Sorption Reactions

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Sorption Reactions

• Pierre Glynn, USGS, March 2003

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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

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Semi-empirical models

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

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Other linear constant-partitioning definitions
(1)
s is amount sorbed per unit surface area b is
fracture aperture Kf is expressed in L/m2
Non-dimensional partition coefficient
mi is molality of i in the solution or on the
surface
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Other linear constant-partitioning definitions
(2)
Hydrophobic sorption
foc is the fraction of organic carbon (foc should
gt 0.001) Koc is the partition coeff. of an
organic substance between water and 100 organic
carbon.
Karickoff (1981)
Schwartzenbach Westall (1985)
Where a b are constants (see Appelo Postma
1993 textbook). KOW is the Octanol-Water
partition coeff.
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The Langmuir adsorption model
At the limits Kc gtgt 1 ? q b Kc ltlt 1 ? q b Kc
where b and Kc are adjustable parameters.
Advantages Provides better fits, still simple,
accounts for sorption max.

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

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

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

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Thermodynamic Speciation-based Sorption Models
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• 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.

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ION EXCHANGEMODELS
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Ion Exchange Calcs. (1)

• Involve small cationic species (Ca2, Na, NH4,
  Sr2, Al3)
• Exchanger has a fixed CEC, cation exchange
  capacity

• PHREEQC speciates the exchanged species
  sorbed on the exchange sites (usually only
  1/element) either
• adjusting sorbed concentrations in response to a
  fixed aqueous composition
• or adjusting both sorbed and aqueous compositions

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Ion Exchange (2)

• 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.

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Ion Exchange (3)

• 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), q is the porosity and rB is the
  bulk density of the soil in kg/L. (If sw 2.65
  q 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)

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Sorption Exercise (S1)

1. Change the default thermodynamic database to
   wateq4f.dat from phreeqc.dat. What are the major
   differences between both databases?
2. Use wordpad to look at the thermodynamic data.
   What are the main ion exchange reactions
   considered?
3. How are they written? Does species X- really
   exist by itself? Is it mobile?

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Sorption Exercise (S2)
Enter the above NaCl brine in PHREEQC. Use Cl to
charge balance the solution. Equilibrate the
brine with 0.1 moles of calcite and 1.6 moles of
dolomite. Save the resulting solution
composition as solution 1. In a new simulation,
find the composition of an exchanger X that would
be at equilibrium with solution 1 (fixed
composition). There is 1 mole of X per kg of
water.
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Exercise S2
EXCHANGE
EQUILIBRIUM_PHASES
SOLUTION_SPREAD
SAVE
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S2 Questions

1. What happens to the brine as a result of the
   mineral equilibration?
2. What is the Na/Ca mole ratio in the brine before
   and after mineral equilibration?
3. What is the Na/Ca mole ratio on the exchanger in
   equilibrium with the calcite and dolomite
   equilibrated brine?
4. Bonus What about the Mg/Ca ratios? What about
   proton exchange? Are the pH and aqueous
   concentrations affected by the exchange
   equilibrium?

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S2 Questions (cont)

1. Re-equilibrate the calcite-and-dolomite
   equilibrated brine (trhe saved solution 1) with
   an exchanger that has 0.125 moles CaX2, 0.125
   moles MgX2 and 0.5 moles NaX.
2. How is the aqueous solution affected by the
   equilibration with the exchanger?
3. What is the ionic strength of the brine? Is
   PHREEQC appropriate for this type of calculation?
   How are the activities of Na and Ca2 species
   related to their total concentrations
4. What is the model assumed for the activity
   coefficients of the sorbed species?

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Ion Exchange thermo. concepts (1)

• Two major issues
• Activity definition for exchanged species
• Convention for heterovalent exchange (eg. Na\Ca
  or K\Sr)
• For homovalent exchange (eg. K\Na), selectivity
  coefficients usually defined as
• where i represents the activity of i.

