Description of partition equilibria for uranyl nitrate, nitric acid and water extracted by tributyl phosphate in dodecane

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Description of partition equilibria for uranyl nitrate, nitric acid and water extractedby tributyl phosphate in dodecane

S.P. Hlushak a,b, J.P. Simonin a,⁎, B. Caniffi c, P. Moisy c, C. Sorel c, O. Bernard a

a Laboratoire PECSA (UMR CNRS 7195), Université Pierre et Marie Curie, 4 Place Jussieu, 75252 Paris Cedex 05, Franceb Institute for Condensed Matter Physics, Svientsitskoho 1, 79011, Lviv, Ukrainec CEA, Nuclear Energy Division, RadioChemistry and Processes Department, 30207, Bagnols-sur-Cèze, France

a b s t r a c ta r t i c l e i n f o

Article history:Received 8 April 2011Received in revised form 31 May 2011Accepted 31 May 2011Available online 12 June 2011

Keywords:Tributyl phosphateUranyl nitrateExtractionPartitionModel

Experiments were carried out on the partitioning of uranyl nitrate in nitric acid solution extracted by 30 vol.%of tributyl phosphate (TBP) in dodecane at 25 °C. The model proposed by Naganawa and Tachimori (Bull.Chem. Soc. Jap. 70, 809, (1997)) for the case of aqueous solutions of nitric acid was used to additionallydescribe the extraction equilibria of uranyl nitrate. The treatment is based on the assumption ofthermodynamic ideality for the organic solution composed of the diluent, the free extractant and thecomplexes. The stoichiometries of the metal complexes were determined one by one by a suitable procedure.The formation of 6 different complexes involving uranyl nitrate was found capable of representing thepartition equilibria for the three extracted compounds: nitric acid, water and uranyl nitrate. This approachsuggests the formation of 2:1 and 3:1 complexes for TBP and uranyl nitrate, respectively.

© 2011 Elsevier B.V. All rights reserved.

1. Introduction

Nuclear reprocessing uses chemical procedures to separate theuseful components, e.g., the remaining uranium and the newly-createdplutonium, from the fission products and other radioactive waste in thespent fuel produced by nuclear reactors. Reprocessing serves multiplepurposes. Originally used solely to extract plutonium for producingnuclear weapons, it is mainly used nowadays for the reduction of thevolume and radiotoxicity of the waste, allowing separate management(destruction or storage) of nuclear waste components. Plutonium isworth being recovered because it can be recycled to produce a new fuel,like the so-called MOX (mixture of oxides) fuel for instance. Thereprocessed uranium, which constitutes about 95% of the mass of thespent fuel material, can be reused as a fuel, but it is extracted mainly todecrease the amount of waste (the former use is profitable only whenprices are high). The rest of thewaste, composed offission products andneutron capture products (minor actinides) (Nash et al., 2006), isextracted to decrease the radiotoxicity of the waste (Baron et al., 2007;Warin et al., 2009).

The extent of the benefits of reprocessing is determined by theefficiency of the separation process. Among the different actinideseparation methods, solvent extraction (Rydberg et al., 2004) hasseveral advantages at industrial scale, including the ability for

continuous operation, high throughput and solvent recycling (Nashet al., 2006). So, it constitutes the basis of the PUREX (Plutonium–

URanium EXtraction) process, which is the standard method for therecovery of uranium and plutonium.

The PUREX process can be roughly described as the extraction ofplutonium and uranium into an organic phase composed of 30% tributylphosphate (TBP) in odourless kerosene or dodecane from an aqueoussolution containing nitric acid, the fission products remaining inaqueous phase. After this first separation stage, further processingleads to the separation of the heavier plutonium from the uranium. Theprocess is based on the complexation of species by TBP.

A description of metal partitioning equilibria may have value for themodelling of extraction stages in the nuclear reprocessing industry.Such a model may be utilised for various purposes including real-timesafety analysis in a plant (in particular to prevent criticality accidents),the implementation of pilot extractors, and the good working of anindustrial process (for instance during its starting phase).

A number of models has been presented in the literature for thedescription of partitioning equilibria: for the extraction of acid andwater (Alcock et al., 1956; Blaylock and Tedder, 1989; Chaiko andVandegrift, 1988; Davis, 1962; Davis et al., 1970; Healy and McKay,1956; Naganawa and Tachimori, 1997a; Rozen et al., 1971; Schaekers,1986; Ziat et al., 2002), of acid and metal (uranyl nitrate) (Comor et al.,1989), and of metal in trace concentrations and water (Hesford andMcKay, 1958).

On the other hand, models describing the extraction of all species(metal, acid and water) are very scarce in the literature. To our bestknowledge, only Mokili and Poitrenaud proposed such a description

Hydrometallurgy 109 (2011) 97–105

⁎ Corresponding author. Tel.: +33 1 44273190; fax: +33 1 44273228.E-mail addresses: [email protected] (S.P. Hlushak), [email protected]

(J.P. Simonin).

0304-386X/$ – see front matter © 2011 Elsevier B.V. All rights reserved.doi:10.1016/j.hydromet.2011.05.014

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for the extraction of lanthanides by TBP (Mokili and Poitrenaud, 1996,1997). However, the latter treatment gives a prominent role to thewater on the deviations from ideality in organic phase.

In contrast, in the present study, all species in organic phase aretreated on an equal footing and the organic phase is globally regardedas ideal. Moreover this latter classic assumption is used on the molefraction scale, in which the diluent is included. This frameworkmay beexpected to be more suited to the description of this phase ascompared to previous studies developed on molality or concentrationscale for the solute species.

