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J. of Supercritical Fluids 46 (2008) 238–244
High-pressure phase equilibria for the binary system carbon dioxide + dibenzofuran Eduardo P´erez, Albertina Caba˜nas, Yolanda S´anchez-Vicente, Juan A.R. Renuncio, Concepci´on Pando ∗ Departamento de Qu´ımica F´ısica I, Facultad CC. Qu´ımicas, Universidad Complutense, E-28040 Madrid, Spain Received 4 October 2007; received in revised form 18 January 2008; accepted 18 January 2008
Abstract The experimental solubility of dibenzofuran in near-critical and supercritical carbon dioxide and the solid–liquid–vapor (SLV) equilibrium line for the CO2 + dibenzofuran system are reported. The built in-house static view cell apparatus used in these measurements is described. The solubility of naphthalene in supercritical CO2 and the CO2 + naphthalene SLV line are also determined in order to assess the reliability and accuracy of the measurement technique. The solubility of dibenzofuran in carbon dioxide is determined at 301.3, 309.0, 319.2, 328.7 and 338.2 K in the 6–30 MPa pressure range. Solubility data are correlated using the Chrastil model and the Peng–Robinson equation of state. This equation is also used to predict the CO2 + dibenzofuran SLV line. Results show the feasibility of using supercritical CO2 to extract dibenzofuran. © 2008 Elsevier B.V. All rights reserved. Keywords: Supercritical carbon dioxide; Dibenzofuran; Solubility; Solid–liquid–vapor equilibrium; High-pressure phase equilibria
1. Introduction Supercritical carbon dioxide (Tc = 304.2 K, Pc = 7.37 MPa ) and supercritical or near-critical water (Tc = 647.1 K, Pc = 22.06 MPa ) are increasingly used as solvents or reaction media in a variety of supercritical processes. Supercritical water oxidation is the method preferred for destroying hazardous waste while either CO2 or H2 O are used in supercritical fluid extraction (SFE) to separate organic pollutants from solid matrixes . Due to its accessible critical parameters, non-toxicity, low cost and non-flammability, carbon dioxide is very often used both for analytical and clean up purposes. Many examples are found of extractive treatment of solids using supercritical CO2 . For instance, polycyclic aromatic hydrocarbons and polychlorinated biphenyls and dioxins were removed from soils [3–9]. Recently, Gabarra et al.  studied the feasibility of using CO2 SFE to remove polychlorodibenzodioxins and dibenzofurans from fly ash in a solid-waste incineration facility and Kawashima et al.  studied the removal of similar compounds from fish oils ∗
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using CO2 SFE. In order to design and optimize these processes, knowledge of the high-pressure phase equilibria of the mixtures involved is required. Dibenzofuran (DB) is a flat organic molecule; it is a precursor of chlorinated pollutants (polychlorodibenzofurans) and a solid at ambient conditions. The chemical structure, molar mass, melting and boiling points and dipole moment of DB and other solutes considered in this paper are shown in Table 1. Critical parameters for DB were reported by Chirico et al. : Tc = 824 K, Pc = 3.64 MPa, the critical temperature is much higher than that of carbon dioxide. In this study, we investigate the behavior of the CO2 + dibenzofuran system that may serve as a model for systems formed by carbon dioxide and the chlorinated dibenzofurans. The thermodynamic study includes two types of measurements: (a) solubilities of DB in compressed CO2 at 301.3, 309.0, 319.2, 328.7 and 338.2 K and (b) the decreasing of the melting point under CO2 pressure, solid–liquid–vapor (SLV) equilibrium line. A static view cell apparatus was used in these measurements. Solubilities of DB in carbon dioxide are also compared to those previously measured by Hansen at 308.2, 323.2 and 343.2 K using a dynamic flow apparatus .
E. P´erez et al. / J. of Supercritical Fluids 46 (2008) 238–244 Table 1 Physical properties of solutes
Table 2 Solid–liquid–vapor equilibrium for the CO2 + dibenzofuran system MW
Tm and Tb taken from Ref. . μ at 25 ◦ C taken from Ref. .
