Ind. Eng. Chem. Res. 1992,31,927-934
to calculate the absorption rate coefficient and then compare it with the experimental values. The results are presented in Figure 9 with mean error no greater than 10%.
Acknowledmnent This work was supported by the Science Foundation of National Education Committee of China. Nomenclature C = concentration in liquid phase, kmol/m3 Co = initial component concentration, kmol/m3 C* = concentration in equilibrium condition, kmol/m3 D = diffueivity in liquid phase, mz/s E = activation energy, kJ/mol H = solubility coefficient, kmol/(m3.MPa) K,, Kb,K, = equilibrium constants k = absorption rate coefficient, kmol/ (m2.s.MPa) kL = mass-transfer coefficient in liquid film, m/s k2, k p = reaction rate constant of reactions 2 and 7,respectively, m3/(kmol*s)
kzapp= apparent firsborder rate constant, kZapp= kzC,, k = apparent first-order rate constant, kp,app= kpCp, fi:Pabsorption rate, kmol/(m2.s) p = partial pressure, MPa p * = partial pressure in equilibrium condition, MPa r = reaction rate, kmol/(m3-s) T = absolute temperature, K X = content of COz absorbed in liquid phase, kmol/m3 y = conversion Greek Symbols r = liquid flow rate per unit width of surface, kg/(ms) p = density of liquid, kg/m3 ec. = viscosity of liquid, Pa/s Subscripts COz = corresponding to COz am = corresponding to MDEA
927
p = corresponding to piperazine Registry No. MDEA, 105-59-9;COz, 124-38-9;piperazine, 110-85-0.
Literature Cited Appl, M.; Wagner, U.; Henrici, H. J.; Kuessner, K.; Voldamer, K.; Fuerst, E. Removal of C02And/or H a And/or COS From Gases Containing These Constituents. U S . Patent 4,336,233,1982. Barth, D.; Tondre, C.; Lappai, G.; Delpuech, J. J. Kinetic Study of Carbon Dioxide with Tertiary Amines in Aqueous Solutions. J. Phys. Chem. 1981,85,3660-3667. Barth, D.; Tondre, C.; Delpuech, J. J. Kinetics and Mechanisms of the Reaction of Carbon Dioxide with Alkanolamines: A Discussion Concerning the Cases of MDEA and DEA. Chem. Eng. Sci. i984,39,i753-i757. Blauwhoff, P. M. M.; Versteeg, G. F.; Van Swaaij, W. P. M. A Study on the Reaction Between CO, and Alkanolamines in Aaueous Solutions. Chem. Eng. Sci. 1983,38,1411-1429. Danckwerta, P. V. Gas-Liquid Reactions; McGraw-Hill: New York, 1970;p 19. Haimour, N.; Bidarian, A.; Sandall, 0. C. Kinetics of the Reaction Between Carbon Dioxide and Methyldiethanolamine. Chem. Eng. Sci. 1987,42,1393-1398. Meissner, R. E.; Wagner, U. Low-energy Process Recovers C02. Oil Gas J. 1983,Feb, 55-58. Stephens, E. J.; Morris, G. A. Determination of Liquid-Film Absorption Coefficients. Chem. Eng. Prog. 1951,May, 232-242. Tomcej, R.A.; Otto, F. D. Absorption of C 0 2 and N20 Into Aqueous Solutions of Methyldiethanolamine. AIChE J. 1989,35,861-864. Versteeg, G. F.; Van Swaaij, W. P. M. On The Kinetics between C02 and alkanolamines both in aqueous and non-aqueous solutions11. Tertiary Amines. Chem. Eng. Sci. 1988,43,587-591. Wang, Y. W. Kinetics of C02 absorption in Activated Methyldiethanolamine. M.S. Thesis, East China University of Chemical Technology, 1988. Yu, W. C.; Astarita, G. Kinetics of Carbon Dioxide Absorption in Solutions of Methyldiethanolamine. Chem. Eng. Sci. 1985,40, 1585-1590. I
Received for review March 13, 1991 Revised manuscript received September 17,1991 Accepted November 8,1991
Diffusion of Phenylacetic Acid and Vanillin in Supercritical Carbon Dioxide Tony Wells,* Neil R. Foster, and Rodney P. Chaplin School of Chemical Engineering and Industrial Chemistry, University of New South Wales, P.O.Box 1, Kensington 2033, N S W Australia
Binary diffusion coefficients, Ol2, of phenylacetic acid and vanillin have been determined in supercritical carbon dioxide using the Taylor-Aris tracer response technique. DI2values are reported for temperatures ranging from 308 to 318 K and densities between 600 and 850 kg/m3. The binary diffusion coefficients, D12,have a magnitude of m2/s. The influence of pressure, temperature, and carbon dioxide density on the D12values is examined. The applicability of Stokes-Einstein based correlations and the free volume diffusion model is also evaluated. Introduction The advantages of utilizing solvents in a supercritical state to perform extractions and achieve separations are documented williams lg81; et 1983)' The use of supercritical COz,the most commonly employed supercritical fluid (SCF),has considerable potential in the *,'
*Address correspondence to this author at Faculty of Chemical Engineering, Delft University of Technology, P.O.Box 5045,2600 GA Delft, The Netherlands.
