207
Ind. Eng. Chem. Fundam. 1900, 19, 287-291
Interphase Transfer Kinetics of Thorium between Nitric Acid and Tributyl Phosphate Solutions Using the Single Drop and the Lewis Cell Techniques. D. E. Horner, J. C. Mailen,’ J. R. Coggins, Jr., S. W. Thlel, T. C. Scott, N. Plh, and R. G. Yates Chemical Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37830
The kinetic rate constants for the interphase transfer of thorium between an aqueous phase and an organic phase of tributyl phosphate-n-paraffin hydrocarbon have been measured using the single drop and the Lewis cell techniques. Results from individual tests performed with the two techniques agree within experimental error. As with uranium, the data are consistent with a model in which the rate-controlling step is the rate of reaction of the components at the phase interface. An organic-soluble complex, represented by Th(N03)4*2TBP,forms in the organic phase. The composition of this complex is confirmed by equilibrium, as well as by kinetic, data. The kinetic data include results from tests showing the effects of TBP concentration and nitrate concentration on the values of the forward and the reverse kinetic constants. Other tests show the effect of temperature on the kinetic constant in both the forward and the reverse transfer directions, and the activation energies and enthalpy for the extraction reactions were estimated from these data. Unlike uranium, thorium extraction was shown to have a Marangoni effect under certain conditions.
Introduction Results of studies of the extraction kinetics of uranium into tributyl phosphate (TBP)-dodecane using the single-drop technique, the Lewis cell technique, and a highspeed mixer/centrifugal separator have previously been reported by Horner and Mailen (1980). Results obtained in similar studies for thorium kinetics are presented in this report. No references t,o work on thorium kinetics have been found in the literature, and only a limited amount of equilibrium extraction data is available. It is likely that future fuel reprocessing facilities will use contactors with short phase contact times, such as centrifugal contactors, for solvent extraction to minimize radiolytic and hydrolytic damage to the organic phases. Transfer kinetics data, such as those presented in this paper, are necessary for understanding and predicting the behavior of these fast contactors. Although the overall extraction of thorium is generally similar to that of uranium, certain definitive differences have been observed. These include the following: (1)The extraction rates are much slower in the forward direction. (2) Unlike uranium, thorium shows a Marangoni effect at high concentrations and low interfacial area-to-volume ratios. (3) The effect of increasing the neutral nitrate concentration is much smaller. On the other hand, the effect of increasing the temperature during the extraction is similar for both thorium and uranium kinetics, resulting in activation energies of the same magnitude. Details of these effects are given below. Experimental Section Reagents. A concentrated stock solution of thorium was prepared by dissolving reprecipitated Th(N0J4.4H,0 in dilute nitric acid. The uranium stock solution was prepared by dissolving a purified hydrated uranyl nitrate solid also in dilute nitric acid. For the organic phase, TBP was diluted with normal paraffin hydrocarbon (NPH) (both obtained from the Savannah River Plant, Aiken, S.C.), and the resulting solution was then purified from possible degradation products by scrubbing twice with sodium carbonate solution, followed by multiple water washes. Apparatus and Procedure. The apparatus used with the single-drop technique was identical with that used for 0196-4313/80/1019-0287$01 .OO/O
uranium; it has been described previously by Horner and Mailen (1980). Initially, the Lewis cell apparatus was also similar to that described earlier by Horner and Mailen (1980). For some of the latter tests, however, several improvements were made both in the apparatus and in the method of sampling. In these cases, samples of the organic phase (when testing aqueous-to-organic kinetics) were taken just above the interface rather than at the top. A major improvement in technique involved the method for initial contact of the phases. Initially, barren phases were introduced into the cell and stirred; then a concentrated aqueous phase was rapidly introduced into the barren aqueous phase through the hollow leg of a stainless steel baffle (Figure 1). In tests of the organic-to-aqueous kinetics, a concentrated organic solution was similarly introduced into the bulk organic phase. To facilitate sampling of the phases, evacuated tubes (Vacutainer, Becton Dickinson and Co., Rutherford, N.J.) were used with a special support. This support contained a puncturing needle connected to a Teflon capillary positioned in the proper phase in the Lewis cell. Analyses of thorium were made either by wet chemical techniques and spectrophotometric measurements or by X-ray fluorescence measurements.