2. Experimental The materials employed were CO2 (Air Liquide 99.98 mol% pure), dibenzofuran (Fluka ≥ 99 mol% pure) and naphthalene (Fluka ≥ 99.0 mol% pure). Commercial materials were used without further purification. Fig. 1 is the schematic diagram of the static view cell apparatus used to perform phase equilibria measurements. The apparatus was designed and built in-house and is similar to that described by McHugh and Krukonis . The main component is a high-pressure, variable-volume cell constructed of stainless steel, working volume ≈15 cm3 , fitted with a sapphire window. The image of the mixture in the cell was obtained by means of a Fiegert Endotech boroscope placed against the sapphire window, fitted with a Moticam 2000 camera and connected to a computer. The cell was electrically heated up to 373 K by means of a silicone heating tape (Omegalux SRT051-040) connected to a Proportional Integral Derivative (PID) temperature controller (Micromega, model CN77322). A type J calibrated thermocouple was used to measure the temperature with a resolution of ±0.05 K. The stability of the thermostat is estimated to be ±0.2 K. A known amount of solute was introduced and purged several times at room temperature with carbon dioxide to remove the entrapped air. Carbon dioxide was transferred into the view cell gravimetrically by means of an auxiliary cell. The mole fraction precision was estimated to be ±0.1%. The contents of the cell were mixed using a magnetic stir-
330.9 331.2 331.3 331.6 331.7
17.00 18.00 16.00 15.00 15.00
332.6 332.7 332.9 333.8 334.8
13.50 18.90 13.50 12.50 11.50
335.1 335.8 337.0 339.0 340.5
11.00 9.50 9.50 8.00 6.30
rer. The solution can be compressed to the desired operating pressure (up to 30 MPa) by displacing a movable piston fitted within the cell using water pressurized by means of a high-pressure generator. This high-pressure generator is connected to a water reservoir through valve V1 and to the cell through valve V2. The water pressure was determined using a Swagelok pressure gauge. The pressure inside the cell was determined using a relative transducer (Druck, model PTX7511-1, ±0.15% uncertainty) provided with a digital display with an uncertainty of 0.01 MPa. The pressure error was estimated to be ±(0.01 + 0.0015 P) MPa. A solubility data point was obtained in the following manner: At a fixed temperature the mixture in the cell was compressed to a single phase at high pressures. The pressure was then slowly decreased until a condensed phase appears. The contents of the cell were periodically agitated using the magnetic stirrer. The solute can be alternatively solubilized and precipitated to obtain a precise pressure value. The solubility was determined from the amounts of carbon dioxide and solute loaded into the cell. The SLV line was determined applying the so-called “first melting point” as follows. An excess of solid DB was placed into the cell that was then filled with CO2 up to a certain pressure. The temperature was then isobarically increased about 0.05 K/min with periodic stirring until the solid in equilibrium with the CO2 -rich gas phase started to melt. At this temperature the three phases SLV coexist. The measurement was repeated after cooling down the cell. As may be seen in Figs. 3 and 4, in some cases a slightly different melting temperature was observed for CO2 + naphthalene or CO2 + DB. Differences of 0.1 and 0.3 K are observed in Table 2 for CO2 + DB at 15.00 and 13.50 MPa, respectively. The greater difference observed at
Fig. 1. Schematic diagram of the static view cell apparatus used to perform phase equilibria measurements.
E. P´erez et al. / J. of Supercritical Fluids 46 (2008) 238–244
Fig. 2. Solubility isotherms of naphthalene in near-critical and supercritical CO2 at: (a) 308.2 K and (b) 328.2 K; () this work; () Tsekhanskaya et al. ; (♦) McHugh and Paulaitis ; () Mitra et al. ; () Chung and Shing ; (×) Reverchon et al. ; () Sauceau et al. .
9.50 MPa (1.2 K) is considered the limit error of present measurements. 3. Results and discussion
close to those of Cheong et al.  (first freezing point method) and White and Lira  (first melting point method), and lie in the middle of those reported by McHugh , and Lemert and Johnston .
