Fluid Phase Equilibria, 81 W#2) l-15 Elsevier Science Publishers B.V., Amsterdam

The Predictive Capability of the UNIFAC Equation for the 6alculation of

Liquid-liquid Equilibria with Chemical Reactions in Tributyl Phosphate

Extraction Systems for Nitric Acid and Uranyl Nitrate

JIAN CHEN, ZONGCHENG LI, JIUFANG LU and YIGUI LI

Department of Chemical Engineering, Tsinghua Universjty, Beijing, RMO84,

(China)

Keywords: theory, application, group contribution, liquid-liquid equilibria,

tributyl phosphate, nitric acid, uranyl nitrate

(Received May 5,1SS2; accepted in final form August 4,19S2)

ABSTRACT

Liquid-liquid equilibria with chemical reactions in the extraction systems

of HzO-diluent-HNO+TBP, H3O-diluent-U01(NOs)3-TBP and DO-diluent-HNOs-

UOz(NO3)3-TBP are correlated and predicted using the UNIFAC equation to the

organic phase and the Piteer equation to the aqueous phase. Considering the

proximity of groups in TBP, HN03 * TBP and U@(N03)2 * 2TBP molecules, a group

assignment method for these molecules is proposed in this paper. By using this

assignment the WNIFAC group interaction parameters and ther~ynami~ constants

of chemical reactions regressed from the extraction systems with n-heptane as

diluent can be used to predict accurately LLE data of the systems with

Amsco125-82 or nCi3Ii38 as diluent.

INTRODUCTION

Extraction systems with chemical reactions are used extensively as the

separation and purification processes in hydrometallurgy, environment

protection and nuclear fuel processing. Measurement and theoretical work has

been extensively carried out on this area(Sekine and Hasegawa, 1977). The

extraction of uranyl nitrate(UOz(NO3)3) by tributyl phosphate(TBP) in acid

medium(HN03) is the most significant process in nuclear chemical engineering

(Schulz and Navratil, 1984). A lot of experimental data of the system have

been reported in literature (e.g., Healy and Kennedy, 1959a and 1959b; Davis,

03783812192/$05.00 01992 Elsevier Science Publishers B.V. All rights reserved

2

1962; Davis, et al., 1970; Goldberg, et al., 1972; Horng, 1984, Li, et al.,

1989 and 1990).

For theoretical approach, Rozen and Khorkhorina(l957) and Glueckauf(l958)

proposed a chemical equilibrium model to calculate the distribution

coefficients of UOz(NO3)3 in the H30-HNO3-TBP system. Forrest and

Hughes(1975), and Hanson(l97’9) pointed out that the application of the

chemical equilibrium model to extraction systems is theoretically limited to a

very dilute concentration range because of the nonideality of the extraction

systems. Then some empirical and semiempirical models were proposed for

correlation of thermodynamic equilibrium constants versus concentrations in

both phases(Li, 1988 and Horng, 1984).

In the previous paper(Li, et al., 1990) we used the UNIFAC equation to

calculate activity coefficients of the species in organic phases for

H30-nC7Hi6-HNOs-TBP and H2O-nC7Hi6-UO2(N03)3-TBP systems. The TBP molecule was

divided into groups of CH3, CH2, CH30 and PG(according to Rozen and

Yurkin(1983)). For the extracted complex HN03. TBP and UO2(NO3)2; BTBP, two,

large groups POHN03 and (PO)3UOa(NO3)3 were assigned respectively. The group

interaction paremeters were regressed from the LLE systems with initial TBP

concentration of 35 and 83 ~01% and used to predict the LLE systems with other

initial TBP concentration of 15, 50, 66, and 100 ~01% satisfactorily. But when

UNIFAC equation with this group assignment is used to predict the systems with

Amsco125-82 as diluent, the deviationk become larger.

In this paper, proximity effect of groups in TBP, HNO3TBP and UO2(NO3)2

2TBP molecules is considered in their group assignment. Group interaction

parameters in the UNIFAC equation and thermodynamic equilibrium constants of

extraction reactions regressed from the extraction systems with n-heptane as

diluent can be used in the calculation of the systems with Amsco125-82 or

nCisH3s as diluent.