In the presentwork, the partitioning of uranyl nitrate, nitric acid andwater extracted by 30 vol.% TBP in dodecane has been studiedexperimentally. This TBP content is that used in the PUREX process.The experimental work was aimed at measuring the concentrations ofall species in organic phase, which was required for the subsequentdevelopment of the model. Indeed, previously published data on thissystem did not provide the amount of extracted water and/or densitydata that are needed in our present model on mole fraction scale. Aquantitative model capable of describing the partition equilibria of allcomponents has been developed. The approach is motivated by aprevious successfulwork byNaganawa and Tachimori formodelling theextraction of nitric acid andwater in awide range of TBP concentrations(Naganawa and Tachimori, 1997a). The latter treatment involved theformation of 8 different complexes in organic phase and was expressedin terms of thermodynamic partition constant that were indeedindependent of the TBP concentration. Thus, it was appealing toexamine whether this purely chemical approach could also describethe extraction of metal from acid aqueous phases.

2. Materials and methods

Theaqueous ternaryUO2(NO3)2/HNO3/H2Osolutionswerepreparedusing Prolabo Normapur hexahydrate uranium nitrate (UO2(NO3)2,6 H2O), Prolabo nitric acid and deionised water. The organic phaseswere made from dry dodecane (Prolabo, 99% purity, without furtherpurification, d=0.7452 kg dm−3) and purified pre-equilibrated tribu-tyl phosphate (TBP) (Prolabo, 99% purity, d=0.9721 kg dm−3, watercontent=0.854 mg g−1). The TBP was purified by shaking it togetherwith a 0.1 M NaOH solution, and then washing it twice with distilledwater (d=0.9760 kg dm−3, water content=66.6 mg g−1).

Aqueous and organic solutions were equilibrated by vigorouslyshaking equal volumes for 20 min at 25 °C. After centrifugation andseparation of the two phases, the densities, the concentrations ofuranyl nitrate and nitric acid in each phase, and the concentration ofwater in organic phase, were measured at 25 °C.

The densities of aqueous and organic phases were measured usingan Anton-Paar DMA 55 tuning-fork density transducer. The concen-trations of uranyl nitrate and nitric acid in the phases weredetermined by spectrophotometric measurement (using a HitachiU-3000 spectrophotometer) and acid–base titration, respectively. Theconcentration of water in organic phasewasmeasured by coulometricKarl Fischer titration with a Metrohm KF 737 titrator.

3. Model

3.1. Partition equilibrium

We consider the extraction of uranyl nitrate, nitric acid andwater byan organic phase composed of tributyl phosphate (TBP) diluted indodecane. At equilibrium the organic phase extracts all the speciescomposing the aqueous phase, viz. uranyl nitrate, nitric acid and water.Dodecaneand TBPare considered to be insoluble inwater (the solubilityof TBP is on the order of 10−3 mol dm−3 in 0–3 mol dm−3 HNO3

(Wright and Paviet-Hartmann, 2010)).

Extraction of the constituents of aqueous phase by TBP is supposedto lead to the formation of well defined complexes of the form

TBPð Þt• UO2 NO3ð Þ2� �

m• HNO3ð Þa• H2Oð Þh

where t, m, a and h are the stoichiometric numbers of TBP, uranylnitrate, nitric acid and water, respectively. To simplify the notationswe will denote a complex by TtUmAaWh, with T standing for TBP, U forthe metal salt (uranyl nitrate), A for nitric acid and W for water. Thisnotation also includes the case of free TBP (t=1, m=a=h=0) andof free water (t=m=a=0, h=1). We will use the letter D fordodecane. Nitric acid and uranyl nitrate will be assumed to be presentin organic phase only in the form of complexes with TBP.

As done before (Naganawa and Tachimori, 1997a), we admit thatfree water may be present in organic phase. Although the solubility ofwater in pure dodecane is low (ca. 2.5×10−3 mol dm−3 (Skurtveltand Olsson, 1992)) the amount of free water in the systems studiedhere is not negligible as compared to the amount of extracted water(see Table 3) when the ionic solute concentration is high.

The partition equilibrium may then be expressed as

m U + a A + h W + t T↔TtUmAaWh ð1Þ

in which T and the complex are in organic phase, and the other speciesare in aqueous phase.

The mass action law applied to the partition equilibrium (Eq. (1))gives

Kt;m;a;h ≡at;m;a;h

aTð Þt aU;aq� �m

aA;aq� �a

aW;aq

� �h ð2Þ

where Kt,m,a,h is the thermodynamic equilibrium constant for theformation of the TtUmAaWh complex, at,m,a,h and aT are the activitiesof the complex and of T, respectively, and aX,aq is the activity ofcomponent X in aqueous phase.

The activities of the ionic compounds A (= H++NO3−) and U

(= UO22++2 NO3

−) appearing in Eq. (8) are defined by

aA;aq ≡ aHþ aNO−3= γ2

Am2A ð3Þ

and

aU;aq ≡ aUO2+2

a2NO−3= 4γ3

Um3U ð4Þ

in which γA and γU represent the stoichiometric activity coefficients ofnitric acid and uranyl nitrate, respectively, and mA and mU are theirmolalities. The stoichiometric activity coefficients were computed asexplained in Section 4.

3.2. Thermodynamic description of organic phase

In this work we make the classic assumption that deviations fromideality in organic phase originate only from association phenomena.In the present case, nonideality is assumed to be due to the formationof complexes with TBP. Besides, the system of the chemical speciescomposing the organic phase (complexes+free TBP+free water+dodecane) is regarded as ideal. This approximation was proposeda long time ago for the description of associating nonelectrolytesolutions. The latter were called physically ideal by Dolezalek (1908)(Prausnitz et al., 1999) and semi-ideal by Scatchard (1921).