0888-5885/92/2631-0927$03.00/0
flavor and fragrance industry as it is inexpensive, nontoxic, and nonflammable. Additionally C 0 2is an effective solvent at ne^ ambient conditions (30-60 oc), and conse-
quently the for thermal degradation, characteristic of alternative distillation is minimized. The potential for the use of SCFs in the extraction of flavor and fragrance has in n u m e r o ~investigations of their solubility in COz (e.g., Wells et al., 1990; Vitzthum and Hubert, 1978; Schutz e t al., 1984). However, there has been little or no information published on the diffusion and mass-transfer characteristics of such 0 1992 American Chemical Society
928 Ind. Eng.Chem. Res., Vol. 31, No. 3,1992
systems. Indeed as several reviewers such as Groves et al. (1984) have observed, there is a notable lack of diffusion data for SCF systems in general. Consequently there are also few theoretical or empirically based models describing diffusion behavior in supercritical systems. The aim of this study was to obtain binary diffusion data for both vanillin and phenylacetic acid in supercritical carbon dioxide. Phenylacetic acid is a constituent of peppermint and rose oils and is the volatile aroma constituent of many foodstuffs, including honey. It is used as a perfume additive to round off blossom odors and is also added to fruit aromas, imparting a sweet honey note. Vanillin is found in many essential oils, in particular the essential oils of the Vanilla planifolia and Vanilla tahitensis beans, as well as in paper mill waste liquors. The main uses for vanillin are as a flavoring agent for foodstuffs and in the rounding off and fixation of sweet, balsamic fragrances. Vanillin is also an important intermediate in pharmaceutical processes such as the production of L-dopa and methyldopa. The data obtained in this study were also used to aaseas the validity of several currently available correlation models. The diffusion Coefficients were measured using the Taylol-Aris tracer response technique. This simple, robust technique has been used to determine diffusion coefficients of gaseous systems (Giddings and Seager, 1960; Bohemen and Purnell, 1961),gas/liquid systems (Pratt et al., 1973), liquid systems (Ouano, 1972; Pratt and Wakeham, 19741, and more recently supercritical fluid systems (Feist and Schneider, 1982; Funazukuri et al., 1989). It is in this last field of study that the relatively uncomplicated nature of the Taylor-Aris technique has led to its extensive use. Theoretical Background Taylor (1953,1954a,b)analyzed the dispersion of a pulse of solute in a solvent in laminar flow as it passed down the length of a circular tube. His analysis of the peak dispersion, and a subsequent more exact description provided by Aris (1956), showed that a narrow pulse of solute will broaden under the combined effects of flow-induced dispersion in the axial direction and molecular diffusion in the radial direction. The analysis conducted by Taylor and Aris was intended only to describe the dispersion of solute pulses in pipelines and was not developed for the prediction of diffusion coefficients. However, an extensive analysis of the pulse dispersion technique as a tool for the determination of D12 values has recently been conducted by Alizadeh et al. (1980). The results of Taylor and Aris show that the initial injected pulse will disperse to form a peak whose concentration profile can be described by the following expression:
r?U& uo 2442 The effective diffusivity, DeB,can be related to the binary diffusion coefficient through 2(X)
=
2D12L
-+ -
Levenspiel and Smith (1957) showed that if the following condition applies the concentration profile resulting from the dispersion of the pulse will be Gaussian in profile. Deff/U& < 0.01 (3) The above expressions were specifically derived for the case where a straight tube was employed. However, the
Figure 1. Schematic of apparatus. 1, syringe pump; 2, COPstream; 3, plug of solute; 4, CO,/solute stream; 5, water bath; 6, coiled capillary tubing; 7, UV detector; 8, rotameter; 9, wet gas meter; 10, pressure transducers; 11, preheat coils; 12, six-port injection valve.
lengths of tubing involved in a typical peak-broadening experiment are quite long and must be coiled in order to be installed in a temperature-regulated bath. As a consequence, secondary flow effects resulting from the action of centrifugal forces on the laminar concentration profile can be introduced. The effect of such forces has been examined extensively (Springston and Novotny, 1986; Alizadeh et al., 1980; Swaid and Schneider, 1979), and it has been determined that provided the following restrictions are adhered to, secondary flow effects can be neglected.
De SCO.~ < 10 (4) In experiments in this study, fluid velocities were maintained such that De Scod< 8. In chromatogaphy the plate height H is defined in the following manner:
H
= a2(x)/L
(5)
By combining eq 1and 5 the binary diffusion coefficient can be expressed in terms of the theoretical plate height:
"[ [ (
D I 2 = -4 H *
I]):
ZP--
(6)
Giddings and Seager (1962) showed that the negative root of the above equation has physical significance when the fluid velocity is greater than the optimal velocity, UoPt, which minimizes H. The optimal velocity is normally very small for liquid and SCF systems and is thus easily exceeded. Experimental Apparatus The final design of the apparatus was determined after a number of different configurations were tested. A schematic of the apparatus is provided in Figure 1. The COz solvent was delivered by a 500-mL syringe pump (ISCO LC-5OOO) to a stainless steel capillary diffusion column. A commercial six-porthigh-pressure injection valve equipped with a 2GpL sample loop was used to inject a solute pulse into the solvent stream. Several options were available for the delivery of the solute to the injection valve. Several authors (Lauer et al., 1983; Funazukuri et al., 1989; Sassiat et al., 1987) chose to dissolve the solid solute in a third component such as methanol. In this study however, to avoid any complexities a r i s i i from the introduction of a third component, it was decided to follow the course taken by Feist and Schneider (1982) and, consequently, dissolve the solute of interest in supercritical COP. To achieve this a 260-mL syringe pump was used to pump COzthrough a 7-pm filter capsule (Nupro ss-2f47-7prn) packed with the solute. The con-
Ind. Eng. Chem. Res., Vol. 31, No. 3, 1992 929 centration of solute in the COzpassing through the sample loop was controlled by adjustment of the fluid flow rate through a line bypassing the filter capsule. In order to reduce the dead volume of the system, low dead volume connections and a low dead volume UV detection cell were utilized. The total dead volume of the apparatus was determined to be less than 40 pL. The injection valve and diffusion coil were both located in a perspex water bath, where the temperature was reg&tad by a Thermoline 170 temperature regulator capable of maintaininga constant bath temperature to within f O . l K. Pressure of both the solute and solvent streams were monitored with Druck Model PDCR610 pressure transducers with an accuracy of h0.2 bar. The purity of liquid COPused was 99.8%. The vanillin and phenylacetic acid were supplied by Ajax Chemicals and were of a minimum 99% purity. An Isco V4 W-visible variable-wavelength detector was employed to monitor the concentration of the solute in the COz stream. A high-pressure cell specifically designed for low dead volume applications was used (Isco Model 0080-072; SCF cell;) dead volume 0.2 pL; pressure rated to 6OOO psig). The wavelengths employed to monitor the solute concentration were maximum absorbance frequencies. These were determined from a UV spectrum obtained for each solute from a commercially available W scanning device (Varian Superscan 3 UV spectrophotometer).
