Mixtures critical point

At every e the mixture critical point (if indeed, the mixture has a critical point) can be found using the procedure described above. 

The critical points in these mixtures are all at pressures higher than the critical pressure of water many are at temperatures higher than the water critical temperature. The mixture critical points indicate that high density phase separations persist to extreme conditions of temperature and pressure. 

Mixtures of C02 and methanol were selected for the initial investigation of the solvatochromic behavior in supercritical fluid systems. This combination is of interest as it combines the low critical temperature and pressure of carbon dioxide with a polar, less volatile modifier. This system exhibits relatively simple Type I phase behavior and several groups have published measurements of mixture critical points (19-21). At intermediate compositions the critical pressure for this fluid is much higher than that of either pure C02 or pure methanol, reaching a maximum of approximately 2400 psi (20). 

This LCEP is a gas-liquid critical point in the presence of the solid phase. A LCEP was not observed for toluene-TPP mixtures at temperatures below 350°C. Measurements were not made at higher temperatures because of thermal degradation of the porphyrin. The results in Tables I-III are also shown on PT projections in Figures 1 and 2. The mixture critical points in Figure 2 are obtained from Figure 4. 

ID MS involves the precise addition of an isotopically labeled form of the analyte to an accurately measured sample of the specimen, e.g., serum. After an appropriate equilibration time, the analyte and its labeled internal standard are isolated from the sample with a suitable extraction and purification step, and an aliquot is introduced, either directly or after (gas) chromatographic separation from remaining interferences, into the mass spectrometer. The latter accurately measures the ratio of analyte to internal standard using the intensities of an equivalent ion in the spectrum of each. From this ratio, the concentration of analyte is calculated by comparison with the ratios of the same ions in standard calibration mixtures. Critical points in this procedure are as follows ... 

A PT diagram for the ethane/heptane system is shown in Fig. 12.6, and a yx diagram for several pressures for the same system appears in Fig. 12.7. According to convention, one plots as y and x the mole fractions of the more volatile species in the mixture. The maximum and minimum concentrations of the more volatile species obtainable by distillation at a given pressure are indicated by the points of intersection of the appropriate yx curve with the diagonal, for at these points the vapor and liquid have the same composition. They are in fact mixture critical points, unless y = x = 0 or y = x = 1. Point A in Fig. 12.7... 

The volumetric expansion of the liquid when it is contacted with the SCF plays the key role in the process. The behaviour reported by Yeo et al. [10] and by Kordikowski et al. [11] for the dymethylsulfoxide (DMSO)-CC>2 system at two temperatures shows that CO2 produces a remarkable volumetric expansion of DMSO near the mixture critical point. The increase of antisolvent amount in the mixed solvent and the evaporation of the organic liquid into the SCF eventually cause the precipitation of the solute. A cleaning step, carried out with pure antisolvent, is necessary after the precipitation, in order to remove completely the liquid solvent from the solid particles the antisolvent pushes the liquid out of the vessel, then it has to extract the residual solvent from the solid and the dry solid particles can be collected. 

Besides these thermodynamic criteria, the most common approach used in the literature is based on the operation at pressures above the binary (liquid - SC-CO2) mixture critical point, completely neglecting the influence of solute on VLEs of the system. But, the solubility behavior of a binary supercritical COj-containing system is frequently changed by the addition of a low volatile third component as the solute to be precipitated. In particular, the so-called cosolvency effect can occur when a mixture of two components solvent+solute is better soluble in a supercritical solvent than each of the pure components alone. In contrast to this behavior, a ternary system can show poorer solubility compared with the binary systems antisolvent+solvent and antisol-vent+solute a system with these characteristics is called a non-cosolvency (antisolvent) system. hi particular, in the case of the SAS process, they hypothesize that the solute does not induce cosolvency effects, because the scope of this process lies in the use of COj as an antisolvent for the solute, inducing its precipitation. 

In the light of these considerations, a different approach based on ternary system thermodynamics could be considered. However, the phase behavior of temaiy systems could be very complex and there is a considerable lack of data on ternary systems containing a component of low volatility therefore, a possible compromise could be to consider that the solute addition can produce the shift of the mixture critical point (MCP) (i.e., the pressure at which the ternary mixture is supercritical) with respect to binary system VLEs and the modification of this kind of system that is formed according to the van-Konynenburg and Scott classification. ... 

In this part of the chapter, a summary of semi-continuous SAS experiments performed on various materials is proposed and an attempt at providing an interpretation of the different morphologies observed in relation to the position of the process operating point with respect to mixture critical point has been made. 

It is important to note that while SCWO is formally defined in terms of the critical point of pure water, addition of any other constituents to the water will alter the critical point, and the system may or may not be supercritical with respect to this mixture critical point. Rather than a single critical point, for a binary system a critical curve exists that in the simplest cases joins the critical point of pure water to the critical point of the second substance across the composition space. For ternary mixtures the critical curve becomes a critical surface, and so on. In general, mixtures of water with higher volatility substances such as noncondensable gases or liquid organics will remain supercritical, while mixtures of water with lower-volatility substances such as salts will become subcritical and liquid or solid phases will precipitate from the vapor/ gas phase. 

