Processes > Reactive transport modelling

Cation Exchange

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avadhoot:
Hi, I am Avadhoot. As part of PhD research I am trying to estimate effect of cation exchange on fresh recharge water. Fresh recharge water chemistry is Ca-Mg-HCO3. It interacts with sandstone aquifer that has higher smectite modal % (15 %). Smectite CEC is approx 120 meq/100g. I am trying to model the following reactions
Na2X + Ca --> 2Na + Cax
Na2X + Mg --> 2Na + MgX
X is the exchange complex

Recharge water chemistry and my code is as follows:

TITLE Cation Exchange MRA
SOLUTION_SPREAD
-units mg/L

SOLUTION 1 Recharge Water
    temp      25
    pH        7.71
    pe        4
    redox     pe
    units     mg/l
    density   1
    Alkalinity 470.05
    Ca        52.02
    Cl        33.59
    Mg        24.26
    Na        24.74
    S(6)      72.90
    -water    1 # kg

EXCHANGE 1
    X       0.06
    MgX2    Dolomite             equilibrium_phase   0.005
    -equilibrate with solution 1
    -pitzer_exchange_gammas true

EQUILIBRIUM_PHASES 1
    Dolomite  0 10


PRINT
-reset false
-totals true
-exchange true
END

My questions are:
1. How do I input rate of reactions?
2. I know that there should be dissolution of calcite based on saturation indices along groundwater flow path < 0
3. How can I estimate the resultant water chemistry after cation exchange?
4. Where do I have to input the CEC of smectite in the above code?

dlparkhurst:

1. How do I input rate of reactions?
Start with equilibrium calculations. KINETICS and RATES are more difficult to implement and you can get more complicated after you decide what you want to simulate.
2. I know that there should be dissolution of calcite based on saturation indices along groundwater flow path < 0
Include calcite and dolomite in your equilibrium phases. Equilibrium for these carbonates is reasonable for an aquifer where they are present.
3. How can I estimate the resultant water chemistry after cation exchange?
The following script models the infiltration of 3 pore volumes of your recharge water into an aquifer that has a Na dominated clay with plenty of calcite and dolomite to maintain equilibrium.
4. Where do I have to input the CEC of smectite in the above code?
The number of sites of X is moles of sites in the cell. In the script, there is approximately 1 L of water. You need to adjust the moles of X to provide the correct number of sites per liter of water.

This may not be what you had in mind, but it should be a start.


--- Code: ---TITLE Cation Exchange MRA
SOLUTION_SPREAD
-units mg/L

SOLUTION 0 Recharge Water
    temp      25
    pH        7.71
    pe        4
    redox     pe
    units     mg/l
    density   1
    Alkalinity 470.05
    Ca        52.02
    Cl        33.59
    Mg        24.26
    Na        24.74
    S(6)      72.90
    -water    1 # kg
END
EXCHANGE 1
    NaX       0.06
END
EQUILIBRIUM_PHASES 1
    Dolomite  0 10
    Calcite   0 10
END
USE solution 0
USE exchange 1
USE equilibrium_phases 1
SAVE solution 1-10
SAVE exchange 1-10
SAVE equilibrium_phases 1-10
END
TRANSPORT
    -cells                 10
    -shifts                30
    -time_step             86400 # seconds
    -dispersivities        10*0.1
    -length                10*1
    -punch_frequency 30
    -print_frequency 30
    -punch_cells 1-10
USER_GRAPH 1
    -headings               dist Ca Mg Na pH
    -axis_titles            "Distance" "Molality" "pH"
    -initial_solutions      false
    -connect_simulations    true
    -plot_concentration_vs  x

  -start
10 GRAPH_X DIST
20 GRAPH_Y TOT("Ca"), TOT("Mg"), TOT("Na")
30 GRAPH_SY -LA("H+")
  -end
    -active                 true
END
--- End code ---

avadhoot:
Dear Dr Parkhurst,

Thank you very much for helping me with the modified code. I could do a manual calculation and validate results with PHREEQC output (not exactly the same but are in the ballpark). I understood the methodology of ion exchange.

For my research, I am trying to understand increase in Na concentrations downgradient due to following processes:
1. Ion exchange (which accounts for Na increase and Ca-Mg decrease downgradient)
2. Diffusion: Based on literature, it is known that there is diffusion of high salinity water from underlying aquitard and addition of equimolar amounts of Na and Cl is needed to maintain electro-neutrality.

My question then is:
1. How can I include ion exchange and addition of equimolar amounts of Na and Cl due to diffusion from aquitard in this code?
2. Moreover, how can I simulate this transport for 500,000 years? (based on 36Cl and 81Kr tracer data, we know groundwater ages are very old)

Thank you very much for the valuable input Dr Parkhurst!

Thanks
Avadhoot

dlparkhurst:
Sorry, I can't help you much with this. TRANSPORT has a stagnant cell option that could represent diffusion from the aquitard. However, I don't know how to set the exchange factors to represent the diffusion, especially when you are trying to model ~1e6 years. I suspect the problem will be intractable at a time scale that long. You are welcome to read the documentation, especially using MIX definitions for the the stagnant cells, to try to set up a simulation. See the section on Dual Porosity in the PHREEQC version 2 manual in the /doc directory for more details of stagnant zones.

Note that example 21 considers diffusion of 36Cl in a diffusion cell.

avadhoot:
Dear Dr Parkhurst,

Thank you very much for answering my query. I think, I will have to read through the manual but as you said rightly the concentrations will not be tractable for such a long time scale.

Thank you very much again for the valuable inputs!
Avadhoot

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