1372
I n d . Eng. Chem. Res. 1992,31, 1372-1378
Paine, P. L.; Sherr, P. Drag Coefficients for the Movement of Rigid Spheres Through Liquid-Filled Cylindrical Pores. Biophys. J. 1975,15, 1087-1091. Shinohara, M.; Haaimoto, H. Force on a Small Sphere Sedimenting in a Viscous Fluid Outside of a Circular Cylinder. J. Phys. SOC. Jpn. 1980,49, 1162-1166. Suge, Y. An Experimental Study on the Effect of a Wall upon a Sphere Falling in a Viscous Fluid. Bull. Inst. Phys. Chem. Res.,
Tokyo 1931,10, 146-156. Tineren, H. Torque on Electric Spheres Flowing in Tubes. J. Appl. Mech. 1982,49, 279-283. Theren, H. Drag on Eccentrically Positioned Spheres Translating and Rotating in Tubes. J . Fluid Mech. 1983,129, 77-90. Received for review July 22, 1991 Accepted January 28, 1992
Solvent Extraction of Holmium and Yttrium with Bis(2-ethylhexy1)phosphoric Acid Kazuharu Yoshizuka,* Yoshitsugu Sakamoto, Yoshinari Baba, and Katsutoshi Inoue Department of Applied Chemistry, Saga University, Saga 840, Japan
Fumiyuki Nakashio Department of Organic Synthesis, Kyushu University, Fukuoka 812, Japan
A kinetic study on the solvent extraction of holmium(II1) and yttrium(II1) with bis(2-ethylhexy1)phosphoric acid (DBEHPA) from nitrate media was conducted a t 303 K using a hollow fiber membrane extractor. Also studied were the distribution equilibria of these metals and interfacial adsorption equilibria of DBEHPA and ita metal complexes between the organic and aqueous phases. It was found that the metals (M3+)were extracted with D2EHPA (HR) as MRg3HR into the organic phase, and the extraction equilibrium constants were evaluated. Furthermore, it was established that dimeric DBEHPA can be adsorbed a t the interface between the organic and aqueous phases, while the interfacial activities of DBEHPA-metal complexes were negligibly small. The apparent orders 2, 1, and 2 of the permeabilities for the extraction of both metals were found with respect to the pH of the aqueous solution and the concentrations of the metal ion and dimeric DBEHPA, while the orders 1, 1,and -1 of the permeabilities for the stripping of both metals were found with respect to the hydrogen ion activity and the concentrations of the metal complex and dimeric DBEHPA, respectively. The diffusional effects were reasonably explained by the diffusion model accompanied by an interfacial reaction, taking into account the velocity distributions of the aqueous and organic phases through the inner and outer sides of a hollow fiber.
Introduction Dialkylphosphoricacids have found extensive use in the hydrometallurgical recovery and refining processes of rare metals such as cobalt, nickel, zinc, actinides, and lanthanides. The separation and refining processes of rare earth elementa have been mainly carried out by solvent extraction with dialkylphosphoric acids, especially bis(2ethylhexy1)phosphoric acid (henceforce, abbreviated to DBEHPA), and many fundamental studies on the extraction of rare earth elements have been conducted (Bauer and Lindstrom, 1971; Bauer et al., 1972; Bhattacharyya and Ganguly, 1986; Coleman and Roddy, 1971; Danesi and Cianetti, 1982; Huato and Toguri, 1989, Imai and Furusaki, 1987; Inoue and Nakashio, 1982; Kolaric et al., 1974; Pierce and Peck, 1963; Sato, 1975,1989). However, most of the previous investigations on the separation of rare earth elements were concerned with the extraction equilibrium, while the studies on the extraction kinetics are few (Danesi and Cianetti, 1982; Hirato and Toguri, 1989; Imai and Furusaki, 1987; Kolaric et al., 1974). Recently, the application of hollow fiber modules to membrane extraction processes has been attempted for metal recovery (Alexander and Callahan, 1987; Kim, 1984) and protein extraction (Dahuron and Cussler, 1988). In order to improve the membrane extraction processes, the kinetics and mechanism of extraction and stripping through the hollow fiber membrane must be elucidated because these processes are governed by kinetics rather than equilibria. If the difference between the extraction and stripping rates of the metals of interest is greater than 0888-5885/92/2631-1372$03.00/0