Then, we may write that the activity of every component oforganic phase is equal to its true mole fraction (Prausnitz et al., 1999),which reads

aY = ζY ð5Þ

98 S.P. Hlushak et al. / Hydrometallurgy 109 (2011) 97–105


in which Y is a complex, free TBP, or free water. This assumptiondiffers from a previous study in which ideality was expressed onconcentration scale (aY=CY) (Naganawa and Tachimori, 1997a).Although the two ways (ζ-scale and C-scale) are equivalent at highdilution, they are expected to give different results at high loading(low mole fraction of diluent).

The true mole fraction of a species X is defined as

ζX =CX

∑t;m;a;h Ct;m;a;h + CDð6Þ

where Ct,m, a,h is the concentration of the TtUmAaWh complex. Let usrecall that the sum appearing in the denominator also includes thefree TBP and the free water: C1, 0, 0, 0=CT, free and C0, 0, 0, 1=CW, free.Moreover CD represents the concentration of dodecane.

The true mole fractions naturally satisfy the normalisationcondition

ζD + ∑t;m;a;h

ζt;m;a;h = 1; ð7Þ

in which ζt,m, a,h designates complex true mole fraction.

3.3. Basic relations

From Eqs. (2) and (5) we therefore obtain the basic relation

ζt;m;a;h = Kt;m;a;h ζTð Þt aU;aq� �m

aA;aq� �a

aW;aq

� �h: ð8Þ

The normalisation condition, Eq. (7), together with Eq. (8), yields afirst equation for ζT and ζD, namely

ζD + ∑t;m;a;h

Kt;m;a;h ζTð Þt aU;aq� �m

aA;aq� �a

aW;aq

� �h= 1: ð9Þ

In this equation, the sum includes the cases {t,m,a,h}={1,0,0,0} forfree TBP (forwhichK1,0,0, 0=1)and {t,m,a,h}={0,0,0,1} for freewater.

Another useful quantity is the stoichiometric mole fraction of acomponent Y (= T, U, A or W), which is given by

xY =CtotY

CtotT + Ctot

U + CtotA + Ctot

W + CD; ð10Þ

with CYtot the total concentration of Y, obtained by summing the

concentrations of the various complexes in which the species appears.So, in the case of T one has

CtotT = ∑

tt Ct;m;a;h; ð11Þ

and similar relations for U, A and W. The diluent (dodecane) isregarded as an inert compound. For a given content of TBP indodecane, the ratio CT

tot/CD is a constant. Its value in the present workis of the order of 0.357 which corresponds to a 30 vol.% solution.

A second equation for ζT and ζD was obtained as follows.The total concentrations of U, A and W were determined

experimentally (see Section 2). Then, the total concentration of TBP,CTtot, was deduced from this data and from the measured molality of

TBP used in the experiment, together with the measured density oforganic phase, dorg, which satisfies the relation

dorg = MUCtotU + MAC

totA + MWCtot

W + MTCtotT + MDCD: ð12Þ

The total concentration of TBP was found to be comprised between1.03 and 1.10 mol dm−3 for the data of Table 2.

The stoichiometric mole fraction of T can therefore be calculatedfrom Eq. (10). Now, the use of Eqs. (6), (10) and (11), leads to

xY =ZY

ZT + ZU + ZA + ZW + ζDð13Þ

for Y=T, U, A or W, and in which the Z's are defined by

ZT = ∑t;m;a;h

t ζt;m;a;h; ZU = ∑t;m;a;h

m ζt;m;a;h;

ZA = ∑t;m;a;h

a ζt;m;a;h; ZW = ∑t;m;a;h

h ζt;m;a;hð14Þ

Eq. (13) applied to Y=T gives a relation between the twounknowns, ζD and ζT, because ζt,m, a,h can be expressed as a function ofζT [Eq. (8)]. The expression of ζD that can be deduced from thisequation can then be inserted into Eq. (9) to yield an equationsatisfied by ζT only.

The resulting equation was solved numerically for ζT by using theclassic Brent method, for given values of the set of equilibriumconstants, Kt,m, a,h. The activities of the components in aqueous phase,aX, aq, were calculated as explained in the next section.

Once the value of ζT is known, the true mole fractions of thecomplexes, ζt,m, a,h, are known by virtue of Eq. (8). Then, the values ofthe stoichiometric mole fraction of U, A andWmay be calculated fromEqs. (13) and (14) (with ζD calculated previously).

The reaction equilibrium constants Kt,m, a,h are adjustable modelparameters. Their values were determined so as to optimallyreproduce the experimental values of xU, xA and xW. The fittingprocedure consisted of solving Eqs. (9) and (13) for every given testedset of Kt,m, a, h values, and checking the quality of fit of thestoichiometric mole fractions [Eqs. (10) and (11)] of the extractedcompounds, U, A and W. In the algorithm, the sum of the relativedeviations of the calculated mole fractions from their experimentalcounterparts was minimised. In the case of uranyl extraction, theweight for the deviation of xU in the fit was taken to be twice that forxA and xW.