Table 1. Equilibrium data (25’C) used in this work

sys t em Equilibrium data data type points source

-_---__-__----_---___~-_--

nC7 Hi 6 -TBP VLE 9 Li J.D. et al.,1990

H3G-nC7H~6-HN03-TBP LLE 35 Li Z.C. et al.,1989

H3 0-nC7Hi a-U03 (NO-3 ) 3 -TBP LLE 28 Li Z.C. et al.,1996

H20-Amsco125182-HN03-TBP LLE 76 Davis , 1962

HzO-Amsco125-82-UO3 (NO3 )I-TBP LLE 56 Davis et al.,1970

H3O-nCi3Hz8-HN03-U02 (N03)3-TBP LLE 210 Go ldberg et al. ,1972 ---------1-------------------

SURVEY OF EXPERIMENTAL DATA

There have been a lot of experimental data reported in

usage of UNIFAC and Piker equation, the mole fractions of

phase, and the molality concentrations of solutes in aqueous

So only some of the experimental data (see Table 1) can

purpose.

LIQUID-LIQUID EQUILIBRIA WITH CHEMICAL REACTION

literature. But for

species in organic

phase are ’ needed.

be used for this

There are two phases in the extraction system. In the organic phase(or the

extract phase)four components are considered : (1) a diluent( nC-rHI6,

Amsco125-82 or nCl3H28), (2) the extractant TBP, (3) the extracted complex

HN03. TBP and (4) the extracted complex Uol(N03)P. BTBP. The subscripts 1, 2, 3,

and 4 are used to denote these components. Although a certain amount of water

can be extracted into the organic phase, its existence as free water or

TBP- Hz0 is controversial. Moreover, many LLE data from literatures do not give

the water concentration in equilibrated organic phase. So in this paper we

omit the dissolved wate,r as one component in organic phase for simplicity and

convenience.

In the aqueous phase(or raffinate phase) H+, UOa” and N03- are the ionic

species and subscripts H, U, and NO3 are used to denote these ions,

respectively.

The extraction chemical reactions between the two phases are written as:

H+<oq) t NO3 <oq> t TBP<org> = HN03.TBPcorg) (I)

UO2 a+ <aq) t 2N03-<aq) t 2TBPcorg) = UO2(NO3)2.2TBP<org, (2)

Where the subscripts (aq) or <or& denote the species in the aqueous phase and

in the organic phase.

The thermodynamic eqilibrium constants of these reactions can be written

as:

a 11110 TDP x3 y3

XII= 3

= __--

‘HNO 2

3 aTDF msmso3Y+HA0 x272 3

(3)

Ku 2 3 a = =-- 2 2 a

a U02<N0 >

3 a ‘TBF’

mm U NO Y3

3 ~U02~N0 3 >

2 x2

(4)

where a is the activity of component i. xi is the mole fraction of a component

i in the organic phase and y,is the relevant activity coefficient with its

pure liquid at the same temperature as the reference state. m is the molality

concentration(mole/hsHzO) of an ion in the aqueous phase. y+ is the mean ionic

activity coefficient of an electrolyte with the infinite dilution at the same

temperature as the reference state.

PITZER EQUATION

The y, of HNOa and UOz(NOs)2 in the aqueous phase are calculated with the

Piteer equation for mixed electrolyte solutions(Pitzer, 1979):

lW,MX = ;I ZgZx I f’(I)+($) Ema [BMa+(~mZ)C,,] a

in which Z is the charged number of a ion and v is the moles of ions

completely dissolved from a mole of electrolyte. The subscripts c or a

indicates a cation or an anion..

