Reaktoro  A unified framework for modeling chemically reactive systems
Calculating the equilibrium reaction path of a H2O–HCl–CaCO3 system

Consider two different chemical states in equilibrium: an initial state and a final state. These states can have different temperatures, pressures, and/or molar amounts of elements. If we gradually adjust temperature, pressure, and elemental amounts in the system to bring the initial state to the final state, slowly enough so that every intermediate state is in equilibrium, the system would trace a path, which we call reaction path.

Let's say we initially have 1 g of calcite (CaCO3) mixed with 1 kg of water. We want to see how the addition of hydrochloric acid (HCl), up to 1 mmol, contributes to the dissolution of calcite. Thus, our initial and final states for a reaction path calculation can be described as follows:

Initial state Final state
1 kg of H2O 1 kg of H2O
1 g of CaCO3 1 g of CaCO3
1 mmol of HCl

We show below the code for doing this reaction path calculation using Reaktoro, followed by comments of each newly introduced C++ component:

#include <Reaktoro/Reaktoro.hpp>
using namespace Reaktoro;
int main()
{
ChemicalSystem system;(editor);
EquilibriumProblem problem1;(system);
problem1.setTemperature(30.0, "celsius");
problem1.setPressure(1.0, "bar");
EquilibriumProblem problem2;(system);
problem2.setTemperature(30.0, "celsius");
problem2.setPressure(1.0, "bar");
ChemicalState state1 = equilibrate(problem1);
ChemicalState state2 = equilibrate(problem2);
EquilibriumPath path;(system);
ChemicalPlot plot1 = path.plot();
plot1.x("elementAmount(Cl units=mmol)");
plot1.y("pH");
plot1.xlabel("HCl [mmol]");
plot1.ylabel("pH");
plot1.showlegend(false);
ChemicalPlot plot2 = path.plot();
plot2.x("elementAmount(Cl units=mmol)");
plot2.y("elementMolality(Ca units=mmolal)", "Ca");
plot2.xlabel("HCl [mmol]");
plot2.ylabel("Concentration [mmolal]");
plot2.legend("right center");
ChemicalPlot plot3 = path.plot();
plot3.x("elementAmount(Cl units=mmol)");
plot3.y("speciesMolality(CO2(aq) units=mmolal)", "CO2(aq)");
plot3.y("speciesMolality(CO3-- units=mmolal)", "CO3--");
plot3.xlabel("HCl [mmol]");
plot3.ylabel("Concentration [mmolal]");
plot3.legend("right top");
ChemicalPlot plot4 = path.plot();
plot4.x("elementAmount(Cl units=mmol)");
plot4.y("speciesMass(Calcite units=g)", "Calcite");
plot4.xlabel("HCl [mmol]");
plot4.ylabel("Mass [g]");
ChemicalOutput output = path.output();
output.filename("result.txt");
path.solve(state1, state2);
}

In the code above, two instances of class EquilibriumProblem are created: problem1 describes the initial state, and problem2 the final state. Two instances of class ChemicalState are then created to store the initial and final equilibrium states calculated by method equilibrate.

Note that, differently from the previous code example, the object editor from class ChemicalEditor was not initialized with a given Database object. Instead, it was initialized using the default built-in database file supcrt98.xml. Also note that the aqueous species were not listed, but the chemical elements composing the phase. When chemical element names are specified during the creation of a phase, like in:

using namespace Reaktoro; {delete}

class ChemicalEditor searches for all species in the database that can be formed by those elements. Only species corresponding to the phase type being created is selected (e.g., only aqueous species are searched in the above case).

Once the initial and final equilibrium states have been calculated, it is now time to trace the reaction path between them, with each intermediate state in chemical equilibrium. For this, we use the class EquilibriumPath. Note that its initialization requires a ChemicalSystem instance:

using namespace Reaktoro; {delete}
EquilibriumPath path(system);

A reaction path calculation is better analyzed using plots. Before the method EquilibriumPath::solve is called, one can configure plots to be generated during the calculation. These plots are generated by Gnuplot, so ensure it is installed in your system to be able to see these plots. There are four configured plots in the above equilibrium path calculation. The first plot is defined as:

using namespace Reaktoro; {delete}
EquilibriumPath path;(system); {delete}
ChemicalPlot plot1 = path.plot();
plot1.x("elementAmount(Cl units=mmol)");
plot1.y("pH");
plot1.xlabel("HCl [mmol]");
plot1.ylabel("pH");
plot1.showlegend(false);

which sets the x-axis to the amount of element Cl, in units of mmol, and the y-axis to the pH of the aqueous phase, resulting in the following figure:

The second plot is defined as:

using namespace Reaktoro; {delete}
EquilibriumPath path;(system); {delete}
ChemicalPlot plot2 = path.plot();
plot2.x("elementAmount(Cl units=mmol)");
plot2.y("elementMolality(Ca units=mmolal)", "Ca");
plot2.xlabel("HCl [mmol]");
plot2.ylabel("Concentration [mmolal]");
plot2.legend("right center");

which now sets the x-axis to the pH of the aqueous phase and the y-axis to the molality of element Ca, i.e., the molar amount of Ca in the aqueous phase, divided by the mass of solvent water H2O(l). This results in the following figure:

The third figure is produced with the following code:

using namespace Reaktoro; {delete}
EquilibriumPath path;(system); {delete}
ChemicalPlot plot3 = path.plot();
plot3.x("elementAmount(Cl units=mmol)");
plot3.y("speciesMolality(CO2(aq) units=mmolal)", "CO2(aq)");
plot3.y("speciesMolality(CO3-- units=mmolal)", "CO3--");
plot3.xlabel("HCl [mmol]");
plot3.ylabel("Concentration [mmolal]");
plot3.legend("right top");

which also sets the x-axis to pH, but the y-axis now contains two plotted quantities: the molality of species CO2(aq) and the molality of species CO3–, both in units of mmolal (i.e., mmol/kgH2O). This produces the following figure:

The fourth and last figure finally plots how the mass of calcite (or calcium carbonate) changes with the addition of HCl in the system:

using namespace Reaktoro; {delete}
EquilibriumPath path;(system); {delete}
ChemicalPlot plot4 = path.plot();
plot4.x("elementAmount(Cl units=mmol)");
plot4.y("speciesMass(Calcite units=g)", "Calcite");
plot4.xlabel("HCl [mmol]");
plot4.ylabel("Mass [g]");

producing the following figure:

Note
Check class ChemicalQuantity for a list of supported quantity names, their default units, and how they can be used in both ChemicalPlot and ChemicalOutput classes.
Warning
The equal sign (=) used to specify the units (e.g., units=mmolal, units=celsius) should not be separated by spaces.

To output quantities to a file or terminal during the calculation, use method EquilibriumPath::output, which returns an instance of class ChemicalOutput:

using namespace Reaktoro; {delete}
ChemicalOutput output = path.output();
output.filename("result.txt");

The method ChemicalOutput::add adds a quantity to be output to the file result.txt (i.e., the file name specified in the call to method ChemicalOutput::file). Each call to ChemicalOutput::add results in a new column of data in the output file, like shown below:

Cl [mmol] Ca [mmolal] pH speciesMass(Calcite units=g)
1.1e-16 0.134437 9.78558 0.986545
6.3132e-06 0.134439 9.78557 0.986544
9.55315e-05 0.134467 9.7853 0.986542
0.000987715 0.134742 9.78268 0.986514
0.00990955 0.137677 9.7559 0.98622
0.029156 0.144655 9.69602 0.985522
0.0484024 0.15261 9.63351 0.984726
0.100331 0.179333 9.45629 0.982051
0.152259 0.213487 9.27833 0.978633
0.204187 0.253494 9.11218 0.974629
0.256115 0.297405 8.96347 0.970234
0.308043 0.343719 8.83241 0.965598
0.397568 0.42662 8.6418 0.957301
0.487093 0.511357 8.48573 0.94882
0.531083 0.553286 8.41877 0.944623
0.575074 0.595296 8.35705 0.940419
0.605964 0.624812 8.31647 0.937465
0.636854 0.654325 8.27795 0.934511
0.68543 0.700704 8.22109 0.929869
0.734007 0.747012 8.16829 0.925234
0.797192 0.807094 8.10488 0.919221
0.860377 0.866961 8.04663 0.913229
0.922344 0.925434 7.99384 0.907376
0.984311 0.983645 7.94481 0.90155
1 0.998339 7.93293 0.900079

When two arguments are provided to method ChemicalOutput::add, the first one is a label used as the heading of the column of data in the output file, and the second argument is the name of the quantity to be output (e.g., time, elementAmount(Cl), ionicStrength). When only one argument is provided, this single argument is both the label and the quantity name.

To output the result directly to the standard output, use:

using namespace Reaktoro; {delete}
ChemicalOutput output; {delete}
output.terminal(true);

Finally, after all plots and output files have been configured, the equilibrium path can be calculated using:

using namespace Reaktoro; {delete}
EquilibriumPath path; {delete}
path.solve(state1, state2);

We now finish by showing the Python code equivalent to the previous C++ code used for the equilibrium path calculation:

using namespace Reaktoro; {delete}
from reaktoro import *
editor = ChemicalEditor()
; {delete}
ChemicalEditor editor; {delete}
; {delete}
; {delete}
system = ChemicalSystem;(editor)
problem1 = EquilibriumProblem;(system)
problem1.setTemperature;(30.0, "celsius")
problem1.setPressure;(1.0, "bar")
problem2 = EquilibriumProblem;(system)
problem2.setTemperature;(30.0, "celsius")
problem2.setPressure;(1.0, "bar")
state1 = equilibrate(problem1)
state2 = equilibrate(problem2)
path = EquilibriumPath(system)
;{delete}
plot1 = path.plot()
plot1.x;("elementAmount(Cl units=mmol)")
plot1.y;("pH")
plot1.xlabel;("HCl [mmol]")
plot1.ylabel;("pH")
plot1.showlegend;(False)
plot2 = path.plot()
plot2.x("elementAmount(Cl units=mmol)")
plot2.y("elementMolality(Ca units=mmolal)", "Ca")
plot2.xlabel("HCl [mmol]")
plot2.ylabel("Concentration [mmolal]")
plot2.legend("right center")
plot3 = path.plot()
plot3.x("elementAmount(Cl units=mmol)")
plot3.y("speciesMolality(CO2(aq) units=mmolal)", "CO2(aq)")
plot3.y("speciesMolality(CO3-- units=mmolal)", "CO3--")
plot3.xlabel("HCl [mmol]")
plot3.ylabel("Concentration [mmolal]")
plot3.legend("right top")
plot4 = path.plot()
plot4.x("elementAmount(Cl units=mmol)")
plot4.y("speciesMass(Calcite units=g)", "Calcite")
plot4.xlabel("HCl [mmol]")
plot4.ylabel("Mass [g]")
output = path.output()
output.filename("result.txt")