Experimental Procedure Prior to injection of a solute pulse into the solvent stream, the apparatus was allowed to attain thermal, pressure, and flow equilibrium. The 20-pL sample loop was flushed with approximately 2OU-300 pL of fresh solute solution. At the time of injection the pressure in the sample loop was equivalent to that of the dispersion column. Three or four pulses were injected onto the column per run and were spaced at 15-20-min intervals to avoid any overlap of peaks at the detector end of the column. To counteract the adverse effects of initial peak dispersion and dead volume, a two column subtraction method was utilized. Duplicate runs were performed on both a short (2.558 m) and long (14.435 m) length of tubing of the same bore (4 = 1.20 X lo9 m). The results were then subtracted in the following fashion:
As the initial peak dispersion and dead volume were equivalent in both the long and short columns, the subtraction of the two values should cancel their deterious effects. This procedure resulted in a maximum correction of 1.4% indicating that the effects of dead volume and initial peak dispersion were minimal. Linear velocities of between 0.4 and 0.5 cm/s were employed in the majority of experimental runs, resulting in residence times of approximately 1 h for the runs with the long column and 10 min for the short column. The pressure drop along the longer column length was generally less than 1bar. This was not expected to greatly influence the diffusion results obtained. The method used for the determination of the theoretical plate height was similar to that employed by Lauer et al. (1983). The dispersion was assessed by measuring the peak half-width at 0.607 of the peak height-the Gauasian half-width. The plate height was then calculated via the following equation: H =U~o.~o,)~/t,~
(8)
Table I. Solvent Conditions under Which Diffusion Coefficients Were Obtained viscosity, temp, K press., bar density, k17/rn-~ 106 Pa-s 308.15 96.7 700.0 5.663 112.0 750.0 6.376 120.0 768.0 6.658 138.5 800.0 7.195 160.0 828.0 7.708 181.3 8.143 850.0 313.15 103.0 5.052 650.0 114.0 5.674 700.0 132.7 750.0 6.385 163.2 7.201 800.0 210.5 850.0 8.146 318.15 109.4 600.0 4.520 650.0 117.9 5.066 700.0 131.7 5.686 153.7 750.0 6.394 188.0 800.0 7.208
"-
-.-
1
80
'.ThisStudy/
1
100
120
140
180
1
- 0 - Knaff [1Q871
180
200
220
240
Pressure (bar) Figure 2. Diffusion coefficienta of naphthalene in supercritical carbon dioxide as a function of pressure at 308 K. For an accurate analysis to be performed the peaks recorded should be symmetrical. It has been found by several researchers (Sassiat et al., 1987; Feist and Schneider, 1982), however, that polar compounds in particular adsorb strongly onto the column wall resulting in severe tailing of the peaks. In order to quantify the extent of the peak tailing, an asymmetric factor, defined as the ratio between the peak half-widths at 0.1 X the peak height is used. Peaks with an asymmetric factor higher than 1.3 were rejected in this study as being unsuitable for analysis. In order to study the role of various solvent parameters in the diffusion process, it was decided to determine the diffusion coefficients a t three temperatures, 35, 40, and 45 OC, for pressures ranging from 90 to 215 bar. Pressures were chosen so that diffusion at constant densities and viscosities could be studied over the temperature range examined. The conditions examined have been listed in Table I. Density values were determined from an empirical relationship (Pitzer and Schreiber, 1988), and viscosity values were obtained from an empirical equation developed by Altunin and Sakhabetinov (1972).
Results and Discussion Comparison with Previous Data. In order to establish the validity of the chromatographic peak broadening (CPB) method and the performance of the individual apparatus, the diffusion coefficients for the naphthalene/C02 system were determined for a variety of pressures a t 35 "C and compared with data obtained by Knaff and Schlunder (1987). As is shown in Figure 2, there is substantial agreement between the values obtained by Knaff and Schlunder (19871, who employed a pseudesteady-state
930 Ind. Eng. Chem. Res., Vol. 31, No. 3, 1992 Table 11. Experimental Binary Diffusion Coefficients for Phenylacetic acid and Vanillin in C02 diffusion coeff, m2/sX108 temD. K Dress.. bar Dhenvlacetic acid vanillin 1.21 96.7 308.15 1.00 1.06 112.0 308.15 1.02 0.95 120.0 308.15 0.89 0.97 138.5 308.15 0.91 0.86 160.0 308.15 0.84 0.86 181.3 308.15 1.27 1.34 103.0 313.15 1.12 114.0 1.18 313.15 0.95 132.7 1.08 313.15 0.92 163.2 0.98 313.15 0.84 0.87 210.5 313.15 1.42 1.52 109.4 318.15 1.28 1.43 117.9 318.15 131.7 1.20 1.26 318.15 1.06 1.14 153.7 318.15 0.96 1.02 188.0 318.15 1.8 ~
308K
3
1.41
1
_.300
302
304
308
308
310
312
314
318
318
320
Temperature (K) Figure 4. Diffusion coefficients of phenylacetic acid as a function of temperature at constant pressures.
