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Isobaric or isothermal Vapor-liquid equilibrium data of any tertiary or quaternary systems may be evaluated when they are calculated as activity coefficients. Residual curve mapping is a triangular diagram which is used to describe the relationship between ternary systems. The VLE of this ternary system has evaluated experimentally by using Othmer still at 101.3 kPa. This ternary system does not form any azeotrope.

Keywords: VLE; Residue Curve Map, Ternary system, Hexane, Cyclohexane, Methyl t-butyl ether.


Distillation is a unit operation which is very common in chemical engineering. It involves separation of two or more liquid components based on their boiling points, when a mixture of compounds is boiling; it will give vapour and liquid components and both should have different compositions. The graph of the molar fractions of the more volatile components in vapour and liquid phases of the mixture in relation to the temperature of the boiling mixture is the vapour-liquid equilibrium curve for the mixture. [1, 2]

Constant pressure VLE data is obtained from boiling point diagrams. The VLE data of binary mixtures is often expressed as a plot as shown in above fig. This plot represents the bubble point and dew point of the binary mixture at constant pressure. The particular VLE plot shows a binary mixture that has a uniform vapor liquid equilibrium that is relatively easy to separate the curve line is as equilibrium curve line and gives the compositions of liquid and vapor in equilibrium at some fixed pressure. Azeotrope is also important concept in VLE. If the equilibrium curve crosses the diagonal line then it should be considered that there are azeotropic points where the azeotrope occurs. When thermodynamics is applied to vapor liquid equilibrium, the goal is to find calculation of the Temperatures, pressures, and compositions of phases which are in equilibrium.[3]

VLE can be calculated as two different ways:

At constant temperature:

First consider a system with the two constituents A and B according to Routs law,

PA = XA P0A (1)

PB = XBP0B (2)

The total pressure, according to Dalton’s law, is given by the sum of the partial pressures:

P = XA P0A + XBP0B (3)

As the system is binary, it is possible to substitute (1-XA) for XB; after this modification:

P = XA (P0A- P0B)+ P0B (4)

According to Dalton’s law we have for the vapour phase:

pA = yAp (5)

pB = yBp = (1 – yA) p (6)

    ( Y_A)/y_B / x_A/( x_B ) = (y_A  (1-x_A ))/(x_A (1-y_A ) ) = (P°_A)/(P°_B ) = α (7)

For an ideal solution α is a constant independent upon the composition, called as relative volatility or enrichment ratio. The isothermal dependence of the total pressure on the composition of the vapour phase is,

p = (P°_A)/('∝' - y_A ('∝' -1)^' ) (8)

The relation giving the dependence between the mole fraction of constituent A in the liquid phase and its mole fraction in the vapour phase is obtained by a simple rearrangement

yA = ('∝'X_A)/(1+X_A ('∝' -1)^' )  (9)

 (b) At constant pressure

Knowledge of the isobaric vapour-liquid equilibrium data is more important in distillation. The total pressure is,

                          P=P_A+P_B+X_A P°(T)+(1-X_A )P°(T)                                           (10)

We can write Poi (T) to emphasize that the vapour pressures of the pure constituent i depends on the Temperature, which in this case is not constant. The relation giving the dependence between the compositions of the vapour and liquid phases is given by the equation

yA = (x_A'∝'(T))/(1+x_A ['∝'(T)- 1] ) (11)

A is a function of temperature; however the ratio of the vapour pressures of the pure constituents varies but little in a short range of temperatures, so that α can often be considered as constant over the entire range of compositions calculation of phase equilibrium from excess enthalpy.

None of the data can be accomplished without models for the behavior of systems in vapor liquid equilibrium.[4]

Residue curve mapping is used to investigate and visualize vapour liquid equilibrium issues affecting the modeling of distillation and liquid liquid extraction column. Most commonly RCMs are generated using commercial process simulation software, such as Aspen Plus, Aspen HYSIS or DISTIL. A residue curve map represents the composition of the residue of a simple batch distillation involving three components over time. It also indicates the liquid residue composition with time as the result of a simple, one stage batch distillation. When all the results plotted on a triangular graph which is called as “residue curve” because the particular plot follows the liquid residue composition in the still. Different residue lines result from different starting compositions. A collection of these curves for a given ternary system is called a “residue curve map”[5]

Fig 2 Basic principal of residue curve mappings

The residue curve mappings are having two main basic characteristics which are as follows:

The presence of azeotrope can create distillation boundaries which cannot be crossed by a residue curve. These distillation boundaries represent the residue curve on which the light or starting residue composition is a lower boiling pure component or azeotrope and the heavy or ending composition residue is a higher pure component or azeotrope.

On the graph any azeotrope or pure component point will be connected to some but not all other pure component points and azeotrope. Those boundaries are thermodynamic in natures which are connected form distillation boundaries.

These boundaries of the distillation make the partition of the map into distillation regions. The nature of these regions is two pure components which lie in different regions cannot be separated using conventional distillation.[6,7]

Apparatus and Procedure.

For VLE experimentation modified Othmer still apparatus was used because it gives best separation. In this circulation apparatus, the total volume of the still was about 250 ml, of which about 150 ml was filled with the liquid solution. Heat was applied to the still through a heating coil which was on the lower extended portion of the boiling flask. As the system is tertiary the feed mixture of three system components

was fed to the boiling section, heated continuously until thermal equilibrium was attained. Equilibrium usually reach in (5 to 6) hours .The system was maintained in the equilibrium state for about 1 hour, and samples of the vapor and liquid phase were collected and analyzed. The equilibrium samples of vapour and liquid composition was determined by using a gas chromatograph equipped with a flame ionization detector. Under these conditions was good separation achieved.

The Tie lines and Residue Map Curves based on the experimental data for the ternary system are shown in Fig.3 and 4

Fig 3. Tie lines for the ternary system MTBE + hexane + Cyclohexane at 101.3 kPa

Fig. 4 Residue Curve Map for MTBE + hexane + Cyclohexane at 101.3 kPa


Activity coefficient is always equal to one (1) in case of Ideal system. The vapour liquid equilibrium data can be quantitatively recorded in the distillation design and the possible way of predicting such data are natural pre-requisites for any course on distillation design. So that particularly heights of the distillation columns are determined by vapor liquid equilibrium (VLE) data for the mixture so that it is very important to study the basic concept of vapour liquid and RCM. It has been found that the feed points near Hexane node shows distillate and residue diverting towards MTBE and Cyclohexane region shift of distillate and residue is been observed

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