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# Binary phase diagrams

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Phase diagrams are graphical representations of the liquid, vapor, and solid phases that co-exist at various ranges of temperature and pressure within a reservoir. Binary phase diagrams describe the co-existence of two phases at a range of pressures for a given temperature.

## Binary phase diagrams

Fig. 1 is a pressure-composition (p-x-y) phase diagram that shows typical vapor/liquid phase behavior for a binary system at a fixed temperature below the critical temperature of both components. At pressures below the vapor pressure of Component 2, pv2, any mixture of the two components forms a single vapor phase. At pressures between pv1 and pv2, two phases can coexist for some compositions. For instance, at pressure pb, two phases will occur if the mole fraction of Component 1 lies between xB and xE. If the mixture composition is xB, it will be all liquid; if the mixture composition is xE, it will be all vapor. At constant temperature and pressure, the line connecting a liquid phase and a vapor phase in equilibrium is known as a tie line. In binary phase diagrams such as Fig. 1, the tie lines are always horizontal because the two phases are in equilibrium at a fixed pressure. For 1 mole of mixture of overall composition, z, between xB and xE, the number of moles of liquid phase is

....................(1)

Eq. 1 is an inverse lever rule because it is equivalent to a statement concerning the distances along a tie line from the overall composition to the liquid and vapor compositions. Thus, the amount of liquid is proportional to the distance from the overall composition to the vapor composition, divided by the length of the tie line.

Phase diagrams such as Fig. 1 can be determined experimentally by placing a mixture of fixed overall composition in a high-pressure cell and measuring the pressures at which phases appear and disappear. For example, a mixture of composition xB would show the behavior indicated qualitatively in Fig. 2. At a pressure less than pd (Fig. 1), the mixture is a vapor. If the mixture is compressed by injecting mercury into the cell, the first liquid, which has composition xA, appears at the dewpoint pressure, pd. As the pressure is increased further, the volume of liquid grows as more and more of the vapor phase condenses. The last vapor of composition xE disappears at the bubblepoint pressure, pb.

If the system temperature is above the critical temperature of one of the components, the phase diagram is similar to that shown in Fig. 3. At the higher temperature, the two-phase region no longer extends to the pure Component 1 side of the diagram. Instead, there is a critical point, C, at which liquid and vapor phases are identical. The critical point occurs at the maximum pressure of the two-phase region. The volumetric behavior of mixtures containing less Component 1 than the critical mixture, xc, is like that shown in Fig. 2. Fig. 4 shows the volumetric behavior of mixtures containing more Component 1. Compression of the mixture of composition x2 (in Fig. 3) leads to the appearance of liquid phase of composition x1 when pressure pd1 is reached. The volume of liquid first grows and then declines with increasing pressure. The liquid phase disappears again when pressure pd2 is reached. Such behavior is called "retrograde vaporization" or "retrograde condensation" if the pressure is decreasing.

If the system temperature is exactly equal to the critical temperature of Component 1, the critical point on the binary pressure-composition phase diagram is positioned at a Component 1 mole fraction of 1.0. Fig. 5 shows the behavior of the two-phase regions as the temperature rises. As the temperature increases, the critical point moves to lower concentrations of Component 1. As the critical temperature of Component 2 is approached, the two-phase region shrinks, disappearing altogether when the critical temperature is reached.

Fig. 6 shows a typical locus of critical temperatures and pressures for a pair of hydrocarbons. The critical locus shown in Fig. 6 is the projection of the critical curve in Fig. 5 onto the p-T plane. Thus, each point on the critical locus represents a critical mixture of different composition, although composition information is not shown on this diagram. For temperatures between the critical temperature of Component 1 and Component 2, the critical pressure of the mixtures can be much higher than the critical pressure of either component. Thus, two phases can coexist at pressures much greater than the critical pressure of either component. If the difference in molecular weight of the two components is large, the critical locus may reach very high pressures. Fig. 7 gives critical loci for some hydrocarbon pairs.[1]

The binary phase diagrams reviewed here are those most commonly encountered. However, more complex phase diagrams involving liquid/liquid and liquid/liquid/vapor equilibriums do occur in hydrocarbon systems at very low temperatures (well outside the range of conditions encountered in reservoirs or surface separators) and in CO2/crude oil systems at temperatures below approximately 50°C. See Stalkup[2] and Orr and Jensen[3] for reviews of such phase behavior.

## References

1. GPSA. 1972. GPSA Engineering Data Book, 9th edition. Tulsa, Oklahoma: Gas Processors Suppliers Association.
2. Stalkup Jr., F.I. 1983. Miscible Displacement, Vol. 8. Richardson, Texas: Henry L. Doherty Monograph Series, SPE.
3. Orr, F.M. Jr. and Jensen, C.M. 1984. Interpretation of Pressure-Composition Phase Diagrams for CO2/Crude Oil Systems. SPE J. 24 (5): 485–497. SPE-11125-PA. http://dx.doi.org/10.2118/11125-PA.