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Ion Exchange thermo. concepts (2)

• Activities of exchanged species calculated
  either
• as molar fractions
• as equivalent fractions
• Activity coefficients typically ignored (but not
  always and Davies and Debye-Huckel conventions
  can be used in PHREEQC)

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Ion Exchange thermo. concepts (3)

• Heterovalent exchange (eg. Na\Ca) what is the
  standard state for the exchanged species, Ca0.5X
  or CaX2 ? In latter case, the law of mass action
  is
• Both the Gaines Thomas (default in PHREEQC)
  and Vanselow conventions use CaX2 as the standard
  state for divalent Ca on the exchanger.
• Gaines Thomas uses equivalent fractions of
  exchange species for activities
• Vanselow uses molar fractions

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Ion Exchange thermo. concepts (4)

• Gapon convention uses Ca0.5X as the standard
  state for Ca2 on the exchanger and uses
  equivalent fractions for sorbed ion activities.
• Gapon convention selectivity coeff. for Na\Ca
  exchange

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Ion Exchange Transport (1)

• Selectivity coeffs. are similar to Kd
  distribution coeffs. (linear adsorption model)
  when
• one of the elements is present in trace
  concentrations
• the concentrations of major ions remains constant

Constant?
Constant if q rB are constant
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Ion Exchange Transport (2)
Unlike most non-linear empirical adsorption
isotherms (Langmuir, Freundlich) used in
reactive transport codes, ion exchange
isotherms can be concave upwards, i.e. exhibit
greater partitioning at higher concentrations Mos
t isotherms usually result in self-sharpening
fronts and smeared-out tails, because of greater
sorption at lower concentrations. Ion exchange
isotherms can result in smearing fronts.
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From Appelo Postma (1993)
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Ionic strength sorbent effects on ion exchange
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From Amrheim Suarez, SSSA, v. 55, 1991
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From Amrheim Suarez, SSSA, v. 55, 1991
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Ion exchange final remarks

• Selectivity preference on exchangers, generally
• Divalents gt monovalents Ca gt Na
• Ions w/ greater ionic radius ( consequently
  lower hydrated radius) Ba gt Ca, Cs gt Na, heavy
  metals gt Ca

• The amount and direction of exchange depends on
• the ratio of ions in solution (and other solution
  properties)
• the characteristics of the exchanger

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From Appelo Postma, 1993, Geochem., groundwater
pollution
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Surface ComplexationModels
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Surface Complexation Principles

• Fully considers variable charge surfaces. of
  sorption of sites is constant but their
  individual charge, total 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 species through the diffuse layer
  (similar to an activity coefficient correction) ?
  Gouy-Chapman theory

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Surface charge depends on the sorption/surface
binding of potential determining ions, such as
H. Formation of surface complexes also affects
surface charge.
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pH edges for cation sorption
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pH edges for anion sorption
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Examples of Surface Complexation Reactions
outer-sphere complex
inner-sphere complex
bidentate inner-sphere complex
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Gouy-Chapman Double-Layer Theory
The distribution of charge near a surface seeks
to minimize energy (charge separation) and
maximize entropy. A charged surface attracts a
diffuse cloud of ions, preferentially enriched in
counterions. The cation/anion imbalance in the
cloud gradually decreasses away from the surface.
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Surface Complexation Double-Layer Model
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• The Double-Layer model assumes
• a surface layer of charge density s and uniform
  potential Y throughout the layer
• a diffuse layer of total charge density sd with
  exponentially decreasing potential away from the
  surface layer

Electroneutrality requires that
The charge density of the surface layer is
determined by the sum of protonated and
deprotonated sites and sorbed charged complexes
Where F is the Faraday const. (96490 C/mol), A is
the spec. surf. area (m2/g), S is the solid
concentration (g/L), ms and ns are the molar
concentrations and charges of surface species.
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According to Gouy-Chapman theory, for a
symmetrical electrolyte
where R is the gas const. (8.314 J/mol/K), T is
absolute temperature (K), m is molar
concentration, e is the dielectric constant of
water (78.5 at 25 Celsius), e0 is the
permittivity of free space (8.854x10-12 C/V/m), Z
is the valence.
Or at 25 Celsius
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Surface complexation equations
1st deprotonation reaction
2nd deprotonation reaction
divalent cation complexation
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For all surface reactions
where DZ is the net change in the charge number
of the surface species
is variable and represents the
electrostatic work needed to transport species
through the interfacial potential gradient. The
exponential factor basically is equivalent to an
activity coefficient correction. Kint strictly
represents the chemical bonding reaction.
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Surface Complexation Calcs. (1)

1. PHREEQC initially ignores electrostatic effects
   and solves the mass action and mass balance
   equations accounting for surface reactions, using
   the intrinsic thermodynamic constants
2. The estimated concentrations of surface species
   are used to calculate s, the surface charge
   density
3. s is used to calculate the potential y
4. y is used to calculate the apparent
   thermodynamic constants
5. Steps 1-4 are repeated using apparent
   thermodynamic constants instead of intrinsic
   ones, until convergence is obtained

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Surface Complexation (2)

• 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 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 phase.

