The predictive capability of the UNIFAC equation for the calculation of liquid-liquid equilibria...
Transcript of The predictive capability of the UNIFAC equation for the calculation of liquid-liquid equilibria...
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 ~,[email protected]
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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