Inverse modeling for exchangeable cations

[MichaelZ20]

Is it possible to solve the inverse problem for exchangeable cations?
In other words, to calculate in what proportions should soluble salts (Halite, Gypsum, Epsomite and Sylvite) be added to the known composition of rain for obtaining a measured composition of exchange cations of the topsoil layer?

[dlparkhurst]

I'm not sure that is a well posed problem. If the ratio of water to exchanger is small enough, the water will be dominated by the exchanger. If the ratio is large, the exchanger will assume equilibrium with the water. Do you want the inverse reaction that affects the clay composition, or affects the solution composition.

If you do the reaction with phreeqc with a large amount of exchanger of the given composition, you can determine a water composition in equilibrium with the exchanger. The initial water could simply be a NaCl solution of an appropriate ionic strength. That of course that calculation relies on the exchange constants in the database.

You can calculate the composition of the exchanger with a given water composition by the option in EXCHANGE.

[MichaelZ20]

David, thank you for your reply.
When I put the rainwater in equilibrium with the known X [eq/kgw] (at differing rainwater masses) I don't obtain the known percents of exchangeable cations. From this I concluded that the dissolved dry fallout may influence, but I don't know how to estimate this influence.

[dlparkhurst]

I'm not following your logic. I was suggesting a large amount of exchanger (many moles) of the known composition relative to a SOLUTION with a given ionic strength. Something like this:

Code: [Select]

SOLUTION 1
-units mol/kgw
pH 7
Na 1
Cl 1
-water 0.1
END
EXCHANGE 1
NaX 1
CaX2 0.5
MgX2 0.1
KX  0.1
END
EXCHANGE_MIX 1
1 100
END
USE solution 1
USE exchange 1
END

The exchange composition basically does not change, and the solution is in equilibrium with the exchanger. Seems like this solution composition might be useful to you as an end-member.

Alternatively, you might be able to add the exchanged moles to SOLUTION (along with an anion) and do inverse modelling, provided the solution can be solved. Any model that you produce will react sufficiently to produce the exchange composition that you want, albeit in solution, which you would logically partition between the real solution and the desired exchange composition.

I'm not sure if either of these approaches are what you are trying to do.

[MichaelZ20]

Thank you, David!