Fundamentals of Fluid Flow in Porous Media
Fluid Phase Behavior: Tertiary Diagram
Ternary or triangular phase diagrams can be used to plot the phase behavior of systems consisting of three components by outlining the composition regions on the plot where different phases exist. The advantage of using a ternary plot for depicting compositions is that three variables can be conveniently plotted in a two-dimensional graph and mixture of different components can be easily represented. A ternary diagram for hypothetical components A, B and C is shown in Figure 5‑7.The phase behavior on ternary diagram is plotted at fixed pressure and temperature and If these three components were miscible at that special temperature and pressure then no multiphase region would appear on the diagram. Every point on a ternary plot represents a different combination of the three components. Compositions could be represented in ternary diagram as weight, mole or volume percentage. The volume percentage is used only when there is not significant volume change during the mixing. The vertexes represent the pure components, and the sides of equilateral triangle are scaled to represent the binary compositions of the three possible pairs.
There are three common methods used to determine the ratios of the three species in the composition. The first method is an estimation based upon the phase diagram grid. The concentration of each species is 100% (pure phase) in its corner of the triangle and 0% at the line opposite it. The percentage of a specific species decreases linearly with increasing distance from this corner, as seen in Figure 5‑7. By drawing parallel lines at regular intervals between the zero line and the corner (Figure 5‑7.a), fine divisions can be established for easy estimation of the content of a species. For a given point, the fraction of each of the three materials in the composition can be determined by the first. For phase diagrams that do not possess gridlines, the easiest way to determine the composition is to set the altitude of the triangle to 100% (that is equal to the sum of all altitudes from the mixture point to three sides) and determine the shortest distances from the point of interest to each of the three sides. The distances (the ratios of the distances to the total height of 100%) give the content of each of the species, as shown in Figure 5‑7.b. The third method is based upon a larger number of measurements, but does not require the drawing of perpendicular lines. Straight lines are drawn from each corner, through the point of interest, to the corresponding side of the triangle. The lengths of these lines, as well as the lengths of the segments between the point and the corresponding sides, are measured individually. Ratios can then be determined by dividing these segments by the entire corresponding line, by the so-called inverse-lever-arm rule, as shown in the Figure 5‑7.c.
In Figure 5‑7.c, point M is a mixture of ( Mb / Bb ) of component ‘B’ and (1 – Mb / Bb ) of binary mixture ‘b’ of ‘A’ and ‘C’. These 3 rules could be applied to the combination of any two mixtures represented on the ternary. Figure 5‑8 shows two different mixtures represented by M1 and M2. Any mixture of M1 and M2 would be along line M1M2 . The point representing the composition of the final mixture would again be determined by applying the inverse-lever-arm rule along the line.
Figure 5-7: Ternary Phase Diagram for a System Consisting of Components A, B, and C Which are Miscible in All Proportions
Phase relationship may also be represented on a triangular phase diagram Figure 5‑11. The diagram shows the phase condition at equilibrium at constant pressure and temperature. The plot is typical for hydrocarbon systems in which vapor-liquid equilibrium exists over regions of the concentration domain.
Figure 5-8: All Mixture of M1 and M2 Would Be Along Line M1M2