I
750 kg/rn3 0 800 kg/rn3
0.8 SO
'
0.6 306
, 100
120
140
180
180
200
220
I
307
309
240
Pressure (bar) Figure 3. Diffusion coefficients of vanillin as a function of pressure at constant temperatures.
technique, and the current study. The similarity of results obtained by the differing methods was encouraging, as it suggested that the results obtained from the CPB apparatus were accurate. The agreement of data also suggests that the dimensions of the CPB apparatus were accurately determined. The data obtained for the diffusion coefficients of both phenylacetic acid and vanillin in supercritical CO, together with the temperatures and pressures at which the results were obtained are presented in Table 11. The experimental diffusivities ranged from 1.52 X lW8 to 0.84 X m2/s. The results represent the average of three to five runs with a standard deviation of less than 2%. Influence of Pressure at Constant Temperatures. The relationship between diffusion coefficients and pressure at constant temperatures for the vanillin/CO, system is shown in Figure 3. Similar trends were found for phenylacetic acid. It was observed that D12decreased with increasing pressure, a trend reported in all previous studies. The greater pressure sensitivity of D,, at low pressures is probably linked to changes in solvent viscosity or density both of which change rapidly with pressure in this region. Influence of Temperature at Constant Pressure. The relationship between the diffusion Coefficients of phenylacetic acid/C02 and temperature at isobaric conditions is illustrated in Figure 4. Similar behavior was observed for vanillin. While the points shown represent interpolated data over a narrow temperature range, Figure 4 clearly shows a marked increase in the diffusion coefficient as the temperature is increased isobarically. A regression analysis of the data indicates that the diffusion coefficient is pro-
311
313
316
317
319
Temperature (K) Figure 5. Diffusion coefficients of phenylacetic acid as a function of temperature at constant carbon dioxide densities.
-
1.4 \ u)
-
N
E
1.2 -
a
sz
1-
2 1 0.8
0.6 660
I 800
860
700
760
800
860
900
960
Density (kg/m3 Figure 6. Diffusion coefficients of phenylacetic acid as a function of carbon dioxide density.
portional to T4 at lower pressures. The results also show that as the pressure is increased, the dependence of diffusion on temperature decreases but is still high at 170 bar (D120: Tm6). Influence of Temperature at Constant Density. In contrast to the behavior shown at isobaric conditions, little change in the value of D12was observed as the temperature was increased at constant fluid density (Figure 5). As the degree of change was only marginally greater than the experimental errors incurred, it was difficult to quantitatively analyze the influence of isopycnic changes in temperature. Effect of Changes in Solvent Density. One of the unique aspects of dealing with supercritical fluids is the
Ind. Eng. Chem. Res., Vol. 31, No. 3, 1992 931 1.0 I 1.4 -
9
-
1.2
-
N
E
(0
9
a
1-
0.0 0.0-
N
0.4 -
0.2r
0
SO
100
160 -1
200
260
-1
i/\liscosity (Pa s *IO -*I Figure 7. Diffusion coefficients of phenylacetic acid as a function of p-1.
possibility of effecting, with small changes in pressure and temperature, significant changes in both the density and viscosity of the SCF. It is, therefore, important that the role of density and viscosity in the diffusional process be understood. The diffusion of phenylacetic acid as a function of C02 density is shown in Figure 6. As the fluid density increases, the path of the molecule through the solution becomes more hindered and the value of the diffusion coefficient consequently declines. It was also observed that, with the exception of values obtained at low densities, the decrease in D12with respect to increasing fluid density was linear. At low COz densities, DI2values were found to be higher than predicted by extrapolating this linear relationship. This divergence has been noted by several authors, notably Sassiat et al. (1987), who observed similar behavior for the solutes benzene and naphthalene diffusing in COz at densities below -700 kg/m3 (40"C). Influence of Solvent Viscosity. In modeling the diffusion behavior of liquids, the Stokes-Einstein relationship has often been used as a starting point for the development of semiempirical equations (e.g., the WilkeChang equation). In all such equations the assumption is made that the diffusion coefficient is inversely proportional to the viscosity of the solvent or the solvent/solute system. More specifically Dl*/T = fn (molar volume of the solute) (9)
In this study the viscosity of carbon dioxide was varied Pass. Similar Viscosity ranges from 4.5 X lo6 to 8.1 X have been employed by previous researchers. The binary diffusion coefficients for phenylacetic acid are shown in Figure 7 plotted as a function of GLc0J1. The results obtained for both phenylacetic acid and vanillin are consistent with the trends found by previous researchers, (e.g., Debenedetti and Reid, 1986), namely, a linear relationship with a small positive intercept. It was observed that the slope of the lines increased as the temperature rose, in accordance with eq 9. Modeling the Diffusion Data. The observed diffusion coefficients were used to evaluate the applicability of several Stokes-Einstein based empirical equations. Table I11 lists the average errors observed for each model. The molar volumes of both vanillin and phenylacetic acid were determined from the Le Bas group contribution technique (Le Bas, 1987). Plotted in Figure 8 are the observed diffusion values versus those predicted from the W i l k e Chang and Hayduk-Minhas equations. Generally it was found that the Wilke-Chang equation gave the best fit. The other equations tested did not correlate the data as well with overpredictions of 40-50%
Table 111. Solute Molar Volumes Calculated Using the Le Bas Method and the Errorso between Predicted Values of DIzand Values Observed in This Study phenylacetic acid vanillin V , (cm3/g-mol) = V , (cm3/g-mol) = 157.0 156.9 Wilke-Chang +5.5% +11.5% (1955) Reddy-Doraiswamy +41.4% +51.3% (1967) Scheibel +42.3% +52.0% (1954) Lusis-Ratcliff +36.1% +45.4% (1968) Tp-Calus +33.3% +42.4% (1987) Hayduk-Minhas +15.1% +23.3% (1987) Error = [Dlz(calcd)/D,z(exptl)lxlOO%. m
%
j
N
E
1
1.6 -
1
Wilke Chang 0
Hayduk Minhas
1
ID
s .-2 .-w
1-
m a
/
c
0.2
0
0.8
0.8
0.4
1
1.2
1.4
1.8
1.8
Measured Diffusivity 10' (rn2 1 s ) Figure 8. Comparison of the predictions of both the Wilke-Chang and Hayduk-Minhas equations with experimental data.
