EXCHANGE module and relation to sorption isotherms

[larsaste]

Dear PhreeqcUsers,
I have deployed the ADVECTION and EXCHANGER datablock to model sorption, based on a script from the PHREEQC manual (Parkhurst and Appelo, 2013):

TITLE Sorption at Ringerike
SOLUTION 0 Manganese-rich infiltrate water
units mg/L
temp 6.9
pH 6.94
pe 12.5 O2(g) -0.68
Na   5.47
Ca   15.43
Mg   4.35
Mn(2)   0.30
K   1.98
Cl   4.81
S(6)   9.54
Alkalinity 85.43 as HCO3   
SOLUTION 1-50 Manganese-free groundwater
units mg/L
temp 6.9
pH 6.94
pe 12.5 O2(g) -0.68
Na   5.47
Ca   15.43
Mg   4.35
Mn(2)   0.007
K   1.98
Cl   4.81
S(6)   9.54
Alkalinity 85.43 as HCO3
END
EXCHANGE 1-50
equilibrate 1
X 0.08904
COPY cell 1 4001
END
ADVECTION
-cells 50
-shifts 4000
-punch_cells 50
-punch_frequency 1
-print_cells 50
-print_frequency 10
PRINT; -reset false; -status false
SELECTED_OUTPUT
-file RingerikePW3.xls
-reset false
-step
-totals Cl Ca Mg Mn
USER_PUNCH
-heading Pore_vol
10 PUNCH (STEP_NO + .5) / cell_no
USER_GRAPH 1 Example 11
-chart_title "Using ADVECTION Data Block"
-headings Cl Ca Mg Mn
-axis_titles "Pore volumes" "Concentration (mg/l water)"
-axis_scale x_axis 0 85
-axis_scale y_axis 0 1 0.1
-plot_concentration_vs time
-start
10 x = (STEP_NO + 0.5) / cell_no
20 PLOT_XY x, TOT("Cl")*35453, symbol = None
30 PLOT_XY x, TOT("Ca")*40800, symbol = None
35 PLOT_XY x, TOT("Mg")*24305, symbol = None
40 PLOT_XY x, TOT("Mn")*54938, symbol = None
60 PUT(1, 1)
-end

Could anyone please help me understand how the sorption is modeled, or possibly direct me to somewhere in the manual where it is elaborated? Is it a linear sorption isotherm that is deployed?

Kind regards,
Lars

[dlparkhurst]

No, you are not using linear isotherms, although example 19 demonstrates calculations with linear, Langmuir, and Freundlich isotherms. These isotherms calculate a distribution between sorbed and unsorbed constituent. There is no competition for sites between multiple species.

The EXCHANGE calculation that you are using is a  competitive exchange process in which sites are filled by cations based on the half-reaction definitions in the database (EXCHANGE_SPECIES). Exchange calculations assume all exchange sites are filled and no charge develops (in SURFACE calculations a surface charge can accumulate). EXCHANGE is an equilibrium calculation such that if you combine two half-reactions the resulting mass-action equation will be satisfied. For example phreeqc.dat contains the following two half reactions:

Code: [Select]

Na+ + X- = NaX
-log_k 0.0

Ca+2 + 2X- = CaX2
-log_k 0.8

When combined, you get the reaction

Code: [Select]

Ca+2 + 2NaX = CaX2 + Na+
-log_k 0.8

and the mass action expression

Code: [Select]

[CaX2][Na+] / [Ca+2][NaX]^2 = 10^0.8 = 6.3

where [] indicates activity. For an ion-association database (like phreeqc.dat), an exchange species activity is equal to the equivalent fraction of exchange sites occupied by the cation; aqueous activities are calculated as part of the distribution of aqueous species and ionic-strength dependent activity coefficients. So, if we consider a cell with a solution of equal aqueous activity of Na+ and Ca+2, the following equality would hold for the exchanger composition:

Code: [Select]

[CaX2]/[NaX]^2 = 6.3

With multiple cations participating in the exchange reactions, the composition of the exchanger and the solution will adjust such that all of the combinations of half-reaction mass-action equations are satisfied and mass balance is satisfied for the total moles of elements in the cell.

"Geochemistry, groundwater and pollution" by Appelo and Postma is a good text for learning to use PHREEQC. It discusses the theory, the literature, and presents PHREEQC examples for most geochemical processes that can be modeled with PHREEQC.

[larsaste]

Thank you once again for a very rapid and elaborate answer, David!
It comes clearer to me also now that we are of course not talking about a linear sorption isotherm, since we are defining a maximum sorption capacity [X].
I guess the question that is left is whether my groundwater system has time to reach equilibrium. My average groundwater system is a quite dynamic one (bank filtration), with a travel time around 2.5 m/d. I see other publications with a 1.5 m/d groundwater travel time using this methodology (i.e., assuming equilibrium is reached).
Have you got any general verdict on whether ion exchange reactions can be considered fast/slow?
Kind regards,
Lars

[dlparkhurst]

Exchange reactions are fairly fast, at least in laboratory experiments.  I'd certainly start with the assumption of equilibrium and use it until you need something more complicated.

In aquifers, there is always the possibility of slower diffusion into clays and dead-end pores. The TRANSPORT capability does allow dual porosity, which may be a way to make exchange more kinetic, if that is what you need. You could put the exchanger in the immobile zone so that there is a slower exchange process to move ions to and from the exchanger (which is in equilibrium). Example 21 considers diffusion and exchange in detail.

[larsaste]

Thank you for the advise!

Lars