Ternary phase diagrams

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. Ternary phase diagrams represent the phase behavior of mixtures containing three components in a triangular diagram.

Properties of ternary diagrams

Phase behavior of mixtures containing three components is represented conveniently on a triangular diagram such as those shown in Fig. 1. Such diagrams are based on the property of equilateral triangles that the sum of the perpendicular distances from any point to each side of the diagram is a constant equal to the length of any of the sides. Thus, the composition of a point in the interior of the triangle can be calculated as

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

where

....................(2)

Several other useful properties of triangular diagrams are a consequence of this fact. For mixtures along any line parallel to a side of the diagram, the fraction of the component of the corner opposite to that side is constant (Fig. 1b). In addition, mixtures lying on any line connecting a corner with the opposite side contain a constant ratio of the components at the ends of the side (Fig. 1c). Finally, mixtures of any two compositions, such as A and B in Fig. 1d, lie on a straight line connecting the two points on the ternary diagram. Compositions represented on a ternary diagram can be expressed in volume, mass, or mole fractions. For vapor/liquid equilibrium diagrams, mole fractions are most commonly used.

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  Fig. 1 – Properties of ternary diagrams.

Features of ternary diagrams

Fig. 2 shows the typical features of a ternary phase diagram for a system that forms a liquid and a vapor at fixed temperature and pressure. Mixtures with overall compositions that lie inside the binodal curve will split into liquid and vapor. Tie lines connect compositions of liquid and vapor phases in equilibrium. Any mixture with an overall composition along a tie line gives the same liquid and vapor compositions. Only the amounts of liquid and vapor change as the overall composition changes from the liquid side of the binodal curve to the vapor side. If the mole fractions of Component i in the liquid, vapor, and overall mixture are x_i, y_i, and z_i, the fraction of the total moles in the mixture in the liquid phase is given by

....................(3)

Plait point

Eq. 3 is another lever rule similar to that described for binary diagrams. The liquid and vapor portions of the binodal curve meet at the plait point, a critical point at which the liquid and vapor phases are identical. Thus, the plait-point mixture has a critical temperature and pressure equal to the conditions for which the diagram is plotted. Depending on the pressure, temperature, and components, a plait point may or may not be present.

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  Fig. 2 – Ternary phase diagram at a constant temperature and pressure for a system that forms a liquid and a vapor.

Phase behavior representation

Any one ternary diagram is given for fixed temperature and pressure. As either the temperature or pressure is varied, the location of the binodal curve and slopes of the tie lines may change. Fig. 3 shows the effect of increasing pressure on ternary phase diagrams for mixtures of C₁, butane (C₄), and decane (C₁₀) at 160°F. The sides of the ternary diagram represent a binary system; therefore, the ternary diagram includes whatever binary tie lines exist at the temperature and pressure of the diagram. Fig. 4 shows the corresponding binary phase diagrams for the C₁–C₄ and C₁–C₁₀ pairs. The C₄–C₁₀ pair is not shown because it forms two phases only below the vapor pressure of C₄, approximately 120 psia at 160°F (see Fig. 8.9).

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  Fig. 3 – Ternary phase diagram for the methane/butane/decane system at 160° F.

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  Fig. 4 – Pressure-composition phase diagram for methane/butane and methane/decane binary systems at 160°F.

As Fig. 3 shows, at 1,000 psia the two-phase region is a band that stretches from the C₁–C₁₀ side of the diagram to the tie line on the C₁–C₄ side. If the pressure is increased above 1,000 psia, the liquid composition line shifts to higher methane concentrations; methane is more soluble in both C₄ and C₁₀ at the higher pressure (see Fig. 4). The two-phase region detaches from the C₁–C₄ side of the diagram at the critical pressure of the C₁–C₄ pair (approximately 1,800 psia). As the pressure increases above that critical pressure, the plait point moves into the interior of the diagram (Fig. 3, lower diagrams). With further increases in pressure, the two-phase region continues to shrink. It would disappear completely from the diagram if the pressure reached the critical pressure of the C 1 –C 10 system at 160°F (nearly 5,200 psia).

According to the phase rule, three phases may coexist at a fixed temperature and pressure for some ternary systems. Fig. 5 shows the general structure of such systems. The three-phase region (3Φ) on a ternary diagram is represented as a triangle in Fig. 5. Any overall composition lying within the three-phase region splits into the same three phases (I, II and III). Only the amounts of each phase change as the overall composition varies within the three-phase region. Given 1 mole of an overall mixture in the three-phase region, the geometrical relations

....................(4)

with ....................(5)

determine the fraction of each phase. The edges of the three-phase region are tie lines for the associated two-phase (2Φ) regions; thus, there is a two-phase region adjacent to each of the sides of the three-phase triangle. Three-phase regions can exist in several phase diagrams applied in the design of EOR processes.

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  Fig. 5 – Generic ternary phase diagram with three-phase region.

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See also

Phase diagrams

Binary phase diagrams

Phase diagrams for EOR processes

Phase diagrams for reservoir fluid systems

Quaternary phase diagrams

PEH:Phase_Diagrams