4A@I f(I)=-----b- ln(l+bIi’2)

f’(r)=*)

B =a <c) 2RCi’

oa CP +z [l-(l+aI’“)e*1i’2]

a21

(6)

(7)

(8)

(9)

(10)

5

The parameters of HNO3 and UOz(NO3)a are listed in Table 2

Table 2. Pitzer parameter of HNO3 and UO3 (N03)2 -

B < 0)

B Cl> 8 -

HN03 0.1119 0.3206 0.0010

UOa (NO3 ) ia 0.4607 1.61326 -0.03154

THE UNIFAC EQUATION

The activity coefficients z.-I of the components in the organic phase are

expressed by the UNIFAC equation(Fredenslund, et al., 1977):

(11)

The combinatorial part is calculated by the Guggenheim-Starvermann

equation(Guggenheim, 1952):

lnr ic ‘i

= In ( 7 @l

)t1-- i I ei 3 (12)

where xi is the mole fraction of component i. The volume and surface fractions

of a component are

x r 0 =

i i "i% . 8 = (13) .i

5: xjrj i . ,

c x 9. .i

j J

The volume and surface parameters (ri and qia are calculated from the

summation of the relevant group values(Rk and %):

(14)

in which uLiJ is the number of the group k in a molecule of component i. Rk

and q are volume and surface parameters for group k. The residual part of the

activity coefficients is expressed by group activity coefficients in mixed

solution(pk) and pure liquid(Ik’ i’ )_:

6

1nr,n = co, ")(lnrk - lnl-k"') k

(15)

empkm

‘llrk = Qk (l- ln( c 9,kmk )-c--------- ) (16)

m In c ??A

n

ek=(xv; %J/(c c v:j’Q,J , i m .i

* mn=exP(-amn/T) (17)

where anin. is the group interaction parameter between group m and n. T is the

absolute temperature.

The structure of TBP, HNO3eTBP and UOa(NCh)a*TBP molecules is as follows:

TBP : I -----------I

CHa-CH2-CH2~CH20\p,0CHz~CH2-CHz-CH3

CHs;CH2-CH2+CH20' 0 I___________

I

___-_______ HNOS~TBP:

CH3-CH2-CH2~CH2O\P,OCH+CH2-CH2-CHt

CH2-CH2-CH2+CH20' OHNOs; I___________

__-__--_-___-____-_-_ WX(N03)z.PTBP:

CHS-CH~-CH~+HIO\ NO3

,OCHaiCHa-CHa-CHs

CH3-CHz-CHa+CH20-PO. *UOa. .OP-OCH~~CH~-CH~-CHS

CH3-CR2-CH&H20 NO3 \ i OCHa+CH2-CH2-CH3

I -_-_____-_,__-_____-_I

Because of the proximity effect between groups CH20, PO, HN03 and UOz(NOt)z

(Fredenslund, 1989) a group assignment is proposed as shown by dashed lines.

Table 3. Group volume and surface parameters

k CH3 CHa (cH20)3PO (cif$3po UOz(N03)2 ((CHzO)sPO)2

Rk 0.9011 0.6744 3.7249 5.3609 10.34

Qk 0.848 0.540 3.216 4.82 9.68

The Rk and Qk values for (CH20)sPO is from summation of the values of CR20 and

PO groups. The Rk and Q kvalues for PO group are empirically equal to those of

the group CN(Rosen and Yurkin, 1983). The volume parameters Rk of groups

HN03(CH20)3PO and UO~(NOS)~((CH~O)~PO)~- are determined by comparison of molar

7

volumes(Li., et al., 1989 and 1990) of TBP, HNOsTBP and UO1(NCkf22TBP. All

these volume and surface parameters are listed in Table 3.

DETERMINATIONOFGROUPINTERACTIONPARAMETERS

of

in

The group interaction parameters are regressed from the experimental data

systems with n-heptane as diluent(see Table 1). All parameters are listed

Table 4.

Table 4. Group interaction parameters a mn and Ks, Ku -- n

m CIi2 fCH20)3PO HN03 UO2(NO2)2

fCii20)3PO ((CH20)3POf3

-- CH2 0.0 1649 61.93 246.5

(CH20)3PO 230.9 0.0 177.3 32.7

HNOs(CH20)2PO 213.0 -236.8 0.0 3513

UOz(N02)2 ((CH20)3PO)3'

29.41 -49.83 -31.97 0.0

Kil = 0.2412 Ku'= 54.64 --

The interaction parameters between CH2 and (CH20)3PO are obtained from VLE

data of the nC7Hia-T3P system.

