Pseudocritical point

The above trend is valid for members of a homologous series. For components which are not members of a homologous series, the reverse trend may occur over a limited temperature range, causing relative volatility to increase as the equilibrium temperature is raised [Eq. (1.12)]. However, as temperature is raised further and approaches the critical point, relative volatility eventually diminishes and will reach unity at the pseudocritical point of the mixture. 

The effect of temperature (or pressure 1 on relative volatility is further illustrated in Fig. 1.2b (29). The diagram clearly shows a reduction in relative volatility as pressure is raised and illustrates that relative volatility approaches unify as the pseudocritical point of the mixture is approached. 

The heat transfer to supercritical carbon dioxide was measured in horizontal, vertical and inclined tubes at constant wall temperature for turbulent flow at Re-numbers between 2300 and lxl 05. The influence of the variation of physical properties due to the vicinity of the critical point was examined, as well as the influence of the direction of flow. Therefore most of the measurements were conducted at pseudocritical points. At those supercritical points the behaviour of the physical properties is similar to the behaviour at the critical point, but to a lesser degree. At such points the heat capacity shows a maximum density, viscosity and heat conductivity are changing very fast. [1]... 

At the pseudocritical points that are nearest the critical point, this behaviour is most accentuated. 

Because of the strong variations of the heat capacity and therefore of the local heat transfer coefficient at a pseudocritical point, the LMTD (logarithmic mean temperature difference) cannot be used for the evaluation of all of our measurements. 

Figure 3. Heat transfer at a pseudocritical point at 120 bar at a small distance from the critical point.

In Figure 3, the predicted P-x-y equilibria for CC>2-toluene system up to 16Mpa is shown uniquely by the group parameters in Table 1 and 2. Also, in Figure 4, the predicted P-x-y equilibria for ethane-acetone system at 298.15K and up to 5Mpa is illustrated. The predictions are included the pseudocritical point of the mixtures. Although we omit here further demonstrations, the GC-EOS is found to be comprehensively applicable to various phase equilibria of... 

We note from Figures 10.3-2 and 10.3-3 that the shapes of the critical loci of mixtures are complicated and that, in general, the critical temperature and/or pressure of a binary mixture is not intermediate to those properties of the pure fluids. It is of interest to note that, in analogy with the properties of a pure fluid, a pseudocritical point of a mixture of a fixed composition is defined by the mechanical stability inflection point,... 

Figures 2, 3, and 4 present isothermal pressure-composition diagrams of the liquid-vapor regions close to the pseudocritical locus, at - 90 , -95°, and -100°F. Since no pseudocritical points were determined in this particular study, the pseudocritical points shown are taken from the work published by Donnelly and Katz [1].

Figures 2, 3, 4, 5, and 6 are diagrams representing the best lines through a considerable amount of data. Some of the data were found to scatter considerably, particularly in the regions near the pseudocritical point and near the triple point. Several times, apparently valid liquid samples were taken in a region which should have contained only vapor and solid, indicating a strong tendency toward a metastable liquid state. Consequently, the brute force method of obtaining a large number of points was used to define the boundaries of the liquid-vapor region.

The above discussion does not seek to invalidate any of the rest of the work by Donnelly. It must be pointed out that Donnelly was determining the outlines of the overall carbon dioxide-methane system and the higher temperature data were probably quite valid. In particular, the locus of pseudocritical points appears to be suitably established and points from this curve were used to supply the pseudocritical points indicated in Figs. 2, 3, and 4. These figures show that data from the present study extrapolate reasonably well to the Donnelly pseudocritical points. 

Another key issue is the prediction of cladding surface temperatures at bulk temperature close to the pseudocritical point. The strong change of almost all coolant properties with temperature may cause a deterioration of heat transfer and associated hot spots, which can hardly be predicted with current computational fluid dynamics (Pioro and Duffey, 2007). A recent blind benchmark exercise on heat transfer in an... 

Pseudocritical line is a hne that consists of pseudocritical points. 

Pseudocritical region is a narrow region around a pseudocritical point where aU thermophysical properties of a pure fluid exhibit rapid variations. For H2O, it is about 25°C from pseudocritical temperature. 

The volumetric expansivity of liquid metals is much smaller than that of the remaining coolants and stays almost constant (see Fig. A2.11). The volumetric expansivity of gases drops almost twice, in a linear fashion, from 250 to 1000°C. Remarkably, the values of volumetric expansivity for SCW at temperatures below the pseudocritical point are close to those for gases. Near the pseudocritical point, the volumetric expansivity of SCW peaks. At higher temperatures, the volumetric expansivity of SCW gradually reaches values corresponding to those of gases. 

Figure A33 Photos of carbon dioxide during transition through (a) critical and pseudocritical points and (h) corresponding pressure—temperature diagram (Gupta et al., 2013).

Pseudocritical point (characterized with P and pc) is the point at a pressure above the critical pressure and at a temperature (Tpc > Ter) corresponding to the maximum value of specific heat at this particular pressure. 

Critical parameters of selected fluids are listed in Table A3.1. For better understanding of general trends and specifics of various thermophysical properties near critical and pseudocritical points, it was decided to show these properties in comparison with subcritical properties for water (see Figs. A3.5—A3.12). Also, thermophysical... 

Figure A3.13 Variations of selected thermophysical properties of water near pseudocritical point (384.9°C at 25 MPa) pseudocritical region is about 25°C around pseudocritical point.

The specific heat of water (see Fig. A3.9(b)) (as well as of other fluids, for example, for carbon dioxide, see Fig. A3.18 and Fig. A3.26 for helium) has a maximum value at the critical point. The exact temperature that corresponds to the specific heat peak above the critical pressure is known as the pseudocritical temperature (see also Figs. A3.23 and A3.24, and Table A3.2 for water and carbon dioxide). For water at pressures approximately above 300 MPa and for carbon dioxide at pressures above 30 MPa (see Fig. A3.24), a peak (here, it is better to say a hump ) in specific heat almost disappears therefore, the term such as a pseudocritical point no longer exists. The same applies to the pseudocritical line. 

In general, it is very difficult or, actually impossible, to define the exact pressure at which a maximum value of specific heat will disappear or cannot be defined. The major problem here is that we need to know uncertainties of specific heat at these very high supercritical pressures, which are not easy to find. If a maximum value of specific heat is within these uncertainties compared to those on a base line, we can assume that at this pressure, a pseudocritical point does not exist ... 

Table A3.3 Peak values of specific heat, volume expansivity, and thermal conductivity in critical and near pseudocritical points (a) water and (h) carhon dioxide... 

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