2854
Ind. Eng. Chem. Res. 1993,32, 2854-2862
Kinetics of Mercury Extraction Using Oleic Acid K a r e n A. Larson and John M. Wiencek' Department of Chemical and Biochemical Engineering, Rutgers University, Piscataway, New Jersey 08855-0909
In the absence of halide ion, Hg2+is the predominant species in water and can be effectively extracted using oleic acid. The organic phase complex that is formed is HgRi2(RH). The presence of polar modifiers in the organic phase facilitates the formation of a complex dimer, [HgR2'2(RH)12. Kinetics of the extraction reaction have been studied as a function of pH, Hg2+ concentration, oleic acid concentration, and mixing rate in a stirred cell reactor. Extraction kinetics are first order in mercury concentration and zero order with respect to oleic acid concentration and pH. This is consistent with filmtheory predictions for an instantaneous reaction that is mass transfer controlled. A diffusion/ reaction model for mercury extraction in a batch stirred tank reactor has been developed that incorporates this information, and includes mass transfer of mercuric ion from the bulk solution t o the droplet surface, equilibrium between aqueous mercury and organic mercury complex at the droplet interface, and diffusion and dimer formation of the complex within the organic phase droplet. Without the use of adjustable parameters, this model successfully predicts mercury extraction rate and equilibrium. Introduction Contamination of aqueous streams with heavy metals, especially mercury, is a serious problem. In addition to contaminatedwater, there is growing concern over leaching of heavy metals from landfills to nearby groundwater. Discarded batteries are a major source of mercury in landfills. In fact, household batteries account for 88% of all mercury found in municipal solid waste, or about 1.4 million lb (Holusha, 1991). The possibility exists that some landfills could be a potential source of mercury contamination of groundwater. As a result, there is a need to not only rectify aquatic regions that are known to be contaminated with mercury, but also to have the technology available to treat aqueousstreams that may become contaminated at some future time. Although a number of methods exist for recovery of mercury from aqueous waste streams, one of the most promising techniques is solvent extraction using liquid ion exchangers. This method has been used extensively in hydrometallurgical operations (Tavlarides et al., 1987). Since mercury can exist as a cation or anion in aqueous solution depending on the amount and type of counterion present, liquid cation exchangers and anion exchangers are appropriate extractants. In halide solutions, equilibrium favors an anionic mercury complex (Tavlarides et al., 1987). For example, mercury in brine waste streams from the chlor-alkali industry, which contain up to 4.5 M chloride, exists primarily as HgClP. High molecular weight amines such as tertiary amines and quaternary ammonium salts are effective anion exchangers for mercuric chloride anion (Larson and Wiencek, 1992; Caban and Chapman, 1972a,b; Moore, 1972; Seeley and Crouse, 1966). In the absence of halide, equilibrium favors the cationic form of mercury; consequently, long-chain carboxylic, phosphoric, or sulfonic acids are appropriate extractants (Larson and Wiencek, 1992;Tavlarides et al., 1987). A separation technique which has been widely investigated for the removal of trace contaminants from aqueous streams is extraction using emulsion liquid membranes.
* To whom correspondence should be addressed. Electronic mail:
[email protected].
By combining extraction and stripping into one step, emulsion liquid membranes minimize equilibrium limitations inherent with conventional solvent extraction. When an ion exchanger is incorporated into the formulation, coarse emulsion liquid membranes have been used to extract a number of heavy metals from aqueous solutions: copper, nickel, cobalt, chromium,and zinc (Gu et al., 1985; Fuller and Li, 1984; Kitagawa et al., 1977; Kondo et al., 1981) as well as mercury (Weiss et al., 1982; Boyadzhiev and Benzenshek, 1983). The work in our laboratory is focused on a subset of emulsion liquid membrane technology-the use of microemulsions. Microemulsions, unlike coarse emulsions, are a class of emulsions that are thermodynamicallystable and, as such, offer potential advantageswhen used as liquid membranes over coarse emulsion liquid membranes which are only kinetically stable (Wiencek and Qutubuddin, 1989). Microemulsions have been used to separate acetic acid from water (Wiencek and Qutubuddin, 1988),copper ions from water by incorporating benzoylacetone (Wiencek and Qutubuddin, 19921, and mercuric ion from water by incorporating oleic acid (Larson and Wiencek, 1992).The goal of our work is to characterize mercury extraction using microemulsion liquid membranesthrough experimentand modeling. In order to successfully model the liquid membrane extraction, both equilibrium and kinetics of the metal: liquid ion exchanger reaction must be characterized and related to the other transport processes occurring during a liquid membrane separation (mass transfer, diffusion, and reaction). A comprehensive study of the extraction of mercury by both cation and anion exchangers over the range of conditions of pH and sodium chloride concentration has been completed (Larson and Wiencek, 1992). Predictive extraction models for mercury extraction using triisooctylamine, Aliquat 336, and oleic acid were developed by identifying and solving the appropriate aqueous phase and organic phase reaction equilibria. Mercury stripping from an oleic acid organic phase using a 6 N solution of sulfuric acid was also characterized and modeled. A microemulsion which incorporated oleic acid as the cation exchanger and 6 N sulfuric acid as the internal phase reduced the aqueous solution mercury content from 460 to 0.25 ppm in a single contacting. This extraction
0888-5885/93/2632-2854$04.00/00 1993 American Chemical Society
