Sorption Reactions

Pierre Glynn, USGS, March 2003

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

Semi-empirical modelsThe Linear adsorption model (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, 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

Other linear constant-partitioning definitions (#1)

s is amount sorbed per unit surface area; b is fracture aperture; Kf is expressed in L/m2

1 2 ff

KsK R

c b

Retardation in a fracture:

,

,

1i sorbedr r

i aq

mK R K

m

Non-dimensional partition coefficient:

mi is molality of i in the solution or on the surface

Other linear constant-partitioning definitions (#2)

foc is the fraction of organic carbon (foc should > 0.001); Koc is the partition coeff. of an organic substance between water and 100% organic carbon.

' /d OC OC OC OC wK K f K c c

Hydrophobic sorption:

log log 0.35OC OWK K Karickoff (1981):

log logOC OWK a K b Schwartzenbach & Westall (1985):

Where a & b are constants (see Appelo & Postma 1993 textbook).KOW is the Octanol-Water partition coeff.

The Langmuir adsorption model:

1c

c

bKq

K

where b and Kc are adjustable parameters.

Assumptions:1) Fixed number of sorption sites of equal affinity2) Ignores speciation, pH, competing ions, redox states…

At the limits:Kc >> 1 q = b Kc << 1 q = b Kc

Advantages: Provides better fits, still simple, accounts for sorption max.

The Van Bemmelen-Freundlich adsorption model:

q Ac

where A and are adjustable parameters with 0 < usually.

Assumptions:1) Assumes a log-normal distribution of Langmuir K

parameters (I.e. affinities)2) Ignores speciation, pH, competing ions, redox states…

Advantages: Provides good fits because of 2 adjustable params. Still simple.

Thermodynamic Speciation-based Sorption Models

• 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.

ION EXCHANGEMODELS

• 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

Ion Exchange Calcs. (#1)

• Involve small cationic species (Ca+2, Na+, NH4+, Sr+2, Al+3)

• Exchanger has a fixed CEC, cation exchange capacity

• 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)

Ion Exchange (#3)

100 / / 1 100 / B

CEC CECX

sw

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?

Sorption Exercise (S2)

pH pe Temp. Ca Mg Na Cl C S As5.713 4 25 0.4655 0.1609 5.402 6.642 0.00396 0.00473 0.05

Oklahoma Brine composition:(units are mol/kg water, except mol/kg water for As; Solution pe must be calculated for equilibrium with atmospheric O2)

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.

Exercise S2

SOLUTION_SPREAD

EXCHANGE

EQUILIBRIUM_PHASES

SAVE

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?

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 Ca+2 species related to their total concentrations

4. What is the model assumed for the activity coefficients of the sorbed species?

• 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.

\K Na

K X NaK

Na X K

Ion Exchange: thermo. concepts (#1)

• Activities of “exchanged” species calculated either:1) as molar fractions 2) as equivalent fractions

• Activity coefficients typically ignored (but not always and Davies and Debye-Huckel conventions can be used in PHREEQC)

Ion Exchange: thermo. concepts (#2)

• 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

Ion Exchange: thermo. concepts (#3)

0.52

\ 0.5

2

Na Ca

Na X CaK

Ca X Na

Ion Exchange: thermo. concepts (#4)

• Gapon convention uses Ca0.5X as the standard state for Ca+2 on the exchanger and uses equivalent fractions for sorbed ion activities.

• Gapon convention selectivity coeff. for Na\Ca exchange:

0.52

\

0.5

GaponNa Ca

Na X CaK

Ca X Na

Ion Exchange & Transport (#1)

Selectivity coeffs. are similar to Kd distribution coeffs. (linear adsorption model) when:1) one of the elements is present in trace concentrations2) the concentrations of major ions remains constant

2

\ 2 2Sr Ca d

Sr X Ca Sr XK K

Sr Ca X Sr

Constant? Constant if & B are constant

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

Most 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.

