Ind. Eng. Chem. Res. 1989,28, 1903-1907 Oil. ASME J. Heat Transfer 1962,84, 339-346. Kirschbaum, E. Neues zum Warmeubergang mit und ohne Anderung des Aggregatzustandes. Chem.-1ng.-Tech. 1952,24(7), 393-400. Krishnamurthy, R.; Gebhart, B. An Experimental Study of Transition to Turbulence in Vertical Mixed Convection Flows. ASME J. Heat Transfer 1989, 111,121-130. Marcucci, B. J.; Joye, D. D. Experimental Study of Transitions in Mixed-Convection, Vertical Upflow Heating of Water in Tubes. In Fundamentals of Forced and Mixed Convection;Kulacki, F. A., Boyd, R. D., Eds.; Heat Transfer/Denver, ASME Publications: New York, 1985; HTD Vol. 42, pp 131-139. Martinelli, R. C.; Southwell, C. J.; Alves, G.; Craig, H. L.; Weinberg, E. B.; Lansing, N. F.; Boelter, L. M. K. Heat Transfer and Pressure Drop for a Fluid Flowing in the Viscous Region Through a Vertical Pipe. Trans. Am. Znst. Chem. Eng. 1942, 38, 493-530. McAdams, W. H. Heat Transmission, 3rd. ed.; McGraw-Hill: New York, 1954; pp 229-235. Metais, B.; Eckert, E. R. G. Forced, Mixed, and Free Convection Regimes. ASME J. Heat Transfer 1964,86, 295-296. Mullin, T. E.; Gerhard, E. R. Heat Transfer to Water in Downward Flow in a Uniform Wall Temperature Vertical Tube at Low
1903
Graetz Numbers. ASME J. Heat Transfer 1977, 99, 586-589. Petuckov, B. S.; Nolde, L. D. Heat Transfer in the Visco-gravitational Flow of Liquid in Pipes. Teploenergetika 1959,6, 72-80 (in Russian). Scheele, G. F.; Hanratty, T. J. Effect of Natural Convection Instabilities on Rates of Heat Transfer at Low Reynolds Numbers. AZChE J. 1963, 9(2), 183-185. Scheele, G. F.; Rosen, E. M.; Hanratty, T. J. Effect of Natural Convection on Transition to Turbulence in Vertical Pipes. Can. J . Chem. Eng. 1960,38, 67-73. Swanson, L. W.; Catton, I. Surface Renewal Theory for Turbulent Mixed Convection in Vertical Ducts. Znt. J . Heat Mass Transfer 1987, 30(11), 2271-2279. Symolou, P. D.; Todreas, N. E.; Rohsenow, W. M. Criteria for the Onset of Flow Recirculation and Onset of Mixed Convection in Vertical Rod Bundles. ASME J. Heat Transfer 1987, 109(1), 138-145.
Received f o r review April 5, 1989 Revised manuscript received August 24, 1989 Accepted September 11, 1989
Critical Locus and Partial Molar Volume Studies of the Benzaldehyde-Carbon Dioxide Binary System Neil R. Foster, Stuart J. Macnaughton, Rodney P. Chaplin,* and P. Tony Wells School of Chemical Engineering & Industrial Chemistry, University of New South Wales, P.O.Box 1, Kensington, N S W , Australia 2033
A fundamental experimental study of the behavior of the benzaldehyde-carbon dioxide binary system has been undertaken. The critical locus for the system has been accurately determined for concentrations up to 1.5 mol % benzaldehyde. Partial molar volume data were also obtained, which exhibited characteristically large negative values near the critical region. The Peng-Robinson equation of state in combination with van der Waals mixing rules proved to be only semiquantitative in the prediction of partial molar volumes. Binary systems comprising supercritical carbon dioxide and both liquid and solid solutes have been extensively studied over the last decade, and a comprehensive phase classification scheme has been compiled (Williams, 1981; Johnston, 1983; McHugh, 1983). In this study, the behavior of the system benzaldehyde-carbon dioxide has been investigated at supercritical conditions. The benzaldehyde-carbon dioxide system is of considerable interest due to the possible commercial extraction of benzaldehyde from Australian flora using supercritical carbon dioxide. The study comprised two interlinked parts. In the first section, the supercritical behavior of the binary benzaldehyde-carbon dioxide system was investigated with the purpose of enabling the system to be classified according to its phase behavior. The investigation was limited to low concentrations of benzaldehyde in carbon dioxide. The objective of the second section was to measure the partial molar volume of benzaldehyde in carbon dioxide at infinite dilution. The justification for this investigation extends beyond its physical significance. The partial molar volume can be used to test the ability of an equation of state to predict derivative-based thermodynamic properties (Eckert et al., 1983). In particular the Peng-Robinson equation of state may be able to predict the shape of the partial molar property correctly provided that the system can be described by adequate mixing rules. Eckert et al. (1983) have shown that this equation of state is the most useful in this region, although lack of adequate mixing rules is still a major limitation. 0888-5885/89/2628-1903$01.50/0