that of the distribution ratios at equilibrium,the separation using the membrane extraction processes could represent an attractive alternative to the conventional solvent extraction processes based on distribution equilibrium. However, only a few investigationshave been reported that deal with the membrane extraction processes since the mechanism is strongly dependent on the combination of metals and the extractanta (Danesi and Cianetti, 1982). In the present study, the extraction and stripping of holmium(III) and yttrium(III) ions, classified to the heavy rare earth element group, with D2EHPA were carried out by a hollow fiber membiane extractor (Yoshizuka et al. 1986b,c),together with the measurements of the distribution equilibria of these metals with DBEHPA and the interfacial adsorption equilibria of D2EHPA and its metal complexes, in order to obtain more detailed information on the kinetics and equilibria of rare earth elements with D2EHPA. 1. Experimental Section Reagents. DP-8R, a commercial metal extraction reagent, was used as D2EHPA (denoted by HR for monomeric species and as Hz& for dimeric species hereafter) as delivered from Daihachi Chemical Industry Co. Ltd. (Lot No. K20801). The purity of the reagent was found to be above 98% by means of neutralization titration with alcoholic potash using phenolphthalein as an indicator. Reagent grade holmium nitrate and yttrium nitrate were also used as received without further purification since the purities of both metal nitrates are above 99.99%. Reagent 0 1992 American Chemical Society
Ind. Eng. Chem. Res., Vol. 31, No. 5, 1992 1373
2.0
-
.-I
0 Ho . Y
10-
a
-m 0
-
0--.-o1
%-
I
9-
Figure 1. (a,top) Schematic d m of the hollow fiber membrane extractor. (b, hattorn) Flow pattern of each phaae in the membrane extractor.
grade toluene was used as an organic dduent. Other inorganic reagents, nitric acid, and sodium nitrate were all commercial reagent grade. The metal complexes, M k , were prepared by adding an aqueous solution of the nitrate salt of holmium or yttrium to a methanol solution of D2EHPA at about 333 K, adjusting to pH = 4.0 by 100 mobrn-' acetic acid-sodium acetate buffer solution. The resulting complexes were fdtered, rinsed with methanol several times, and dried in vacuo. These were analyzed by elementary analysis. Anal. CalcdforC&O&~ C,51.04,H,9.11. Found C, 50.44, H, 9.03. Anal. Calcd for C,H,O,,Y C, 54.72; H, 9.77. Found C, 54.80; H, 9.85. Distribution Equilibria of Holmium and Yttrium. Organic solutions were prepared by dissolving D2EHPA and/or the metal complex in toluene to the desired concentrations gravimetrically. The aqueous solutions were prepared by dissolving the nitrate salt of holmium or yb trium in the aqueous mixtures of 100 mol.m-' sodium nitrate and 100 m ~ l . m -nitric ~ acid solution; the pH was adjusted by changing the volume ratios of the two solutions. Nitric acid solutions were used for stripping. Distribution equilibria of the metals between the aqueous and organic phases were measured batchwise in a conventional method (Nakashio et al., 1982; Yoshizuka et al., 1985), under various experimental conditions as follows: initial concentration of metals was 10 m 0 1 d . analytical concentration of D2EHPA as a monomeric and the pH range was 0.6-1.5. species was 1WoOm~hm-~, Interfacial Tension. Interfacial tension between the organic and aqueous phases was measured at 303 K by the pendant drop method to examine the interfacial adsorption equilibria of the extractant and the metal complexes (Yoshizuka et al., 1986a). Since the solubilities of metal complexes in toluene are too low to measure the interfacial tension of metal complexes alone, DZEHPA was added in the organic phase together with the metal complexes when the interfacial tension was measured. Extraction and Stripping Rates. A hollow fiber membrane extractor for measuring the permeabilities for the extraction and stripping and the experimental procedure were the same as described in the previous papers (Yoshizuka et al., 1986b,c). As shown in Figure la, the membrane extractor consists of one hollow fiber inserted in a cylindricalglaas tube. The aqueous solution containing metal ion flowsthrough the lumen of the fiber, while the organic solution containing D2EHPA and metal complex flows through the annulus in the extractor conurently. Since the hollow fiber used in this study is made of poly(tetrafluoroethylene),the interface between the aqueous
-1.0 -1.0
-0.5
0
0.5
Figure 2. Equilibrium distribution of holmium and yttrium.