Practical Aspects of SCWO Processing 429 Table 10 Gas and Organic Mixture Critical Points at 250 Bar... 

Compound Formula Mixture Critical T,"C Wt% Compound at Mixture Critical Point Reference... 

It is necessary to find the appropriate solvent for the given solute and the optimum temperature and pressure conditions for instantaneous crystallization of the solute from its solution, at which the antisolvent, CO2 either is totally miscible in the solvent or has a very high solubility in it. The solvent and CO2 are completely miscible as the binary mixture reaches the mixture critical point. There is an exponential increase in the total volume of the solution with increasing dissolution of CO2. Originally, the relative total volume expansion (RTVE) of the solvent was the criterion for the GAS crystallization, which was defined (45) as... 

Where and LH are the corresponding activation energy and enthalpy of phase transition and the coefficient defines the maximum probability that molecules will cross the interface between the liquid and SCF (vapor) phases. This simple relationship can explain the behavior of the mass transfer coefficient in Figure 15 when it is dominated by the interfacial resistance. Indeed, increases with temperature T according to Eq. (49) also, both parameters E and A// should decrease with increase of pressure, since the structure and composition of the liquid and vapor phases become very similar to each other around the mixture critical point. The decrease of A/f with pressure for the ethanol-C02 system has been confirmed by interferometric studies of jet mixing described in Section 3.2 and also by calorimetric measurements described by Cordray et al. (68). According to Eq. (43) the diffusion mass transfer coefficient may also increase in parallel with ki as a result of more intensive convection within the diffusion boundary layer. 

A standard operating temperature of 60 C was chosen for two reasons. First, a rough approximation for estimating binary mixture critical points is that (15)... 

If an experiment is performed at an overall composition equal to x in figure 3.2d, the vapor-liquid envelope is first intersected along the dew point curve at low pressures. The vapor-liquid envelope is again intersected at its highest pressure, which corresponds to the mixture critical point at T2 and x. This mixture critical point is identified with the intersection of the dashed curve in figure 3.2b and the vertical isotherm at T2. At the critical mixture point, the dew point and bubble point curves coincide and all the properties of each of the phases become identical. Rowlinson and Swinton (1982) show that P-x loops must have rounded tops at the mixture critical point, i.e., (dPldx)T = 0. This means that if the dew point curve is being experimentally determined, a rapid increase in the solubility of the heavy component will be observed at pressures close to the mixture critical point. The maximum pressure of the P-x loop will depend on the difference in the molecular sizes and interaction energies of the two components. 

If the temperature is raised to Tj, the phase behavior shown in figure 3.7e occurs. This temperature is greater than the UCEP temperature, therefore two phases exist as the pressure is increased as long as the critical mixture curve is not intersected. The two branches of the vapor-liquid phase envelope approach each other in composition at an intermediate pressure and it appears that a mixture critical point may occur. But as the pressure is further increased, a mixture critical point is not observed and the two curves begin to diverge. To avoid confusion, the phase behavior shown in figure 3.7e is not included in the P-T-x diagram. 

Figure 3.12d shows the phase behavior if the temperature is increased to T2, a temperature greater than the critical temperature of component 1. In this instance, the left-hand side of the vapor-liquid envelope no longer contacts the pressure axis and a vapor-liquid mixture critical point occurs at the highest pressure of the vapor-liquid envelope. The vapor-liquid envelope is much larger at T2 than at T because T2 is higher than Tj. Again, there are... 

If the operating temperature is now increased to T, the phase behavior shown in figure 3.15d occurs. At Ty the mixture critical point pressure of the vapor-liquid envelope occurs precisely at the same pressure at which the three-phase SLV line is intersected. Hence, a vapor-liquid mixture critical point is observed in the presence of excess solid. This vapor-liquid mixture critical point in the presence of excess solid is the lower critical end point (LCEP) (Diepen and Scheffer, 1948a). If the temperature is increased slightly above the LCEP temperature, only solid-SCF phase behavior is observed at all pressures, since the three-j)hase (SLV) line ends at the LCEP. 

Consider first the schematic P-T and P-x diagrams for the naphthalene-ethylene system. Figure 3.18b depicts the solubility behavior of naphthalene in supercritical ethylene at a temperature greater than the UCEP temperature. Solid-gas equilibria exist at low pressures until the three-phase SLV line is intersected. The equilibrium vapor, liquid, and solid phases are depicted as points on the horizontal tie line at pressure Pj. As the pressure is further increased a vapor-liquid envelope is observed for overall mixture concentrations less than Xl- A mixture critical point is observed for this vapor-liquid envelope, as described earlier. If the overall mixture composition is greater than Xl, then solid-gas equilibria are observed as the pressure is increased above Pj. 

When working with a liquid solute, a bubble point, dew point, or mixture critical point can be visually detected. A bubble point is defined as the... 

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