The present model relies on the assumption of a finite number ofcomplexes formed in organic phase. However, besides the generallyadmitted T2U species (whose existence is suggested by slope analysis inpartition experiments), none of these complexes has been revealedexperimentally. In the absence of this information, it was chosen todetermine the minimum set of complexes leading to a satisfyingrepresentation of experimental data. For this purpose, an optimisationapproachwas developed in which the stoichiometries of the complexeswere found one by one, by successive approaches. At each step of theprocedure, the stoichiometry of thenext likely complexwasdeterminedby a fit of experimental data using a differential evolution globaloptimisation algorithm (Price et al., 2005; Storn and Price, 1997). Thenthe newly found complex was added to the set and the equilibriumconstants for all complexes were adjusted again. The procedure wasrepeated until a satisfying description of experimental data wasobtained.

The global optimisation procedure employed here is a type of metaheuristic algorithm called differential evolution (Price et al., 2005;Storn and Price, 1997). It is capable of finding global minima of theobjective function. While the algorithm chosen is less numericallyefficient than the classic Marquardt algorithm, it is easier toimplement because it does not require the derivatives of the objectivefunction. Moreover it is more reliable because it cannot be trapped inlocal minima of the objective function.

Using the above described procedure, we identified a set of probablecomplexes, which appeared to fit well the experimental data.

3.4. Deviations from ideality in aqueous phase

Let us underline first that the quantities γA and γU appearing inEqs. (3) and (4) denote activity coefficients for the unhydrated species

99S.P. Hlushak et al. / Hydrometallurgy 109 (2011) 97–105


A and U (Simonin et al., 2006). These quantities are thereforenaturally suited to use in Eq. (2).

In this work we employed the extended Pitzer model (Pitzer, 1973;Pitzer and Kim, 1974) in the version given by Goldberg et al. (1988) torepresent the thermodynamic properties of the aqueous phase. It wasrefitted to describe simultaneously experimental osmotic coefficientdata for pure nitric acid (Hamer and Wu, 1972), for pure uranyl nitrate(Goldberg, 1979), and for the ternary mixture of these compounds(Ruas et al., 2006).

The formulation of the extended Pitzer model is based on theassumption that the contribution of the three-ion interaction terms toexcess Gibbs energy could be approximated by a polynomial in ionicstrength. Thus, the excess Gibbs energy of solution reads (Goldberget al., 1988)

Gex= RT = nWf Ið Þ + 2nW ∑

c∑amcma Bca Ið Þ + E ∑

NQ

n=1Q nð Þ

ca In−1

" #ð15Þ

where subscripts a and c denote anion and cation, respectively,∑c and∑a denote sum over all cations and anions in the mixture, nW is themass of water in the mixture,mi and zi are molality and charge of ion i,

I =12∑i miz2i is ionic strength of the mixture, E =

12∑i mi jzi j , and

NQ is thenumber ofQca(n) coefficients in the sum. The function f is givenby

(Pitzer and Mayorga, 1973)

f Ið Þ = −Aϕ4I1:2

ln 1 + 1:2 I1=2� �

where Aϕ is the Debye–Hückel constant, Aϕ=0.392 at 25°.The quantities

Bca = β 0ð Þca + 2

β 1ð Þca

α2I1− 1 + αI1=2� �

e−αI1 = 2� �

;

are responsible for the two-ion interactions contribution to excessGibbs energy, whileQca

(n) denote the coefficients of the polynomial thatapproximates the three-ion interactions contribution.

The osmotic and activity coefficients of the electrolyte mixture areobtained by differentiating the excess Gibbs energy,

ϕ−1 = − 1∑i mi

∂Gex= RT

∂nW; ð16Þ

lnγi =∂Gex

= RT∂ni

; ð17Þ

where ni denotes the number of moles of ion i in the mixture. Aftersome calculations, one gets from Eqs. (15) and (16) (withmi=ni/nW),

ϕ−1ð Þ∑imi = 2If ϕ + 2∑

c∑amcma Bϕ

ca + E∑NQ

n=1n + 1ð ÞQ nð Þ

ca In−1

" #;

ð18Þ

lnγCX =��zCzX��f γ +

2νC

ν∑ama BCa + E∑

NQ

n=1Q nð ÞCa I

n−1

" #

+2νX

ν∑cmc BcX + E∑

NQ

n=1Q nð ÞcX In−1

" #

+ ∑a∑cmamc

" ��zCzX��B′ca +νXzX + νCzC

ν∑NQ

n=1Q nð Þca In−1

+��zCzX��E∑

NQ

n=1n−1ð ÞQ nð Þ

ca In−2

#; ð19Þ

where C and X denote cation and anion, respectively, lnγCX=(νClnγC+νXlnγX)/ν is the activity coefficient of theneutral salt CνC

XνX,νC andνX are

the stoichiometric numbers of ions C and X in the salt, and ν≡νC+νX.The other introduced above quantities are as follows.

f ϕ =12Id f = Ið Þ

dI=

−AϕI1=2

1 + 1:2I1=2� � ; ð20Þ

BϕCX = β 0ð Þ

CX + β 1ð ÞCX e

−αI1 = 2

; ð21Þ

f γ = −AϕI1=2

1 + 1:2I1=2+

21:2

ln 1 + 1:2I1=2� �" #

; ð22Þ

BCX = β 0ð ÞCX + 2

β 1ð ÞCX

α2I1− 1 + αI1=2� �

e−αI1 = 2� �

; ð23Þ

B′CX = 2β 1ð ÞCX

α2I2−1 + 1 + αI1=2 +

α2I2

!e−αI1 = 2

" #; ð24Þ

with α=2 (Pitzer, 1973).The activity of water is obtained from the osmotic coefficient using

the relation

aW ;aq = exp − νAmA + νUmUð ÞMWϕ½ �; ð25Þ

with MW the molar mass of water, and νA=2 and νU=3 the totalstoichiometric numbers of HNO3 and UO2 NO3ð )2, respectively.