and organic phases is at the inner surface of the hollow fiber. For evaluation of the experimental results, the permeabilities for the extraction and stripping of metal, PMand PM',respectively,were defmed by the following equations:
PM (=Jd[MId = EQW/(2miL)
(1)
PM'(=JM'/[%*~HRIo) = E'Qm,/(2mL)
(2)
2. Results Distribution Equilibria of Holmium and Yttrium. Extraction equilibria of trivalent metal ion ( M 9 with DZEHPA in aromatic dduents can be expressed as follows:
M3+ + 3FR2 + MRg3HR + 3H+
K,
(3)
where DZEHPA is known to dimerize in aromatic diluenta, such as benzene and toluene (Coleman and Roddy, 1971; Danasi and C i e t t i , 1982; Hmto and Toguri, 1989;Huang and Juang, 1986; Imai and Furusaki, 1987; Kolaric et al., 1974; Komasawa and M e , 1983; Pierce and Peck, 1963; Vandegrift and Horwitz, 1977). The extraction equilibrium constant, Kex,is written as follows:
where [MI and aH are the total concentration of metal in the aqueous phase and the hydrogen ion activit~calculated by the pH of the aqueous solution, respectively. Expressed in logarithm form, eq 4 gives the following equation.
1% DM
3 1% ( [ r k ] /(Id + log Kex
(5)
The experimental results are plotted in Figure 2 according to eq 5. Straight lines with a slope of 3 were obtained for both metals. The extraction equilibrium constants, ICex,at 303 K were evaluated from the intersection of the straight line and the ordinate in Figure 2 as K , = 8.53 for holmium and K , = 17.3 for yttrium, respectively. It was found that the extraction equilibrium constant of yttrium is 2 times greater than that of holmium. Interfacial Tension. Parta a and b of Figure 3 show the relation between interfacial tension and the concen-
1374 Ind. Eng. Chem. Res., Vol. 31, No. 5, 1992 o.o+
I
z
a
t
OL
0
7 i
1
8-0
O + r -
-
1
00 3 k
0021
1 0ao
1 .o
30
20
PH
I
0.03
'
'
I
[m10 I I I III
Figure 4. Relation between PM and pH of feed aqueous solution.
' ' 1 " ' 1 Key pH'35 H o Y [molWl 0 0 500
10-5LIlIIII
I
I111111
I
I I Ill11
[~;~,!,:100rnolrn~
'
I
t
c
c
J
1.0 10' [ m l o [mol m-31
lo2
30
~ ~ - ~ 1 1 1 1 1
A
Figure 3. (a, top) Interfacial tension of DBEHPA. (b, bottom) Interfacial tension of holmium and yttrium complexes with DPEHPA.
104
10 [ M IO
-
trations of dimeric DBEHPA, [H2R2I0,and the complexes of holmium and yttrium with DBEHPA, [MR3.3HRIo,respectively. From these figures,since the interfacial tension of each metal complex is not affected by the concentrations of the metal complex, is can be concluded that the adsorption of the metal complex at the interface is negligibly small compared with that of D2EHPA. The adsorption equilibrium of dimeric D2EHPA is expressed as follows: H2R2 HzR2(ad) Kad (6) where Kad is the adsorption equilibrium constant of the dimeric species of DPEHPA. The relation between interfacial tension, y ,& the concentration of H2R2in the organic phases, [HzR2],is derived from the Gibbs equation for adsorption, assumlng a Langmuir adsorption isotherm for expressing the relation between the amount of HzR2 adsorbed and [H,R,], as follows: (7) y = yo - (RT/s,,) In (1+ Kad[W21) where yois the interfacial tension between toluene and the aqueous phases and Sadis the interfacial area occupied by unit mole of dimeric species of DBEHPA. From the experimental results shown in Figure 3a and eq 7, the values of Kad and s a d obtained by nonlinear regression are Kad = 12.6 m3.moi-l and s a d = 6.7 x 105 m2.mo1-' (=HO A2/molecde), respectively. Kd is 7 times greater than that of (2-ethylhexy1)phosphonic acid mono(2-ethylhexyl) ester measured in the n-heptaneaqueous acetate buffer solution system (Nakashio et al., 1982), while S a d are nearly equal to each other. Extraction Rates of Holmium and Yttrium with D2EHPA. Figure 4 shows the relation between the permeability for the extraction of metal, PM,and pH of the feed aqueous solution. The plots fall on a straight line with slope of 2 at low pH, while PM is not affected by pH at high pH.
pH
0 0
-;-;;;lj
0.01
0
I I l l
Ho Key Y
A
10'
r
102
[rnol.m3]
Figure 5. Relation between PM and feed concentration of metal ions.
