CHAPTER THREE
CHAPTER 3 VAPOUR-LIQUID EQUILIBRIUM
I
Separation of Waste acid StreamI
~
....
Ke)' components
I I
Nonkey componentsAre there any VLE data No Measure VLE data
lI"ailahlc for key Predict binary VLE
COIllP<)IlClltS ill litcrature?
Yes ..
Reduce experimental data and select hest-fit model
Calculate interaction
nar:lI11eters for selected model
I
Proceed with slIllulationI
Figure 3-1: Outline for starting distillation simulations
29
CHAPTER 3 VAPOUR-LIQUID EQUILIBRIUM
3 .1 Relative volatility
Distillation is a technique of separating components according to their relative volatility (a).
Therefore. the relative volatility is a measure of the ease of separation. For a binary mixture (component I & 2) relative volatility can be defined as;
.\'1 (1-XI)
= -'-'-':_'-'- x,(l-y.)
In the ubove equation above XI and YI are the equilibrium mole fractions of component liquid and vapour phase respectively. Component I is the more volatile component.
(3·1) in the
VLE data is generally presented as vapour-liquid (x-y) diagrams and temperature-composition (T- x-y) diagrams. These are shown in Figures 3-2 and 3-3 respectively. In Figure 3-2a the x and yaxes show the concentration of the more volatile component in the liquid and vapour phase respectively.
The 45() diagonal represents points at which vapour and liquid compositions are the same. The curve in Figure 3-2a is the equilibrium curve and shows how the more volatile component concentrates in the vapour. Tracing the dashed lines in Figure 3-2a shows how a liquid mixture containing 0.4 mole fraction of the more volatile component in the liquid is in equilibrium with vapour containing 0.6 mole fraction of the same component. Therefore if this vapour is collected and condensed one will end up with a mixture in which the more volatile component mole fraction has been enriched from 0.4 to 0.6.
Figure 3-2b illustrates the effect of relative volatility on the tendency of the more volatile componcnt to concentrate in the vapour. The higher the relative volatility the greater the separation.
For example. when the relative volatility is 5. a liquid mixture containing 0.2 mole fraction of the more volatile component is in equilibrium with vapour containing 0.56 mole fraction of the more volatile component. For this mixture it will take only a few steps to obtain a pure liquid of the more volatile component. Conversely. when the reh.ltive volatility is lower (e.g. a = 2). a liquid mixture containing 0.2 mole fraction of the more volatile component is in equilibrium with vapor containing
CHAPTER 3 VAPOUR·LlQUID EQUILIBRIUM
Figures 3-2<1 ;md 3-2b are x-y diagrams of "normal" mixlUres. For certain systems there exists Cl
composition (the point of intersection of the equilibrium curve and the 450 line) for which the vapour and liquid compositions are identical. Such systems 3re known as azeotropic. The x-y diagram for such a system is shown in Figure 3-4. At point A. once this vapour and liquid composition is reached the componems can no longer be separated by simple distillation and other allernalives (c.g. eXlmclive distillation and liquid-liquid extraction) need to be considered.
0.8 Equilibrium
0.6
0.4
0.2
0 "
o
0.2 0.4~-L/
\
0.6
a=2
0.8 0.2 0.4 0.6 0.8
Figure 3-2: x-y diagrams. (a) Concentration of morc volatile component in liquid (x) vs.
,·apour concentration (yl. (b) Effect of relative volatility on the concentration of the more vol • ..tilc component in the vapour.
31
CHAPTER 3 VAPOUR-LIQUID EQUILIBRIUM
mole fraction x, or y, Figure 3-3: T-x-)' diagram
,,~~---~
x,
Figure 3-4: x-)' curve for an azcotropie system
CHAPTER 3 VAPOUR-LIQUID EQUILIBRIUM
3 . 2 Theoretica l Aspects of VLE
As discussed earlier. measuremenl of VLE IS expensive and time consuming. It is therefore imponant that the data be correctly theoretically interpreted as this allows for interpolation.
extrapolation and prediction of data to new conditions which subsequently provides 11 designer to explore a wide range of design alternatives in process simulation.
The developmcllI of the criterion for thermodynamic equilibrium between two phases is covered in Appendix 8-1. For the case of VLE. a vapour phase (V) and liquid phase (L) are in equilibrium at the same temperature and pressure when their respective fugacities (fi) are equal:
• •
r." = rL
J, .I,
In the above equation .. 11" denotes the mixture property.
(3·2)
To use Equation 3-2. it is useful to define the mixture fugacities in terms of measurable quantities such as temperature. pressure and phase compositions. This is achieved by introducing dimensionless auxiliary functions. These are known us the fugucity coefficient and activity coefficient for the vapour and liquid phases respectively. The fugacity coefficient is related to the
vapour phase as follows:
•
•
~"
•tfJ,
=,.'p
. , (3·3)
In the above equation
q>,
is the fugacity coefficient of the vapour phase. y, the vapour mole fraction :.IIld P is the system pressure.Similarly. the activity coefficient (y,) is related to the liquid phase fugacity as follows:
-
~'. •y,--~
x , ,
In Equation 3-4. x, is the liquid mole fraction andI, is the pure component fugacity.
33
(34)