Results and Discussion Mathematical Equation. The overall chemical reaction representing thorium extraction is similar to that for other tetravalent ions and for uranium. Thus Th(N03),(4-m)(aq)+ 4 - m N03-(aq) + 2TBP(org) e Th(N03)4-2TBP(org)(1) where the subscript “aq” refers to the aqueous phase and the subscript “org” refers to the organic phase. The following equations are based on pseudo-first-order kinetics, where the effects of nitrate and TBP concentrations are included in the rate constants de’ _ - --k’c’a dt
U’
kca
+
- (change
u’
in aqueous-phase concentration) (2)
0 1980 American Chemical Society
288
Ind. Eng. Chem. Fundam., Vol. 19, No. 3, 1980
dc = --kca dt
U
+
E 2
STlRRER
k’c‘a
-(change in organic-phase concentration) (3) U
At equilibrium
In these equations, c is the molar concentration of thorium, a is the interfacial area, u is the phase volume, and k is a rate constant; the primed and unprimed symbols refer to the aqueous and the organic phases, respectively. As a guide to inspecting the rate data, it is observed that the ratio of the forward rate constant to the reverse rate constant should be equal to the equilibrium constant (the distribution coefficient, D, in this case) if the transfer rate is reaction controlled. Therefore, the power effect of a variable on the forward rate constant minus that on the reverse rate constant must be equal to the power effect on the equilibrium constant. The integrated final working equations for the different modes of extraction in the single-drop technique are given below; the equations for use in the Lewis cell technique are also included. Aqueous-to-organic transfer of thorium in the rising drop mode can be described by
The corresponding equation for organic-to-aqueous transfer is akt = -In C (6)
u
.L,
CELL
Figure 1. Apparatus for Lewis cell determinations.
/
4 ,IO+
CO
Aqueous-to-organic transfer in the falling drop mode can be described by C’ --k ’at - In 7 (7) CO
U’
The corresponding equation for organic-to-aqueous transfer is
Derivatives of these equations were given by Horner and Mailen (1980). All of these equations are used by plotting the appropriate functions such that the slopes of the resulting straight lines give the values of the kinetic constants desired. For aqueous-to-organic transfer in the Lewis cell near time = 0, where cf c( and using eq 4 to eliminate k’, eq 3 becomes dc = --kca kh’a (9) Du dt u This equation can be integrated to give
-
+-
-
k f = - @a t In
‘1
JACKETED
1
-
ciDj
1--
for organic-to-aqueous transfer near time = 0, where c co, the equation is
-
c
In eq 10 and 11,D is the equilibrium distribution coefficient; all the other terms are as previously defined.
1
2 x 10-1
I
l , l o ! l l
1
I
1 1 1 1 1 1
10-1 FREE-TBP
100
CONCENTRATION It41
Figure 2. Kinetic constants for both transfer directions as a function of free TBP concentration.
Effect of TBP Concentration. Both aqueous-to-organic and organic-to-aqueous transfers were determined as a function of the “free TBP” concentration (i.e., initial TBP concentration minus that complexed with thorium but not with HNOJ by using the rising drop technique and the Lewis cell. An aqueous thorium concentration of 10 g/L was used to avoid possible Marangoni effects (Sternling and Scriven, 1959) and third phases in the aqueousto-organic transfer by the drop technique. Under these conditions the Lewis cell and drop methods gave the same rate constants. A log-log plot of TBP concentration vs. k and k’yielded straight lines for both transfer directions (Figure 2). The slopes of the lines were 1.3 and -0.66 for the aqueous-to-organic and the organic-to-aqueous transfer directions, respectively. The difference in these slopes is approximately 2.0, which agrees both with the assumed combining ratio of thorium with TBP (eq 1)and with the effect of TBP on the equilibrium constant. Also, the ratio of k’/k at each TBP concentration was approximately equal to the equilibriumdistribution coefficient of thorium (Figure 3), as would be expected for a chemically controlled reaction. Extraction Rates vs. Initial Thorium Concentration. As in the studies with uranium, it was necessary to determine if a Marangoni effect (Sternling and Scriven, 1980) occurs at relatively high thorium concentrations and to establish the reaction order. Although the mechanics of this phenomenon are somewhat complex, the overall
Ind. Eng. Chem. Fundam., Vol. 19, No. 3, 1980
-0
C
one
-+ k 2
-
1
-
I
289
I 1 1 1 I l
U FORWARD EXTRACTION IMARANGONI)
/
LLZ
03
o m u z
E’:
--
* w
2a $
0’
Th FORWARD (MARANGONII EXTRACTION
uE XFORWARD) TRACTION
0
INON-MARANGONII
/
/
a 5 / L T h FORWARD EXTRACTION INON-MARANGONI)
.03
/ 0 01
os
004 OC 2 5 (0 FREE TBP CONCENTRATION (MI
-__
05
0 2
10
12
F R E E TBP CONCENTRATION ( H I
Figure 3. Agreement of the ratio k ‘ / k with the equilibrium distribution coefficients. 7
0.1
1
Figure 5. Marangoni effects in a mixed thorium-uranium solution vs. free TBP concentration.