Ind. Eng. Chem. Res., Vol. 32, No. 11,1993 2855 represented a 32-fold improvementin extraction over the equilibrium-limited solvent extraction case. This paper represents the second phase of work and will focus on an examination of the kinetics of mercury extraction with oleic acid. This liquid ion exchanger was chosen because, as mentioned previously, it forms a microemulsion that is stable when used as a liquid membrane. In our previous work, the equilibrium extraction behavior of mercury and oleic acid was modeled by postulating theextraction of Hg2+by anoleic acid dimer (Larson and Wiencek, 1992): Hg2++ 2(HR),
-
HgR&RH
+ 2H+
IC, = 0.449 (1)
Equilibriumexperimentswere alsoperformedwitholeic acid in the presence of a long-chain alcohol or nonylphenol surfactants in order to help solubilize organic phase mercury complex which tends to precipitate, especially at high mercury:oleic acid loadings. The second purpose for the presence of these particular organic soluble surfactanta is that they have a chemical structure that is similar to that of surfactants used to formulate microemulsions. These particular surfactants, however, do not form microemulsions. Equilibrium studies which incorporated surfactant, along with oleic acid, in the organic phase showed that the presence of surfactant enhances the equilibrium extraction of mercury. This enhancement is related to the oxygen content of the surfactant. Mercury equilibrium was best modeled bypostulatingthe formation of a dimer of the mercury/oleic acid complex of the form:
(0.yge")
2HgRz.2RH
(HgR2.2RH),
K z = 1600 (2)
where
Kz =
[(HgRz.ZRH)zI [HgR2~2RH12[oxygenl
In this work, the kinetics of the mercury:oleic acid reaction are evaluated as a function of mixing, mercury, oleic acid, and hydrogen ion concentration, and are compared to film theory models for two-phase reactions. Finally, a diffusionlreadion model is developed for extraction of mercury with oleic acid in a hatch stirred tank reador. Experimental Section
Materials. The chemicals used in this study are oleic acid (food grade, Fisher Scientific), mercuric nitrate monohydrate (Fisher Scientific), heptanoic acid (Fisher Scientific),and tetradecane (Fisher Scientific and Humphrey Chemical). The surfactantused in this kineticstudy is Igepal CO-210 (Rhone-Poulenc) {nonylphenoxypoly(ethyleneoxy),ethanoI, n = 1.5). Procedures. Aqueous solutions of mercury were prepared by dissolving mercuric nitrate monohydrate in distilled water and adjusting the pH to the desired value using "03 and NaOH as required. The organic phase was prepared by weighing the desired amount of oleic acid and diluting with tetradecane. The CO-210 was added to the organic phase on a weight/weight basis. Kinetics of mercury extraction with oleic acid were evaluated in a stirred cell contactor, shown in Figure 1.In these experiments, 175mL of aqueous solution was added to the cell. An equal volume of organic phase was poured on top of the aqueous phase. Great care was taken to minimize mixing of the two phases. The agitation was started (Lightnin DSlOlO motor), and 2-mL samples of
UghVlin Motor
rgank
I Fila%
Figure 1. Schematic representation of the stirred cell contactor.
the aqueous phase were taken every minute for 10 min. In order to reduce the change in the liquid level of the cell, 2 mL of deionized (DI) water was added to the aqueous phase via the sampling port after alternate samples were taken. The addition of 8 mL of water to the reaction solution represents a dilution effect of less than 5% over the course of the experiment. The degree of extraction over thesame timeperiodwasroughly50%;consequently, the change in mercury concentration due to dilution was neglected. Mercury in the aqueous phase was measured using a Perkin-Elmer Model 3030 atomic absorption spectrophotometerata wavelengthof 253.7. The precision of multiple readings of the same sample was generally within 5% while that of duplicated experiments ranged from 3 to 10%. For the purpose of modelingthe kinetics and measuring drop size, the model experimental system of Skelland and Lee (1981) was used. The stirred tank reactor consisted of an 8-L glass tank having a diameter of 22.5 cm and a height of 25 cm and containing four aluminum baffles havingdimensions of 2 X 22 em. Mixingwasaccomplished using asingle-stage,sixflat bladeRushton turbine powered by a Lightnin Model DSlOlO motor. Photographs of the dispersed oil phase were taken using an Olympus Boroscope Model OES F100-OHH-000-30 attached to an Olympus Model OMPC 35-mm camera. The light source wasanOlympusModelKM1-5multifunctionallight source fitted with a fiber opticcable. A schematicrepresentation of the tank setup is shown in Figure 2. Kodak Gold 1600 color film was used in the camera, which was set at the fastestshutter speed, 1/1OOO8. Exactly 200 droplets were counted at each agitation setting, and the Sauter mean diameter was calculated. The mass transfer coefficients for the stirred cell contactor and the stirred tank reactor were calculated by measuring the rate of transfer of heptanoic acid from the organic phase to the aqueous phase. The extraction rate is known from the literature to be aqueous phase mass transfer limited (Skelland and Lee, 1981). The organic phase consisted of 20 wt/wt % heptanoic acid in tetradecane with 10 wt/wt % CO-210. The aqueous phase was DI water. The experimental procedure for determination of the mass transfer coefficient in the stirred cell contador was similar to that of the mercury extraction experiment. The aqueous phase samples were analyzed for heptanoic acid using a Dionex Series 4500 ion chromatograph equipped with the AI-450 software package. Heptanoic
2856 Ind. Eng. Chem. Res., Vol. 32, No. 11,1993 Lightnin Motor
Fiber Optic Light Soume
25
i
cm
2501 . . . . . . . . . . . . . . . . . . . . . . . . 0 2 4 6 8 10 12
Time (min)
Figure 3. Effect of mixing on extraction kinetics in a stirred 1
-22.5
Cm
+
\-
Figure 2. Schematic representation of the photographic setup in the batch stirred tank.
