# 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

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()