Theoretical Background To enable a pressure-explicit cubic equation of state to predict partial molar volumes, a derivative form must be used (Edmister, 1974). The ability of an equation of state to maintain accuracy under differentiation is a better measure of its usefulness than the ability to match P, V, and T data. Most of the important thermodynamic properties of mixtures such as entropy and enthalpy can only be determined by differentiating cubic equations of state. While the prediction of such bulk properties relies essentially on the form of the equation of state, the prediction of partial molar properties is also heavily influenced by the choice of mixing rules. The partial molar volume at infinite dilution of a solute, VZm,can be determined from the standard thermodynamic relation
The symbol y1 refers to the mole fraction of component 1 in the supercritical phase. In this series of experiments, the magnitude of Vzmwas determined both experimentally and also calculated by using the Peng-Robinson equation of state. The method adopted for the calculation of partial molar volumes requires that the experimental procedure be designed such that the values for the derivative (dV/dy!)T,p at infinite dilution may be obtained. A t this low dilution, the relationship between molar volume and composition is sufficiently linear such that graphical determination of 8 1989 American Chemical Society
1904 Ind. Eng. Chem. Res., Vol. 28, No. 12, 1989 Digital thermometer
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Figure 1. Critical locus experimental apparatus.
the derivative required is justified (Eckert et al., 1983,1986; Eckert, 1983).
Experimental Section Apparatus and Procedures for Critical Locus Determination. The critical locus experiments were performed in a specially designed high-pressure test apparatus which incorporated a sight gauge. The apparatus is shown schematically in Figure 1. The technique for determining the critical point of the binary mixtures involved visual observation of the transition from a two-phase state to a single-phase state, and vice versa. In the studies reported in this paper, the disappearance of the meniscus was rapid and was usually accompanied by cloudiness or opalescence. In order to determine the critical locus of the benzaldehydecarbon dioxide binary mixture, the critical points of mixtures of the two components were determined for a range of compositions. This range was limited by the maximum temperature to which the apparatus could be safely taken. The major item of the apparatus was a Jerguson sight gauge rated to 240 bar and 40 "C, with a borosilicate glass window on one face. The sight gauge was fitted with a thermocouple and pressure transducer (DRUCK Model DPI 260). A needle valve was used to seal off the volume inside the sight gauge, enabling the volume to be held constant throughout each experiment. A three-way valve mounted externally to the apparatus provided access to a wet gas meter or carbon dioxide. A manually operated magnetic agitator was used to ensure that the contents of the sight gauge were well mixed. Tests conducted with industrial-grade C 0 2 yielded critical values of P, = 73.1 atm and T,= 31.0 "C representing deviations of 0.4% and 0.1%, respectively, from the accepted values of 72.8 atm and 31.1 "C. Equipment limitations, though, suggest that the likely errors for each data point were larger than these values. The overall error for each temperature measurement was zt0.2 "C, and the pressure transducer error was judged to be h0.5 atm. The mass of C02 present in the Jerguson gauge was determined by venting the gas through a wet gas meter after the critical values were ascertained. Calibration of the meter against known weights of C 0 2 produced a standard deviation in error of 1.5%. The syringe used to inject benzaldehyde into the gauge was weighed before and after injection on a balance accurate to hO.1 mg (representing less than 0.03% of the injected amount). It can therefore be assumed that the compositions are accurate to within h1.5%. After considerable experimentation, it was found that greater accuracy and reproducibility in the critical point
Figure 2. Critical locus for the system benzaldehyde-carbon dioxide. The composition range is 0-1.5 mol % benzaldehyde.