eell-long times. Over the range 5W90rpm, extraction kineties are strongly affected by mixing rata when all other variables are held constant. 0.345 M Oleic Acid pH 2.6
./
70 rpm
acid extraction rate in the stirred tank reactor was monitored continuously using an Orion Model 140 conductivity meter interfaced with a computerized data collection program that collected data at a rate of 2 readingshecond. Results and Discussion Mercury Extraction Kinetics i n the Stirred Cell Contactor. Initial experiments for determination of mercury:oleic acid extraction kinetics were carried out in the 8-L stirred tank reactor using a 1 0 1 aqueous:organic ratio; however, the extraction rate was so fast that >90% extraction wascompletein lees than 1min. Consequently, experiments were conducted in the stirred cell contador. Danckwerta (1970) first used a stirred cell contactor as an experimental model of a packed column to evaluate the kinetics of gas-liquid reactions. Stirred cells have also been used extensively by Nanda and Sharma (1966,1967, 1983) for examination of the kinetics of liquid-liquid extraction with reaction. More recently, stirred cell contadorshave been used for the evaluation ofthe kinetics of metal extraction by liquid ion exchangers. Such examples include extraction of copper by benzoylacetone (Kondoet al., 1978),extraction ofcobalt,copper, andnickel by bis(2-ethylhexy1)phosphoric acid (Komasawa and Otake, 1983; Brisk and McManamey, 1969). extraction of zinc by bis(2-ethylhexy1)phosphoric acid (Huang and Juang, 1986; Uribe et al., 1988). This apparatus has the advantage of a well-defined interfacial area for reaction. The area per unit volume is also small (compared to a stirred tank reactor); thus, extensive reaction rates are considerablyreduced. Different regimes of a reaction can be studied by varying the mixing rate in the stirred cell (effect of mass transfer coefficient on reaction rate) and by varying the concentration of different species involved in the reaction to deduce a rate expression. For these reasons, the stirred cell contactor is ideal for examining the kinetics of Hg2+extraction with oleic acid. Figure 3 shows the effect of mixing speed in the stirred cell on mercury extraction kinetics. Over the range examined, 5W30 rpm, the extraction kinetics are strongly affected by mixing speed when all other variables such as
y = 6.8854e-06 * x^(l.2019)R= 0.98885
100 I 0.001
0.002
0.003
0.004
0.
5
Initial Hg Concentration (molll) Figure 4. Effect of initial mercury concentrationon extractionrate. The slope of the line is 1.2. This can effectively be interpreted to be first.order kinetics with respect to mercury concentration over the range examined.
[Hg**l~,[oleic acidlo, and [H+lo are held constant. At speedsgreaterthan lWrpm,someripplingattheinterface was observed; therefore, experiments were confined to the 3C-90 rpm range. Theinitialextractionrateofmercwyfromtheaqueoua phase can be calculated as follows:
",
dx 1 1 --- -[moV(cm2.s)l (3) Odt A 601ooO where [Hglo is the initial mercury concentration in the aqueous phase (mol/L), X is the dimensionless mercury concentration in the feed phase at time, t b i n ) , V, is the volumeoftheaqueousphase(mL),andAistheinterfacial area (an2). In general, evaluation of the intrinsic kinetics of a two-phase reaction requires that the experiments be performed in the region where the rate of reaction is no longer affected by the mixing rate. In that region, mass transfer to the aqueouslorganic phase interface is sufficiently high that the reaction is controlled by the intrinsic kinetics. Figure 3 shows that the rate of reaction has not leveledoffat thehighest mixingspeed, whichimpliesthat the reaction is still in the mass transfer regime. Theeffectofinitialmercuryconcentrationontheinitial extraction rate is shown in Figure 4 for the following conditions: pH 2.65, [oleic acidlo = 0.345 M,70 rpm. The data fall on a straight line having a slope of 1.2. Within R = [Hg]
Ind. Eng. Chem. Res., Vol. 32, No. 11, 1993 2857 Table I. Rate of Reaction for Different Metals and Ion Exchangers ion metal exchanger Hg2+ oleic acid Zn2+ DPEHPA
rate [mol/(cm2.s)l comment reference 3 X le9 this work 5 x 10-10 Huana and JuAg, 19% 5 x 10-10 Komasawa and Ni2+ DPEHPA Otake, 1983 pH 5.5 Kondo et al., 1978 Cu2+ benzoylacetone 2 X 10-lo pH 7.5 Kondo et al., 1978 Cu2+ benzoylacetone 8 X 1 P 10-8 ,
1
-
9 I
I
-.-m .e -
= I
IHSl,=500 PPm pH-2.65 50 rpm
!