Figure 6. Relation between PM and feed concentration of dimeric
D2EHPA.
Figure 5 shows the relation between PM and the feed concentration of holmium or yttrium, [MI,. At low pH, PM is independent of [MI,, which means that the permeability for the extraction of metal is proportional to [MI,. At high pH, PM is independent of [MI, in the range of low [MI,, while in the range of high [MI, PM is inversely proportional to [MI,. Figure 6 shows the relation between PM and the feed concentration of dimeric DBEHPA, [H2R,],. At high pH, the plots are lying on the straight line witha slope of 1at low [H2R210, while PM is not affected by [HzRJo at high [H2R2]@At low pH, the plots are lying on the straight line with a slope of 2 a t low [H2R,IO. P M values approach constant with increasing [H2R2],in the same manner as at high pH. Stripping Rates of Holmium and Yttrium with Nitric Acid. Figure 7 shows the relation between the
Ind. Eng. Chem. Res., Vol. 31, No. 5, 1992 1375 (I,,,,
1
I
I
I 1 1 1 1 1 1
Kw
I
I I I I ! !
103
1 02 OH0
10‘
[mol m-31
Figure 7. Relation between PM’and hydrogen ion activity of feed aqueous solution. Figure 9. Relation between PM’and feed concentration of’ dimeric
DPEHPA. 10‘6
10’8
Ho Y lmdm+l 0 0 3000
10’
[ f n - m l o [mclm-31
Figure 8. Relation between PM’and feed concentration of metal complexes.
permeability for the stripping of metal, PM’, and the hydrogen ion activity of the feed aqueous solution, aHO.The acid concentration used in this study was so high that the hydrogen ion activity was used in place of the concentration, [HI,. The plots are lying on the straight lines with while they approach constant at the slope of 1at low aHO, high uH@ Figure 8 shows the relation between PM’and the feed concentration of the metal complex, [MR3*3HRIwPM’ is independent of [MR3-3HRlo,over the whole range of experimental conditions, which means that the permeability for the stripping of metal is proportional to [MR3-3HRIo. Figure 9 shows the relation betweenPM’and the feed a high concentration of dimeric DBEHPA, [H2R2],. At concentration of nitric acid, PM’ is independent of [H2R210 at low [H2R2I0,while at high [H2R2I0,the slopes of this linear relation were about -1. At low acid concentration, the slopes of this linear relation are also about -1. This suggests that the shielding effect caused by the adsorption of DPEHPA at the interface is high. From the experimental results in the ranges of low permeabdities for the extraction and stripping of metals where they are controlled by the interfacial reaction step, the apparent orders 2, 1, and 2 were found for the permeabilities for the extraction of metals with respect to the pH of the aqueous solution and the concentrations of metal ion and dimeric DBEHPA, while the orders 1,1,and -1 were obtained for the permeabilities for the stripping of metals with respect to the hydrogen ion activity and the concentrations of the metal complex and dimeric D2EHPA. These apparent orders are the same with the experimental results reported by Hirab and Toguri (1989) who measured the extraction and stripping rates of yttrium(II1) with DBEHPA from the chloride media in a stirred transfer cell.
3. Discussion From the measurements of interfacial tensions, it was found that D2EHPA is adsorbed at the interface, while the metal complexes are scarcely adsorbed. In addition, the experimental results shown in Figures 4-9 suggest that the diffusional effect of each species and shielding due to the adsorption of DOEHPA at the interface on the extraction and stripping rates should be taken into account. On the basis of the experimental results mentioned above, the following interfacial reaction scheme between metal ions and DBEHPA was inferred:
MR2+-HR(ad)+ H+
M3++ H2FLJad)
+
+
MR2+qHR(ad) r R 2 + MR2+.2HR(ad) H+ -
k
e
MR2+-2HR(ad)+ H2R2
K , (8) K2 (9)
MR3-3HR+ H+
K3 (10) From the fact that the apparent order of permeability with respect to the concentration of dimeric DSEHPA is 2 at low [H2R2IOand that with respect to pH of the aqueous solution is 2 at low pH, the interfacial reaction step described by eq 10 was considered to be the ratecontrolling step among the interfacial reaction steps described by eqs 6 and 8-10. The interfacial reaction rate for the elementary step of eq 10, R, is expressed as follows: R = k3[MR2+*2HR(ad)] [ W 2 I - k3’[MR3-3HR]aH (11) On the basis of the Langmuir adsorption isotherm for the adsorbed D2EHPA and intermediate complexes, H&(ad), MR2+-HR(ad),and MR2+.2HR(ad)and with the assumption that the interfacial area occupied by the unit mole of H2R2,s a d , is equal to those of the intermediate complexes, the interfacial reaction rate, R, is ultimately expressed by the following equation:
R = [k&lK2(Kad/sad)[Ml [mZl3/aH2= ki[MR3*3HRlaHI/ [1 + Kad[H2RZI + ( K a d ( l [ M l [ ~ l / a H ) ( l+ K 2 [ m I / a H ) l ( 1 2 ) where the third and fourth terms in the denominator represent the extent of intermediate complexes adsorbed at the interface (MR2+.HR(ad)and MR2+-2HR(ad)). Under the present experimental conditions, the third and fourth terms in the denominator are considered to be much less than 1 + Kad[H2R2]since the concentration of DPEHPA is much higher than those of the intermediate complexes.
