Two-phase region

Best ternary predictions are usually obtained for mixtures having a very broad two-phase region, i.e., where the two partially miscible liquids have only small mutual solubilities. Fortunately, this is the type of ternary that is most often used in commercial liquid-liquid extraction. 

Figure 15 shows results for a difficult type I system methanol-n-heptane-benzene. In this example, the two-phase region is extremely small. The dashed line (a) shows predictions using the original UNIQUAC equation with q = q. This form of the UNIQUAC equation does not adequately fit the binary vapor-liquid equilibrium data for the methanol-benzene system and therefore the ternary predictions are grossly in error. The ternary prediction is much improved with the modified UNIQUAC equation (b) since this equation fits the methanol-benzene system much better. Further improvement (c) is obtained when a few ternary data are used to fix the binary parameters. 

In most cases only a single tie line is required. When several are available, the choice of which one to use is somewhat arbitrary. However, our experience has shown that tie lines which are near the middle of the two-phase region are most useful for estimating the parameters. Tie lines close to the plait point are less useful, since no common models for the excess Gibbs energy can adequately describe the flat region near the... 

The continuous line in Figure 16 shows results from fitting a single tie line in addition to the binary data. Only slight improvement is obtained in prediction of the two-phase region more important, however, prediction of solute distribution is improved. Incorporation of the single ternary tie line into the method of data reduction produces only a small loss of accuracy in the representation of VLE for the two binary systems. 

Figure 17 shows results for the acetonitrile-n-heptane-benzene system. Here, however, the two-phase region is somewhat smaller ternary equilibrium calculations using binary data alone considerably overestimate the two-phase region. Upon including a single ternary tie line, satisfactory ternary representation is obtained. Unfortunately, there is some loss of accuracy in the representation of the binary VLB (particularly for the acetonitrile-benzene system where the shift of the aceotrope is evident) but the loss is not severe. 

Outside the two-phase region, ELIPS yields a value of 0 for E/F on the R-phase side and 1 for E/F on the E-phase side. Con-, vergence to these values again requires about eight or fewer iterations, except near the plait-point region where convergence is somewhat slower. 

The criterion used for "too near the plait point" is that ratio of K s for the two "solvent" components is less than seven with the feed composition in the two-phase region. 

The subroutine is well suited to the typical problems of liquid-liquid separation calculations wehre good estimates of equilibrium phase compositions are not available. However, if very good initial estimates of conjugate-phase compositions are available h. priori, more effective procedures, with second-order convergence, can probably be developed for special applications such as tracing the entire boundary of a two-phase region. 

It is important to remember the significance of the bubble point line, the dew point line, and the two phase region, within which gas and liquid exist in equilibrium. 

When the two components are mixed together (say in a mixture of 10% ethane, 90% n-heptane) the bubble point curve and the dew point curve no longer coincide, and a two-phase envelope appears. Within this two-phase region, a mixture of liquid and gas exist, with both components being present in each phase in proportions dictated by the exact temperature and pressure, i.e. the composition of the liquid and gas phases within the two-phase envelope are not constant. The mixture has its own critical point C g. 

Moving back to the overall picture, it can be seen that as the fraction of ethane in the mixture changes, so the position of the two-phase region and the critical point change, moving to the left as the fraction of the lighter component (ethane) increases. 

The initial condition for the dry gas is outside the two-phase envelope, and is to the right of the critical point, confirming that the fluid initially exists as a single phase gas. As the reservoir is produced, the pressure drops under isothermal conditions, as indicated by the vertical line. Since the initial temperature is higher than the maximum temperature of the two-phase envelope (the cricondotherm - typically less than 0°C for a dry gas) the reservoir conditions of temperature and pressure never fall inside the two phase region, indicating that the composition and phase of the fluid in the reservoir remains constant. 

On compression, a gaseous phase may condense to a liquid-expanded, L phase via a first-order transition. This transition is difficult to study experimentally because of the small film pressures involved and the need to avoid any impurities [76,193]. There is ample evidence that the transition is clearly first-order there are discontinuities in v-a plots, a latent heat of vaporization associated with the transition and two coexisting phases can be seen. Also, fluctuations in the surface potential [194] in the two phase region indicate two-phase coexistence. The general situation is reminiscent of three-dimensional vapor-liquid condensation and can be treated by the two-dimensional van der Waals equation (Eq. Ill-104) [195] or statistical mechanical models [191]. 

With a further increase in the temperature the gas composition moves to the right until it reaches v = 1/2 at the phase boundary, at which point all the liquid is gone. (This is called the dew point because, when the gas is cooled, this is the first point at which drops of liquid appear.) An unportant feature of this behaviour is that the transition from liquid to gas occurs gradually over a nonzero range of temperature, unlike the situation shown for a one-component system in figure A2.5.1. Thus the two-phase region is bounded by a dew-point curve and a bubble-point curve. 

It is important to note that, in this example, as in real seeond-order transitions, the eiirves for the two-phase region eaimot be extended beyond the transition to do so would imply that one had more than 100% of one phase and less than 0% of the other phase. Indeed it seems to be a quite general feature of all known seeond-order transitions (although it does not seem to be a themiodynamie requirement) that some aspeet of the system ehanges gradually until it beeomes eomplete at the transition point. 

