The Phase Envelope

The phase envelope of a mixture is analogous to the vapor pressure curve of a pure component. The vapor pressure curve defines temperature and pressure conditions at which a pure component can exist as vapor and liquid at equilibrium. In this two-phase regime only one parameter, the temperature or the pressure, may be varied independently. 

Bubble points and dew points may be generated as described above for a given mixture over ranges of temperature and pressure. The locus of bubble points is the bubble point curve and the locus of dew points is the dew point curve. The two curves together define the phase envelope. In addition to the bubble point curve (total liquid saturated) and the dew point curve (total vapor saturated), other curves may be drawn representing constant vapor mole fraction. All these curves meet at one point, the critical point, where the vapor and liquid phases lose their distinctive characteristics and merge into a single, dense phase. 

Unlike a pure component, the critical point of a mixture is not necessarily the 

In areas surrounding the phase envelope, the system exists as a single phase. Below the dew point curve and at higher temperatures, it is a superheated vapor, while areas above the bubble point curve and to the left of it represent a sub-cooled liquid. In areas above the phase envelope between the sub-cooled liquid and the superheated vapor, the mixture is a dense or supercritical fluid, with properties changing gradually from those typical of a liquid to those typical of a vapor. 

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Figure 5.21 helps to explain how the phase diagrams of the main types of reservoir fluid are used to predict fluid behaviour during production and how this influences field development planning. It should be noted that there are no values on the axes, since in fact the scales will vary for each fluid type. Figure 5.21 shows the relative positions of the phase envelopes for each fluid type. 

Comparison of the phase envelopes for different hydrocarbon types... 

Figure 5.23 shows the phase envelopes for the different types of hydrocarbons discussed, using the same scale on the axes. The higher the fraction of the heavy components in the mixture, the further to the right the two-phase envelope. Typical separator conditions would be around 50 bara and 15°C. 

The composition points, the tie-lines and the phase envelope showing the multiphase regions were then plotted on the ternary diagram. Micellar solutions were selected... 

When the pressure of interest exceeds the critical pressures of both components, the phase envelope exhibits two critical points. For instance, mixtures of methane and ethane exhibit critical points at 900 psia and minus 62°F and at 900 psia and 46°F. 

A common use of three-component phase diagrams is in analysis of miscible displacement. For instance, Figure 2-30 gives the phase envelope of an oil mixed with carbon dioxide.6 The oil is plotted as an artificial two-component mixture, with methane as one component and all other constituents added together as the other component. 

Mixture 2 on Figure 2-37 illustrates a mixture containing a large quantity of the light component. The phase envelope is relatively small and is located at low temperatures. The critical point is located far down the left-hand side of the phase envelope and is fairly close to the critical point of the pure light component. There is a large area in which retrograde condensation can occur. 

As heavy component is added to the mixtures—lines 3 and 4, for instance—the phase envelope increases in size and covers wider ranges of temperature and pressure. The critical point moves up closer to the top of the envelope. 

Black oils consist of a wide variety of chemical species including large, heavy, nonvolatile molecules. The phase diagram predictably covers a wide temperature range. The critical point is well up the slope of the phase envelope. 

The phase diagram of a typical black oil is shown in Figure 5-1. The lines within the phase envelope represent constant liquid volume, measured as percent of total volume. These lines are called iso-vols or quality lines. Note that the iso-vols are spaced fairly evenly within the envelope. ... 

Additional gas evolves from the oil as it moves from the reservoir to the surface. This causes some shrinkage of the oil. However, separator conditions lie well within the phase envelope, indicating that a relatively large amount of liquid arrives at the surface. 

The phase diagram for a typical volatile oil, Figure 5-2, is somewhat different from the black-oil phase diagram. The temperature range covered by the phase envelope is somewhat smaller, but of more interest is the position of the critical point. The critical temperature is much lower than for a black oil and, in fact, is close to reservoir temperature. Also, the iso-vols are not evenly spaced but are shifted upwards toward the bubble-point line. 

A wet gas exists solely as a gas in the reservoir throughout the reduction in reservoir pressure. The pressure path, line 12, does not enter the phase envelope. Thus, no liquid is formed in the reservoir. However, separator conditions lie within the phase envelope, causing some liquid to be formed at the surface. 

The point e to the left on Figure 15-3A is the position of the bubble point at the temperature of the isotherm, and the point e to the right is the position of the dew point. If the above analysis were performed at various temperatures below the critical temperature, the phase envelope would be defined. Figure 15-4 shows the position of the phase envelope along with three isotherms. 

Important Note Use Z.mak when at less than the critical pressure and/or in the phase envelope. 

RK.mak. When out of the phase envelope, use this program, the well-known Soave-Redlich-Kwong (SRK) equation-of-state simplified program [12], The student here may immediately detect the standard SRK... 

Please note that both Z.mak and RK.mak exhibit the same problem for finding the gas density of propane at 100 psia and 200°F. Note also that Z calculations from each are appreciably different, 0.86 vs. 0.94 (see Figs. 1.3 and 1.4). Why the difference Remember the previous warning about using the Z.mak program out of the phase envelope Well, this is a classic example, as these conditions are definitely out of... 

Now for those of you who may say, This table has its place but what about enthalpy values far to the right of this saturated liquid line or far to the left of this saturated vapor line Chap. 2 addresses this question most specifically. Please consider the fact that pressure increase has little effect on liquid enthalpy at constant temperature. Similarly, notice how pressure lines tend to converge on the vapor dew point line of the phase envelope. This indicates that at constant temperature, increasing the pressure of vapor tends to approach the enthalpy value of the saturation vapor dew point line of the phase envelope of a P vs. H enthalpy figure. See Fig. 2.1 in Chap. 2. 