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Surface complexation (3)
PHREEQC speciates the surface, determining the
surface species either adjusting surface
concentrations in response to a fixed aqueous
composition or adjusting both surface and
aqueous compositions

• Calculation options include
• calculating the diffuse layer composition with
  the -diffuse_layer option (which allows charge
  neutrality to be maintained in the solution)
• ignoring electrostatic calculations with the
  -no_edl option

SAVE and USE keywords can be applied to
SURFACE phase compositions.
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Sorption parameters for HFO(from Dzombak
Morel, 1990)
HFO Specific surface area 600m2/g (range
200-840) Site density for type 2 sites (weak)
0.2 mol/mol Fe (range 0.1-0.3) Type 2 sites apply
to sorption of protons, cations and anions Site
density for type 1 sites (strong) 0.005 mol/mol
Fe (range 0.001-0.01) Type 1 sites account for a
smaller set of high-affinity cation binding
sites. Dzombak Morel assume HFO to be
Fe2O3.H2O, i.e. 89g HFO/mol Fe Note the above
values apply to HFO only, an amorphous solid.
With significant aging, HFO transforms to
goethite (a-FeOOH), a crystalline oxide with
lower and less reactive surface area. 2-10
goethite appears in HFO after 12-15 days of aging.
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Successful application of a DDLSC model
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Successful application of DDLSC DTLSC models
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Sorption Exercise (S3)

1. You may modify the PHREEQC input file created in
   exercise S2.
2. In a first simulation, equilibrate the OK brine
   with 0.1 moles calcite 1.6 moles Dolomite.
   Save the resulting solution as solution 1.
3. In a second simulation, equilibrate 1 mol of an
   EXCHANGE surface (with initially undefined
   composition) with solution 1. Also, equilibrate
   with solution 1, a surface complexation SURFACE,
   with 0.07 moles of surface site Hfo_w, a specific
   surface area of 600 m2/g and a mass of 30 g. The
   composition of this surface is initially
   undefined.

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Sorption Exercise (S3 cont.)

• In the same second simulation, use the
  SELECTED_OUTPUT keyword to output to a file, the
  following information
• total concentrations of Na, Ca, Mg, As
• Molalities of NaX, CaX2, MgX2, Hfo_wOH2, and any
  significant sorbed arsenic species
• Amounts and mass transfers of calcite and
  dolomite
• Use the USER_PUNCH keyword to sum and print out
  total sorbed arsenic.
• Also, use the SURFACE_SPECIES keyword to
  effectively eliminate the species, Hfo_wMg and
  Hfo_wCa, by defining very small association
  constants (log K -15)

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Thermodynamic and printing toolbars
Access from view toolbars
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USER_PUNCH keyword
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Sorption Exercise (S3 cont)
Oklahoma recharge water composition (units are
mmol/kg water Solution pe must be calculated for
equilibrium with atmospheric O2)

• For the third simulation, enter the above
  recharge water in PHREEQC as solution 0. Use SO4
  for charge balance. Equilibrate the solution
  with calcite, dolomite, and a soil log pCO2 of
  1.5. Save the resulting solution as solution
  0.

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Sorption Exercise (S3 cont)

• In simulations 4-13, model the infiltration of 10
  pore volumes of recharge water (solution 0) as it
  contacts the solid phases, and the exchange and
  surface complexation surfaces. In each
  simulation, USE solution 0 to equilibrate with
  EQUILIBRIUM_PHASES 1, SURFACE 1, EXCHANGE 1.
  SAVE the new solid and surface and exchange phase
  compositions, to USE them in the following
  simulation. Do not save solution 0 after each
  simulation.

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Exercise S3 Questions

• How do solution pH and As content vary with time
  in a given volume of initially brine-filled
  aquifer, as recharge water passes through it? Is
  ion exchange important? Why? Is surface
  complexation important? Why? What is the maximum
  As concentration seen? How long does it take
  (how many pore volumes?) to get As concentrations
  down to the 10 ppb threshold. How soon will the
  carbonate minerals be depleted? Are surface
  complexationpH in the solution

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Exercise S3 Questions (cont)

• Is the partitioning of As, Ca, and Na between the
  aqueous and sorbed phases constant with time?
  (You can use excel to calculate and plot the
  partitioning. You may also use the USER_PUNCH
  keyword in PHREEQC to calculate the
  partitioning).
• What do you expect will happen once the
  carbonates are depleted?
• What would a reversal in flow direction with an
  upward movement of brine do?