Ion Exchange using Rothmund-Kornfeld convention

[mwleeds]

Hi,

I asked a question about PHAST back in May. Since then we have abandoned attempts to build a 2D model and have instead built a 1D model using PHREEQC to simulate our push-pull tracer test, which was completed successfully. The test was undertaken on a borehole which penetrates the Triassic Sandstone aquifer at the University of Birmingham.

I'm now attempting to match my PHREEQC model to the analytical data. The test involved the injection of ~95 L of a mixed NaCl solution with a concentration of 0.18 mol/L and the subsequent extraction of around 1230 L over a period of 2 hrs 35 minutes.

My initial model has been calibrated by changing CEC and the selectivity coefficients for Ca and Mg exchange. Here is an extract of the file.

EXCHANGE_MASTER_SPECIES
X X-

EXCHANGE_SPECIES
X- = X-
log_k 0.0

Na+ + X- = NaX
-log_k 0.0
Ca+2 + 2X- = CaX2
-log_k 1.05 # KNa/Ca=0.3
Mg+2 + 2X- =MgX2
-log_k 0.6 # KNa/Mg=0.5
K+ + X- = KX
-log_k 0.7

I have been attempting to build a model that will allow the Rothmund-Kornfeld convention to also be tested. I'd like to start with a model that replicates the same results as the GT model shown above (i.e. start with no stoichiometric adjustments).

This is the exchange part of my R-K model.

EXCHANGE_MASTER_SPECIES
X X-

EXCHANGE_SPECIES # Rothmund-Kornfeld n=1 for Ca and Mg exchange

Na+ + X- = NaX
-log_k 0.0
-gamma 4.0 0.075

Na+ + 0.5CaX2 = NaX + 0.5Ca+2
-log_k 1.05
-no_check
-mole_balance NaX
-gamma 4.0 0.075

Na+ + 0.5MgX2 = NaX + 0.5Mg+2
-log_k 0.6
-no_check
-mole_balance NaX
-gamma 4.0 0.075

Na+ + KX = NaX + K+
-log_k 0.7
-no_check
-mole_balance NaX
-gamma 4.0 0.075

These two exchange inputs don't produce the same results, but I'm not sure why.  Is it perhaps because I need to change the selectivity coefficients, as the reactions above are not the same as the half reactions in G-T exchange extract? Or have I missed something else?

I would greatly welcome any feedback on what I've done wrong :)

Thanks,

Mike

[dlparkhurst]

There is a pdf on using different ion exchange conventions with PHREEQC at Tony Appelo's web site (hydrochemistry.eu):

http://hydrochemistry.eu/pub/ap_pa02.pdf

Note that -no_check is needed only if the chemical reaction does not balance, and -mole_balance is needed only if you want a different stoichiometry for the mole balance equations than the species that is being defined. Usually, these options are not necessary, and in general should be used rarely.

[mwleeds]

Thanks for the reply.

I have the pdf which shows how to modify input files for different exchange conventions. It's been quite helpful but the Rothmund-Kornfeld example is quite restrictive as it uses a study specific selectivity coefficient (I think), so it isn't easy to compare with the other examples in the pdf or in Tony Appelo's Geochemistry Book. But perhaps I'm over-complicating things by wanting to build a model where the selectivity coefficients and the exponent n can be changed.

[dlparkhurst]

Tony's example is as follows, where n is defined by the coefficients of K+ and Na+ (the given reactions define the mass action equation) and the K is defined for the KX reaction. In this case it is necessary to use -no_check and -mole_balance so that the coefficients of the mass action equation is different than the mole balance equations. Perhaps you will need to change these values to your preference, but what else do you want?

Code: [Select]

EXCHANGE_SPECIES
 Na+ + X- = NaX
  log_k 0
  -gamma 4.0 0.075
 0.789K+ + NaX = KX + 0.789Na+
  -log_k 0.705
  -no_check
  -mole_balance KX

The equivalent mass action equation is
K = ([Na+]/[K+])^0.789([KX]/[NaX])

[mwleeds]

In a previous model I defined the exchange reaction:

0.1Na+ + 0.5CaX2 = NaX + 0.05Ca+2

based on the mass action equation:

K = ([Ca2+]^0.5/[Na+])^0.1*([NaX]/[CaX2]^0.5)

This seemed to be a better fit to the analytical data and I'd like to investigate this further. However, I'm not sure what log_k to use with the equation

0.1Na+ + 0.5CaX2 = NaX + 0.05Ca+2.

My calibration using the default GT approach suggested that log_k of 1.05 for CaX2 and 0.6 for MgX2 were best. It seemed sensible to start with equivalent values with the RK model. I'm just not sure what they are.

I guess I'm also concerned that in creating the R-K exchange input (see below) I've made a mistake and the ^0.1 in the mass action equations for Ca and Mg exchange are not the only difference between this model and my previous GT model. This was why I wanted to start with a model that replicates the same results. I hope this makes sense.

EXCHANGE_MASTER_SPECIES
X X-

EXCHANGE_SPECIES # Rothmund-Kornfeld n=0.1 for Ca and Mg exchange

Na+ + X- = NaX
-log_k 0.0
-gamma 4.0 0.075

0.1Na+ + 0.5CaX2 = NaX + 0.05Ca+2
-log_k 1.05
-no_check
-mole_balance NaX
-gamma 4.0 0.075

0.1Na+ + 0.5MgX2 = NaX + 0.05Mg+2
-log_k 0.6
-no_check
-mole_balance NaX
-gamma 4.0 0.075

Na+ + KX = NaX + K+
-log_k 0.7
-no_check
-mole_balance NaX
-gamma 4.0 0.075

Thanks for your time in answering my questions.

[dlparkhurst]

Seems like n and K are both fitting parameters.

[mwleeds]

I have managed to model the push-pull tracer test using the R-K method. It didn't work as well as I had hoped. In fact the cation breakthrough curves were best matched by including a small amount of immobile porosity in my model.

Thanks for your help.