&Cluster
g
* N
size
100
t F
'
0.1 0
lo 100
200
CO,
300
400
600
800
700
Density (kg/rn3 1
Figure 9. Diffusion coefficients and cluster sizes near the LCEP of the naphthalene/C02 system. Cluster sizes estimated from partial molar volume data (Eckert, 1986). Diffusion data obtained from Tsekhanskaya (1971).
being common. The failure of the Stokes-Einstein based equations is especially evident in regions of low C02 density where the solvent compressibility is high. In such regions the calculated diffusion is much higher than that observed. The highly negative partial molar volumes readily observed in regions of high C02 compressibility (Foster et al., 1989; Eckert et al., 1986) indicate that many solvent molecules may cluster in the region of each solute molecule severely impeding solute diffusion. Evidence of this effect is shown in Figure 9. In this figure the approximate cluster size of the naphthalene/C02 cluster has been plotted in conjunction with the diffusion behavior
932 Ind. Eng. Chem. Res., Vol. 31, No. 3, 1992
of naphthalene in C02 (Tsekhanskaya, 1971) at the same temperature (35 "C) and over the same range of COz densities. The cluster size was estimated from partial molar volume data obtained from Eckert et al. (1986). Clearly as the lower critical end point (LCEP) is approached the cluster size increases and diffusion is seen to decrease rapidly. The equation of Hayduk and Minhas (1987) was observed to give a slightly better correlation than most of the Stokes-Einstein based correlations. As has been noted previously, the assumption that ( D 1 g / T )is constant is not true for either of the systems studied. The more flexible viscoisity term employed by the following equation appears to better correlate such behavior. p.47
P
D12
This is similar in form to eq (12) proposed by Batschinski (Hildebrand, 1971) to relate the viscosity of liquids = Cs(V - V,)
(12)
to their specific volume, V, and a hard-core volume, V,, similar in concept to the constant V, shown in the above correlation. Batschinski showed that eq 12 correlated the viscosity behavior of many nonassociated liquids extremely well. He also observed that the ratio Vv/Vc for each fluid was generally close to 0.31. The success of the Batschinski equation and its similarity to the hard-sphere model of Dymond suggeata that a successful correlation for diffusion behavior may be derived from an analysis of hard sphere diffusion models. Such a model was proposed by Dymond (1974): 7Q.5
D = Cd-M O . 5
v - c,vo V00.66
40
80
80
Solvent Molar Volume (cm3 /gmol) Figure 10. Free volume diffusion plot of the diffusion Coefficients of both vanillin and phenylacetic acid in supercritical carbon dioxide.
6
13.3 X 1 0 - ' ~
where [ = (10.2/V1) - 0.791. It can be seen from Table I11 that the Le Bas estimates of the molar volumes of both solutes are nearly identical. AB a result, all of the above-mentioned equations predict a virtually identical D12value for both solutes at any given solvent condition. Clearly our data do not support this prediction. It appears that there are several disadvantages to using the Stokes-Einstein style diffusion equations. Firstly, deviations from the D120: p-l relationship lead to overprediction of the diffusion values. Secondly, the solute is inadequately characterized by its molar volume. It has been noted in a previous study (Swaid and Schneider, 1979) that it is possible for solutes of similar molar volume to display differing diffusion characteristics probably as a result of their differing molecular shapes. In this study the DI2values for phenylacetic acid were approximately 6% higher than those of vanillin while the molar volumes were computed to differ by less than 0.1 %. Additionally, the molar volume of the solute must in many cases be calculated from a group contribution method (e.g., the Le Bas method), and as the contribution of many functional groups is still unknown such estimations are at best guesswork. Dymond (1974) determined from computer analysis that the viscosity of a fluid comprised of hard spheres can be modeled using the following free volume form: p-' = C1(MT)0.5( V - C2V0)/ V2,33 (11)
p-1
~~~
20
(13)
Using eq 13 as a starting point, Chen et al. (1982) and more recently Matthews and Akgerman (1987) adopted the
following equation to describe binary diffusion in liquid systems:
D/7".5 = c5(v- v d )
(14)
In order to test the proposed model, diffusion data obtained in this study for both vanillin and phenylacetic acid in C02have been plotted as Figure 10 in the form indicated by eq 14. The regression lines have been constructed on the assumption that the value of Vd is equal to O.31Vc. This is the value recommended by Matthews and Akgerman (1987) for the minimum free diffusion volume ( v d ) and corresponds to the ratio of Vv/ V, proposed by Batschinski (Hildebrand, 1971). The lines shown in Figure 10 are therefore of the form