The interaction parameters between HNCb(CH20)3PO and CH2 or (CH20)3PO and

the thetmodynamic constant of HNG? extraction reaction are obtained from LLE

data of the ~~n~Hi6-HN~-TBP system,

The interaction parameters between U~(N~)2((~N20)3PO)3 and CH2 or

(CH20)3PO and the thermodynamic constant of UM(N@)2 extraction reaction are

obtained from LLE data of the H2O-nC?IHla-UCn(NCn)2-TBP system.

PREDICTIONOFLLEWITHONEEXTRACTIONREACTION

The group interaction parameters thus regressed are used to predict LLE

xt+x2+x 3 = 1

(x2tx3)/(xitx2tx3) = x; (18)

Kll = x3y3 / mHrnNO y+:no ry2

3- 3

8

data for H2O-nC@rHi6-HNOs-TBP, HZ~~~HI~-U~(NO~)Z-TBP, H10-Amsco125-82- HNOs-

TBP and ~O-Amsco125-82-U(h(NOs)3-TBP extraction systems. The equations(l8)

are used for prediction of extraction systems of HNCh.

0.80

Fig. 1

c.00 2.00 4.00 6.X 8.

m(HNO~,) ‘0

Mole fractions of the extracted complex HNO3* TBP in the

equilibrated organic phase with molality concentration of HNOs in

aqueous phase in the H20-nCvHia-HNCu-TBP system.

(m : experimental data; - : predicted by UNIFAC)

And equations for extraction systems of UOa(NCb)z are:

I x1+x2+x

4 = 1

(x2t2x4)/(xttx2*2x4) = x;

Ku = x4 Y, ’ mums: 3

Y*Zo <no > 2 32

xi Y:

(19)

where the activity coefficients Yi of organic components are calculated by the

UNIFAC equation with the group parameters listed in Table 3 and Table 4 and

the mean ionic activity coefficients 7+sIyo and Y+“o tno , of aqueous solutes - 3 - 2 32

are calculated by the Pitzer equation with the parameters listed in Table 2.

xz is the mole fraction of the extractant TBP in the organic phase when x3=0

and x4=0.

The diluent Amsco125-82 has the mean molecular weight of 185 and molar

volume of 246.7ml/mol(Davis et al., 1970) which are very close to those of

9

Fig.2

Fig.3

0.00

0.34895

&c ,,,,,, (,,_

>

2.00 0.20 0.40 0. 0 n’s0 1 r- .O 0

Mole fractions of the extracted complex UCh(NCa)~PTBP in the

equilibrated organic phase with molality concentration of

UOz(NOs)Z in aqueous phase in the H2C-nC7Hi6-UOI(N03)I-TBP system.

(8 : experimental data; - : predicted by UNIFAC)

1.00 ,

0.80

i /

x*O= 1 .o

/ 0.61476

10

Mole fractions of the extracted complex HNCsTBP in the equilibrated organic phase with molality concentration of HNOs in

aqueous phase in the H2C-Amsco125-82-HNCa-TBP system.

(m : experimental data, - : predicted by UNIFAC)

10

nCi3Has(l84.4 and 244ml/mole), so in our calculation the group assignment of

Amsco125-82 is carried out as that of nCl3H28.

The prediction results are listed in Table 5 in which Ax is the standard

absolute deviation of a component in the organic phase. In Figures l-4 the

predicted mole fractions of the extracted complexes HNO3. TBP or UOz(NO3)z. 2TBP

are compared with the experimental ones.