Figure 2.1 presents the simplistic basis upon which all separations are commonly made in our industry. Even membrane separations depend to a large degree upon the vapor pressure and temperature effects shown. A typical temperature dashed line shows how the temperature variance effects a vapor-liquid separation. Notice also the variance for pressure and enthalpy. Inside the phase envelope, the temperature and pressure remain constant while the enthalpy varies. This constant T and P occur in what is called the flash zone. 

The bubble point is defined as that hydrocarbon component condition at which the system is all liquid, with the exception of only one drop (infinitely small) of vapor present. The amount of vapor is specified as a matter of convenience so that the composition of the liquid is the composition of the total system. This means that if we want to find the bubble point of a liquid composition, we simply flash it for a very small amount of vapor specified. You can do this with the RefFlsh program quickly by trial and error. How Simply try varied temperatures with the pressure held constant. The program RefFlsh will tell you if your temperature is out of the phase envelope by stating SYSTEM IS ALL... 

Referring to Fig. 2.1, notice the vast temperature difference between the bubble point and the dew point. This is 313 - 106 = 207°F. Figure 2.1 displays a single discrete component temperature constant line. A system mixture like the preceding example mixture, debutanizer feed bubble point minus dew point, would yet have a varied-temperature horizontal line running through the phase envelope. 

These vertical constant temperature lines (Fig. 2.1) are the same for a mixture as for a single component. Outside the phase envelope, the temperature lines tend to hold a constant enthalpy value or have very limited variance with variance of pressure. Compare Figs. 2.1 and 2.2. In particular, notice that the constant temperature line approaches verticality outside the phase envelope. This vertical temperature line indicates that outside the phase envelope there is no significant enthalpy variance with pressure variance. Again, outside the phase envelope, temperature variance is most effective to enthalpy. Observe how limited enthalpy is between 1.0 and 100.0 atm pressure. 

An interesting feature of the phase equilibrium behavior is the relative insensitivity of the phase envelope and positions of the tielines to variations in pressure in the two-phase region, as evidenced by comparison of the diagrams at 100 and 150 bar in Figure 4. This would seem to imply that similar separations can be achieved by operation at a range of pressures above the upper critical solution pressure of -95 bar. 

For mixtures, the phase envelopes expand from a curve to a region for the single component. Recall that in order for a single component to exist in two phase (vapor + liquid), the conditions had to fall exactly on the vapor pressure curve. For a mixture, there is a region over the pressure-temperature plane where two phases exist. 

The condition at which the liquid just begins to form is called the dew point. The condition at which the vapor just begins to form is called the bubble point. A curve can be plotted showing the temperature and pressure at which a mixture just begins to liquefy. Such a curve is called a dew-point curve or dew-point locus. A similar curve can be constructed for the bubble point. The phase envelope is the combined loci of the bubble and dew points, which intersect at a critical point. The phase envelope maps out the regions where the various phases exist. 

Figure 3.2 shows a phase envelope for an acid gas mixture. Note that the locus at lower pressure is the dew-point curve, whereas the one at higher pressure is the bubble-point curve. In fact, any point inside the phase envelope is a two-phase point. 

Phase envelopes for typical natural gas tend to be fairly broad. That is, they cover a large range of temperature and pressure. On the other hand, the phase envelopes for acid gas mixtures tend to be quite narrow. Figure 3.2 shows the phase envelope for a mixture containing 50 mol% H2S and 50 mol% C02. This phase envelope was calculated using the Peng-Robinson equation of state, and the bubble, dew, and critical points are labeled. 

For rapid approximations of the phase envelope, the process engineer is wise to keep this chart handy. With some insight, the design engineer can use this chart to obtain estimates of the phase equilibrium for mixtures other than those shown. 

Methane, a common impurity in acid gas, tends to broaden the phase envelope because it is lighter than the acid gas components. Figure 3.6 shows two phase envelopes. The first is the phase envelope for an equimolar mixture of hydrogen sulfide and carbon dioxide. This is the same phase envelope shown in figure 3.2. The other phase envelope is for a mixture with 2 mol% methane. 

The phase envelope with the methane is broader than the one without. In essence, the dew point loci are the same for the two... 

To demonstrate the effect of ethane and propane on the phase envelopes of acid gas mixtures, consider figures 3.7 and 3.8, which... 

Figure 3.9 shows the effect of n-butane on the phase envelope of an equimolar mixture of H2S and COz. Note how the butane decreases the dew point pressure but has only a small effect on the bubble point pressure. 

Figure 3.11 Comparison of the phase envelopes for two acid gas mixtures 1. Clarke et al. (1998) and 2. Kellerman et al. (1995) for mixtures containing approximately 90 mol% C02. Curves are from the Peng-Robinson equation of state.

CSMGem software (Sloan and Koh, 2007). The broken portion of these curves is where the acid gas liquefies and crosses the phase envelope. The steep portion is for the hydrate for the liquefied acid gas. 

Figure 5.5 shows the phase envelope and two hydrate loci for this acid gas mixture. The first curve labeled "Saturated" assumes that there is plenty of water present. The other hydrate locus is labeled "3.2 g/m3[std]," and this is the hydrate curve for the acid gas containing the specified amount of water. 

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