Study of the Equilibrium of Nitric Acid with a Solution of TBP/IP6

2.1 Propose system

The purpose of this work is to study an LLE-IE system to establish a new PUREX variant. Variants refer to change in some of the original conditions which in this case is adding a new molecule to the system. Original PUREX consist in TBP with HNO3 in a hydrocarbon. The proposed system consists in TBP with IP6 in solution con dodecane.

The IP6 presents 6 phosphates, it is water soluble and lightly soluble in ethanol and has a boiling point of 150 °C. The respective constants for calculations have been obtained from the literature [6].

The full chemical reaction with the purpose LLE-IE system is as present in Figure 2 . It can be observed the interaction between the characteristic’s actinides of a spent nuclear fuel and the TBP-IP6. In this reaction, the radiolitic effects are not considered.

2.2 Effects of water on the activity of TBP/IP6 in the H2O-dodecane system

The study system comprises 30% of TBP and 10% of IP6 (TBP/IP6) in solution with water and n-dodecane.

Considering that the distribution of water in the H2O–TBP/IP6–dodecane system be described using the Equation [7] (1)

Where x_i, ai and φ_i are the molar fraction, activity, and volume fraction of the i component in solution respectively; indices 1, 2 and 3 refer to water, TBP/IP6 and dodecane respectively; in this work, by recommendation, we used n = 2.10; and the volume fractions of TBP/IP6 and dodecane were calculated neglecting water by:

Table 1 present the value of x₁calculated by Eq. (1). The following constants were used: K1 = 0.0795, K2 = 0.0029 and b₁ = 1.783 (used for dodecane too); V₂ = 273.8 cm³ [1], v₃ = 228.6 cm3 [1], n = 2.10 and k₂ = 0.1.

From Eq. (1) we can derive an equation for the molar coefficient of the activity of water.

The result of the Eq. (4) is a molar coefficient of a_w f₁ = 22.432452and lnf₁ = 3.11050866. To derive an equation for the molal coefficient of the activity of TBP, we used the cross-equation.

Where the derivatives with respect to the molar concentration m₂y m₁were calculated for constant m₁and m₂respectively. Differentiating (5), we obtain

The value m₂can be calculated from the mole fractions of TBP/IP6 and dodecane,

Where x₂₀and x₃₀are the mole fraction of TBP/IP6 and diluent in anhydrous solution; x₃₀ = 1-x₂₀; and M3 is the molecular mass of the solvent (170.33 g/mol). Then from (2), we obtain

From (9) we determinate the derivative δφ2/ δm2for (7),

Now, substituting the Eq. (10) in (7),

The right side of the Eq. (11) does not contain any value dependent on m₁. Then, integrating the Eq. (6), we obtain

Where f₂₀is the TBP-IP6 activity coefficient in a binary (considering tri-n-butylphosphate and inositol hexaphosphate as one) anhydrous solution, which can be set at 1 in the first approximation. Table 2 presents the results of the calculation by (12).

The deviations from the ideal values are moderate and increase with the activity of water and TBP/IP6 concentration.

2.3 Dissociation of nitric acid

Nitric acid is integral to the reprocessing of irradiated fuel and other LLE, the understandings its behavior is important. Nitric acid undergoes thermal and radiolytic degradation, the products of which include nitrous acid (HNO2) and nitrogen oxide species (NOX).

Eq. 13 shows the generic dissociation reaction of nitric acid.

The equation for calculating the degree of dissociation is as follows:

Where K is the equilibrium constant, AB is the reagent, A+ and B- ions (cation and anion respectively), C acid concentration and α dissociation degree. For alpha calculation purposes, we have an equilibrium constant of K = 2.598.

We will consider the dissociation of nitric acid using the polynomial Eq. (15), which has been adjusted from the data reported by [8]. In Eq. 15, the concentration of nitric acid [C] is in mol/dm3 and α the dissociation degree where α = 1 shows a complete dissociated acid and α = 1 a completely associated acid

The following calculation describes the concentration of associated and dissociated nitric acid.

Where [HNO_3total] is the sum of dissociated and associated nitric acid, [NO₃ ⁻] and [HNO₃] are respectively the associated and dissociated acid concentration.

It can be observed that after the 23 M the value increases again: due to the point of saturation of nitric acid and coexistence with non-associated species.

In nitric acid solutions, nitrogen oxide species, including HNO₂, NO₂ and NO, have been observed. The presence of these species in the absence of other reactants or radiation is attributed to the thermal decomposition of nitric acid. Non-dissociated nitric acid is thermally decomposed to produce NO₂• as shown in Eq. 18; notice that this reaction is non-elementary. This thermal decomposition of nitric acid in aqueous solution has been widely reported in the literature for different concentrations, high acidity and at high temperatures.

2.4 Calculations of the equilibrium

The calculation method used in this research work is as follow:

1. The nitric acid and water activities are calculated from the data of [8].

2. The calculation of equilibrium implies the formation of the non-hydrated HNO₃·TBP/IP6 monosolvate and the hydrated HNO₃·2TBP/IP6 disolvate and 2HNO₃·TBP/IP6 semisolvate of nitric acid, and the equilibrium between them obeys the mass action law.

where aa and a₂are the nitric acid and TBP/IP6 activities, x_ijand f_ijare the molar fraction and rational activity coefficient of a solvate consisting of i acid molecules and j complex molecules (TBP/IP6). The parameter f_ijis calculated within the nonstoichiometric hydration concept by the equation

where h_ijis the hydrate number of a solvate, and a₁is the water activity.

1. The molar fraction of free water (nonbonded with solvates) is calculated by the equation

Eq. (21) is very similar to Eq. (1). As in (1), x_i, a_i, and ϕ_iare the molar fraction, activity, and volumetric fraction of the ith component in a solution. The volumetric TBP/IP6 and n-dodecane fractions are calculated without allowance for water as (2) and (3).

4. Organic phase nonideality is considered using the activity solvate coefficients calculated as

5. The molar fraction x_iis determined as

where the sum Σc_jis calculated for the first time as

c_a, c₂, and c_dare the molar acid, TBP/IP6, and dodecane concentrations, respectively, and

where c_T is the total complex (TBP/IP6) concentration in a solution, i.e., the formation of the monosolvate alone was initially assumed.

6. To calculate the molar fraction of free complex x_2f, we write the equation

7. The value of x_2fcalculated by the Eq. (26) is used to determine the molar fractions x_ij. The molar concentrations c_ijare then estimated by the equations

where dis the density of a solution, and x_iand M_iare the molar fraction and mass of the ith component.

The values of c_jare used to correct the molar fractions in compliance with Eqs. (23) and (24).

The calculated acid molar concentration c_acis further found as (28) and the calculated complex molar concentration c_tcis estimated as (29)

Table 4 presents all the principal input parameters. The values presented in the table are the one who has been used to solve the equilibrium equations.

The concentration of the acid allowed to know the activity of water in the system, which have a value of 0.6 which represents a large amount of water to form the aqueous phase, since a water activity value equal to 1 would represent that we have the total disposition of water to hydrate.

Table 5 presents the results of the calculation in the equilibrium.