Table 5. Standard absolute deviations between predicted and experimental mole fractions of extracted complexes

----- system AXIS Axla

H30-nC7Hls-HNOs-TBP 0.003

HaO-nC7HI6-U02 (NO3 )3&TBP 0.005

HaO-Amsco125-82-HN03LTBP 0.006

HzO-Amsco125-82-U02 (N03)a-TBP 0.007

HzO-nCi3Ha8-HN03-UOz(NO3)2~TBP 0.010 0.005 -----

0: Axi=

OZO l------ -- 2 ~,~=@.51472

Fig.4 Mole fractions of the extracted complex UOz(NO3)32TBP in the

equilibrated organic phase with molality concentration of

UOz(NO3)a in aqueous phase in the HaO-Amsco125-82-UO3(NOs)2-TBP

system. (m : experimental data; i ‘: -predicted by UNIFAC)

11

0.25 -J--- -

0.20 mu=O.OO1

C.00 2.00 --Y?ir--x 4.00

m(HN03) IO

Fig.5 Mole fractions of the extracted complex HNOsTBP in the

equilibrated organic phase with molality concentration of HNOs in

aqueous phase in the H~O-C~~~S-HNC~-U~~(N~~)~-TBP system.

(m : experimental data; - : ‘predicted by UNIFAC)

PREDICTION OF LLE WITH TWO EXTRACTION REACTIONS

In nuclear fuel seperation and purification processes the extraction of

UOz(NOs)a is carried out in acid medium(HNOs), so the extraction of HNOs

happens simultaneously with the extraction of UO2(NO3)2.! The prediction of LLE

in the presence of both reactions is important in practice.

The interaction parameters between groups i#N@(CH20)3PO and UO2(NOa)2-

((CH20)sPO)s are regressed from LLE data of the system HzO-nCisHss- HNOs-

UOs(NOs)z-TBP (see Table 3). The equations(20) are used for the system with

xI+x2+x3tx c

= 1

(x2tx3t2x4)/(xi +x2+x3+2x*) = x;

Ks = x3r3 /mm Y 11 I40 3 t:No3x272

Ku = x4 7, ’ mums: Go <so > xi 7:

3 - 2 32

(20)

both chemical reactions. The prediction results are shown in Figure 5 and

12

Figure 6. The stendard absolute deviations of gand x+ are shawn in Triblt 5.

The prediction results are in good agreement with literature data.

Fig*6 Mote fractions oi the extracted complex V~~~~~22T~F in the

e~ui~b~a~~d organic phase with 3aolality concentration of

U~(N~~Z in aqueous phase in the Hlo-Ci3H38-HXlfas-UOn8-~~~3-w~(rJCb)2-TBP

system. (r t experimental data; - : predicted by UNIE’AC)

The VEIFAC group h&era&on paraa~&rs and t~~~y~a~~ e~u~b~~~~

eon&ants of reactions regressed irant the extraction syateras ot ffK% OS

UOz(No3fz with n-heptane as diluent are au&able for prrsdictien of the systeme

with Amsco125-82 or nCi3HPs as dtiulsnt and the system with both extraction

reactions. Predictian results coincide very well with the experimental ones.

The results prove the great predictive power OE the WNIFAC model in

con&deration of the proximity effect of groups in TBPt HNfm- TBP and

V~(~~~~ - 2TBP lkwA?eures*

a activity c;if a component in the aqueous or organic phase

a group interaction parameter between groups m and n

13

A@ = O.S19(at 25*C), a parameter used in the Pitzer equation

C@ a parameter used in the Pitzer equation

K thermodynamic equilibrium constant of a extraction reaction

I ionic strength in the aqueous phase

L

molality concentration of an ion in the aqueous phase

group surface parameter

r

R’

volume parameter of component I

gas constant(8,314J/K mol)

RL group volume parameter

T absolute temperature(K)

‘i mole fraction of component i

Z =lO, coordination number or contact number in the UNIFAC equation

Z the charged number of an ion

Greek symbols

a

R

*xi

*,

*i rk

rk Ci)

f mn

9 m

co “k V

= 1.2, a parameter used in the Pitzer equation

the parameters used in the Pitzer equation(see Table 2)

standard absolute deviation between predicted and experimental

mole fractions of a component in the organic phase

mean ionic activity coefficient of an electrolyte in the aqueous

phase

activity coefficient of component i in the organic phase

activity coefficient of group k in mixture

activity coefficient of group k in pure component i

group interaction energy parameter between groups m and n

surface fraction of group m in an organic solution

number of group k in a molecule of component 1

the moles of ions completely dissolved from a mole of electrolyte

volume fraction of component i in the organic phase

surface fraction of component i in the organic phase

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14

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15

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