0 0
:t d
-
2 0.6
4
3
2
4
CONC.
/ ; I N I T I A L “03
6
(Mi
Figure 6. Kinetic constant vs. initial nitric acid concentration. -0
’
0
100
THORIUM CONCENTRATION
I 200
100
260
Ipll)
Figure 4. Marangoni effect vs. initial thorium Concentration.
result is that the high mass transfer causes turbulence in the interfacial area leading to higher-than-expected rate constants. For the Marangoni test in the aqueous-to-organic extraction direction, data were obtained in a Lewis cell with solutions whose thorium concentrations ranged between 5 and 235 g/L. The calculated values of k’ were essentially constant for initial concentrations of 5,10, and 29 g/L, thus confirming a first-order reaction as initially assumed. At concentrations -29 g/L, however, the value of h’ increased rapidly up to -100 g/L, indicating the occurrence of a Marangoni effect (Figure 4). A Marangoni effect was also observed during a test using the single-drop technique in which a solution containing 117 g of thorium and 10 g of uranium was used. In this case, the k ’ values for both thorium and uranium were increased above those expected for TBP concentrations between 0.1 and 0.5 M. This is illustrated in Figure 5, where the data obtained with high thorium concentrations (solid lines) are compared with those for low thorium concentrations (dashed lines). The observed decrease in rates above 0.5 M TBP (Marangoni conditions) may be due to formation of a second organic phase at the surface of the drop. Extraction Rates vs. Nitric Acid Concentration. In contrast with uranium in which essentially no effect of nitric acid concentration was obtained, the thorium kinetic rate was shown to increase slightly with acidity. Thus, over an acid concentration range of 1.0 to 4.0 M, the rate constant obtained in a Lewis cell increased from 3.0 X to 6.8 X cm/s (Figure 6). Extraction Rates vs. Neutral Nitrate Concentration. The distribution coefficient for thorium between
w
0
8 0 m ’”
-
-
>
-
0
-
3
c
-
LINE OF SLOPE = 2 LEASTSLOPE SOUARES 2 06
i
I
I
I l l l l l
I
1
10
‘I
NO NO^
CONCENTRATION
(MI
Figure 7. Thorium distribution coefficient between sodium nitrate solutions and 1.09 M free TBP solutions.
sodium nitrate and TBP-NPH solutions (corrected to 1.09 M free TBP) is shown in Figure 7. The slope of the log-log plot is about 2. The effect of increasing nitrate concentration on the forward rate constant is about 0.6, as shown by the slope of a log-log plot of k’ vs. nitrate concentration (Figure 8). Increasing the nitrate concentration decreases the reverse rate constant with the log-log slope being between 4 7 and -1.2 (Figure 9). The scatter seen in this plot is due to very low thorium concentrations found in the aqueous phase. The difference in the slopes of the kinetic constants is 1.3 to 1.8, which is in reasonable agreement with the effect of nitrate on the distribution coefficient of thorium (Figure 7). Based on these data, it appears that m of eq 1must be such that addition of about two nitrate ions, on the average, completes the formation of the neutral species Th(N03)4-2TBP(eq 1). These conditions are consistent with data on the formation constants of the thorium nitrate complexes (Bjerrum et
290
Ind. Eng. Chem. Fundam., Vol. 19, No. 3, 1980 7
I
I
I
I
I
I
1
/
/
/
oa
/
U
:to-' z P
SLOPE = 2 05 f.36 7 .
