should start like this, with numerical values substituted:

KINETICS 1Sulfate_reduction -formula CH2O n -m DOC value in moles/kgw

Exercise K1 (cont)*

Use the SELECTED_OUTPUT keyword to have PHREEQC output total concentrations on S(6), S(-2), S, C(4), and information on the kinetics of Sulfate_reduction.

Specify output steps at 0 seconds, and 0.1, 0.2, 0.4, 0.6, 0.8, 1, 2, 4, 6, 8, 10, and 20 years.

Graph the decay of SO4, the increase in S(-2), and the decrease in the number of moles of reactant available (CH2O) w/ time.

Exercise K1 (cont)*

Exercise K1 (cont)

What happens to TDIC?

Calculate or estimate how long it would takes to oxidize all the dissolved organic carbon?

What are the final concentrations of SO4, S(-2), and DOC after 20 years? *

Exercise K1 (cont) Examine the SO4 concentration (the limiting substrate) in the initial water and compare it to the Michaelis-Menten constant, Km. Which one is significantly smaller? What is the actual limiting rate law?

Re-run the exercise with the full Michaelis-Menten expression described in the RATES block, with SO4 as the limiting substrate. Add some additional time steps to carry out the simulation to 200 years.

*

Michaelis-Menten kinetics for sulfate reduction(constants from Ulrich et al., ES&T, 2003) *

Exercise K1 (part 2) Ulrich et al. claim that barite dissolution provides the source of most of the S(6) in the Norman waters. In a new simulation, use the background water from near the Norman landfill. Maintain equilibrium with barite. Use the rate law and the kinetics keywords previously defined in part 1.

Specify output steps at 0 second, 0.1, 0.2, 0.4, 0.6, 0.8, 1, 2, 4, 6, 8, 10 and 20 years.

Graph the decay of SO4, and the increase in S(-2) and Ba with time.

How do the values compare with those observed in the leachate-contaminated water? *

Exercise K2 (optional if time)Examine the rate and kinetic blocks for Organic carbon reaction, using Monod kinetics, present in the phreeqc.dat file. Write out, and explain the rate laws and equations used.Simulate the kinetic reaction specified using a water equilibrated with atmospheric O2 and and a log pCO2 of 1.5. What is the initial organic carbon concentration specified? How long does it take for the reactants to disappear?Repeat the problem using the background water from the Norman landfillRepeat the problem using the contaminated water from the Norman landfill

*

**ANSWER: Provides BASIC functions and mechanism to code in rate laws.*ANSWER: Provides the block KINETICS to use previously defined reaction rates, specify reaction parameters, and integrates the rate equations over a specified number of time steps. *Graphs providing answers to problem k1 can be found in the k1 excel file. PHREEQCi input files k1-part-1 and k1-part-2 are also available but you should try to derive them independently if possible.