7.5 Distillation

Distillation is a thermal separation process that splits liquid mixtures based on differences in how easily each component vaporizes. It's one of the most widely used unit operations in chemical engineering, showing up everywhere from petroleum refining to pharmaceutical purification.

This topic covers the core principles, vapor-liquid equilibrium, column design methods, and energy considerations you'll need to understand how distillation columns work and how engineers design them.

Fundamentals of Distillation

Principles and Components of Distillation

Distillation works by exploiting differences in volatility between components in a liquid mixture. The more volatile components (lower boiling points) preferentially move into the vapor phase, while less volatile components stay in the liquid. By repeating this vaporization-condensation cycle many times inside a column, you achieve progressively better separation.

A distillation column has several key components:

• Reboiler: Sits at the bottom of the column and supplies heat to vaporize liquid. This drives the upward vapor flow that makes separation possible.
• Condenser: Sits at the top and cools the rising vapor back into liquid. Some of this liquid is collected as the distillate (your light product), and some is returned to the column as reflux.
• Column internals: Either a series of trays (plates) or packing material that creates surface area for vapor-liquid contact. Each contact point allows mass transfer between the rising vapor and the falling liquid.

The feed stream enters the column at a specific tray location. Above the feed point is the rectifying section (enriches the vapor in the more volatile component), and below it is the stripping section (strips the more volatile component out of the liquid). The liquid collected at the bottom is the bottoms product, enriched in the less volatile component.

Factors Influencing Distillation Separation

Relative volatility ($\alpha$) is the single most important parameter for judging how easy a distillation separation will be. It measures the ratio of the tendency of two components to vaporize relative to each other. Higher $\alpha$ values mean the components have very different volatilities, making separation straightforward. When $\alpha$ is close to 1, separation becomes difficult and requires many more stages.

For example, benzene (boiling point: 80.1°C) and toluene (boiling point: 110.6°C) have a relative volatility around 2.3, making them fairly easy to separate. Ethanol and water, on the other hand, have a much lower relative volatility, especially as the ethanol concentration increases, making that separation much harder.

Boiling point difference between components is a related factor. Separating methanol (64.7°C) from water (100°C) is easier than separating ethanol (78.4°C) from water because the boiling point gap is larger for the methanol-water system. Larger gaps generally correspond to higher relative volatilities and easier separations.

Vapor-Liquid Equilibrium in Distillation

Vapor-Liquid Equilibrium (VLE) and Phase Diagrams

Vapor-liquid equilibrium (VLE) describes the relationship between the composition of a liquid mixture and the composition of the vapor in contact with it at a given temperature and pressure. VLE data is the foundation of all distillation design because it tells you what vapor composition you'll get from a given liquid composition on each stage.

VLE behavior is typically represented on phase diagrams:

• T-xy diagrams (temperature vs. composition at constant pressure): These show the bubble point curve (temperature where the first bubble of vapor forms) and the dew point curve (temperature where the first drop of liquid condenses). The region between these curves is the two-phase region.
• x-y diagrams (vapor composition vs. liquid composition): These are especially useful for the McCabe-Thiele method. A 45° diagonal line represents $y = x$, and the equilibrium curve shows how the actual vapor composition relates to the liquid composition.

The relative volatility can be calculated from VLE data:

$\alpha = \frac{y_1 / x_1}{y_2 / x_2}$

where $y$ is the vapor-phase mole fraction and $x$ is the liquid-phase mole fraction for each component.

Ideal and Non-Ideal VLE Behavior

Ideal mixtures follow Raoult's law, which states that the partial vapor pressure of each component equals its pure-component vapor pressure multiplied by its mole fraction in the liquid:

$p_i = x_i \cdot P_i^{sat}$

Benzene-toluene is a classic example of a nearly ideal system because the molecules are chemically similar and interact with each other much like they interact with themselves.

Most real mixtures deviate from Raoult's law due to intermolecular interactions. Ethanol-water is a textbook non-ideal system because hydrogen bonding between ethanol and water molecules changes the effective vapor pressures. These deviations are accounted for using activity coefficients ($\gamma$), which modify Raoult's law:

$p_i = x_i \cdot \gamma_i \cdot P_i^{sat}$

When $\gamma > 1$, the component has a higher effective vapor pressure than Raoult's law predicts (positive deviation). When $\gamma < 1$, it has a lower effective vapor pressure (negative deviation). Models like the Margules, Van Laar, and Wilson equations estimate activity coefficients from mixture composition and component properties.

Azeotropes are a special consequence of non-ideal behavior. At an azeotrope, the vapor and liquid have the same composition, so no further separation is possible by conventional distillation. The ethanol-water azeotrope occurs at 95.6 wt% ethanol (78.2°C), which is why you can't distill ethanol beyond about 95.6% purity without special techniques like pressure-swing distillation or adding an entrainer.

Distillation Column Design and Optimization

Design of Binary Distillation Columns

Designing a distillation column means determining four main things: the number of theoretical stages, the feed stage location, the reflux ratio, and the column diameter.