3
! I
I
I
1
I
2
3
4
5
c L" 40-2
N E U T R A L NITRATE CONCENTRATION IbJ)
Figure 8. Forward rate constant vs. neutral nitrate concentration. 0~2.06en [TEP] + l n 199: AOUEOUS.2M "03
Pn
r - 1 SLOPE
-
51
d q 5 a 16' to-' i F R E E TSP CONCENTRATION (MI
-0 7
\"
4
Figure 10. Equilibrium distribution coefficient vs. free TBP concentration.
5 1
cc 4
5
1 0 - ~
U
Table I. Effects of Fluoride and Aluminum o n Thorium Kinetics. (Organic: 30% TBP-NPH; Aqueous: 2 M HNO, containing 1 0 g Th/L;Technique: Rising Drop ; Aqueous -+ Organic)
-
W
c
-
a W in
SLOPE
-
-1 2
W
10-5
t
0
Ld 10
TOTAL N I T R P T E CONC. I!)
Figure 9. Reverse rate constant vs. nitrate concentration, 0.5 M "OB + sodium nitrate.
al., 1958) which show that the dominant aqueous species under the conditions described in this report are Th(N03)3+and Th(N03)9+. Equilibrium Distribution of Thorium. The equilibrium distribution of thorium was determined as a function of TBP concentration between 1 and 30% in batch contacts with 2 M HN03 containing 10 g of thorium/L. Each phase was analyzed by X-ray fluorescence. When the logarithm of the calculated distribution coefficient was plotted vs. the logarithm of the "free TBP" concentration, a straight line with a slope of 2.05 f 36% (fit by hast squares) was obtained (Figure 10). This slope represents the combining ratio of TBP to thorium for the extracted complex [Le., Th(N0J4-2TBP]under the conditions given above. Previous work by other workers (Flagg, 1961, p 227) showed that a 3:l complex was obtained at high TBP concentrations; also, a ratio of 2.3 has been noted when the TBP was saturated with thorium (Flagg, 1961, p 228). Activation Energy. The kinetic constants for thorium extraction in both directions (2 M "03-30% TBP-NPH) were determined at -25, 40, and 60 " C by the single-drop technique. The activation energies were then estimated as the slopes of straight lines found when log k was plotted vs. 1/RT. Average values of 5.53 and 7.56 kcal/mol were
te0mp, C
F/Th/Al mole ratio
22 22 22 22 22 22 22 22
11111.25 21112.5 31113.75 41115 11112 21114 31116 41118
kinetic constant, k ' , cmls
Average of t w o determinations. tion.
1.62 1.28 1.22 1.2 1.67 1.53 0.86 1.08
x 10-30 x 10-30 x 10-30 8 ~1 0 - 3 0
x x x x
10-~b 1 0 - ~ b
Single determina-
found in the aqueous-to-organicand the organic-to-aqueous directions, respectively. The subtraction of the organic-to-aqueous value from the aqueous-to-organic value resulted in an enthalpy, AH, of -2.03 kcal/mol for the conditions of these tests. This compares with a value of -3.7 kcal/mol for uranium, indicating that the energy of complexation of the metal nitrate and TBP is relatively small in each case. Effects of Fluoride and Aluminum. The effect of increasing the fluoride-to-thorium ratio from 0 to 4 in a 2 M HN03 solution (also containing aluminum a t Al/F ratios of 1.25 and 2.0) was to decrease the forward kinetic constant by about a factor of 2.3. These results (see Table I) are consistent with the high stability of the thorium fluoride complex and with its probable nonextractability. Although aluminum also forms a complex with fluoride, it is not as strong as the thorium fluoride complex. Thus, over the concentration range used, the aluminum complex had little or no effect on the rate constant of thorium. Nomenclature k = reverse rate constant (organic to aqueous) k' = forward rate constant (aqueous to organic) c = concentration of organic phase after time t c' = concentration of aqueous phase at time t u = volume of organic phase u' = volume of aqueous phase
Ind. Eng. Chem. Fundam. 1980, 19, 291-294
a = interfacial area
t = interphase contact time co = initial concentration in organic phase at t = 0 cd = initial concentration in aqueous phase at t = 0 D = aqueous to organic equilibrium distribution coefficient At = time change corresponding to concentration changes ct - co or C< - cd AH = heat of reaction, AH = H,- Hf [CTho] = molar concentration of thorium in organic phase [TBP] = free TBP concentration ([TBPiJ - 2[CTh,O] (excludes TBP complexed with HNOJ Ht = reverse (0-A) activation energy Hf= forward (A-0) activation energy
29 1
Literature Cited Bjerrum, J., Schwarzenbach, G., Slilen, L. G., "Stability Constants. Part 11. Inorganic Ligands", p 54, The Chemical Society, London, 1958. Flagg, J. E., "Chemical hocessing of Reactor Fuels", pp 227, 228, Academic Press, New York, 1981. Horner, D. E., Mallen, J. C., Thiel, S. W., Scott, T. C., Yates, R. G., Ind. f n g . Chern. Fundarn., 19, 103 (1980). Strenllng, C. Y., Scrlven, L. E., AIChEJ., 5(4), 514 (1959).
