Uranium (VI) speciation as a function of pH at fixed CO2 partial pressure
Uranium (VI) speciation as a function of pH at fixed CO2 partial pressure#
Written jointly by Svetlana Kyas (ETH Zurich) and Dan Miron (PSI) on April 4th, 2022
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This tutorial shows an example of the calculation of uranium speciation with changing pH values at fixed CO2 partial pressure. This example uses the thermodynamic database
psinagra-12-07, which is based on the Nagra/PSI Chemical Thermodynamic Data Base 01/01. The database supports the ongoing safety assessments for the planned low and intermediate-level (L/ILW) and high-level (HLW) radioactive waste repositories in Switzerland.
If your main interest is in calculating thermodynamic properties rather than modeling chemical equilibria and kinetics, you should check out ThermoFun, an excellent project dedicated to this task.
First, we set up the chemical system with the aqueous phase only. We are only interested in the U(VI) species distribution in the aqueous solution.
from reaktoro import * # Define the Thermofun database db = ThermoFunDatabase("psinagra-12-07") # Define the aqueous phase solution = AqueousPhase(speciate("C Cl H O P S U")) solution.set(chain( ActivityModelHKF(), ActivityModelDrummond("CO2") )) # Define chemical system by providing a database and an aqueous phase system = ChemicalSystem(db, solution)
The equilibrium specifications given below indicate that the equilibrium calculations are performed for fixed T, P, pH, and partial pressure of CO2. The corresponding equilibrium conditions and the equilibrium solver are initialized with the instance
specs. The conditions will be provided to the chemical solver later when we call it to calculate equilibrium.
A detailed explanation of
EquilibriumConditions as well as a variety of problems with different boundary conditions are presented in the tutorial Chemical equilibrium with constraints.
# Specify conditions needed to be satisfied at chemical equilibrium specs = EquilibriumSpecs(system) specs.temperature() specs.pressure() specs.pH() specs.fugacity("CO2(g)") # Define the value of conditions needed to be satisfied at the chemical equilibrium state conditions = EquilibriumConditions(specs) conditions.temperature(25.0, "celsius") conditions.pressure(1.0, "bar") conditions.fugacity("CO2(g)", 0.01, "bar") # Define the equilibrium solver solver = EquilibriumSolver(specs)
The initial chemical state is defined according to the following recipe:
1000 g of water and
1e-5 mol of UO₂(OH)₂.
# Define initial equilibrium state state = ChemicalState(system) state.set("H2O@" , 1e3, "g") state.set("UO2(OH)2@", 1e-5, "mol")
The amount of uranium can be calculated based on the chemical properties of this chemical state. We define the range of pH values and the list of uranium-containing species of interest in our evaluation. We also create the list
coeffs_u, which contains the number of uranium atoms in each species needed to correctly scale the amount of U in the species.
# Calculate the amount of uranium element props = ChemicalProps(state) bU = props.elementAmount("U") # Defined an auxiliary array of pH values import numpy as np pHs = np.linspace(3, 10, num=101) # Create list of species names, list of Species objects, and auxiliary amounts array species_list_str = "UO2+2 UO2OH+ UO2(OH)2@ UO2CO3@ (UO2)3CO3(OH)3+ (UO2)2CO3(OH)3- (UO2)2(OH)+3 " \ "UO2(CO3)3-4 UO2(CO3)2-2 (UO2)2(OH)2+2 (UO2)3(OH)5+ (UO2)4(OH)7+".split() percentages = np.zeros(len(species_list_str)) amounts = np.zeros(len(species_list_str)) # Collect the coefficients of U in the selected species coeffs_u =  for species_str in species_list_str: # Fetch species as well as the lists of elements and corresponding coefficients species = system.species().getWithName(species_str) symbols = species.elements().symbols() coeffs = species.elements().coefficients() # Loop over all the elements and select coefficients for uranium for [symbol, coeff] in zip(symbols, coeffs): if symbol == "U": coeffs_u.append(coeff) # Define dataframe to collect amount of the selected species import pandas as pd columns = ["pH"] \ + ["amount_" + name for name in species_list_str] \ + ["perc_" + name for name in species_list_str] df = pd.DataFrame(columns=columns)
Finally, we run simulations in the for loop on the pH values that we provide to the equilibrium conditions. There we previously set the temperature, pressure and the CO2 gas partial pressure.
for pH in pHs: # Set the value of pH for the current equilibrium calculations conditions.pH(pH) # Equilibrate the initial state with given conditions and component amounts res = solver.solve(state, conditions) # If the equilibrium calculations didn't succeed, continue to the next condition if not res.optima.succeeded: continue # Otherwise, calculate U(VI) speciation in mols and % for j in range(0, len(species_list_str)): amounts[j] = float(state.speciesAmount(species_list_str[j])) percentages[j] = float(coeffs_u[j] * amounts[j]) / bU * 100 # Update dataframe with obtained values df.loc[len(df)] = np.concatenate([[pH], amounts, percentages])
In the following, we plot the obtained values of U(VI) speciation in %.
from reaktplot import * fig1 = Figure() fig1.xaxisTitle('pH') fig1.yaxisTitle('U(VI) Speciation [%]') fig2 = Figure() fig2.xaxisTitle('pH') fig2.yaxisTitle('log(U(VI)) Speciation [mol]') for species in species_list_str: fig1.drawLine(df["pH"], df["perc_"+species], name=species) fig2.drawLine(df["pH"], df["amount_"+species], name=species) fig1.height(800) fig2.height(800) fig1.show() fig2.show()