I
0.01
0.1
! I
1
Initial Oleic Acid Conc (mol/l)
N -
E
Y L
-
10q9
In
E
lo'*
m=-0.19,-0.17
1 I
I
[Hglo = 475 ppm Oleic Acid = 0.345 M 1 0 9 ~ , , , , , , , , , ~ , 1 , , ~ 1 , , , 1 , , , 1.4 1.6 1.0 2 2.2 2.4 2.6
Equilibrium pH
Figure 5. Effect of pH on extraction rate. While the overall rate of extraction at each pH increases with mixing speed, for a given mixing speed, the rate of extraction is essentially independent of pH. The letter -m'' is the slope of the regressed line.
experimental error, the rate can effectively be interpreted to be first order with respect to mercury concentration over the range 0.001-0.004 mol/L. The initial extraction rate of mercury at 0.004 mol/L is compared to the rates of extraction of other heavy metals by ion exchangers in Table I. Mercury extraction rate is well over an order of magnitude higher than any of the other metalion exchange systems with the exception of copper extraction at pH 7.5, where the rates are of the same order of magnitude. At pH 7.5,copper extraction kinetics are known to be mass transfer limited (Kondo et al., 1978). In Figure 5,the rate of mercury extraction is plotted as a function of pH at several different mixing speeds. As in Figure 3, the overall rate of extraction at each pH increases with mixing speed; however, a t a given mixing speed, the rate of extraction is essentially independent of pH over the range 1.8-2.55. In addition, the lines are parallel indicating that there is no transition between different reaction regimes. Figure 6 shows the initial extraction rate as a function of oleic acid concentration over the range 0.032-0.32 mol/L. The rate at these conditions is essentially independent of oleic acid concentration. This range of oleic acid concentration was also utilized in the microemulsion experiments. Film Theory Models for Interpretation of the Kinetics of Two-PhaseReactions. Mercury extraction kinetics can be interpreted using film theory predictions for two-phase reactions (Sharma, 1983). In fact, film theory was used to interpret copper extraction kinetics with benzoylacetone in a stirred cell (Kondo et al., 1978). In attempting to determine which of the reaction regimes is controlling, several assumptions are made: (1) The reaction is irreversible; (2) Hg2+is insoluble in the organic phase; (3) oleic acid is sparingly soluble in the aqueous phase and as a consequence,the reaction is homogeneous; and (4)there is no mass transfer resistance in the organic
Figum 6. Effect of oleic acid concentration on extraction rate. The rate of extraction is essentiallyindependent of oleicacid concentration overtherange0.0324.32M. Theletter 'm"isthes1opeoftheregressed line.
phase. Assumption 1 is reasonable considering that initial rate data is used to calculate the extraction rate. In addition, the equilibrium experiments indicate that the experimental conditions overwhelmingly favor the forward extraction (mercuryinto the organic phase). Assumption 2 is valid because control experiments show that Hg2+is not extracted into tetradecane without the presence of oleic acid. For assumption 3,the solubility of oleic acid in water is estimated by measuring the total organic carbon of an aqueous sample after prolonged contact with the organic phase. The solubility is approximately 1 X 10-4 moUL, which is considerably lower than typical "sparingly soluble" materials (1 X 10-"1 X 103 mol/L) (Nanda and Sharma, 1966). This clearly is the weakest of the four assumptions because the low solubility suggests that the reaction occurs at the interface rather than in the bulk solution. However, in analyzing the results of the stirred cell experiments, it is useful to employ the basic principles of film theory models to help discern between different reaction regimes. Assumption 4, no mass-transfer limitations in the organic phase, is valid because oleic acid is in excess compared to mercury. In addition, the distribution coefficient for the mercury:oleic acid complex is favorable. Film theory predicts four possible reaction regimes dependingupon the relative rates of diffusion and reaction. 1. Very Slow Reaction. In this regime, the reaction is so slow that only the kinetics are important; diffusional factors are unimportant. For this reaction regime, the reaction rate is not affected by mixing since the rate is controlled by the intrinsic reaction kinetics. Clearly, this is not the case for the mercury:oleic acid system, as shown in Figure 3. 2. Slow Reaction. In this regime, the concentration of the ion exchanger in the bulk aqueous phase is zero, but is finite in the mass transfer film. The rate expression in this case would be first order in oleic acid concentration. In this system, however, the rate is essentially independent of oleic acid concentration for the range of interest for microemulsion extractions (0.032-0.32 M), as shown in Figure 6. This regime does not account for the observed kinetics. 3. Very Fast Reaction. The ion exchanger is depleted within the mass transfer film while the concentration of metal is constant. This regime is a special case where a first-order reaction in ion exchanger has an observed rate that is proportional to the ion exchanger concentration
2858 Ind. Eng. Chem. Res., Vol. 32, No. 11, 1993
Sh, = c,(Sc,)o.6We[Re
+ (2)(:)Re2]o's[
1+
(;)( $(
1)""]
(4)
where
Q
0
0 consequently
k,
