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# Quaternary 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. Quaternary phase diagrams represent the phase behavior of mixtures containing four components in a pyramid-shaped diagram (a tetrahedron).

## Quaternary phase diagrams

Phase diagrams for systems with four components can be represented conveniently on a tetrahedral diagram like that shown in Fig. 1a, which shows a quaternary phase diagram calculated with the Peng-Robinson[1] equation of state for mixtures of methane (C1), C3, C6, and hexadecane (C16) at 200°F and 2,000 psia. These phase diagrams have a property similar to that of ternary diagrams: the sum of the lengths of perpendicular lines drawn from a composition point in the interior of the diagram to the four faces of the diagram is a constant length. Hence, the fractions of four components can be represented by an extension of Eq. 8.4 to four components.

The faces of the quaternary diagram are ternary phase diagrams. Fig. 1b shows the ternary diagram for the ternary methane (C1)/hexane (C6)/hexadecane (C16) system, which is the bottom face of the quaternary diagram. The two-phase region is a band across the diagram, and there is no critical point on that face. Fig. 1c shows the C1/C3/C16 system, which is the left face of the quaternary diagram. That ternary system does have a critical point. While the ternary diagram for C1/C3/C6 is not shown separately, it is qualitatively similar to the diagram for the C1/C3/C16 system in Fig. 1c.

The two-phase region in the interior of the quaternary diagram is a 3D region of composition space bounded by the ternary two-phase regions on the faces. Within that region, every mixture composition forms two phases, and each composition point lies on a tie line that connects equilibrium vapor and liquid compositions. A vertical slice through the two-phase region is shown in Fig. 1a, along with a few tie lines that lie in the interior of the diagram. The mole fraction of liquid phase is still calculated with Eq. 8.6, which applies to systems with any number of components.

....................(8.6)

The boundary of the two-phase region in the interior of the quaternary diagram is divided into two parts: a surface that includes all the vapor-phase compositions and a corresponding surface of liquid-phase compositions. The dividing line between the liquid and vapor surfaces is a critical locus (the dotted line in Fig. 1c) that connects the critical point in the C1/C3/C16 face (Fig. 1a) with the critical point in the C1/C3/C6 face. The critical locus is a set of compositions at which the liquid and vapor phases have identical compositions and properties. The compositions and limiting tie lines on the critical locus play important roles in the description of EOR processes (see Phase diagrams for EOR processes).

## References

1. Peng, D.-Y. and Robinson, D.B. 1976. A New Two-Constant Equation of State. Industrial & Engineering Chemistry Fundamentals 15 (1): 59–64. http://dx.doi.org/10.1021/i160057a011