Effect of calcite dissolution on exchangeable cations#

Written by Svetlana Kyas (ETH Zurich) on Mar 10th, 2022

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In this tutorial, we study the effect of calcite dissolution on determination of CaX₂ using 1-molal NH₄-acetate. We will vary the acidity of the solution from 9.3 to 7.0 by adding NH₄⁺ to the porewater.

As all the tutorials above, the numerical experiment start from importing necessary python-packages, initializing database, and defining aqueous and exchange phases to form chemical system.

from reaktoro import *
import numpy as np
import pandas as pd

# Load Phreeqc database
db = PhreeqcDatabase("phreeqc.dat")

# Define an aqueous phase
solution = AqueousPhase(speciate("H O C Na N Cl Ca Mg"))
solution.set(ActivityModelPhreeqc(db))

Since we are mainly concerned with the extraction of Ca⁺², we only include two ion exchange species into ion exchange phase. Below, we also define a single mineral phase represented by calcite.

# Define an ion exchange phase
exchange = IonExchangePhase("NaX CaX2")
exchange.set(ActivityModelIonExchangeGainesThomas())

# Define an ion exchange phase
mineral = MineralPhase("Calcite")

After all the phases are prepared, the chemical system as well all other building blocks of equilibrium simulation, i.e., equilibrium solver and aqueous properties, can be initialized.

# Create the chemical system
system = ChemicalSystem(db, solution, exchange, mineral)

# Define equilibrium solver and equilibrate given initial state with input conditions
solver = EquilibriumSolver(system)

# Define ion exchange properties and aqueous properties
aqprops = AqueousProps(system)

Bellow, we define the range of NH₄⁺ amount as well as the array with NaX values in the initial chemical state. We also collect the parameters and arrays of the data we are trying to study.

# Sampling arrays of NH4 ions' amounts and NaX exchange species
num_ph = 31
num_exchangers = 4
mols_NH4 = np.linspace(0, 60.0, num=num_ph)
mols_NaX = 1e-3 * np.array([0.0, 2.5, 12.5, 25])

# Output dataframe
data = pd.DataFrame(columns=["amount_NaX", "amount_NH4", "pH", "I",
                             "amount_Ca", "amount_CaX2", "delta_Calcite"])

Next, we perform a sequence of equilibrium calculations by varying amounts of NH₄-acetate and NaX. At the end of each calculation, we’ll extract the following properties from the computed chemical state:

pH,
ionic strength I,
amount of Ca⁺²,
amount of CaX₂,
amount of Calcite.

During each equilibrium calculation, the following two major equilbrium calculations will be defining the solubility of calcite and to formation of CaX₂: $$

(5)#\[\begin{alignat}{4} {\rm CaCO{_3}} + {\rm H_2O} & \rightleftharpoons {\rm Ca}^{+2} + {\rm HCO}_3^- + {\rm OH}^- \\ \tfrac{1}{2} {\rm Ca^{+2}} + {\rm NaX} & \rightleftharpoons {\rm Na}^+ + \tfrac{1}{2} {\rm CaX}_2\\ \end{alignat}\]

for mol_NaX in mols_NaX:

    for mol_NH4 in mols_NH4:

        # Initial amount of Calcite
        m0Calcite = 10.0

        # Define initial chemical state
        state = ChemicalState(system)
        state.setTemperature(25.0, "celsius")
        state.setPressure(1.0, "atm")
        # Seawater
        state.set("H2O" , 1.0    , "kg")
        state.set("Na+" , 1.10   , "mmol")
        state.set("Mg+2", 0.48   , "mmol")
        state.set("Ca+2", 1.90   , "mmol")
        state.set("NH4+", mol_NH4, "mmol")
        # Ammonia
        state.set("Calcite", m0Calcite, "mol")

        # Equilibrate chemical state corresponding to the seawater
        res = solver.solve(state)
        # Stop if the equilibration did not converge or failed
        if not res.succeeded(): continue

        # Update aqueous properties and evaluate pH
        aqprops.update(state)
        pH = float(aqprops.pH())

        # Exchanger
        state.set("NaX", mol_NaX, "mol")

        # Equilibrate the seawater with carbonates
        res = solver.solve(state)
        # Stop if the equilibration did not converge or failed
        if not res.succeeded(): continue

        # Update aqueous properties to evaluate ionic strength
        aqprops.update(state)
        chemprops = state.props()

        # Collect the value to be added to the dataframe in the following order
        # "amount_NaX", "amount_NH4", "amount_pH", "I", "amount_Ca", "amount_CaX2", "delta_Calcite"
        data.loc[len(data)] = [mol_NaX, mol_NH4, pH, float(aqprops.ionicStrength()),
                              float(chemprops.elementAmountInPhase("Ca", "AqueousPhase")), float(state.speciesAmount("CaX2")),
                              m0Calcite - float(state.speciesAmount("Calcite"))]

First, we plot the dependence of the dissolved calcite on the levels of pH and for different initial values of NaX providing the exchanger X^-. We see that the solubility of calcite grows with an increase in acidity.

from reaktplot import * 

fig = Figure()
fig.title("DEPENDENCE OF CALCITE SOLUBILITY ON PH")
fig.xaxisTitle('pH')
fig.yaxisTitle('Dissolved Calcite [mol]')

for mol_NaX in mols_NaX:
    df_NaX = data[data['amount_NaX'] == mol_NaX]
    fig.drawLineWithMarkers(df_NaX["pH"], df_NaX["delta_Calcite"], f'{mol_NaX} mol of NaX')

fig.show()

Finally, we represent the amount of CaX₂ resulting from the reaction NaX + Ca⁺² = CaX₂ + Na⁺, where the level of Ca⁺² ions grows from the dissolved calcite. We see that at lower pH values, we obtain higher amounts of precipitated CaX₂.

fig = Figure()
fig.title("DEPENDENCE OF CAX2 DISTRIBUTION ON PH")
fig.xaxisTitle('pH')
fig.yaxisTitle('CaX2 [mol]')

for mol_NaX in mols_NaX:
    df_NaX = data[data['amount_NaX'] == mol_NaX]
    fig.drawLineWithMarkers(df_NaX["pH"], df_NaX["amount_CaX2"], f'{mol_NaX} mol of NaX')

fig.show()

The numerical experiment performed in this study showed the effect of carbonate mineral solubility (represented by calcite) on the exchangeable cations in the presence of the ion exchanger X^- occupied by sodium ions.