Separations analysis fundamentals - Principles of Chemical Separations with Environmental Applications - page 44

Here, V i L

= molar volume of pure liquid component i

λ ij = interaction energy between components i and j , λ ij = λ ji

T = absolute temperature, in Kelvin, K

=

R gas law constant.

UNIQUAC equation

C
i

R

ln γ i = ln γ + ln γ , (3.9)

i

where

ln ϕ i

z

2 q i ln ϑ i

C

ln γ =

x i +

x i l j (3.10)

i

ϕ i

j

and

ln

j = 1 ϑ j τ ji

m m

,

ϑ j τ ij
m

R

ln γ = q i 1 − − (3.11)

i

k = l ϑ k τ kj

j = 1

with

z
2 ( r i −

l i = q i ) − ( r i − l ) , z = 10 (3.12)

exp

u ji − u ii

τ ji = − , τ ii = τ jj = 1 . (3.13)

RT

Here, q i = area parameter of component i

r i = volume parameter of component i

u ij = parameter of interaction between components i and j , u ij = u ji

z = coordination number

γ i C = combinatorial part of activity coefficient of component i

γ i R

= residual part of activity coefficient of component i

q i x i / j q j x j = ϑ i = area fraction of component i

r i x i / j r j x j = ϕ i = volume fraction of component i .

3.4.3 Triangular diagrams

Extraction, to be covered in Chapter 5, is a three-component process in which a solute is
transferred from a diluent into a solvent. Binary phase diagrams at constant temperature and
pressure used in analyzing distillation are insufficient to characterize a three-component
system. Triangular diagrams (at constant T and P ) represent the equilibrium phase behavior
of a three-component partially miscible system. The equilateral triangular diagram is
easy to read, but somewhat difficult to draw. The right triangle diagram is much easier
to produce, but equilateral diagrams are often found in literature so it is important to
understand how to read them.