Page 252 - Process Equipment and Plant Design Principles and Practices by Subhabrata Ray Gargi Das

252 Chapter 9 Phase equilibria

ternary composition and when the point is outside the dome OPQ, it represents composition of a
homogeneous mixture phase. A mixture with a composition corresponding to the point M
within the partial miscibility region splits into two phases that are in equilibrium. Composition of
the two phases in equilibrium are E and R that lie on the equilibrium curves. The line RE is a
typical “tie line” that passes through the point M with the endpoints corresponding to the equi-
librium compositions in the two liquid phases. The phase composition represented by E has a
higher proportion of solvent S and is termed extract phase, and R represents the “raffinate phase”
composition.
Tie lines are rarely parallel and gradually change their slope in one direction. As evident from
Fig. 9.6A, the tie lines become shorter in length as one approaches the top part of the dome until it
reduces to a point at “P.” This point of inflection near the top of the two-phase envelope is termed the
plait point. It signifies the condition at which the compositions of the two liquid phases in equilibrium
become identical and transform into a single phase. Thus, the “plait point” composition is obviously
the limit of composition where no phase separation takes place. The plait point is ordinarily not at the
maximum value of B on the solubility curve.
Henceforth, the equilibrium solubility curve of the extract and raffinate phase will be referred to as
the “extract curve” and the “raffinate curve,” respectively. In this book, the composition in the raffinate
phase is denoted by x and that in the extract phase by y, with subscripts denoting the components. The
composition can be expressed in terms of mass, mole, or any other quantity basis of each substance.
The curves are different for different physical quantity selected, but the material balance, equilibrium
principles, and the results obtained are the same in all cases.
One may note that the composition M actually results from mixing the feed and the solvent streams,
and it splits into two phases with the compositions represented by E and R. On removing S from the
ternary mixture M, the binary solution regains its original composition, which lies on line AB.
It is often more useful to plot LLE data in rectangular coordinates with the concentration of solute
(B) plotted against the concentration of solvent (S), and the concentration of feed solvent (A) is the
remaining fraction, such that all weight fractions sum to unity. Similar to triangular plots, the two-
phase region and single-phase homogeneous liquid region are demarcated by the extract and raffi-
nate curves, as shown in Fig. 9.6B. Tie lines connecting the two equilibrium phase compositions are
also shown.
The distribution of the solute in the two phases can also be conveniently shown as a distribution
curve (Fig. 9.6C) of solute B In this case, the concentration of B in the extract phases is plotted on the
y-axis and that in the raffinate on the x-axis. The equilibrium curve lying above the diagonal (y ¼ x)
denotes that the distribution of B favors the S-rich phase (% of B in E is more than that in R). The slope
of the curve is quantitatively expressed as the distribution coefficient K Di , for component i.
K Di ¼ y i =x i (9.7)
Similar to vapor-liquid systems, K Di is found from the thermodynamic considerations by equating
the chemical potential of each component in the two phases.
Often distribution curves are plotted with concentration of solute in raffinate and extract phase
expressed on solvent-free basis denoted as X B ¼ x B =ð1 x S Þ and Y B ¼ y B =ð1 y S Þ respectively.