From Appelo & Postma (1993)

Ionic strength & sorbent effects on ion exchange

From Amrheim & Suarez, SSSA, v. 55, 1991

From Amrheim & Suarez, SSSA, v. 55, 1991

Ion exchange: final remarksSelectivity preference on exchangers, generally:

1) Divalents > monovalents: Ca > Na2) Ions w/ greater ionic radius (& consequently lower

hydrated radius): Ba > Ca, Cs > Na, heavy metals > Ca

The amount and direction of exchange depends on:1) the ratio of ions in solution (and other solution

properties)2) the characteristics of the exchanger

From Appelo & Postma, 1993, Geochem., groundwater & pollution

Surface ComplexationModels

• 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

Surface Complexation Principles

Surface charge depends on the sorption/surface binding of potential determining ions, such as H+. Formation of surface complexes also affects surface charge.

pH “edges” for cation sorption

pH “edges” for anion sorption

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

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.

Surface Complexation Double-Layer Model

The Double-Layer model assumes:1) a surface layer of charge density and uniform

potential throughout the layer2) a “diffuse” layer of total charge density d with

exponentially decreasing potential away from the surface layer

Electroneutrality requires that: 0d

The charge density of the surface layer is determined by the sum of protonated and deprotonated sites and sorbed charged complexes:

s s

Fm

AS

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 s are the molar concentrations and charges of surface species.

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, is the dielectric constant of water (78.5 at 25 Celsius), 0 is the permittivity of free space (8.854x10-12 C/V/m), Z is the valence.

1/ 2

08000 sinh2

ZFRT m

RT

Or at 25 Celsius:

1/ 20.1174 sinh 19.46m Z

Surface complexation equations

0 - +

2 0

SOH SO H

appa

SO HK

SOH

1st deprotonation reaction:

+ 0 +2

0

1

2

SOH SOH H

appa

SOH HK

SOH

2nd deprotonation reaction:

divalent cation complexation:

0 2+ + +

0 2

SOH M SOM H

appM

SOM HK

SOH M

For all surface reactions:0 0 0 0

exp

total intrinsic coulombic intrinsic

app int

G G G G ZF

ZFK K

RT

where Z 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.

0coulombicG

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 , the surface charge density

3 is used to calculate the potential 4 is used to calculate the “apparent” thermodynamic

constants5) Steps 1-4 are repeated using “apparent” thermodynamic

constants instead of intrinsic ones, until convergence is obtained

Surface Complexation Calcs. (#1)

• 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.

Surface Complexation (#2)

Calculation options include: 1) calculating the diffuse layer composition with the “-

diffuse_layer” option (which allows charge neutrality to be maintained in the solution);

2) ignoring electrostatic calculations with the “-no_edl” option

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

“SAVE” and “USE” keywords can be applied to “SURFACE” phase compositions.

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 (-FeOOH), a crystalline oxide with lower and less reactive surface area. 2-10% goethite appears in HFO after 12-15 days of aging.

Successful application of a DDLSC model

Successful application of DDLSC & DTLSC models

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.

Sorption Exercise (S3 cont.)

4) In the same second simulation, use the SELECTED_OUTPUT keyword to output to a file, the following information: a) total concentrations of Na, Ca, Mg, Asb) Molalities of NaX, CaX2, MgX2, Hfo_wOH2+, and any

significant sorbed arsenic speciesc) Amounts and mass transfers of calcite and dolomite

5) Use the USER_PUNCH keyword to sum and print out total sorbed arsenic.

6) 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)

Thermodynamic and printing toolbars

Access from “view “ toolbars

USER_PUNCH keyword

Sorption Exercise (S3 cont)

Oklahoma recharge water composition:(units are mmol/kg waterSolution pe must be calculated for equilibrium with atmospheric O2)

7) 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.

pH pe Temp Ca Mg Na Cl C S4.6 4 25 0.191625 0.035797 0.122668 0.133704 0.01096 0.235153

Sorption Exercise (S3 cont)

8) 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.

9) 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

Exercise S3: Questions

10)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).

11)What do you expect will happen once the carbonates are depleted?

12)What would a reversal in flow direction with an upward movement of brine do?

Exercise S3: Questions (cont)