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 models
The Linear adsorption model (constant Kd):
q
Kd 
c
b
R  1
Kd

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 sites
2) 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)
Retardation in a fracture:
s
Kf 
c
R  1 2
Kf
b
s is amount sorbed per unit surface area; b is fracture
aperture; Kf is expressed in L/m2
Non-dimensional partition coefficient:
mi ,sorbed
Kr 
mi ,aq
R  1  Kr
mi is molality of i in the solution or on the surface
Other linear constant-partitioning definitions (#2)
Hydrophobic sorption:
K d'  KOC fOC
 KOC  cOC / cw
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.
Karickoff (1981):
log KOC  log KOW  0.35
Schwartzenbach & Westall (1985):
log KOC  a log KOW  b
Where a & b are constants (see Appelo & Postma 1993 textbook).
KOW is the Octanol-Water partition coeff.
The Langmuir adsorption model:
bK c
q
1  Kc
At the limits:
Kc >> 1  q = b
Kc << 1  q = b Kc
where b and Kc are adjustable parameters.
Advantages: Provides better fits, still simple, accounts for
sorption max.
Assumptions:
1) Fixed number of sorption sites of equal affinity
2) Ignores speciation, pH, competing ions, redox states…
The Van Bemmelen-Freundlich adsorption model:
q  Ac 
where A and  are adjustable parameters with 0 <  < 1 (usually).
Advantages: Provides good fits because of 2 adjustable
params. Still simple.
Assumptions:
1) Assumes a log-normal distribution of Langmuir K
parameters (I.e. affinities)
2) Ignores speciation, pH, competing ions, redox states…
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 EXCHANGE
MODELS
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 “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 (#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.
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:
CEC
CEC
X 

(100 / sw) ( / (1   ) ) 100 ( /  B )

• 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)
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)
Oklahoma Brine composition:
(units are mol/kg water, except mmol/kg water for As;
Solution pe must be calculated for equilibrium with atmospheric O2)
pH
5.713
pe
4
Temp.
Ca
Mg
25
0.4655 0.1609
Na
5.402
Cl
C
S
6.642 0.00396 0.00473
As
0.05
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
EXCHANGE
SOLUTION_SPREAD
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?
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),
coefficients usually defined as:
 K  X   Na  
K K \ Na 
 Na  X   K  
• where [i] represents the activity of i.
selectivity
Ion Exchange: thermo. concepts (#2)
•
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 (#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:
K Na \Ca 
 Na  X  Ca 2 
0.5
Ca  X 2 0.5  Na  
• 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 (#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:
Gapon
K Na
\ Ca 
 Na  X  Ca 2 
0.5
Ca0.5  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 concentrations
2) the concentrations of major ions remains constant
K Sr \Ca 
2


Sr

X
Ca


 Sr  Ca  X 
2
Constant?
Sr  X 


K
 Sr 
2
d
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 remarks
Selectivity preference on exchangers, generally:
1) Divalents > monovalents: Ca > Na
2) 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 Complexation
Models
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
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
SOH + (M 2+ )aq  SOH(M 2+ )aq
outer-sphere complex
SOH + (M 2+ )aq  SOM +  H +
inner-sphere complex
2 SOH + (M 2+ )aq  (SO)2 M 0  2H +
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 s and uniform
potential Y throughout the layer
2) a “diffuse” layer of total charge density sd with
exponentially decreasing potential away from the
surface layer
Electroneutrality requires that:
s sd  0
The charge density of the surface layer is determined by the
sum of protonated and deprotonated sites and sorbed charged
complexes:
F
s
ms s

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:
s  (8000 RT ee 0m )
1/ 2
 ZF Y 
sinh 

 2 RT 
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:
s  0.1174m1/ 2 sinh (19.46Z Y)
Surface complexation equations
1st deprotonation reaction:
2nd deprotonation reaction:
SOH +2  SOH 0  H +
SOH )  H
(

( SOH )
0
K
app
a1

SOH 0  SO-  H +


K aapp
2

2
divalent cation complexation:
SOH 0  M 2+  SOM +  H +
SOM )  H
(

( SOH )  M

K
app
M
SO )  H 
(

( SOH )
0

2



0
For all surface reactions:
0
0
0
0
Gtotal
 Gintrinsic
 Gcoulombic
 Gintrinsic
 ZF Y
 ZF Y 
K app  K int exp 

 RT 
where Z is the net change in the charge number of the surface species
0
is variable and represents the electrostatic work
Gcoulombic
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.
Surface Complexation Calcs. (#1)
1)
2)
3)
4)
5)
PHREEQC initially ignores electrostatic effects and
solves the mass action and mass balance equations
accounting for surface reactions, using the “intrinsic”
thermodynamic constants
The estimated concentrations of surface species are
used to calculate s, the surface charge density
s is used to calculate the potential y
y is used to calculate the “apparent” thermodynamic
constants
Steps 1-4 are repeated using “apparent” thermodynamic
constants instead of intrinsic ones, until convergence is
obtained
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.
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:
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
“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 (a-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, As
b) Molalities of NaX, CaX2, MgX2, Hfo_wOH2+, and any
significant sorbed arsenic species
c) 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 water
Solution pe must be calculated for equilibrium with atmospheric O2)
pH
4.6
pe
4
Temp
25
Ca
Mg
Na
Cl
C
0.191625 0.035797 0.122668 0.133704 0.01096
S
0.235153
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.
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.
Exercise S3: Questions
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 (cont)
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?