3.1. Veriﬁcation of the method
3.2. CO2 + dibenzofuran solid–liquid–vapor equilibrium
To test the reliability and accuracy of our measurement technique, naphthalene was used as a calibration standard. Fig. 2 shows a comparison of the solubility data of naphthalene in CO2 at 308.2 and 328.2 K reported in this paper to those reported in the literature [17–22]. The agreement is very good for most of the pressure range. At high pressures, results obtained in this paper are slightly lower than those reported in the literature. These differences may be due to the different techniques used; data presented in this paper are the only ones measured using a synthetic method. Fig. 3 shows a similar comparison for the CO2 + naphthalene SLV line [23–26]. CO2 + naphthalene presents a type III diagram in the classification of Scott and van Konynenburg ; the liquid–gas line intersects with a solid phase. Considerable differences occur between the literature sets of results for this system. Results presented in this paper are very
Temperatures and pressures for CO2 + dibenzofuran solid–liquid–vapor equilibrium are listed in Table 2. The SLV line is shown in Fig. 4 together with the critical point and vapor pressure curve for carbon dioxide [1,12] and dashed lines indicating the conditions of the solubility isotherms. A minimum of the melting temperature is observed at 17 MPa. The shape of the SLV line suggests a liquid–gas type III diagram in the classification of Scott and van Konynenburg , which intersects with a solid phase. In this case, the three-phase line should begin at the DB triple point (T = 355.31 K ) and end at the upper critical end point (UCEP) where it would intersect the critical line. At the UCEP, a vapor–liquid mixture critical point occurs in the presence of a solid phase. This
Fig. 3. Solid–liquid–vapor equilibrium for the CO2 + naphthalene system: () this work; () McHugh ; (♦) Cheong et al. ; () Lemert and Johnston ; () White and Lira ; ( ) upper critical end point .
Fig. 4. Solid–liquid–vapor equilibrium for the CO2 + dibenzofuran system, CO2 critical point ()  and vapor pressure curve (- - -)  and conditions of the solubility isotherms reported in this paper (- - -): () P, T coordinates of the SLV line, this work; (—) predicted using the Peng–Robinson EOS.
E. P´erez et al. / J. of Supercritical Fluids 46 (2008) 238–244
Table 3 Mole fraction solubility of dibenzofuran in near-critical and supercritical CO2 P (MPa)
301.3 K 6.74 9.27 10.48
3.00 3.56 3.97
309.0 K 8.96 9.40 10.65 12.11 13.35
3.00 3.56 4.06 4.65 5.14
15.55 14.42 16.92 18.41
5.78 5.80 6.35 6.89
20.95 22.50 21.46 27.48
7.56 7.95 8.04 8.65
319.2 K 10.66 11.19 11.37 12.35 12.50 13.16
3.00 3.56 3.97 4.65 4.83 5.80
13.40 13.97 13.65 14.27 14.84 15.69
6.00 6.34 6.43 6.57 6.85 7.42
16.55 17.72 19.36 20.70 22.40
8.04 8.65 9.44 10.39 11.17
328.7 K 12.80 13.16 13.48 13.59 13.75 14.63 14.60 14.83
3.00 3.56 4.06 4.59 4.65 5.32 5.80 6.00
15.22 14.99 14.96 15.06 14.99 15.20 15.63 15.80
6.33 6.35 6.43 6.57 6.74 6.85 7.42 8.04
16.24 16.75 17.27 17.53 17.70 17.83 18.47 18.51
8.65 9.07 9.99 10.04 10.08 10.39 11.07 11.17
338.2 K 13.50 14.10 14.94 15.49 15.97
3.44 4.04 5.03 5.76 6.58
16.48 16.77 17.24 17.56 18.37
7.39 7.83 7.66 8.60 9.79
18.90 18.92 19.43 19.97
11.10 10.70 11.52 12.20
SLV line is similar to that reported in the literature for the CO2 + naphthalene system. For the CO2 + DB system, the SLV line appears at temperatures higher than those measured for the former system. At temperatures close to a critical end point, there is a solid solubility enhancement that is currently exploited in SFE experiments. 3.3. Dibenzofuran solubility The mole fraction solubility (y2 ) of dibenzofuran in carbon dioxide was determined at 301.3, 309.0, 319.2, 328.7 and 338.2 K in the 6.5–30 MPa pressure range. Results are summarized in Table 3. Fig. 5 shows plots of the five solubility isotherms obtained. An inspection of Fig. 4 and Table 3 indicates that carbon dioxide is a liquid for data taken at 301.3 K while for data taken at 309.0, 319.2 and 328.7 K carbon dioxide is a supercritical fluid. On the other hand, data taken at 338.2 K correspond to liquid–vapor equilibrium. At the studied conditions, dibenzofuran mole fraction solubility ranges from 10−3 to 10−2 . These values show the feasibility of using supercritical CO2 fluid to extract dibenzofuran. For a given temperature, the solubility increases with pressure due to the higher density of the solvent. The effect of temperature is
Fig. 5. Solubility isotherms of dibenzofuran in near-critical and supercritical CO2 at: () 301.3 K; (䊉) 309.0 K; () 319.2 K; () 328.7 K; () 338.2 K; (—), correlated using a second degree polynomial.