measurement for this system was obtained by taking each binary mixture into the supercritical region first and determining the conditions at which a meniscus formed upon cooling. Each data point required between 4 and 6 h for an accurate determination. While the method outlined above was used to determine the actual critical locus for the mixture, the phase behavior of the system was also observed. Each mixture was examined for evidence of immiscibility or other unusual behavior. Apparatus and Procedure for Partial Molar Volume Measurements. The relationship between molar volume and composition was determined indirectly by using a constant volume apparatus similar to that used in the critical locus experiments, except that the Jerguson sight gauge was replaced with a length of 3/4-in.-o.d. stainless steel tube. The tube served as the main experimental vessel and occupied over 90% of the internal volume of the rig. A constant volume was charged with a solute-solvent mixture a t a very low concentration and raised to the supercritical state. The supercritical mixture contained within the vessel was bled out in small amounts, and the change in pressure and the volume removed were recorded. As the vessel contents were in the one-phase region, the whole evacuation process was assumed to occur at constant composition. Partial molar volume experiments were performed at 35 and 41.8 "C, with at least six experiments being completed at each temperature. The method relied on its success for measurements being obtained at constant composition, and thus the mixture in the vessel had to be above its critical point and well mixed. The results from the critical locus experiments were used to determine the temperature conditions at which the measurements could be made, while ensuring supercriticality.
Results and Discussion The experimentally determined critical locus for the system carbon dioxide-benzaldehyde, for the composition range 0-1.5 mol % benzaldehyde, is shown in Figure 2. The composition dependence of the critical mixture temperature and critical mixture pressure are shown in Figures 3 and 4. As the data in Figures 2-4 illustrate, small concentrations of benzaldehyde in carbon dioxide resulted in a sharp rise in the mixture critical point. At 1 mol % benzaldehyde, the critical pressure was altered by 15%, which is an indication of a large solute-solvent interaction. Reported literature values are usually much less than this. For example, for the hydrogen sulfide-carbon dioxide system at 1% hydrogen sulfide, the critical pressure is only
Ind. Eng. Chem. Res., Vol. 28, No. 12, 1989 1905 I
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Figure 3. Critical mixture temperature for the system benzaldehyde-carbon dioxide as a function of composition.
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Figure 6. Infinite dilution partial molar volumes for the system benzaldehyde-carbon dioxide as a function of pressure. (+) Experimental; (- - -) predicted from the Peng-Robinson equation of state with a binary interaction parameter value of 0.185.
Useful partial molar volume data were only obtained at 41.8 "C, with considerable scatter occurring with the results at 35 "C. The results at the lower temperature will be discussed later. The data presented in Figure 6 are experimental partial molar volumes, as well as those predicted by using the Peng-Robinson equation, as a function of pressure. The value of the interaction parameter was optimized to give a least-squares fit of the experimental values. It is clear from the graph that the Peng-Robinson equation provides a good qualitative representation of the experimental data. However, quantitatively, the correlation between the experimental and predicted data sets is not good. The experimental errors, while quite large in the region of maximum compressibility, compare favorably with other published data obtained by using a different experimental method (Eckert et al., 1983; Eckert, 1983). The errors in temperature and pressures involved in the determination of the partial molar volumes are equivalent to those already discussed in the section dealing with the critical locus experiment. However, the uncertainty in the mixture composition was substantially reduced from the earlier value of f1.5% to less than 3~0.2%as the reduction in the bulkiness of the rig made possible the direct gravimetric determination of both the benzaldehyde and CO, weights. The internal volume of the "partial molar volume" apparatus was determined by filling the vessel with nitrogen until a known pressure was obtained at a given temperature. The mass of N, was then calculated from the volume of gas subsequently vented through a wet gas meter. The volume obtained was 37.1 f 0.2 mL (0.5%). The same procedure was also followed employing C 0 2 (at 35 "C), in the place of N2. The values obtained at both high pressures (>lo0 bar) and lower pressures (
