Separation Methods & Governing
Equations
2.1 Introduction
Separation processes are fundamental in chemical engineering, employed to isolate
desired components from mixtures based on differences in physical or chemical
properties. These processes may use phase changes, solubility differences, molecular
size, adsorption, or volatility to achieve separation. The correct selection and design
of separation methods are crucial for energy efficiency, product purity, and economic
viability in industrial operations [1].
In this project, two primary separation methods are used: liquid–liquid extraction
(LLE) and evacuated (vacuum) distillation. Liquid–liquid extraction is chosen for
its ability to remove benzene from n-hexane without large temperature requirements,
while vacuum distillation is used to recover benzene overhead by lowering boiling
points, reducing thermal stress and solvent losses.
This chapter begins by reviewing common separation methods, then describes in more
detail LLE and vacuum distillation, and finally presents the governing equations for
each method as applied in this work.
2.2 Overview of Separation Methods
There are several classes of separation techniques. Common methods include:
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Distillation: separating components based on volatility differences; vaporliquid equilibrium and relative volatility are key parameters.
Absorption and stripping: using gas-liquid contact; species are absorbed into
a liquid or stripped from one.
Adsorption: separation via differential affinity of components to a solid
surface.
Liquid-Liquid Extraction (LLE): partitioning of solute between two
immiscible or partially miscible liquid phases; useful when distillation is
impractical due to low volatility or thermal instability of components [2].
Membrane separation, chromatography, crystallization, etc.: applicable in
specialized contexts.
When heat-sensitive compounds, low volatility, or close boiling points are present,
LLE often outperforms distillation in energy and purity trade-offs. Conversely,
distillation is highly developed, scalable and widely used when feed mixtures are
vaporisable and volatility differences are sufficiently large.
2.3 Liquid-Liquid Extraction (LLE)
Liquid-liquid extraction exploits the difference in solubility of a solute between two
liquid phases, typically one organic and one polar solvent. The phases are brought
into contact under equilibrium conditions; after separation, the solute is enriched in
the solvent phase. Key considerations include solvent selection, phase equilibrium
(distribution coefficient), number of theoretical stages, and stage efficiency [3].
LLE is particularly advantageous when dealing with thermally sensitive components
or when components form azeotropes making simple distillation inefficient or
impossible. In the petroleum industry, LLE has been used historically to extract
aromatic hydrocarbons using solvents such as sulfolane and furfural [4].
2.4 Vacuum (Evacuated) Distillation
Distillation separates based on volatility; in vacuum distillation, the operating
pressure is reduced below atmospheric, lowering boiling points and enabling
separation at lower temperatures. This reduces thermal decomposition or solvent loss,
and permits separation of components with very high boiling points or nearazeotropic behavior under atmospheric pressure [5].
Vacuum distillation columns include feed stages, rectifying and stripping sections.
Under vacuum, heavy keys (non-volatile or less volatile components) may be
assumed negligible in vapor, simplifying vapor-liquid equilibrium models.