A residue curve describes the change in the composition of the liquid phase of a chemical mixture during continuous evaporation at the condition of vapor–liquid equilibrium (open distillation). Multiple residue curves for a single system are called residue curves map.
Residue curves allow testing the feasibility of a separation of mixtures and therefore are a valuable tool in designing distillation processes. Residue curve maps are typically used for examining ternary mixtures which can't be easily separated by distillation because of azeotropic points or too small relative volatilities.
Pure components and azeotropic points are called nodes. Three different types are possible:
The distillation regions and the nodes are the topology of the mixture.
The calculation of residue curves is done by solving the mass balance over time by numerical integration with methods like Runge-Kutta.
with
x: vector of liquid compositions in mole fractions [mol/mol]
y: vector of vapor compositions in mole fractions [mol/mol]
ξ: dimensionless time
The integration of this equation can be done forward and backward in time allowing the calculation from any feed composition to the beginning and end of the residue curve.
The ternary mixture of chloroform, methanol and acetone has three binary azeotropes and one ternary azeotrope. Together with the three pure components the system has seven nodes which altogether form four distallation regions. Two nodes are stable (pure methanol and the binary azeotrope of chloroform and acetone which have both the lowest vapor pressure (isothermal calculation) in their two regions where they are part of. The other two binary azeotropes are unstable nodes. They have the highest vapor pressure in their regions.
The other nodes are saddles (the ternary azeotrope, the pure acetone and the pure chloroform).
The border lines in this system connect the ternary azeotrope (saddle) with the two stable nodes and the two unstable nodes.
The residue curves are always moving away from an unstable node to a saddle but never reaches that because they then turn to a stable node.
A residue curve describes the change in the composition of the liquid phase of a chemical mixture during continuous evaporation at the condition of vapor–liquid equilibrium (open distillation). Multiple residue curves for a single system are called residue curves map.
Residue curves allow testing the feasibility of a separation of mixtures and therefore are a valuable tool in designing distillation processes. Residue curve maps are typically used for examining ternary mixtures which can't be easily separated by distillation because of azeotropic points or too small relative volatilities.
Pure components and azeotropic points are called nodes. Three different types are possible:
The distillation regions and the nodes are the topology of the mixture.
The calculation of residue curves is done by solving the mass balance over time by numerical integration with methods like Runge-Kutta.
with
x: vector of liquid compositions in mole fractions [mol/mol]
y: vector of vapor compositions in mole fractions [mol/mol]
ξ: dimensionless time
The integration of this equation can be done forward and backward in time allowing the calculation from any feed composition to the beginning and end of the residue curve.
The ternary mixture of chloroform, methanol and acetone has three binary azeotropes and one ternary azeotrope. Together with the three pure components the system has seven nodes which altogether form four distallation regions. Two nodes are stable (pure methanol and the binary azeotrope of chloroform and acetone which have both the lowest vapor pressure (isothermal calculation) in their two regions where they are part of. The other two binary azeotropes are unstable nodes. They have the highest vapor pressure in their regions.
The other nodes are saddles (the ternary azeotrope, the pure acetone and the pure chloroform).
The border lines in this system connect the ternary azeotrope (saddle) with the two stable nodes and the two unstable nodes.
The residue curves are always moving away from an unstable node to a saddle but never reaches that because they then turn to a stable node.