Question

Describe tie lines in a ternary diagram.

Answer 1

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.

This figure 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.

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. The next figure 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. The other figure 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

   

Now for the tie lines, If any two ternary alloys are mixed together, tie lines can be shown. The composition of the mixture will lie on a straight line joining the original two compositions. This is true regardless of the proportions of the two alloys in the mixture. Conversely, if an alloy decomposes into two fractions of differing composition, the compositions of the two portions will lie on opposite ends of a straight line passing through the original composition point. Consider Fig. 10.9. Points S and L represent two ternary alloys of respective composition: 20% A + 70% B + 10% C and 40% A + 30% B + 30 % C. Suppose that one part of S is mixed with three parts of L and the mixture is analyzed.

As can be seen by inspection of the following figure,, this composition lies at P, which is a point on the straight line connecting S and L. Regardless of the compositions chosen or in what proportions they had been mixed, the total composition would have occurred on the line joining the two original compositions. It is evident that the line SL has the characteristics of a tie line: It is both isobaric and isothermal, because it lies in the composition plane, which is drawn perpendicular to the temperature axis and corresponds to the case of constant atmospheric pressure (i.e., it would be drawn perpendicular to the pressure axis if a fourth dimension were available).

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