-y = 0.97738 e"(-0.046671~)R= 0.98949 90 rpm, 18% Heptanoic acid in C14+10% CO-210 I
"
I
I
,
"
I
~
~
'
I
' r
whereas for reactions that are zero order in ion exchanger, the observed rate is proportional to the l/2 power. This is most likely not the reaction regime for mercury extraction with oleic acid since the observed rate is independent of oleic acid concentration. 4. Instantaneous Reaction. The reaction is so fast that it is assumed to occur in an infinitesimally thin plane. In this case, the rate is independent of ion exchange concentration but is proportional to metal concentration and the aqueous phase mass transfer coefficient. This rate expression is consistent with the first-order kinetics in mercury concentration, shown in Figure 4. Thus, the rate of mercury extraction with oleic acid is concluded to be instantaneous and controlled by aqueous phase mass transfer. In fact, given this interpretation of the data, the mass transfer coefficients for the stirred cell can be calculated from the slope of the data at each agitation rate in Figure 3. The mass transfer coefficients range from 0.001 to 0.004 cm/s. These values are within the range of mass transfer coefficients determined for stirred cells (Nanda and Sharma, 1967; Danckwerts, 1970). The next section will discuss the actual measurement of the mass transfer coefficient in the stirred cell to allow for a direct comparison with the mercury extraction rate. Mass Transfer Coefficient Determination in the Stirred Cell. The mass transfer coefficient was measured for the stirred cell at a mixing rate of 90 rpm. The organic phase consisted of 18 wt/wt % heptanoic acid solution in tetradecane with 10% CO-210. Heptanoic acid is a good reagent for studies of aqueous phase controlled mass transfer because the distribution coefficient between the organic and aqueous phases is large. Thus, most of the mass transfer resistance is maintained on the aqueous side (Skelland and Lee, 1981). The rate of transport of heptanoic acid is shown in Figure 7. Plotted as a firstorder rate expression, the data follow a straight line having a slope of 0.0467. By taking into account the interfacial area and volume of the aqueous phase, the mass transfer coefficientfor heptanoic acid at the given stirring condition is calculated to be 0.002 48cm/s. McManamey et al. (1973) developed a correlation for mass transfer coefficients in stirred cells:
D112 (5) Here, p , p, and D are density, viscosity, and diffusivity of phases 1and 2, respectively. The diffusivity of heptanoic acid reported by Skelland and Lee (1981) is 6.00 X lo4 cm2/s . The diffusivity of Hg2+was estimated using the Nernst-Haskell equation (Reid et al., 1977)and has a value of 1.22 X 10-5 cm2/s. The mass transfer coefficient measured for heptanoic acid can be converted into a mass transfer coefficient for Hg2+by taking into account the difference in diffusivities using the proportionality described in eq 5. The mass transfer coefficient calculated for Hg2+,then, is 0.003 53 cm/s. This value compares very favorably to 0.0031 cm/s, which is the mass transfer coefficient calculated for the stirred cell from the slope of the mercury extraction data (Figure 3) at 90 rpm. These results provide additional support for the conclusion that mercury extraction is mass transfer limited. This information can now be incorporated into a diffusion/reaction model for batch extraction of mercury in a stirred tank reactor. Modeling Mercury Extraction Kinetics in a Batch Stirred Tank Reactor. On the basis of the results presented in the previous sections, the following assumptions are made: mercury extraction with oleic acid is a mass transfer limited process; at the aqueous/organic interface, mercury is in equilibrium with oleic acid per reaction 1; as mercury diffuses into the drop, the complex dimerizes per reaction 2. The mathematical description of this process is as follows: Bulk Phase: 0:
where (7) The following initial condition applies: at t = 0, [Hgl, = [Hgli = [Hgl,, for r < R, [Cl = 0, [Bl = [BlO,[Hgli = 0
Organic Phase: In the organic phase, the active oleic acid (Le. dimer) concentration is Vm at a[Bl = VmDB[
$.
2
""'1
(9)
r ar The concentration of the mercury:oleic acid complex is
Ind. Eng. Chem. Res., Vol. 32, No. 11, 1993 2859 Table 11. Effect of Mixing Speed on Mass-Transfer Coefficient in Stirred Tank
C2 represents the complex dimer that is formed in the organic phase as a result of the presence of oxygen in the surfactant, where [C21= KJoxyI [C12 (11) Because the oxygen concentration of the 10 w t 5% CO-210 is approximately 0.7 mol/L compared to the typical mercury complex concentration in the organic phase of 10-4 mol/L, the oxygen concentration can be taken to be constant over the course of the extraction. Consequently, a new equilibrium constant can be defined as follows: K’ = K2[oxyl (L/mol)
a[ci, a -- - K’ $CI2 at
am at
This expression can now be substituted into eq 10. The initial conditions are at t = 0, [Bl = [BI,, [Cl = 0, and [C21= 0 The boundary conditions are
~ [ B--I a[ci --0 ar
ar
at r = O
Sauter mean diama (cm) 0.0166 0.0152 0.0145 0.0141
heptanoic acid kLa (cm/s) 0.00462 0.00525 0.00787 0.00901
Hg2+kLb (cm/s) 0.00658 0.00748 0.0112 0.0128
a Experimentally measured value. Value calculated from heptanoic data, corrected for Hg diffusion coefficient (see text).