The McCabe-Thiele method is a graphical approach for binary systems that you'll likely use extensively in this course. Here's how it works:

1. Plot the x-y equilibrium curve for your system at the column's operating pressure.
2. Draw the rectifying section operating line from the distillate composition ($x_D$) on the 45° line, with a slope determined by the reflux ratio: $y = \frac{R}{R+1}x + \frac{x_D}{R+1}$, where $R$ is the reflux ratio.
3. Draw the stripping section operating line from the bottoms composition ($x_B$) on the 45° line to the intersection of the rectifying operating line and the q-line (which depends on the feed condition).
4. Step off stages between the equilibrium curve and the operating lines, starting from $x_D$ and working down. Each step represents one theoretical stage.
5. The stage where you switch from the rectifying operating line to the stripping operating line is the optimal feed stage.

This method assumes constant molar overflow (the molar flow rates of liquid and vapor are roughly constant in each section), which is reasonable for many systems but breaks down when components have very different heats of vaporization.

The Fenske equation estimates the minimum number of stages ($N_{min}$) at total reflux:

$N_{min} = \frac{\ln\left[\left(\frac{x_{D,LK}}{x_{D,HK}}\right)\left(\frac{x_{B,HK}}{x_{B,LK}}\right)\right]}{\ln(\alpha_{avg})}$

This gives you the absolute fewest stages needed if you had infinite reflux (no product withdrawal), serving as a lower bound for your design.

The Underwood equation determines the minimum reflux ratio ($R_{min}$), which is the smallest reflux ratio that could achieve the desired separation with an infinite number of stages. The actual reflux ratio is typically set at 1.2 to 1.5 times $R_{min}$ as a practical compromise between capital cost (more stages) and operating cost (more energy).

Multicomponent Distillation and Optimization

Real industrial distillation rarely involves just two components. For multicomponent systems, engineers identify key components:

• Light key (LK): The lightest component you want to keep mostly out of the bottoms product.
• Heavy key (HK): The heaviest component you want to keep mostly out of the distillate.

The column is designed around separating these two key components. All components lighter than the LK go almost entirely to the distillate, and all components heavier than the HK go almost entirely to the bottoms.

The Fenske-Underwood-Gilliland (FUG) method is a shortcut approach for initial multicomponent column design:

1. Use the Fenske equation to find $N_{min}$ (minimum stages at total reflux).
2. Use the Underwood equations to find $R_{min}$ (minimum reflux ratio).
3. Use the Gilliland correlation to relate the actual number of stages $N$ to the actual reflux ratio $R$, given $N_{min}$ and $R_{min}$.

This gives you a solid starting point, but detailed design requires rigorous simulation using process simulators like Aspen Plus or HYSYS. These tools handle non-ideal VLE, detailed mass and energy balances, tray hydraulics, and equipment sizing. They also let you optimize operating conditions (reflux ratio, feed location, pressure) to balance energy costs against capital costs.

Energy Efficiency of Distillation Processes

Energy Consumption and Influencing Factors

Distillation is energy-intensive. The reboiler consumes the bulk of the energy by generating the vapor flow needed for separation. In many chemical plants, distillation accounts for 40-60% of total energy use.

Several factors determine how much energy a column requires:

• Relative volatility: Higher $\alpha$ means fewer stages and less vapor flow needed, which directly reduces reboiler duty.
• Product purity requirements: Going from 95% to 99% purity might require significantly more stages and energy than going from 80% to 95%.
• Reflux ratio: Increasing the reflux ratio improves separation per stage but requires more vapor to be generated and condensed, raising energy consumption. There's always a trade-off between the number of stages (capital cost) and the reflux ratio (operating cost).
• Feed condition: A feed entering as a saturated liquid (at its bubble point) is the baseline case. Preheating the feed or introducing it as partially vaporized reduces the reboiler load. A subcooled feed increases it.

Common metrics for evaluating energy efficiency include:

• Heat duty per unit of product: Lower values mean better efficiency.
• Vapor-to-feed ratio: Lower ratios indicate more efficient use of vapor flow.
• Thermodynamic efficiency: The ratio of the minimum theoretical separation energy to the actual energy consumed. For most distillation columns, this is surprisingly low (5-20%), which is why energy optimization matters so much.

Energy Integration and Advanced Distillation Configurations

Pinch analysis is a systematic method for identifying where heat can be recovered and reused within a process. Applied to distillation, it helps you find the best places to exchange heat between hot streams (like the condenser output) and cold streams (like the feed), minimizing the need for external heating and cooling utilities.

Practical heat integration strategies include:

• Feed-effluent heat exchange: Use the hot bottoms or distillate streams to preheat the incoming feed. This is often the simplest and most cost-effective energy saving.
• Intermediate condensers and reboilers: Adding heat exchange points partway up or down the column reduces the load on the main condenser and reboiler, improving thermodynamic efficiency.

Advanced column configurations push energy savings further:

• Divided wall columns (DWCs): A single column shell with an internal partition that effectively performs the work of two conventional columns. DWCs can separate a three-component mixture in one column, reducing both capital investment and energy use by up to 30%.
• Heat-integrated distillation columns (HIDiCs): These couple the condenser of one column section with the reboiler of another, transferring heat internally. The high-pressure section rejects heat to the low-pressure section, significantly reducing external energy input.