D12/16.5= C1(Vmmlvent - 29.8)
(15)
Matthew and Akgerman (1987) correlated the slope of the line C, with the molecular weight of the solute (MI) and the minimum free diffusion volume ( v d ) , obtaining the following relationship: C1
~1-0.61Vd-1.04
(16)
As C02 was the only solvent employed in this study, it was impossible to confirm the effect of vd on the slope C1. However, a difference of 7% in the values of C1 was observed (seeFigure 10) between vanillin (MW = 152.14) and phenylacetic acid (MW = 136.14). This agrees with the molecular weight dependence stated in the above equation. The average error between predicted and observed D12 values for the two solutes was 3.5% (phenylacetic acid) and 4.7% (vanillin). While this may seem satisfactory, it would appear from the trends for both vanillin and phenylacetic acid (Figure 10) that the true z-axis intercepts are significantly lower than the value of (0.31VJ suggested by Matthews and Akgerman (1987). Conclusion The binary diffusion coefficients of phenylacetic acid and vanillin in supercritical carbon dioxide were determined at 308,313, and 318 K for densities ranging from 600 to 850 kg/m3. The experimental diffusivities obtained ranged from 1.52 X down to 0.84 X lo-* m2/s. The influence of temperature and pressure on the diffusion coefficients was found to be largely the result of consequent changes in the carbon dioxide density. The relationship between D12and C02 density was observed to be linear except in regions of high COPcompressibility. An examination of the effect of carbon dioxide viscosity on D12showed that the Stokes-Einstein relation ( D 1 g / T
Ind. Eng. Chem. Res., Vol. 31, No. 3, 1992 933 = constant) did not hold for either solute. This and the use of the molar volume as the solute descriptor led to large errors when correlating the observed data with StokesEinstein based models. The free volume diffusion model was able to correlate the experimental data with greater accuracy resulting in average errors of approximately 3-5%. A plot of the data indicated, however, that the minimum free diffusion volume was significantly lower than that predicted by Matthews and Akgerman (1987).
Nomenclature C1= constant (kg-m~l~/~.kg'/~.m-~.s-') C2 = constant (m3.kg-mol-') C3= constant characteristic of the solvent (kg-mol.kg-'.m-2.s) C4 = constant (kg-mol-1/6.kg1/2.ms-1.K-1/2) C5 = constant for a given solute-solvent pair (kg-rno1.m-l. s-LK-1/2)
D12= diffusion coefficient ( m 2 d ) Deff= effective diffusivity (m2.s-') De = Dean number = (pUOdtube/p)(dtube/dcoil)1/2 H = plate height (m) L = length of the tubing (m) M = solvent molecular weight (kgkg-mol-') M I= solute molecular weight (kg-kg-mol-') ri = internal radius of the diffusion tubing (m) S c = Schmidt number = p/pD12 T = temperature (K) t, = peak retention time (8) U, = mean fluid velocity (ms-') V = molar volume of the fluid (m3.kg-mol-') Vo = hard-sphere close-packed molar volume (m3.kg-mol-') V , = molar volume of the solute (m3*kg-mol-') V , = critical molar volume of the solvent (m3.kg-mol-l) Vd = minimum free volume for diffusion (m3.kg-mol-') Vmsolvent= molar volume of the solvent (m3.kg-mol-') V , = minimum free volume for viscous flow (m3-kg-mol-') Wo.,7 = peak width at 0.607 of the peak height ( 8 ) Greek Characters u2(x) = variance of p
the dispersed peak (m2) = solvent (or solution) viscosity (kg-m-ld) Registry No. C02, 124-38-9;phenylacetic acid, 103-82-2;
vanillin, 121-33-5.
Literature Cited Alizadeh, A.; Nieto de Castro, C. A.; Wakeham, W. A. The Theory of the Taylor Dispersion Technique for Liquid Diffusivity Measurements. Znt. J. Thermophys. 1980,l (3),243. Altunin, V. V.; Sakhabetinov, M. A. Teploenergetika 1972,8, 85. h i s , R. On the Dispersion of a Solute Flowing Through a Tube. London 1956,235,67. Proc. R. SOC. Bohemen, J.; Purnell, J. H. Diffusional Band Spreading in Gaschromatographic Columns. Part I. The Elution of Unsorbed Gases. J. Chem. SOC. (01961,360. Chen, S.-H.; Davis, H. T.; Evans, D. F. Tracer Diffusion in Polyatomic Liquids. 111. J. Chem. Phys. 1982,77 (51, 2540. Debenedetti, P. G.; Reid, R. C. Diffusion and Mass Transfer in Supercritical Fluids. AIChE J . 1986,32 (12),2034. Dymond, J. H. Corrected Enskog Theory and the Transport Coefficients of Liquids. J. Chem. Phys. 1974,60 (3),969. Eckert, C. A.; Ziger, D. H.; Johnston, K. P.; Kim, S. Solute Partial Molal Volumes in Supercritical Fluids. J. Phys. Chem. 1986,W (12),2738. Feist, R.; Schneider, G. M. Determination of Binary Diffusion Coefficients of Benzene, Phenol, Naphthalene and Caffeine in Supercritical COPbetween 308 and 333K in the Pressure Range 80 to 16 Bar with Supercritical Fluid Chromatography (SFC). Sep. Sci. Technol. 1982,17 (l),261. Foster, N. R.; MacNaughton, S. J.; Chaplin, R. P.; Wells, P. T. Critical Locus and Partial Molar Volume Studies of the Benzaldehyde/COz Binary System. Znd. Eng. Chem. Res. 1989,B (12),1903.