Sauter mean diameter, defined below, is typically used as the length scale in mass transfer systems (Ho et al., 1982).
(12)
Therefore,
= 2K’[Cl-
mixing rate (rpm) 350 400 450 500
(14)
The following dimensionless variables are defined: length scale, X = r/R; time, T = D,t/R2; bulk Hg, A = [Hgl/[Hglo; oleic acid, BB = [BI/[B]o; complex 1, CHG = 2[CI/[Blo; complex2,CC = 4[C2]/[B]o;volumefraction, 4 = (Vi + Vm)/Ve;Biot number, Bi = kd/De. The model equations are solved using an implicit finite difference method (Carnahan et al., 1969). Two simplifying assumptions are made: 1. The pH of the bulk is fixed at the experimentally measured equilibrium pH. This assumption is reasonable because the pH range for the most efficient extraction of mercury (pH 2.7-3.2) occurs in the horizontal portion of the percent mercury extracted vs pH curve-the range where mercury extraction is not very pH sensitive (Larson and Wiencek, 1992). A similar simplification is made by Lorbach et al. (1986) for copper extraction. 2. The diffusivity of the free oleic acid and the complex are assumed to be equal. Although the diffusivities of CHG and BB differ based on calculation using the WilkeChang correlation (Dc = 1.002 X l@cm2/sand D B= 1.53 x 10-6 cm2/s), this assumption is commonly used in facilitated transport modeling (Ho and Li, 1992). Equal diffusivities of complex and carrier are used to simplify the model equations for zinc extraction with bis(2ethylhexy1)phosphoric acid (DSEHPA) (Lorbach and Marr, 1987). Physical Properties of the Batch Stirred Tank. Dropsizes in t h e stirred tank system were measured at four agitation rates and converted to Sauter mean diameter, d32. The results are summarized in Table 11. The
The aqueous phase mass transfer coefficient of the stirred tank system was measured at several mixing speeds by measuring the rate of transfer of heptanoic acid. From the slope of the first-order plot of the heptanoic acid extraction rate and the Sauter mean diameter, calculated from the experimentally measured droplet sizes, the aqueous phase mass transfer coefficient for heptanoic acid can be calculated a t each mixing speed. The corresponding mass transfer coefficient for Hg2+can then be determined using the relationship between the mass transfer coefficient and the square root of the diffusivity from Skelland and Lee (1981). These results are also presented in Table 11. Mass transfer coefficients for this system range from 0.006 58 to 0.0128 cm/s for stirring speeds ranging from 350 to 500 rpm. Recall that the stirred cell contactor experiments showed mercury extraction with oleic acid to be mass transfer limited for the conditions corresponding to a mass transfer coefficient of 0.003 53 cm/s. Because of instabilities at the interface, experiments at higher mixing speeds in the stirred cell (concomitanthigher mass transfer coefficients) could not be performed. Unfortunately, mixing speeds in the stirred tank of less than 350 rpm (concomitant lower mass transfer coefficients) could not be examined because of the inability to adequately disperse the organic phase. Consequently, for the purposes of modeling the extraction kinetics, the conclusion drawn from the stirred cell experiments, namely that of mass transfer control, is extrapolated to the conditions of the stirred tank system. Results of Model Calculations. In the experiments to verify the model, the aqueous phase volume was 5 L and the organic phase volume was 0.5 L. The agitation rate was 350 rpm. Under these conditions, as discussed, the Sauter mean diameter,d32 was 0.0166 cm and the mass transfer coefficient was 0.006 58 cm/s. The results of model simulations, shown in Figures 8-10, illustrate the effect of Biot number on the mercury extraction kinetics and organic phase concentration profiles. The Biot number is a dimensionless number that relates the diffusion time scale in the droplet to that of external mass transfer. In these simulations, the Biot number is varied by changingthe value of the masstransfer coefficient. In Figure 8, dimensionless feed phase concentration is plotted as a function of dimensionless time for different values of the Biot number at short (Figure 8a) and long (Figure 8b) times. Biot numbers of 251,54.5, 31.1,15.1, and 7.58 correspond to mass transfer coefficients of 0.033, 0.006 58, 0.0041, 0.0018, and O.OOO1 cmls, respectively. Because mercury extraction is instantaneous, the extraction kinetics are greatly affected by the feed phase mass transfer coefficient. The points on the graph
2860 Ind. Eng. Chem. Res., Vol. 32, No. 11, 1993 1~ ~ ' " " " ' " " ' " " ' " " ' " " ' " " " " "
Hgo=460 pprn pHzl.94
:
.
Phase
0 0
0.2
0.1
0.3
0.4 0.5 Tau (DVI?)