4. Results and discussions

4.1. Activities in aqueous phase

The activities of species in aqueous phases were computedaccording to Section 3.4. The molalities were obtained by conversionof the experimental molarities of solutions by using fits of density dataand a formula for the density of mixtures, given in the compilations ofSöhnel and Novotny (Novotny and Söhnel, 1988; Söhnel and Novotny,1985).

The result for the activity of water can be visualised in Fig. 1 wherethe osmotic coefficients of the aqueous solutions of nitric acid anduranyl nitrate are plotted, and in Table 1, in which the numericalvalues of the osmotic coefficients for the mixture of uranyl nitrate andnitric acid in water are compared. Since excellent fits were obtainedfor NQ=1, it was not sought to further improve the quality of fit byincreasing the value of NQ. The following parameter values wereobtained (for NQ=1): βA

(0)=0.1083, βA(1)=0.4165, βU

(0)=0.5104,βU(1)=1.0677, QH+,NO3

−(1) =−2.014×10− 3, QUO2

2+,NO3−

(1) =−1.6552×10−2. The fit was performed in the concentration range 0–4 mol kg−1

for uranyl nitrate and0–10 mol kg−1 for nitric acid. The average absoluterelative deviations (AARD) of fit are: AARDϕ=0.52% for pure uranylnitrate solution, AARDϕ=0.30% for pure nitric acid solution andAARDϕ=0.97% for their mixture. The AARD of a quantity X is defined as

AARDX %ð Þ = 1001N

∑N

n=1

��Xcaln −Xexp

n

Xexpn

�� ð26Þ

with N the number of points.This adjustment of parameters in the Pitzer model was then used

to estimate the activities of ionic solutes in aqueous phase, for U and A.



4.2. Partitioning in the absence of metal

The first part of the modelling work was devoted to the case ofaqueous solutions of pure nitric acid. We used the data given ingraphical form in the work of Naganawa and Tachimori (1997a) andwe refitted them with our model. The concentration of the dodecanewas obtained from the concentrations of the other components.

Following previous work (Naganawa and Tachimori, 1997a),8 complexes were assumed to form in organic phase besides freewater (the species AW10 was not included): AW, TW, T2W2, T3W6, TA,TAW, T2AW, T3AW4. The structure of some of these complexes has beendiscussed in the literature (Osseo-Asare, 1991). The values of thecorresponding equilibrium constants that were obtained from the fitare: K0, 0, 1, 1=1.076×10− 6, K1, 0, 0, 1=0.1093, K2, 0, 0, 2=1.0442,K3, 0, 0 , 6= 0.5064, K1, 0, 1 , 0= 0.1663, K1, 0, 1 , 1= 2.338 × 10− 2,K2, 0, 1,1=2.287,K3,0,1,4=4.047andK0, 0, 0,1=6.421×10−4, respective-

ly. Thevalues of the constants found fromafit on concentration scale areK1,0, 0, 1(C)

=0.1124, K2,0,0,2(C)

=0.2109, K3,0, 0, 6(C)

=4.038×10−2, K0,0,1,1(C)

=4.669×10−6, K1, 0, 1, 0

(C)=0.1672, K1, 0, 1, 1

(C) =2.398×10− 2, K2, 0, 1, 1(C) =

0.4769, K3, 0, 1, 4(C) =0.3037, and K0, 0, 0, 1

(C) =2.816×10−3. These lattervalues are very close to those reported by Naganawa and Tachimori(1997a) as expected. One notices that the value of the constant for theformation of AW is very low (K0,0,1,1=1.076×10−6), in agreementwith the value given by Naganawa and Tachimori (1997b). This speciescould therefore be overlooked in further studies, thus leaving onlycomplexes with TBP for consideration in organic phase.

Among the complexes proposed by Naganawa and Tachimori(1997a) some contain two or three TBP molecules and several watermolecules. Alternatively, they might be regarded as TBP aggregates ormicelles, consisting of aqueous polar core with a few TBP moleculesforming the outer shell. These structures are in agreement with theresults of neutron and X-ray scattering experiments (Nave et al.,2004) which suggested the existence of aggregates with a number ofTBP molecules per aggregate ranging between 2 and 5, depending onTBP concentration.

The results for the extracted amounts of nitric acid and water as afunction of TBP and aqueous nitric acid concentrations are shown inFigs. 2–5. Very good fits are obtained with the model, as observed inearlier work (Naganawa and Tachimori, 1997a).

4.3. Partitioning in the presence of metal

The values of the organic phase densities are given in Table 2. Theywere used to calculate the concentration of dodecane in organic phase(see the comments before Eq. (12)) and the true mole fractions of theconstituents.

The densities were empirically fitted by a linear function of thesolute concentrations, which gave

dorg = 0:7452 + 0:26915CU−1:1785 × 10−2CA + 4:467 × 10−3CW

+ 8:7868 × 10−2CT ð27Þ

with dorg given in kg dm−3. In this relation, the coefficient of CA is ofnegative sign. This peculiarity is due to the fact that Eq. (28) is a purelyempirical correlation devoid of physical meaning (one cannotintroduce A into the organic phase without also introducing W). The

Fig. 1. Osmotic coefficients of aqueous solutions of pure uranyl nitrate and of pure nitricacid as a function of ionic strength (in mol kg−1). Uranyl nitrate: (●)=experimental;(—)=result of fit. Nitric acid: (△)=experimental; (–)=result of fit.