Funazukuri, T.; Hachisu, S.; Wakao, N. Measurement of Diffusion Coefficients of CIS Unsaturated Fatty Acid Methyl Esters, Naphthalene and Benzene in Supercritical Carbon Dioxide by a Tracer Response Technique. Anal. Chem. 1989,61 (2),118. Giddings, J. C.; Seager, S. L. Rapid Determination of Gaseous Diffusion Coefficients by Means of Gas Chromatography Apparatus. J. Chem. Phys. 1960,33,1579. Giddings, J. C.; Seager, S. L. Method for Rapid Determination of Diffusion Coefficients. Znd. Eng. Chem. Fundam. 1962,l (4),277. Groves, F. R.; Brady, B.; Knopf, F. C. State-of-the-Art on the Supercritical Extraction of Organics from Hazardous Wastes. CRC Crit. Rev. Environ. Control 1984,15 (3),237. Hayduk, W.; Minhas, B. S. In The Properties of Gaaes and Liquids, 4th ed.; Reid, R. C.; Prausnitz, J. M., Poling, B. E., Eds.; McGraw-Hill: New York, 1987;Chapter 11, p 602. Hildebrand, J. H. Motions of Molecules in Liquids: Viscosity and Diffusivity. Science 1971,174,490. Knaff, G.; Schlunder, E. U. Diffusion Coefficients of Naphthalene and Caffeine in Supercritical Carbon Dioxide. Chem. Eng. Proc. 1987,21, 101. Lauer, H. H.; McManigill, D.; Board, R. D. Mobile-Phase Transport Properties of Liquefied Gases in Near-Critical and Supercritical Fluid Chromatography. Anal. Chem. 1983,55(8),1370. Le Bas. In The Properties of Gases and Liquids, 4th ed.; Reid, R. C., Prausnitz, J. M., Poling, B. E., EMS.; McGraw-Hill. New York, 1987;Chapter 3,p 53. Levenspiel, 0.;Smith, W. K. Notes on the Diffusion-Type Model for the Longitudinal Mixing of Fluids in Flow. Chem. Eng. Sci. 1957, 6,227. Lusis, M. A.; Ratcliff, G. A. Diffusion in Binary Liquid Mixtures at Infinite Dilution. Can. J. Chem. Eng. 1968,46,385. Matthews, M. A.; Akgerman, A. Diffusion Coefficients for Binary Alkane Mixtures to 573K and 3.5 MPa. AZChE J. 1987,33(6), 881. Ouano, A. C. Diffusion in Liquid Systems. 1. A Simple and Fast Method of Measuring Diffusion Constants. Ind. Eng. Chem. Fundam. 1972,ll (2),268. Paulaitis, M. E.; Krukonis, V. J.; Kurnik, R. T. Supercritical Fluid Extraction. Rev. Chem. Eng. 1983,1, 179. Pitzer, K. S.;Schreiber, D. R. Improving Equation-of-State Accuracy in the Critical Region; Equations for Carbon Dioxide and Neopentane as Examples. Fluid Phase Equilib. 1988,41,1. Pratt, K. C.; Wakeham, W. A. The Mutual Diffusion Coefficient of Ethanol-Water Mixtures: Determination by a Rapid, New Method. Proc. R . SOC. London, A. 1974,336,393. Pratt, K. C.; Slater, D. H.; Wakeham, W. A. A Rapid Method for the Determination of Diffusion Coefficients of Gases in Liquids. Chem. Eng. Sci. 1973,28,1901. Reddy, K. A.; Doraiswamy,L. K. Estimating Liquid Diffusivity. Znd. Eng. Chem. Fundam. 1967,6(l),77. Sassiat, P. Mourier, P.; Claude, M. H.; Rosset, R. H. Measurement of Diffusion Coefficients in Supercritical Carbon Dioxide and Correlation with the Equation of Wilke and Chang. Anal. Chem. 1987,59(€0,1164. Scheibel, E. G. Liquid Diffusivities. Znd. Eng. Chem. 1954,46,(9), 2007. Schutz, E.; Vollbrecht, H.-R.; Sandner, K.; Sand, T.; Muhlnickel, P. Method for Extracting the Flavoring Substance from the Vanillin Capsule. US. Patent 4,470,927,1984. Springston, S. R.; Novotny, M. Coil-Induced Secondary Flow in Capillary Supercritical Fluid Chromatography. A d . Chem. 1986, 58 (13),2699. Swaid, I.; Schneider, G. M. Determination of Binary Diffusion Coefficientsof Benzene and Some Alkylbenzenes in Supercritical COz between 308 and 328K in the Pressure Range 80 to 160 bar with Supercritical Fluid Chromatography (SFC). Ber. BunsenGes. Phys. Chem. 1979,83,969. Taylor, G. Dispersion of Soluble Matter in Solvent Flowing Slowly London 1953,219,186. Through a Tube. Proc. R. SOC. Taylor, G. The Dispersion of Matter in Turbulent Flow Through a Pipe. Roc. R. SOC. London 19548,223,446. Taylor, G. Conditions under which Dispersion of a Solute in a Stream of Solvent can be used to Measure Molecular Diffusion. R o c . R. SOC. London 1954b,225,473. Tsekhanskaya, Yu. V. Diffusion of Naphthalene in Carbon Dioxide Near the Liquid-gas Critical Point. Ruse. J. Phys. Chem. 1971, 45 (51,744. Tyn, M. T.; Calus, W. F. In The Roperties of Gases and Liquids, 4th ed.; Reid, R. C., Prausnitz, J. M., Poling, B. E., Eds.; McGraw-Hill: New York, 1987;Chapter 11, p 600.