0.6
0.7
Feed
L
0.2
0.6
0.4
0.8
0.8
1
1.2
rR
b
Biot#=67.1, $=0.0081 cm/s
-
y
0.8
-
-
E
a
0
5
10
15
20
0
25
are experimental data, and the highlighted curve represents model predictions using the experimentally measured d32 and kL (Biot number = 54.5). The agreement between calculated and measured values is quite acceptable considering that there are no adjustable parameters in the model. The model consistently overpredicts the extraction rate at the initial stages of the extraction. The model predicts the final mercury concentration in the aqueous phase quite well (16.1 ppm predicted vs 20 ppm experiment). There are several possible explanations for the difference between the experimentally measured and predicted kinetics. These differences could be a result of theoretical and/or experimental error. One possibility is that kinetic factors may come into play in the batch stirred tank reactor as a result of the high mass transfer coefficient compared to that of the stirred cell (0.006 58 vs 0.0035 cm/s). The mercury:oleic acid reaction is assumed to be under mass transfer control at kL = 0.006 58 cm/s. If the intrinsic kinetics of the reaction become important at this mass transfer rate, the rate of extraction would be overpredicted by the model. Another factor that may affect experimentally measured mercury concentration at initial times is the time required for complete dispersion of the organic phase compared to the time of the first extraction sample. Experimentally, the clock is startedafter the organic phase is charged to the reactor. It takes 15-20 s for complete
0.4
0.6
0.8
1
rR
Tau ( O W 2 )
Figure 8. Effect of Biot number on extraction of Hg2+ at short (a) and long (b)times. Since mercury extractionis mass transfer limited, extractionkineticsare greatlyaffected by the maea transfercoefficient (Biot number). The highlighted curve is the model calculation representing the experimentalconditions. The discrepancy between model and experiment may be due to sample-handling difficulties or organic phase precipitation.
0.2
c
1 I " " " ' " " " " " " I
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a
Figure9. Effect of Biot numberon distributionof mercury complex dimer in the organic phase.
dispersion of the organic phase, during which time mercury is being extracted. However, the model assumes that the organic phase is completely dispersed a t t = 0. This type of error would tend to overpredict the theoretical extraction rate because complete dispersion implies availability of all the mass transfer area. Clearly this is not the case when the organic phase is first added to the reactor. The discrepancy between theory and experiment at the longer times may be due to inhibition of extraction kinetics due to partial precipitation of organic phase mercury complex. Precipitation of mercury in the organic phase would tend to "coat" the droplets, making them impermeable. This would have the effect of reducing the mass transfer area. Solids in the organic phase would also hinder diffusion of
Ind. Eng. Chem. Res., Vol. 32, No. 11, 1993 2861
a 1
-b
mercury:oleic acid dimer near the surface at short times. At longer times, as the complex diffuses to the interior of the drop and equilibrium is established a t every point in the drop, the concentration profile flattens out and eventually becomes completely horizontal. The concentration profiles for unreacted oleic acid are shown for different values of the Biot number in Figure 10. Again, at low Biot numbers, very little of the oleic acid is consumed because so little mercury has been transported to the interface. As the Biot number increases, the concentration profile for oleic acid changes dramatically a t short times. Much of the oleic acid is consumed; however, at longer times, the concentration profile flattens because equilibrium between oleic acid, the monomer, and dimer complexes must be satisfied at every point.
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Figure 10. Effect of Biot number on distribution of free oleic acid in the organic phase.
the unreacted oleic acid-making it unavailable for reaction at the surface. Figures 9 and 10 illustrate the effect of Biot number on the distribution of the organic phase complexes in the emulsion globule. In Figure 9, the effect of Biot number on the distribution of complex dimer is shown as a function of dimensionless time. At low Biot numbers (Figure 9a), very little mercury is transported to the organic phase for reaction; consequently, mercury complex dimer does not build up at the surface, but diffuses to the interior. The concentration gradient between the bulk feed phase and emulsion surface is high throughout the extraction. A t larger Biot numbers, as shown in Figure 9b,c, much more mercury is transported to the feed phase/organic phase interface for reaction. This results in a build-up of
~