Some binary systems show a minimum at a lower eritieal-sohition temperature a few systems show elosed-loop two-phase regions with a maximum and a minimum.) As the temperature is inereased at any eomposition other than the eritieal eomposition v = the eompositions of the two eoexisting phases adjust themselves to keep the total mole fraetion unehanged until the eoexistenee eurve is reaehed, above whieh only one phase... 

Figure A2.5.7. Constant temperature isothenns of reduced Helmlioltz free energy A versus reduced volume V. The two-phase region is defined by the line simultaneously tangent to two points on the curve. The dashed parts of the smooth curve are metastable one-phase extensions while the dotted curves are unstable regions. (The isothenns are calculated for an unphysical r = 0.1, the only effect of which is to separate the isothenns...

At the critical pohit (and anywhere in the two-phase region because of the horizontal tie-line) the compressibility is infinite. However the compressibility of each conjugate phase can be obtained as a series expansion by evaluating the derivative (as a fiuictioii of p. ) for a particular value of T, and then substituting the values of p. for the ends of the coexistence curve. The final result is... 

Figure A2.5.17. The coefficient Aias a fimction of temperature T. The line IRT (shown as dashed line) defines the critical point and separates the two-phase region from the one-phase region, (a) A constant K as assumed in the simplest example (b) a slowly decreasing K, found frequently in experimental systems, and (c) a sharply curved K T) that produces two critical-solution temperatures with a two-phase region in between.

Figure A3.3.6 Free energy as a function of the order parameter cji for the homogeneous single phase (a) and for the two-phase regions (b), 0.

For the phase separation problem, the maximum and minima in Fig. 8.2b and the inflection points between them must also merge into a common point at the critical temperature for the two-phase region. This is the mathematical criterion for the smoothing out of wiggles, as the critical point was described above. 

The procedure outlined in this example needs only one modification to be applicable to the critical point for solution miscibility. In Fig. 8.2b we observe that there are two inflection points in the two-phase region between P and Q. There is only one such inflection point in the two-phase region of the van der Waals equation. The presence of the extra inflection point means that still another criterion must be added to describe the critical point The two inflection points must also merge with each other as well as with the maximum and the minima. 

The accompanying sketch qualitatively describes the phase diagram for the system nylon-6,6, water, phenol for T > 70°C.f In this figure the broken lines are the lines whose terminals indicate the concentrations of the three components in the two equilibrium phases. Consult a physical chemistry textbook for the information as to how such concentrations are read. In the two-phase region, both phases contain nylon, but the water-rich phase contains the nylon at a lower concentration. On this phase diagram or a facsimile, draw arrows which trace the following procedure ... 

Unusual behavior has also been observed in soHd mixtures of He and He. In principle, all soHd mixtures should separate as absolute 2ero is approached, but because of kinetic limitations, this equiHbrium condition is almost never observed. However, because of high diffusivity resulting from the large 2ero-point motion in soHd helium, this sort of separation takes place in a matter of hours in soHd mixtures of He and He (53,61). The two-phase region for the soHd mixture is outlined by the dashed curve in Figure 4. The two-phase dome is shallow, and its temperature maximum is 0.38 K. 

Fig. 3. Vapor—liquid-phase diagram for the HCl—H2 O system (5) where (-) represents the demarcation between the two-phase region and the gas...

Fig. 6. Phase diagram showing the composition pathway traveled by the casting solution during precipitation by cooling. Point A represents the initial temperature and composition of the casting solution. The cloud point is the point of fast precipitation. In the two-phase region tie lines linking the...

Selection of Fractionator 11 gives pure hexane, which can be recycled to Mixer 1. The distillate Dll, however, is a problem. It cannot be distilled because of its location next to a distillation boundary. It is outside of the two-phase region, so it cannot be decanted. In essence, no further separations are possible. However, using the Recycle heuristics, it can be mixed into the MSA recycle stream without changing the operation of Mixer 1 appreciably. However, as both outlet streams are mixed together. Fractionator 11 is not really needed. The mixture of hexane and isopropanol, 07, could have been used as the MSA composition in the first place. 

Iron, cobalt, and nickel catalyze this reaction. The rate depends on temperature and sodium concentration. At —33.5°C, 0.251 kg sodium is soluble in 1 kg ammonia. Concentrated solutions of sodium in ammonia separate into two Hquid phases when cooled below the consolute temperature of —41.6°C. The compositions of the phases depend on the temperature. At the peak of the conjugate solutions curve, the composition is 4.15 atom % sodium. The density decreases with increasing concentration of sodium. Thus, in the two-phase region the dilute bottom phase, low in sodium concentration, has a deep-blue color the light top phase, high in sodium concentration, has a metallic bronze appearance (9—13). 

FIG. 2-11 Enthalpy-concentration diagram for aqueous hydrogen chloride at 1 atm. Reference states enthalpy of liquid water at 0 C is zero enthalpy of pure saturated HCl vapor at 1 atm (—85.03 C) is 8000 kcal/moL NOTE It should he observed that the weight basis includes the vapor, which is particularly important in the two-phase region. Saturation values may be read at the ends of the tie lines. [Van Nuys, Trans. Am. Inst. Chem. Eng., 39, 663 (1943).]... 

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