more complex and a crossover is observed in the solubility versus pressure curves at approximately 15 MPa for the different temperatures studied. At pressures above the crossover pressure, the solubility increases with temperature, while the opposite trend is observed at pressures below the crossover pressure. This behavior results from a compromise between the decreasing of density as the temperature rises (that leads to lower solubilities at lower pressures) and the higher vapor pressure of the solute (that leads to higher solubilities at higher pressures). On the other hand, solubilities of dibenzofuran in carbon dioxide at 309.0 and 328.7 K are lower than those of naphthalene at 308.2 and 328.2 K. Solubilities of dibenzofuran at 309.0 K are very close to those of xanthene at 308.2 K . This could be expected: an inspection of Table 1 reveals that the three compounds have aromatic rings that lead to low solubilities but dibenzofuran and xanthene have similar molar masses much higher than those of naphthalene and similar chemical structures with polar groups that cause a further decrease of the solubility in carbon dioxide. The solubility isotherms reported in this paper are compared to those obtained by Hansen at 308.2, 323.2 and 353.2 K using a dynamic flow apparatus  in Fig. 6. Except for data taken at 308.2–309.2 K, the agreement is satisfactory. The 323.2 K isotherm is intermediate between those at 319.2 and 328.7 K. A 15◦ temperature increase explains the differences between the liquid–vapor equilibrium data taken at 338.2 and 353.2 K; the shape of the two isotherms is similar and clearly different from those of solid–vapor equilibrium data. The solubility data reported by Hansen at 308.2 K are lower than data reported in this paper at 309.2 K both at high and low pressure and will not be considered in the simultaneous data correlation described in the next section. 3.4. Correlation of experimental solubility data and prediction of the SLV line Solubility data of solid dibenzofuran in liquid and supercritical CO2 obtained in this paper (301.3, 309.0, 319.2 and 328.7 K) and those reported by Hansen at 323.2 K were correlated using
E. P´erez et al. / J. of Supercritical Fluids 46 (2008) 238–244
Fig. 6. Comparison of solubility isotherms of dibenzofuran in carbon dioxide reported in this paper (full symbols) and those reported by Hansen  (empty symbols). (a): () 308.2 K; () 309.2 K. (b): () 319.2 K; () 323.2 K; () 328.7 K. (c) (䊉) 338.2 K; () 353.2 K.
the Chrastil model  that relates the solute solubility, y2 , and the solvent density, ρ: a2 lny2 = a0 + a1 lnρ + (1) T where a0 , a1 and a2 are adjustable parameters. Solvent densities were obtained from NIST . A least square-procedure was used to determine values for a0 , a1 and a2 by minimizing the average absolute relative deviation between experimental and calculated solubilities (AARD) and giving the same weight to each isotherm. AARD is defined as: N
T |ycal − yexp | 1 1 4 NT yexp
where NT is the number of experimental points for a given temperature, ycal is the calculated solubility, and yexp is the experimental solubility. Results from this correlation are shown in Fig. 7. Chrastil model is shown to describe well the temperature effect on solubilities; three parameters are used to fit all the experimental data. At high pressures, the solubility is observed to increase monotonically and linearly with pure solvent den-
sity. At the low pressures, solubilities deviate from the linear dependence. The solubility of a solid solute in equilibrium with a fluid at high pressure at a given temperature can be calculated using the equation: s P2sat 1 v2 (P − P2sat ) y2 = exp (3) P φ2G RT where P2sat is the saturated vapor pressure, φ2G is the fugacity coefficient and vs2 is the solid-state molar volume of the solute. Values used for the vapor pressure were obtained from the following equation : 302.724 92761.912 35.96 T − − ln (4) P2sat = R RT R 298.15 A value of 1.30 × 10−4 m3 mol−1  was used for the solid molar volume. The fugacity coefficient is given by V ∂P 1 RT G − + dV − ln z (5) φ2 = RT ∂ni T,V,ni =j V ∞ where z is the compressibility factor. This coefficient may be calculated using an equation of state (EOS) such as the Peng–Robinson EOS . The mixture constants a and b were evaluated using the classical mixing rule: a= xi xj aij ; aij = (aii ajj )1/2 (1 − kij ) i
Fig. 7. Solubility of dibenzofuran in carbon dioxide as a function of the density of pure CO2 : () 301.3 K; (䊉) 309.0 K; () 319.2 K; () 328.7 K, this paper; () 323.2 K Hansen ; simultaneous correlation using Chrastil model .
