Critical line, mixture

Figure A2.5.11. Typical pressure-temperature phase diagrams for a two-component fluid system. The fiill curves are vapour pressure lines for the pure fluids, ending at critical points. The dotted curves are critical lines, while the dashed curves are tliree-phase lines. The dashed horizontal lines are not part of the phase diagram, but indicate constant-pressure paths for the T, x) diagrams in figure A2.5.12. All but the type VI diagrams are predicted by the van der Waals equation for binary mixtures. Adapted from figures in [3].

The mole fraction of the component whose critical point is the origin of the critical line has been indicated as a parameter along each of the lines. It should be noted from these numbers that there are compositions in each of the binary pairs for which there is no critical point. It should also be noted that some C02 - CO mixtures have two critical points. 

The general shape of the binary critical lines dictates the shape of critical lines in the reacting mixtures. 

Critical points have been calculated for such mixtures with various initial H20/C0 ratios. The results are shown in Figure 2. In this figure, the line of zero conversion is the critical line for H20 - CO binary. For mixtures with initial H20/C0 ratios greater than about 4, it is possible to find critical points for all conversions. When the initial ratio is less, this is no longer possible. Lines of 25%, 50% and 75% conversion are also shown in Figure 2. 

Figure 2. Critical lines in reacting mixtures of CO with excess HtO...

The study described above for the water-gas shift reaction employed computational methods that could be used for other synthesis gas operations. The critical point calculation procedure of Heidemann and Khalil (14) proved to be adaptable to the mixtures involved. In the case of one reaction, it was possible to find conditions under which a critical mixture was at chemical reaction equilibrium by using a one dimensional Newton-Raphson procedures along the critical line defined by varying reaction extents. In the case of more than one independent chemical reaction, a Newton-Raphson procedure in the several reaction extents would be a candidate as an approach to satisfying the several equilibrium constant equations, (25). 

Mixtures of equisized charged spheres were also treated by the MSA. Such a system is then uniquely characterized by the ratio of the critical temperatures of the pure components. Harvey [235] found that a continuous critical curve from the dipolar solvent to the molten salt is maintained until the critical temperature of the ionic component exceeds that of the dipolar component by a factor of about 3.6. This ratio is much higher than theoretically predicted for nonionic model fluids. We recall that for NaCl the critical line is still continuous at a critical temperature ratio of about 5. Thus, the MSA of the charged-hard-sphere-dipolar-hard-sphere system captures, at least in part, some unusual features of real salt-water systems with regard to their critical curves. 

These fluctuations, which are referred to as order-parsmeter fluctuations in studies of critical phenomena (3). comprise the driving forces for transport in the system. For liquid mixtures near a critical mixing point, the order parameter is concentration, and for pure gases near the vapor-liquid critical point, the order parameter is density. For gas mixtures such as supercritical solutions near the critical line, the order parameter is again density, which is a function of composition and temperature compared to a pure gas where density is a function of only temperature at constant pressure. 

CO -benzene, and CO -n-decane. The critical densities and the corresponding compositions are plotted in Figure 1. The three hydrocarbons in order of higher to lower solubility in C0 were heptane, benzene, and decane. The measured binary diffusion coefficients or the decay rates of the order-parameter fluctuations at various temperatures and pressures are listed in Tables I, II, and III for CO -heptane, CO -benzene, and CO -decane systems respectively. In Figure 2, the critical lines of the three binary systems in the dilute hydrocarbon range are shown in the pressure-temperature space. dP/dT along the critical lines of CO.-heptane and CO -benzene systems are similar and lower than dP/dT along the critical line of CO -decane system, which indicates that C02 and decane form more asymmetric mixtures relative to CO with heptane or benzene. 

Z. Vaporization of a mixture of two liquids critical line dew surface, ebullition surface.—It is the same when the two phases into which the liquid mixture is divided are a liquid phase (lower... 

The line is projected in its true magnitude along the line syp, which is the limiting line of the mixture of composition x e is its ebvUitian line, and p the dew line they meet in the point y, projection of the critical point F, and at this point they are tangent to the projection of the critical line. 

The critical point for the vaporization of a single fiuid, page 812.—236. Double liquid mixtures. The temperature at which the two layers have the same composition does not correspond to an indifferent point, 814.—237. This temperature is a critical temperature, 816.—238. Mixtures which separate into two layers at temperatures lower than the critical temperature, 817.—239. Mixtures which separate into two layers at temperatures above the critical point, 818.—240. Infiuence of pressure on the critical temperature of a double liquid mixture, 819.—241. Vaporization of a mixture of two liquids critical line dew surface surface of ebullition, 819.—... 

The locus of the critical points corresponding to a series of mixtures of different composition is the critical line shown in fig. 16.6. 

The phase behavior that is exhibited by a critical or supercritical mixture of several components is usually not simple Street (jO reports six classes of phase behavior diagrams In the simplest classes of systems (classes 1 and 2), the critical lines are continuous between the critical points of pure components Study of reaction equilibrium at SCF conditions requires knowledge of critical properties of the reacting mixture at various levels of conversion Three different approaches to evaluate critical properties are available, viz, empirical correlations, rigorous thermodynamics criteria and the theory of conformal solutions (10) The thermodynamic method is more general and reliable because it is consistent with the calculation of other thermodynamic properties of the reacting mixture (11) ... 

P. Van Konynenburg and R. L. Scott (1980) Critical lines and phase-equilibria in binary vanderwaals mixtures. Philos. Trans. Soc. London Series A 298, pp. 495-540... 

Van Konynenburg, P.H. Scott, R.L. Critical lines and phase behavior in binary van der Waals mixtures. Phil. Trans. Roy. Soc. London Ser. 1980, A298 (1442), 495-540. 

CRITICAL LINES IN BINARY MIXTURES OF COMPONENTS WITH MULTIPLE CRITICAL POINTS... 

Keywords critical lines, equation of state, multiple critical points, binary mixtnres, one fluid mixture model... 

It is most likely the critical line asymptotes observed for the conventional types II, III, and IV (Figure 8) should end not at the infinite pressure but at the pure component second (or third) critical point. To study the possibility of continuous critical line path from stable critical point of one component to metastable critical point of other component the t5 e III of phase behavior was chosen. The selection criterion of thermod5mamic model parameters for t5 e III was extracted from global phase diagram for the binary van der Waals mixture... 

Figure 9. Critical lines for a binary mixture of components with several critical points. Solid lines (A, B, C) indicate binary mixture critical lines dashed lines are phase existence curve of pure components Cn rn are the m critical point ( w > i) for the pure component (n = 1,2% m = 1 identifies the vapor-liquid critical point m > 1 corresponds to the fluid-fluid critical points.

We have studied one-fluid model of binary fluids with polyamorphic components and found that multicritical point scenario gives opportunity to consider the continuous critical lines as the pathways linking isolated critical points of components on the global equilibria surface of binary mixture. It enhances considerably the landscape of mixture phase behavior in a stable region at the account of hidden allocation of other critical points in metastable region. 

The critical locus in Figure I0.3-3n is very much like that for the ethane-propylene system in Fig. 10.3-2 this is referred to as category I phase behavior. For such systems the critical line starts at the critical point of pure component 1 (C ), and as the mixture... 

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