Triangular coordinate graphics

The methods for doing so are described in Chapter 9. The basic principles remain unchanged—the primary difference is the choice of a consistent basis for calculation, such as a solvent-free basis. Graphic techniques based on triangular coordinates provide approximate answers, but modern computational techniques are to be preferred. 

If inlet conditions (F, S, xF, and ys) are known, we have four unknown variables (R, E, x, and y). However, since we have only three equations, we need additional information to be able to solve for the unknown variables, which are the equilibrium data of the ternary system solute, solvent, and diluent, which are usually described graphically in triangular coordinates (Treybal, 1980). 

The phase behaviour of a mixed biopolymer solution is quantitatively characterized by a phase diagram, which graphically describes the boundary conditions of phase separation, the partitioning of the components between the phases and the effects of different variables (temperature, pH, salt concentration, etc.) on the phase behaviour of biopolymers. Conventionally, phase diagrams of three-component (ternary) systems are presented in triangular coordinates. However, an excess of solvent water... 

Finally, it should be remembered that the quantities characterizing sequence distribution may be plotted on suitable diagrams, based either on triangular coordinate systems 15) or on cartesian orthogonal coordinates (76). It is also possible to express these quantities as a function of the mole ratio of the monomers in the feed see, for example, the graphical synopsis of pair and triplet sequences published by Kinsinger and Colton (77). 

Covering chemical phenomena of 1,2, 3, 4, and multiple component systems, this standard work on the subject (Nature, London), has been completely revised and brought up to date by A. N. Campbell and N. O. Smith. Brand new material has been added on such matters as binary, tertiary liquid equilibria, solid solutions in ternary systems, quinary systems of salts and water. Completely revised to triangular coordinates in ternary systems, clarified graphic representation, solid models, etc. gth revised edition. Author, subject indexes. 236 figures. 505 footnotes, mostly bibliographic, xii -f- 494pp. 536 x 8. 

The graphical approach to solution is developed in Figure 7.11 on right-triangular coordinates. A total material balance around the entire cascade is... 

To simplify the procedure of solving extraction problems, equilibrium curves may be transposed from triangular coordinates to rectangular coordinates [0.1, vol. 2, p. 546]. Figure 1-13 shows different graphical methods used to represent the distribution equilibrium. 

Graphical determination of stages required for such operations is usually inconvenient to cany out on triangular coordinates [72] because of crowding, and only the use of Ny X, Y coordinates will be described. For the stages in the raffinate stripping section (Fig. 10.27) the developments for simple countercurrent extraction, Eqs. (10.31) to (10.34) apply, and this section of the plant needs no further consideration. 

For the first time through a liqmd-liquid extrac tion problem, the right-triangular graphical method may be preferred because it is completely rigorous for a ternary system and reasonably easy to understand. However, the shortcut methods with the Bancroft coordinates and the Kremser equations become valuable time-savers for repetitive calculations and for data reduction from experimental runs. The calculation of pseudo inlet compositions and the use of the McCabe-Thiele type of stage calculations lend themselves readily to programmable calculator or computer routines with a simple correlation of equilibrium data. 

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