xi xj bij ;
(bii + bjj ) (1 − δij ) 2
where kij = kji and δij = δji denote binary interaction parameters between unlike molecules i and j. The pure component constants aii and bii for carbon dioxide and dibenzofuran were evaluated using the values of the critical constants given in the introduction and values of 0.225 and 0.397 for the CO2 and DB acentric factors, respectively [1,14]. Solubility data of solid dibenzofuran in liquid and supercritical CO2 (301.3, 309.0, 319.2, 323.2 and 328.7 K) were simultaneously correlated using one binary parameter (k12 ) or two binary param-
E. P´erez et al. / J. of Supercritical Fluids 46 (2008) 238–244 Table 4 Parameters and standard deviations, σ, for CO2 + dibenzofuran solubility correlations using the Chrastil model and the Peng–Robinson EOS with one or two binary interaction parameters Chrastil model a0 a1 a2 /K σ
−14.637 3.6805 −4675 5.8 × 10−4
k12 − − σ
−0.08441 − − 15 × 10−4
k12 δ12 − σ
0.01937 −0.1486 − 10 × 10−4
eters (k12 and δ12 ). The Peng–Robinson EOS correlation is not substantially improved if binary interaction parameters are fit to each set of isothermal data. A least square-procedure was used to determine parameter values by minimizing the average absolute relative deviation between experimental and calculated solubilities (AARD) defined by Eq. (2). Results for the Chrastil and Peng–Robinson EOS correlations are shown in Table 4 along with values for the standard deviations between experimental and calculated solubilities, σ. 1/2 N 1 σ= (ycal − yexp )2 (7) (N − 1) i=1
where N is the total number of experimental points. A prediction of the CO2 + dibenzofuran SLV line was also made following the procedure described by McHugh and Kukronis . To this end, the Peng–Robinson EOS and the classical mixing rule with values for the binary parameters k12 and δ12 obtained from the solubility data correlation were used. The SLV line calculated using two binary interaction parameters is not accurate: predicted melting temperatures rise as pressure increases. The predicted SLV line shown in Fig. 4 was calculated using one binary interaction parameter (k12 = −0.08441). A value of 1.9 K is obtained for the standard deviation between experimental and predicted melting temperatures. 4. Conclusions The solubility behavior of dibenzofuran in pure CO2 was investigated at 301.3, 309.0, 319.2, 328.7 and 338.2 K in the 6.5–30 MPa pressure range. Data taken at 338.2 K correspond to vapor–liquid equilibrium. At the other temperatures studied, the solubility of solid dibenzofuran in liquid or supercritical CO2 is reported. These data show the feasibility of using supercritical CO2 to extract dibenzofuran from contaminated soils. The solid–liquid–vapor (SLV) equilibrium for the CO2 + dibenzofuran system was also measured. The shape of the SLV line suggests a liquid–gas type III diagram in the classification of Scott and van Konynenburg  which intersects with a solid phase. The solubility data obtained in this paper at 301.3, 309.0, 319.2 and 328.7 K and those previously reported at 323.12 K by Hansen  were simultaneously correlated using the Chrastil density-based model and the Peng–Robinson equation of state. In spite of its empirical character and simplicity, the Chrastil model provided a correlation of better accuracy than the Peng–Robinson correlation. Nevertheless, it must be noted that
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