1376 Ind. Eng. Chem. Res.,Vol. 31, No. 5, 1992 Table I. Constants Used for Numerical Analysis kinetic and equilibrium constanta Kad= 12.6 m3.mol-1, Sad= 6.7 X lo5 m2.mol-' DM= 1.0 X 104 m 2 d , D H 2 R a = 1.0 X lo* m 2 d DlrlRg.BHR' = 5.0 X m2.s-* physical properties of membrane extractor: hollow fiber material, poly(tetrafluoroethylene)b r1 = 5.3 x 10"' m, r2 = 9.0 x 10-~m, r3 = 1.2 x m L = 0.25 m, T = 1.60,t = 0.70 Qas = (1-3)X 10" m 3 d Q, = (2-6)X 10" m 3 d a Estimated value by Wilke-Chang correlation. Goretex Co. Ltd.
1>0, r=0;
Source: Japan
Table 11. Reaction Rate Constants Obtained from Analysis kf/(m4.mol-1.s-1) k,'/(~~~~.mol-~.s-~) k d k i metal holmium 1.8 x 10-6 3.2 x 10-7 56.3 2.2 x 10-1 112.7 3.8 x 10-5 yttrium ~~
Hence, the interfacial extraction and stripping rates are approximately as follows: kf(tMl[H,R213/a~2 - [a3°3HRla~/K,,) R= (13) 1 + Knd[m21 R'= k3'([m3-3HR]a~- K,,[Ml [H2R213/a~2)(14) + Kad[m21 where kf(=k&,Kad/Sad) is the overall forward reaction rate constant. The data in the region of high permeabilities for the extraction and stripping were analyzed on the basis of the diffusion model accompanied by an interfacial reaction, taking into account the velocity distributions of the laminar flows in aqueous and organic phases as shown in Figure lb. The diffusion equations for metal ion and hydrogen ion in the aqueous phase (0 < r < rl) are expressed as follows:
Those for H2R2and MR3-3HRin the organic phase (r2< r < r3) are expressed as follows: Uorg(r)
uorg(r)
= DH,, ai
(
a2[rn2i
+--1 aim2](17) )
dr2
r
ar
d[MR3*3HR] DMR3*3HR
(
-
B2[M€ii3HR]
)
+ -1d[MR3BHR] r
dr
(18)
Those for H2R2and MR3*3HRin the porous membrane of the hollow fiber (rl C r C r2) are expressed as follows:
a2[MR3.3HR] DMR3.3HR
+ -1r B[MR,BHR] )=O ar
(20) The boundary conditions for the above-described diffusion equations are expressed as follows: 1 = 0, 0 < r < r,; [MI [MI,, UH = uHO (21)
1 > 0, r = r3;
In laminar flow, the linear velocities of the aqueous and organic phases, uaq(r)and u,,&), are expressed as follows:
The above-mentioned diffusion equations and the boundary conditions can be solved with the numerical analysis by means of the implicit finite difference approximations, to obtain the permeabilities for the extraction and stripping of metal, PM and PM',from eqs 1 and 2. The values of the constants used for the calculation are listed in Table I. The unknown parameters in eqs 13 and 14 are the overall forward and backward reaction rate constants, kf and ki. These constants were evaluated by the trialand-error method 80 as to minimize the standard deviation between the experimental and calculated results, as listed in Table II. Solid lines in Figures 4-9 represent the reaults calculated by using these constants. The calculated results satisfactorily agree with the experimental results. The overall forward reaction rate constant, kf, of yttrium is 2 times greater than that of holmium. This may suggest that the yttrium(II1) ion has a smaller mass than the holmium(II1) ion. The ratio of the overall forward reaction rate constant, k , to the backward reaction rate constant, k i , may be considered to be equal to the extraction equilibrium constant of each metal, Kex. However, it was found that the ratio of kf to ki obtained from extraction kinetics of holmium and yttrium are about 7 and 10 times greater than the K,, values obtained from the extraction equilib-
Ind. Eng. Chem. Res.,Vol. 31, No. 5, 1992 1377 rium, respectively. This result is due to the fact that the ionic strength of aqueous phases in the extraction is significantly different from that in the stripping. The ratio of kf/ki of yttrium to that of holmium is 3.0, which agrees well with the ratio of K,, of yttrium to that of holmium. This suggests that an efficient separation process using the difference of the extraction rate between holmium and yttrium could be possible.