Table 1Experimental and calculated osmotic coefficients for ternary aqueous mixtures of nitricacid and uranyl nitrate at 25 °C. Molalities are given in mol kg−1, RMSD designates rootmean square deviation.

mU mA ϕexp ϕcal mU mA ϕexp ϕcal

1.381 7.056 1.498 1.482 2.409 3.032 1.580 1.5951.392 8.045 1.478 1.468 2.438 2.005 1.617 1.6211.422 7.083 1.508 1.482 2.518 0.033 1.671 1.6671.436 6.997 1.509 1.484 2.556 1.052 1.687 1.6551.438 8.027 1.485 1.467 2.673 1.059 1.664 1.6701.515 7.905 1.457 1.468 2.707 0.543 1.710 1.6891.590 5.916 1.513 1.500 2.739 1.071 1.657 1.6771.621 5.812 1.497 1.503 2.755 0.032 1.716 1.7101.840 5.008 1.512 1.523 2.756 0.545 1.714 1.6951.894 0.461 1.546 1.521 2.788 1.097 1.662 1.6821.917 5.041 1.494 1.527 2.808 0.077 1.734 1.7171.972 0.028 1.533 1.534 2.841 0.028 1.733 1.7242.024 5.015 1.512 1.531 2.846 0.576 1.717 1.7062.027 4.015 1.506 1.549 2.894 0.028 1.743 1.7312.105 5.006 1.523 1.533 2.920 0.563 1.714 1.7152.114 4.031 1.515 1.555 2.943 0.061 1.735 1.7372.203 0.981 1.618 1.596 2.995 0.032 1.748 1.7452.217 3.026 1.571 1.580 3.019 0.061 1.764 1.7462.222 4.009 1.520 1.561 3.071 0.028 1.755 1.7542.310 3.034 1.566 1.588 3.077 0.078 1.757 1.7522.404 0.073 1.646 1.643 3.131 0.059 1.757 1.7592.407 0.512 1.673 1.639RMSDϕ=0.019a

a RMSD=root mean square deviation.

Fig. 2. Concentration of extracted nitric acid as a function of organic TBP concentration fordifferent nitric acid concentrations in (metal-free) aqueous phase. Line a) CA,aq=0.03 mol dm−3, b) 0.05 mol dm−3, c) 0.07 mol dm−3, d) 0.1 mol dm−3, e) 0.5 mol dm−3,f) 1 mol dm−3, g) 1.5 mol dm−3, e) 2 mol dm−3, f) 2.5 mol dm−3, h) 3 mol dm−3.(●)=experimental data; (—)=results from the model.



average absolute relative deviation of fit was AARDd=0.37%. This fit isslightly more accurate than the fit of Kumar and Koganti (1998)(AARDd=0.53% for the same data set) which does not take intoaccount the dependence of the density on water concentration.

Next, we started to determine the stoichiometries of complexesinvolving uranyl nitrate, as described in Section 3. The values of thepartition constants found in Section 2 for the metal-free complexeswere kept unchanged. In the search for an additional complex, theequilibrium constants values of the previously found complexes wereoptimised again together with the stoichiometric numbers and theequilibrium constant of the new complex. Thus, in the search of thelast complex, T3U, the optimisation procedure consisted of finding sixequilibrium constants and four stoichiometric numbers. The latterwere allowed to take only integer values smaller than six. Evolution-ary optimisation was performed by means of differential evolutionalgorithm (Price et al., 2005; Storn and Price, 1997) with population

number of 100 vectors (10 for every dimension) for a few thousandsof iterations.

Six additional complexes with uranyl nitrate were thus identifiedstep by step, in the following order T2U, T2UW, T2UA, T3UA, T3UW andT3U,with the values for the equilibriumconstants:K2,1, 0, 0=8.636×104,K2, 1, 0, 1=9.135×103, K2, 1, 1, 0=2.004×102, K3, 1, 1, 0=6.306×105,K3,1, 0, 1=2.789×106 and K3,1,0, 0=6.679×106, respectively. Conver-sion of these values to concentration scale (using the formulaK Cð Þt;m;a;h = Kt;m;a;hC1−t

D;0 with CD, 0=4.375 mol dm−3 the concentrationof dodecane in pure dodecane) are K2, 1, 0,0

(C) =1.974×104, K2,1,0,1(C) =

2.088×103,K2,1, 1, 0(C) =45.81,K3,1,1,0

(C) =3.295×104,K3,1,0,1(C) =1.457×105

and K3,1,0, 0(C) =3.489×105.

Therefore, our results suggest the formation of the complexes TnU,TnUA and TnUW with n=2,3.

It may be pointed out that coordination chemistry, which issometimes used to interpret the formation of the (hypothetical) T2Ucomplex, does not preclude the possibility of formation of T3U. This

Fig. 3. Concentration of extracted nitric acid as a function of nitric acid concentration in(metal-free) aqueousphase for different TBP concentrations. Line a)CT,org=0.005mol dm−3,b) 0.01 mol dm−3, c) 0.03 mol dm−3, d) 0.3 mol dm−3, e) 0.5 mol dm−3, f) 0.7 mol dm−3,g) 0.9 mol dm−3, e) 1 mol dm−3, f) 1.3 mol dm−3, h) 1.5 mol dm−3, i) 1.7 mol dm−3,j) 1.9 mol dm−3, k) 2 mol dm−3, (●)=experimental data; (—)=results from the model.

