THERMODYNAMICS OF SEPARATION OPERATIONS Aseotropes The increased repulsion between molecules can result in the formation of an azeotrope, which is a liquid mixture whose equilibrium vapor has the same composition as the liquid ( i.e. xi = yi for an azeotrope). Minimum-Boiling Homogeneous Azeotropes: This type of azeotropes occurs due to repulsion between the molecules ChE 334: Separation Processes Dr Saad Al-Shahrani

THERMODYNAMICS OF SEPARATION OPERATIONS subcooled vapor Pxy diagram (T constant) > 1.0 (+) deviation from ideality Txy diagram P constant subcooled vapor ChE 334: Separation Processes Dr Saad Al-Shahrani

THERMODYNAMICS OF SEPARATION OPERATIONS xy diagram, ether P or T= constant X=y 45 o line ChE 334: Separation Processes Dr Saad Al-Shahrani

THERMODYNAMICS OF SEPARATION OPERATIONS b) Maximum-Boiling azeotropes This type of azeotropes occurs due to attraction between the molecules. Txy diagram Pxy diagram < 1 (-) deviation from ideality ChE 334: Separation Processes Dr Saad Al-Shahrani

THERMODYNAMICS OF SEPARATION OPERATIONS xy diagram x=y ChE 334: Separation Processes Dr Saad Al-Shahrani

THERMODYNAMICS OF SEPARATION OPERATIONS Example: Ethanol and n-hexane from a minimum boiling point azeotrope at 3.2 mole% ethanol at 58.68 oC and 760 mmHg pressure. The vapor pressure of ethanol and n-hexane are 6 psia and 12 psia respectively, at 58.68 oC, determine iL for ethanol and n-hexane at the azeotropic condition solution At azeotrope x=y For methanol ChE 334: Separation Processes Dr Saad Al-Shahrani

THERMODYNAMICS OF SEPARATION OPERATIONS For methanol Note: foe ethanol and n-hexane L> 1.0, indicating repulsion (positive deviation from ideality ChE 334: Separation Processes Dr Saad Al-Shahrani

THERMODYNAMICS OF SEPARATION OPERATIONS DePriester Charts For Light Hydrocarbons Figures (a,b) give K-value charts for some Iight hydrocarbons. These arts do not assume ideal vapor-phase behavior. Some corrections for pressure effects are included. Figure (a) is used for low temperatures and Figure (b) high temperatures. To find the appropriate K-values, a straight line is drown on the diagram connecting the temperature and pressure of the system. intersection of this line with the K-value curve for each hydrocarbons its K-value at this temperature and pressure. ChE 334: Separation Processes Dr Saad Al-Shahrani

THERMODYNAMICS OF SEPARATION OPERATIONS RELATIVE VOLATILITY The relative volatility is the ratio of K-values For two component j and k If the system is ideal (i,e. obeys Raoult’s law, i.e. no attraction or repulsion between molecules or =1.0) ChE 334: Separation Processes Dr Saad Al-Shahrani

THERMODYNAMICS OF SEPARATION OPERATIONS For component j For component k ChE 334: Separation Processes Dr Saad Al-Shahrani

THERMODYNAMICS OF SEPARATION OPERATIONS Relative volatility for binary system For two components system under equilibrium conditions (j,k): Solve for yj This equation is very important in distillation operation ChE 334: Separation Processes Dr Saad Al-Shahrani

THERMODYNAMICS OF SEPARATION OPERATIONS Relative volatilities (are essentially constant. In general, they are functions of temperature and composition. jk= f ( T and composition) In most systems, () decreases as temperature increases, which means that separation of components becomes more difficult. Therefore, It is often desirable to keep temperatures as low as possible (use low pressure) to reduce energy consumption. The following figure shows some VLE curves on an xy diagram for various values of . The bigger the relative volatility, the fatter the VLE curve and the easier the separation (low number of stages required). ChE 334: Separation Processes Dr Saad Al-Shahrani

THERMODYNAMICS OF SEPARATION OPERATIONS As  → 1.0, the VLE curve approaches the 45o line x = y. It is impossible to separate components by distillation if the value of  is too close to unity. Distillation is seldom used if  < 1.0 5. X ChE 334: Separation Processes Dr Saad Al-Shahrani

THERMODYNAMICS OF SEPARATION OPERATIONS Relative volatility For a multicomponents system. For a multi-component system, the relative volatilities are defined with respect to some component, typically the heaviest one. If we have multi-components system containing components (1,2,3, H), H is the heaviest one and (1) is the lightest one. ChE 334: Separation Processes Dr Saad Al-Shahrani

THERMODYNAMICS OF SEPARATION OPERATIONS By the same manner . . ChE 334: Separation Processes Dr Saad Al-Shahrani

THERMODYNAMICS OF SEPARATION OPERATIONS ChE 334: Separation Processes Dr Saad Al-Shahrani

THERMODYNAMICS OF SEPARATION OPERATIONS Substitute (6) in (4) ChE 334: Separation Processes Dr Saad Al-Shahrani

THERMODYNAMICS OF SEPARATION OPERATIONS Example: A multi-component liquid mixture has the compositions and relative volatilities given in the table below. Calculate the composition of the vapor phase. ChE 334: Separation Processes Dr Saad Al-Shahrani

THERMODYNAMICS OF SEPARATION OPERATIONS Vap. yi V, mol/h Liq. xi L, mol/h The lever rule F = L + V F zi zi F = xi L + yi V ChE 334: Separation Processes Dr Saad Al-Shahrani

THERMODYNAMICS OF SEPARATION OPERATIONS The ratio of the product flows (L,V) is the inverse of the ratio of the lengths of the lines connecting the feed mole fraction of each of the products. This is known as ”Lever Rule” T2sat y x T Temperature T1sat xi zi yi 1.0 Note: the two phases must be under equilibrium conditions ChE 334: Separation Processes Dr Saad Al-Shahrani