T = temperature (K) u = linear velocity (ma-') ti] = concentration of species j (m~l.m-~) Greek Letters y = interfacial tension (N-m-l) t = porosity of hollow fiber T = tortuosity of hollow fiber Superscript
Conclusion Kinetic studies on the extraction of holmium(II1) and yttrium(III)with bis(2-ethylhexy1)phosphoric acid and the stripping with nitric acid were conducted at 303 K using a hollow fiber membrane extractor, together with the extraction equilibria of metals and interfacial adsorption equilibria of the extractant and metal complexes. The following can be concluded. (1) The extracted species of holmium and yttrium with bis(2-ethylhexy1)phosphoric acid are MR3*3HR,and the extraction equilibrium constants for these metals were evaluated. (2) Bis(2-ethylhexy1)phosphoric acid is adsorbed at the interface, while ita metal complexes are scarcely adsorbed. (3) The experimental results for the permeabilities for both the extraction and stripping can be explained by the diffusion model accompanied by an interfacial reaction, the rate expressions of which are described by eqs 13 and 14,taking into account the velocity distributions of laminar flows of both phases in the extractor. (4) The ratios of the overall forward reaction rate constant to the backward reaction rate constant for both metals are significantly greater than the extraction equilibrium constants. Acknowledgment We gratefully acknowledge the kind supply of the hollow fiber from Japan Goretex Co. Ltd. and of DP-8R from Daihachi Chemical Industry Co. Ltd. Nomenclature aH = activity of hydrogen ion (m~l-m-~) Dj= diffusivity of species j (m2&) D M = distribution ratio of metal E = extent of metal extracted E' = extent of metal stripped JM = extraction rate of metal (mol-m-2d) JM' = stripping rate of metal (mol-m-2*s-') Kd = adsorption equilibrium constant of H2Rz(m3.mol-') K,, = extraction equilibrium constant of metal K1= equilibrium constant of eq 8 Kz= equilibrium constant of eq 9 K3 = equilibrium constant of eq 10 (m-l) kf = overall forward rate constant (m4-mo1-'-s-') k3 = rate constant of forward reaction of eq 10 (m3.mol-'.s-') ki = rate constant of backward reaction of eq 10 (mkmol-'.s-') L = length of membrane extractor (m) 1 = horizontal distance from point of contact between aqueous and organic phases (m) PM = permeability for extraction of metal (ms-') PM' = permeability for stripping of metal (mas-') Q = volumetric flow rate ( m 3 d ) R = interfacial reaction rate in extraction (mol.m-2d) R' = interfacial reaction rate in stripping (mol.m-2.s-') R = gas constant (N-m-rnol-'-K-l) r = distance of radial direction of extractor (m) rl = inner radius of hollow fiber (m) r2 = outer radius of hohw fiber (m) r3 = inner radius of membrane extractor (m) Sad= interfacial area occupied by unit mole of H A (m2-mol-')
_ -- organic phase Subscripts
ad = adsorption state aq = aqueous phase j = species (=M3+,HR, H2R2,H+, MR2+.HR, MR2+.2HR, MR3.3HR) org = organic phase 0 = initial state Registry NO.Ho, 7440-60-0;Y,7440-65-5;DBEHPA, 298-07-7. Literature Cited Alexander, P. R.; Callahan, R. W. Liquid-liquid extraction and stripping of gold with microporow hollow fibers. J. Membr. Sci. 1987, 35, 57-62. Bauer, D. J.; Lindstrom, R. E. Differential extraction of rare-earth elements in quaternary ammonium compound-chelating agent systems. U.S. Bur. Mines Rep. Invest. 1971, 7524. Bauer, D. J.; Schultze, L. E.; Lindstrom, R. E. Extraction process for upgrading Sm203wing selective stripping techniques. U.S. Bur. Mines Rept. Invest. 