Fig. 4. Concentration of extracted water in organic phase as a function of nitric acidconcentration in (metal-free) aqueous phase for different TBP concentrations. (●)=experimental data; (—)=results from themodel. Lines a), b),… have the samemeaning asin Fig. 3.

Fig. 5. Concentration of dodecane in organic phase as a function of nitric acidconcentration in (metal-free) aqueous phase for different TBP concentrations. (●)=experimental data; (—)=results from themodel. Lines a), b),… have the samemeaningas in Fig. 3.

Table 2Experimental and calculated densities of organic phases for different compositions at25 °C. Densities are given in kg m−3, concentrations are in mol dm−3.

CUtot CA

tot CWtot CT

tot dorgexp dorg

cal

0.126 0.220 0.251 1.098 886.40 878.900.178 0.390 0.217 1.056 878.67 886.910.187 0.360 0.199 1.071 891.59 891.050.250 0.250 0.128 1.084 917.95 910.230.267 0.183 0.158 1.065 907.09 914.100.323 0.131 0.096 1.068 927.31 929.780.350 0.160 0.073 1.064 936.07 936.200.365 0.150 0.078 1.066 942.42 940.500.398 0.120 0.066 1.057 947.09 948.860.444 0.100 0.053 1.046 955.14 960.560.447 0.080 0.045 1.052 959.42 961.910.482 0.182 0.044 1.031 969.72 968.430.491 0.148 0.038 1.029 969.88 970.960.489 0.122 0.029 1.034 970.70 971.160.494 0.210 0.055 1.036 980.00 971.660.495 0.141 0.046 1.030 971.44 972.290.498 0.162 0.039 1.026 971.13 972.420.500 0.129 0.029 1.027 970.39 973.400.502 0.136 0.040 1.035 977.70 974.550.501 0.148 0.048 1.036 978.67 974.29

RMSDd=4.4a




may be justified as follows. The coordination number of the uranyl isgenerally comprised between 4 and 6 (the more likely being 5, then 6and lastly 4) (Burns, 2005). Besides, the TBP is monodentate but thenitrate ion is a versatile ligand: it may be bidentate or monodentate(Addison et al., 1971). Then, a T3U complex may be formed in whichthe uranyl has a coordination number of 5 with two monodentatenitrates, or it has a coordination number of 6 with one nitrate beingmonodentate and the other one being bidentate. The structure of theTnUW and TnUA complexes may be interpreted along these lines,together with the additional possible role of hydrogen bonding or ionpairing.

It is observed that the formation constants for complexescontaining U have large values. Comparison may be made with the

metal-free case if one looks at the value for the formation of T2UW,which is of the order of 104, as compared to that for the formation ofT2W2 or T2AW which are of the order of unity. The high constants foruranyl complexes are indicative of strong metal-extractant binding.

The experimental results for the equilibrium concentrations of thespecies are presented in Tables 3 and 4 together with the valuescomputed from the model, and in Figs. 6–8. In the tables are alsoreported the values of the root mean square deviations (RMSD)between calculated and experimental values for this quantity.

The RMSD on a quantity Q is calculated according to

RMSDQ =

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi∑N

i=1Qcali −Qexp

i

� �2=N

s

with N the number of values.

Table 3Experimental and calculated (adjusted) total concentrations (in mol dm−3) of speciesU, A andW in organic phase for different concentrations of uranyl nitrate and nitric acidin aqueous phase at 25 °C.

CU, aq CA, aq CU, org CA, org CW, org

exp cal exp cal exp cal

0.103 1.790 0.316 0.358 0.110 0.067 0.133 0.0870.285 1.800 0.420 0.433 0.060 0.036 0.078 0.0650.210 1.890 0.433 0.400 0.080 0.047 0.095 0.0680.0426 1.921 0.267 0.261 0.183 0.143 0.158 0.1320.0202 1.940 0.126 0.138 0.220 0.273 0.251 0.2610.189 1.950 0.398 0.396 0.100 0.054 0.106 0.0700.0952 2.019 0.323 0.351 0.131 0.088 0.096 0.0860.322 2.830 0.447 0.447 0.080 0.078 0.045 0.0510.039 2.890 0.250 0.244 0.250 0.293 0.128 0.1360.203 2.890 0.444 0.407 0.100 0.107 0.053 0.0560.129 2.900 0.398 0.374 0.120 0.141 0.066 0.0640.0820 2.920 0.350 0.335 0.160 0.185 0.073 0.0780.102 2.960 0.365 0.355 0.150 0.167 0.078 0.0700.846 2.997 0.489 0.492 0.122 0.044 0.029 0.0390.840 3.976 0.500 0.487 0.129 0.079 0.029 0.0330.391 4.029 0.491 0.446 0.148 0.117 0.038 0.0360.839 4.989 0.502 0.489 0.136 0.127 0.040 0.0270.399 5.002 0.498 0.443 0.162 0.160 0.039 0.0290.384 5.985 0.482 0.440 0.182 0.212 0.044 0.0230.825 5.990 0.501 0.487 0.148 0.183 0.048 0.022RMSDC

a= 0.026 0.036 0.018


Table 4Experimental and calculated concentrations (in mol dm−3) of total TBP and dodecanein organic phase for different concentrations of uranyl nitrate and nitric acid in aqueousphase at 25 °C.