9
Ind. Eng. Chem. Res. 1992,31,934-941
934
Vitzthum, 0.; Hubert, P. Process for the Production of Spice Extracts. U.S.Patent 4,123,559,1978. Wells, P. A.; Chaplin, R. P.; Foster, N. R. Solubility of Phenylacetic Acid and Vanillin in Supercritical Carbon Dioxide. J. Supercrit. Fluids 1990, 3 (l),8. Wilke, C. R.; Chang, P. Correlation of Diffusion Coefficients in Di-
lute Solutions. AZChE. J. 1955, 1 (2),264. Williams, D. F. Review Article No. 5 Extraction with Supercritical Gases. Chem. Eng. Sei. 1981, 36 (ll),1769. Received for review April 17, 1991 Accepted September 6,1991
Recovery of Amine and Paints from Electrodeposition Wastewater by an H-Form Ion Exchanger: Desorption Process Hiroyuki Yoshida,* Kazuyuki Shimizu, and Takeshi Kataoka Department of Chemical Engineering, University of Osaka Prefecture, 4-804, Mozu-Umemachi, Sakai 591, Japan
Wastewater of anodic electrodeposition painting process contained diisopropanolamine, three unknown paints, and solvents (butyl Cellosolve and/or ethyl Cellosolve). The amine (R’-NH2) was immobilized on H-form resin by the neutralization reaction R-H + R’-NH2 R.NH,-R’. The paints were adsorbed on the resin, too. Here we propose a desorption method of the immobilized amine NaOH from the wastewater-H-form resin complex by using the irreversible reaction R.NH,-R’ R.Na + R’-NH2 + H20. The experimental equilibrium isotherms and elution curves showed the amine and paints were desorbed well by NaOH aqueous solution. Experiments of adsorption, elution, and regeneration also have been reported. The adsorption capacity of the amine did not change with repeat times. The intraparticle effective diffusivities of the amine and Na+ in the elution process were constant after the third cycle, and the intraparticle effective diffusivity of the amine in adsorption process was constant after the second cycle.
-
-
+
1. Introduction Organic amines are used commonly as the dispersing agents for water-soluble paints in the anodic electrodeposition painting process which is widely used to paint metal panels with complicated shapes, such as office instruments and office furniture. Washing of the finished products gives a dilute aqueous solution of the amine and paints as an undesirable wastewater byproduct. Recovery of the amines and paints from these effluents is highly desirable both for the overall economics and for meeting environmental standards. An H-form strong acid ion exchanger adsorbs amine and ammonia almost irreversibly (Yoshida and Kataoka, 1986, 1987),and the amine is eluted almost irreversibly from the amineH-form resin complex by using the aqueous solution of caustic soda (Yoshida and Kataoka, 1989). This makes it possible to have a process that has the advantages of amine recovery and higher removal efficiency. In contact with an H-form strong acid ion exchanger, the amine species are immobilized on the resin by the acidlbase neutralization reaction: R*H R’-NH2 RoNH3-R (1) where R’-NH2 denotes the amine and R.NH,-R’ is the amineH-form resin complex. The amine is desorbed by the following irreversible neutralization reaction: R-NH3-R’ + NaOH R-Na + R’-NH2 + H 2 0 (2) and the resin is finally regenerated by acid: (3) R-Na + HX F! R.H + NaX Yoshida et al. (1990) have applied eq 1 to adsorption of amine from the wastewater of electrodeposition painting, which contained diisopropanolamine, two solvents, three paints which are not pigments but polymers, and Fe2+. The equilibrium isotherm for adsorption of the amine on the H-form resin was very favorable. The experimental breakthrough curves for adsorption of the components showed that the amine and paints were removed well by
+
-+
-
the H-form resin and this method may be feasible technically. In this paper, we present experimental data for desorption of the amine and paints from the wastewater-Hform resin complex to show that they are desorbed well by aqueous caustic soda solution (irreversible reaction, eq 2). We measured the equilibria for desorption of the amine by caustic soda. The experimental elution curves for the desorption of each component from the virgin wastewater-H-form resin complex and for repeat experiments are presented to demonstrate that it is feasible for the proposed process to recover the amine and paints from the wastewater of the electrodeposition painting process. 2. Electrodeposition Painting Process The electrolytic cell contains various polymers (hereafter called paints), amines, and solvents that are dissolved in distilled water or deionized water. Amines are used as dispersing agents for the water-soluble paints. A metal panel is set at the anode, and painting is carried out by applying the electric current for several minutes. The finished products are then removed from the electrolytic cell and are washed. After washing, the solution flows through an ultrafilter (UF)to reuse the paints. Although high molecular weight paints can be recovered from the UF,the amine, low molecular weight paints, Solvents, and Fe2+pass through the filter; 90% of the solution which passes through the filter is recycled to wash finished products. To avoid accumulation of the contents in the solution of the washing process, 10% of the solution is exchanged for distilled water or deionized water. This is the wastewater of the electrodeposition painting process. Table I shows the contents and their concentrations in the three wastewaters. The paints are not pigments but the low molecular weight polymers as mentioned above. The wastewater contained diisopropanolamine,one or two solvents, three paints, and Fez+. Concentration of diisopropanolamine was relatively high, and it had to be removed. The concentration of Fez+was very low. The three
0888-5885f 92f 2631-0934$03.00f 0 0 1992 American Chemical Society
