Ternary Diagram Plotting Software Design Using The "Tie-Line Slope" Method
Authors: Chen S.M. , Cheung V. 
Published: March 2010

Abstract
Ternary diagrams or pseudo ternary diagrams are commonly used to provide a graphical representation of equilibrium fluid phase behavior for systems as diverse as distillation columns and miscible gas floods of oil reservoirs. The phase envelope and the position of the critical point on it are important to enhanced oil recovery engineers who are involved with miscible gas flood design. In the past, phase equilibrium data were laboriously plotted on the pseudo ternary diagram and special graphical techniques were utilized to locate the critical point on the phase envelope. Presented in this article is a computerized curve fitting method to, firstly, generate the phase envelope from a given set of phase equilibrium data and then use the ‘tie-line slopes’ to position the critical point. Experimental data are included and show excellent agreement with this new method.

Introduction
Miscible gas displacement processes have recently gained wide attention within the enhanced oil recovery arena. Prior to spending time, money and exhaustive effort to design and implement such processes in the field, the engineers require certain studies and tools to identify and evaluate which one of these processes is technically and commercially feasible. One of these fundamental tools that can be used is the pseudo ternary diagram, which graphically displays equilibrium phase behavior for fluid systems under investigation. An idealized pseudo ternary diagram is shown in Figure 1.
Two pieces of information from this diagram are of great value to enhanced oil recovery engineers. These include the phase envelope and the position of the critical point on it. Normally, a set of vapour-liquid equilibrium data either obtained through a series of laboratory experiments or calculated from published phase behavior correlations or equations of state is used to generate the phase envelope. Some graphical techniques(1,2) can then be used to locate the critical point. For well-behaved fluid systems, these techniques can easily approxiatmate the correct critical points. In many other instances, difficulties do arise. In addition, these techniques often require laborious manual graph plotting.
To facilitate enhanced oil recovery engineers who are extensively involved with the phase equilibrium data handling and pseudo ternary diagram preparations, a simple computerized curve fitting method was developed. This method includes a conventional polynomial curve fitting routine with optional weight factors and a new "tie-line slope " algorithm. The procedures to design this software package are also presented in this article.

Review of Previous Methods
Several methods have been developed to position the critical point on the phase envelope generated from a set of phase equilibrium data. Among these, Sherwood's and Coolidge's methods are the most recognized. Both are based on the so called "conjugation curve " which represents the locus of the onjugate points derived from vapour-liquid equilibrium data pairs.
FIGURE 1: An idealized ternary diagram. (Available in full paper)
FIGURE 2: Sherwood's method. (Available in full paper)

Sherwood's Method
Referring to Figure 2, points Gi and Li on the phase envelope represent the compositions of equilibrium gas phase (Agi, Bgi, Cgi) and liquid phase (Ali, Bli, Cli).