Receiued for review October 24, 1979 Accepted May 14, 1980
Research sponsored by the Division of Chemical Sciences, U.S. Department of Energy, under Contract W-7405-eng-26with the Union Carbide Corporation.
Three-Parameter Cubic Equation of State for Normal Substances A. Harmens' Petrocarbon Developments Ltd., Manchester M22 4TB, England
H. Knapp Technische Universitat Berlin, Instifut fur Thermodynamik und Anlagentechnik, 1000 Berlin 12, Germany
A cubic equation of state is proposed which possesses three adjustable parameters and therefore is more flexible than the well-known Redlich-Kwong and Peng-Robinson equations. The three parameters are adapted to give an optimal representation of the critical isotherm up to about pr = 5 and in addition are fitted to the vapor pressure from about T, = 0.3 to T, = 1 and to the volume along the critical isobar up to about T, = 2.5. The parameters were correlated in terms of T,, pc, and acentric factor w . The equation was then subjected to tests on pure substances, covering an extensive area of the p , Tfield. It was found in overall performance to be superior to four other generalized cubic equation of state procedures.
Introduction For process calculations particularly in petroleum and cryogenic technology, cubic equations of state have proved to be extremely useful. They are simple and can be solved with a straightforward algebraic procedure, so that they lead to robust computer programs for the prediction of thermodynamic data and t o relatively short computing times. They contain only a small number of adaptable parameters which can easily be related to the critical properties, so that the equations lend themselves well for generalization and application to mixtures. A t least one of the parameters must be treated as an empirical function of temperature, but such a function can also be generalized. Comparisons have shown (Oellrich et al., 1977) that thermodynamic computation procedures with generalized cubic equations of state are on the whole not noticeably inferior to the more expensive procedures using extended virial equations. However, the very fact that these equations are cubic in volume also imparts to them their main characteristic weakness: their failure to give a good account of the volume a t the critical point and at temperatures and pressures immediately above the critical. In that region the pressure changes not as a third-order function but as a fifth-order function of volume (Levelt Sengers, 1976) so that the cubic equation of state is fundamentally inadequate. Fortunately, for technical reasons of flow stability and process control it would be extremely unattractive to run a chemical process at or immediately above the critical 0196-4313l80/1019-0291$01.OO/O
point of one of its fluids: process designers avoid such conditions. The prediction of phase equilibrium can of course suffer from said inadequacy, but in many cases this leads to only minor errors since the calculated fugacity is much less seriously affected than the calculated volume itself (Harmens, 1975). So the shortcomings of the cubic equation are not always experienced as particularly troublesome. The various cubic equations of state also differ as to the extent and the severity of their supercritical unreliability. From the various cubic equations of state and associated procedures for parameter evaluation, two have acquired wide popularity: the Redlich-Kwong-Soave (Soave, 1972) and the Peng-Robinson (1976) procedure. They employ different two-parameter equations of state, but the treatment of the parameters is very similar. In both cases the repulsion parameter is kept constant at i h critical point value, while the attraction parameter contains a generalized function of temperature, fitted to the vapor pressure. For superheated vapors that subcritical temperature function is simply extrapolated above the critical temperature. The present study originated in the conviction that not all avenues had been explored which might lead to even better procedures. In particular, the use of a three-parameter equation and the actual fitting of the generalized temperature function in the region of superheated vapor seemed to deserve further investigation. Three different three-parameter equations were subjected to an explora-
0 1980 American Chemical Society