The kinetics of extraction of Hg2+with oleic acid are first order in [Hg2+loover the range 0.001-0.004 mol/L, zero order with respect to pH for the range 1.8-2.55, and zero order with respect to [oleic acid10for the range 0.0320.32 mol/L. These ranges encompass the practical range of interest for extraction of mercury, and the results are consistent with instantaneous reaction kinetics that are controlled by aqueous phase mass transfer. This conclusion is supported by an independent measurement of the stirred cell mass transfer coefficient in which the masstransfer rate and mercury extraction rate were virtually identical for the same mixing condition. A diffusion/ reaction model for batch extraction of mercury is developed using experimentally determined equilibrium extraction, reaction kinetics, drop size, and mass-transfer coefficient. The effect of feed phase mass transfer coefficient on extraction kinetics follows the expected trends. Without the use of adjustable parameters, the comparison between theory and experiment is quite good, although the experimentally observed extraction rate is somewhat slower than the model prediction. The powerful feature of the model is the ability to probe the inside of the organic phase; consequently, it is also possible to "observe" the effect of mass transfer coefficient on the concentration profile of the organic phase species. Future work will be directed at incorporating the internal phase stripping reaction into the model to describe microemulsion extraction kinetics. Acknowledgment This work has been funded by Hazardous Substance Management Research Center of New Jersey, Grant No. PHYS-28 (a NSF Industry/University Cooperative Research Center and an Advanced Technology Center of the NJ Commission on Science and Technology), New Jersey Water Resources Research Institute (USGS Grant No. G-1577-02),and Merck and Company, Inc. The authors also greatly appreciate the assistance of Dr.B. Raghuraman. Nomenclature a = surface area per unit volume (cm2/crn3)
[Bl = oleic acid dimer concentration, (HR)2 (mol/cm3) [Cl = mercury/oleic acid complex 1 concentration, (HgR2.2RH) (mol/cm3) [Czl = mercury/oleic acid dimer concentration (mol/ cm3) D = diffusivity (cm2/s) [HI = hydrogen ion concentration (mol/cm3) [Hgl = mercury ion concentration (mol/cm3) Keg = equilibrium constant for extraction
2862 Ind. Eng. Chem. Res., Vol. 32, No. 11, 1993
Kea2 = equilibrium constant for dimer formation (mol/’L)2 K’ = eauilibrium constant for dimer, simplified (mol/L) k~ = mass-transfer coefficient (cm/s) [oxy] = oxygen concentration in surfactant (mol/cm3) R = emulsion droplet radius (cm) t = time ( 8 ) V = volume (cm3) Ve = volume of external or bulk phase (cm3) Vi = volume of internal or stripping reagent phase (cm3) V, = volume of membrane (oil) phase (cm3) Subscripts e = external or bulk phase i = interface 0 = initial concentration s = surface
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Komasawa, I.; Otake, T. Kinetic Studies of the Extraction of Divalent Metals from Nitrate Media with Bis(2-ethylhexy1)phosphoricAcid. Znd. Eng. Chem. Res. 1983,22, 367-371. Kondo, K.; Takahashi, S.; Tsuneyuki, T.; Nakashio, F. Solvent Extraction of Copper by Benzoylacetone in a Stirred Transfer Cell. J. Chem. Eng. Jpn. 1978,11, 193-198. Kondo,K.; Kita, K.; Nakashio, F. Extraction Kinetics of Copper with Liquid Surfactant Membranes in a Stirred Transfer Cell. J.Chern. Eng. Jpn. 1981,14,20-25. Larson, K. A.; Wiencek, J. M. Liquid Ion Exchange for Mercury Removal from Water over a Wide pH Range. Znd. Eng. Chem. Res. 1992,31,2714-2722. Lorbach,D.; Marr,R. Emulsion Liquid Membranes: Part 11.Modeling Mass Transfer of Zinc with Bis(2-ethylhexy1)dithiophosphoric Acid. Chem. Eng. Process. 1987,21,83-93. Lorbach, D.; Bart, H.; Marr, R. Maes Transfer in Liquid Membrane Permeation. Ger. Chem. Eng. 1986,9,321-327. McManamey,W. J.; Davies,J. T.; Woollen,J. M.; Coe, J. R. Influence of molecular diffusion on mass transfer between turbulent liquids. Chem. Eng. Sci. 1973,28,1061-1071. Moore, F. Solvent Extraction of Mercury from Brine Solutions with High-Molecular-Weight Amines. Curr. Res. 1972,6,525-529. Nanda, A.; Sharma, M. Effective Interfacial Area in Liquid-Liquid Extraction. Chem. Eng. Sci. 1966,21,707-714. Nanda, A.; Sharma, M. Kinetics of Fast Alkaline Hydrolysisof Esters. Chem. Eng. Sci. 1967,22,769-775. Reid, R.;Prausnitz, J.; Sherwood, J. The Properties of Gases and Liquids; McGraw Hill: New York, 1977;p 590. Seeley, F.; Crouse, D. Extraction of Metals from Chloride Solutions with Amines. J. Chem. Eng. Data 1966,11,424-429. Sharma, M. Extraction with Reaction. In Handbook of Solvent Ertraction; Baird, M., Hanson, C., Eds.; Wiley Interscience: New York, 1983; p 37. Skelland, A.; Lee, J. Drop Size and Continuous-Phase Mass Transfer in Agitated Vessels. AZChE J. 1981,27,99-108. Tavlarides, L.; Bae, J.; Lee, C. Solvent Extraction, Membranes, and Ion Exchange in Hydrometallurgical Dilute Metals Separation. Sep. Sci. Technol. 1987,22,581-616. Uribe, I.; Wongswan, S.; Ortiz,E. A Systematic Method for the Study of the Rate-Controlling Mechanisms in Liquid Membrane Permeation Processes. Extraction of Zinc by Bis(2-ethylhexy1)phosphoric Acid. Znd. Eng. Chem. Res. 1988,27, 1696-1701. Webs, S.;Grigoriev,V.; Muhl, P. The Liquid Membrane Process for theseparation of Mercuryfrom Waste Water. J.Membr. Sci.1982, 12,119-129. Wiencek, J.; Qutubuddin, S. Solubilization in Microemulsions and Application to Separations. Colloids Surf.1988,29, 119-131. Wiencek, J.; Qutubuddin, S. Microemulsion versus Macroemulsion. J. Membr. Sci. 1989,45,311-312. Wiencek, J.; Qutubuddin, S. Microemulsion Liquid membranes. 11. Copper Ion removal from buffered and Unbuffered Aqueous Feed. Sep. Sci. Technol. 1992,27,1407-1422. Receiued for review March 11, 1993 Revised manuscript received August 6,1993 Accepted August 12, 1993O Abstract published in Advance ACS Abstracts, October 1, 1993.