1972,7663. Bhattacharyya, S. N.; Ganguly, K. M. The effect of complexing agent on the extraction of lanthanides by di(2-ethylhexy1)phosphoric acid. Radiochim. Acta 1986,39, 199-203. Coleman, C. F.; Roddy, J. W. In Solvent Extraction Reviews; Marcus, y., Ed.; Marcel Dekker: New York, 1971; Vol. l, pp 63-91. Dahuron, L.; Cussler, E. L. Protein extraction with hollow fibers. AZChE J. 1988,34,130-135. Danesi, P. R.; Cianetti, C. Kinetics and mechanism of the interfacial mass transfer of Eu(II1) in the system: bis(2-ethylhexy1)phosphoric acid, n-dodecane-NaC1, lactic acid, polyaminocarboxylic acid, water. Sep. Sci. Technol. 1982, 17, 969-984. Hirato, T.; Toguri, J. M. Kinetics of solvent extraction of yttrium with di(2-ethylhexy1)phosphoric acid. Today's technology for the mining and metallurgical indwtries; IMM London, 1989; pp 15-20. Huang, T.-C.; Juang, R.4. Kinetics and mechanism of zinc extraction from sulfate medium with di(2-ethylhexy1)phosphoric acid. J. Chem. Eng. Jpn. 1986,19, 379-385. Imai, M.; Furusaki, S. Extraction kinetics of lanthanum with bis(2ethylhexy1)phosphoric acid. Kagaku Kogaku Ronbunshu 1987, 13, 355-360. Inoue, K.; Nakashio, F. Industrial organophosphorus extractants, their developments and recent advances. Kagaku Kogaku 1982, 46, 38-44. Kim, B. M. Membrane-based solvent extraction for selective removal and recovery of metals. J. Membr. Sci. 1984,21, 5-19. Kolaric, Z.; Koch, G.; Kuhn, W. Acidic organophosphorus extractants-XVIII, the rate of lanthanide(II1) extraction by di(2-ethylhexyl)-phosphoric acid from complexing media. J. Znorg. Nucl. Chem. 1974,36,905-909. Komasawa, I.; W e , T. Kinetics studies of the extraction of divalent metals from nitrate media with bis(2-ethylhexy1)phosphoricacid. Znd. Eng. Chem. Fundam. 1983,22, 367-371. Nakashio, F.; Kondo, K.; Murakami, A.; Akiyoshi, Y. Extraction equilibria of copper and zinc with alkylphosphoricacid monoester. J. Chem. Eng. Jpn. 1982,15,274-279. Pierce, T. B.; Peck, P. F. The extraction of the lanthanide elements from perchloric acid by di-(2-ethylhexyl)hydrogen phosphate. Analyst 1963, 88, 217-220. Sato, T. The extraction of indium(III), lanthanum(II1) and bismuth(II1) from sulphuric acid solutions by di(2-ethylhexy1)phosphoric acid. J. Znorg. Nucl. Chem. 1975, 37, 1485-1488. Sato, T. Liquid-liquid extraction of rare earth elements from aqueous acid solutions by acid organophosphorus compounds. Hydrometallurgy 1989,22, 121-140. Vandegrift, G. F.; Horwitz, E. P. The mechanism of interfacial mass transfer of calcium in the system: di(2-ethylhexy1)phosphoric acid
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in dodecane-dilute nitric acid. J. Inorg. Nucl. Chem. 1977, 39, 1425-1430. Yoshizuka, K.; Kondo, K.; Nakashio, F. Extraction equilibria of Cu(II), Zn(I1) and Co(I1) with N-8quinolylsulfonamide. J. Chem. Eng. Jpn. 1985,18,383-384. Yoshizuka, K.; Kondo, K.; Nakashio, F. Effect of hydrophobicity on distribution and interfacial adsorption equilibria of N-8quinolylsulfonamide. J . Chem. Eng. Jpn. 1986a, 19, 258-262. Yoshizuka, K.; Kondo, K.; Nakashio, F. Effect of interfacial reaction
on rates of extraction and stripping in membrane extractor using a hollow fiber. J. Chem. Eng. Jpn. 1986b, 19, 312-318. Yoshizuka, K.; Kondo, K.; Nakashio, F. Effect of hydrophobicity of extractant on extraction kinetics of copper with N-8quinolylsulfonamide. J. Chem. Eng. Jpn. 1986c,19, 396-400.