CU, aq CA, aq CT, org CD, org

exp cal exp cal

0.583 1.650 1.030 1.030 2.951 2.9630.103 1.790 1.076 1.063 2.985 2.9900.285 1.800 1.054 1.049 2.958 2.9650.210 1.890 1.037 1.025 2.957 3.0090.043 1.921 1.065 1.054 2.998 3.0340.020 1.940 1.098 1.107 3.044 3.0010.189 1.950 1.048 1.035 2.960 2.9990.095 2.019 1.068 1.063 2.981 2.9870.322 2.830 1.052 1.053 2.934 2.9330.039 2.890 1.084 1.091 2.964 2.9420.203 2.890 1.046 1.045 2.933 2.9580.129 2.900 1.057 1.058 2.946 2.9530.082 2.920 1.064 1.068 2.955 2.9520.102 2.960 1.066 1.065 2.947 2.9470.846 3.000 1.034 1.026 2.905 2.9440.840 3.980 1.027 1.021 2.902 2.9390.391 4.030 1.029 1.023 2.897 2.9500.839 4.990 1.035 1.031 2.888 2.9070.399 5.000 1.026 1.020 2.889 2.9370.384 5.980 1.031 1.028 2.886 2.9090.825 5.990 1.036 1.034 2.882 2.881RMSDC

a= 0.0069 0.029


Fig. 6. Concentration of uranyl nitrate in organic phase (30 vol.% of TBP), as a function ofthe concentrations of nitric acid and uranyl nitrate in aqueous phase. (●)=exper-imental results, (△)=corresponding results from the model. The mesh was calculatedassuming constant stoichiometric mole fraction of TBP in organic phase.

Fig. 7. Concentration of nitric acid in organic phase of (30 vol.% of TBP), depending onaqueous concentration of nitric acid and uranyl nitrate. (●)=experimental results,(△)=corresponding results from the model. The mesh was calculated assumingconstant stoichiometric mole fraction of TBP in organic phase.



The experimental uncertainties on themeasured values of the totalconcentrations of U, A and W were estimated from the standarddeviation on three different measurements. The resulting uncertaintyranges from ca. 10% for the lower U contents to 1% for the higher. It isof the order of 1% for A and W concentrations.

The values of the statistical correlation coefficients between theexperimental and calculated total concentrations of U, A and W inorganic phase are R2=0.958, 0.793 and 0.942, respectively. Thecorresponding values of the slopes kX in the fit, CX, orgcal =kXCX, org

exp withX=U, A or W, are 0.992, 1.031 and 0.983, respectively. Therefore, theaccuracy of the description decreases in the order U, W and A. Therepresentations of the contents of U and W are very good, especiallyfor the highest values of these contents. The representation of the acidcontent is fair. The result for the description of the acid concentrationcould be improved by introducing further complexes containing thisspecies. However, we did not try to do so because we gave greaterimportance to the description of the uranyl content.

The average deviations of the calculated concentrations ofdodecane and TBP from the experimental values are very small, ofthe order of 1%.

The results show rapidly increasing extraction of uranyl nitratewith the concentration of the latter in aqueous phase. This seems toresult predominantly from the formation of the T2U complex, and isparticularly visible at high aqueous uranyl nitrate concentrationswhere the concentration of extracted uranyl is independent of nitricacid activity and approaches 0.5 mol dm−3, which is twice smallerthan the concentration of TBP. Sharp increase of uranyl nitrateextraction is accompanied by strong back extraction of nitric acid andwater to the aqueous phase. The latter phenomenonmay be explainedby a competition between uranyl nitrate, nitric acid and water for TBPmolecules. As more uranyl nitrate is added to the aqueous phase, theweak complexes in the organic phase, composed of TBP with nitricacid and water, are superseded by stronger ones with uranyl nitrate.The nitric acid and the water produced by dissociation of weakcomplexes are then extracted back to the aqueous phase. Nonetheless,some amounts of water and nitric acid remain in the organic phasethrough complexes of the form TnUW and TnUA, with n=2,3.

The speciation, i.e. the concentrations of the complexes and of freeTBP in organic phase, is presented in Fig. 9 for an aqueous nitric acidconcentration of 3 mol dm−3. At sufficiently high metal loading(above ca. 0.1 mol dm−3 uranyl nitrate in aqueous phase) the more

abundant complex is T2U. On the other hand, at low uranyl nitrateconcentrations where there is more free TBP, the results from themodel indicate higher concentrations of T3U and T3UA complexes.When the concentration of uranyl nitrate in water is increased theamounts of free TBP and of these latter complexes decrease. Thus, thecomplexes with three TBP molecules are mainly responsible for theinitial slope of the concentrations of the extracted species, while thosewith two TBP molecules govern the extraction at high concentrationsof uranyl nitrate.

5. Conclusions

A simple thermodynamic model for the extraction of uranylnitrate, nitric acid and water into the organic phase composed of TBPin dodecane is described. It is applied to represent experimentalpartitioning data for an organic phase composed of 30 vol.% TBP indodecane. It shows good quantitative agreement with experiment forthe extraction of uranyl nitrate and water, and fair agreement for theextraction of nitric acid. The model should be applicable for variousTBP concentrations. This will be examined in future work.

A number of complexes have been proposed that involve two andthree TBP molecules per uranyl nitrate molecule. The complexes withthree TBPs are important only at low uranyl nitrate concentrations.Some of the uranyl complexes include nitric acid and water moleculesand are the main complexes responsible for the extraction of thesespecies to the organic phase at high uranyl nitrate concentrations.

Acknowledgements

This work and the stay of one of us (SH) were supported by“Agence Nationale de la Recherche” (ANR) through grant ANR-07-BLAN-0295 CSD 3. SH acknowledges hospitality fromUniversité Pierre& Marie Curie in Paris.

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Description of partition equilibria for uranyl nitrate, nitric acid and water extracted by tributyl phosphate in dodecane

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