Received for review June 12, 1991 Revised manuscript received January 21, 1992 Accepted February 20, 1992
PVT Calculations on Petroleum Reservoir Fluids Using Measured and Estimated Compositional Data for the Plus Fraction Karen Schou Pedersen* CALSEP AIS, Lyngby Hovedgade 29, DK-2800 Lyngby, Denmark
Ann Lisbeth Blilie and Knut Kristian Meisingset STATOIL, Forus, N-4001 Stavanger, Norway
Molar compositions to Cm are presented for 17 North Sea oil mixtures. These extensive analytical data have been made available using a high-temperature gas chromatography technique. It is shown that a simple exponential distribution fits the C7+distribution of all 17 oil mixtures very well. Because of this simple exponential relation, it is possible from a compositional analysis (to for example Clo+ or C20+)to generate an extended composition that can be used to perform accurate PVT and phase equilibrium calculations. There appears to be little or no advantage of having measured compositional analyses beyond CzO+.
Introduction The compositions of petroleum reservoir fluids are most often reported to C,+, CIW,or Cm and in rare cases to CW (Pedersen et al., 1989a). To be able to perform phase equilibrium calculations (PVT calculations) on this kind of mixtures, it is necessary to estimate the molar composition of the plus fraction. The final calculation results are very sensitive to the molar distribution assumed for the plus fraction. Pedersen et al. (1985,1989b) have obtained accurate PVT calculation results by using the Soave-Redlich-Kwong (SRK) equation of state (Soave, 1972) and assuming the following dependence of the mole fraction on carbon number: z, = exp(A + BC,) (1) z, is the total mole fraction of components with C, carbon atoms and A and B are constants. It has previously been shown (Pedersen et al., 1984) that this distribution function may be used to represent reservoir fluid compositions to at least Clg. With the use of a high-temperature gas chromatography technique, analytical data have now been made available to CW+for 17 North Sea oil mixtures. These data have made it possible to check the validity of the distribution function expressed in eq 1, and to investigate whether the PVT-calculation accuracy can be improved by using analytical data to CBocas compared to the use of a distribution function for the Cl0+,C20+,or C30+fraction.
Experimental Data This paper deals with 17 different reservoir fluids (gas condensates and oils). The molar compositions of the reservoir fluids are determined from compositional analyses of the gas and liquid phases resulting from a flash of the reservoir fluid to atmospheric conditions or of the well test separator gas and liquid phases. In the latter case the 0888-5885/92/2631-1378$03.00/0
Table I. P l u s Fractions of the Standard Molar ComDositions for 15 of the Reservoir Fluids of This S t u d s oil plus oil plus oil plus no. fraction no. fraction no. fraction ~
1
3 4 5
~~
~~
clot
6
c30t c20t
7 8 9 10
Go+
c20+
Go+
cm cm czot Got
~
11 12 13 16 17
~~
ClOC
czo+ c17t
Go+
CZOC
separator liquid is flashed to standard conditions before the analysis is performed. The molar composition to Clo of all samples was determined by capillary gas chromatography. For the liquid samples at atmospheric conditions (in the following referred to as oils or stable oils) the CIWcomposition to Cm or to CN+is usually determined by TBP distillation (Osjord et al., 1985). The resulting molar compositions are given in terms of carbon number fractions, as described by Katz and Firoozabadi (1978). A carbon number fraction, C,, consists of all components with boiling points higher than that of the n-alkane with n - 1carbon atoms and lower than or equal to that of the n-alkane with n carbon atoms. Molecular weights are calculated from the single-component distribution for the C6-Cgfractions and measured for the distillate fractions. Molar compositions determined in the described manner are in the following referred to as standard molar compositions. In Table I is shown at what plus fraction the standard molar composition stops for the oil referred to in the PVT calculations. The extended molar compositions to Cm presented in this paper have been obtained using high-temperature capillary gas chromatography (GC) to analyze the stable oils (this technique is of no interest for gas phases because the content of CIWcomponents is negligible). The applied technique is similar to that used by Curvers et al. (1989). The residue which does not pass through the high-tem0 1992 American Chemical Society
