Separation Processes and Distillation Engineering Exercises

These exercises practise first-pass calculations used in separation processes and distillation engineering. They connect component balances, recovery, reflux, reboiler duty, absorption removal, extraction losses, membrane concentration, filtration flux, dryer solvent removal, and operating-window risk controls.

Assume simplified nominal values unless an exercise states otherwise. Real separation design requires thermodynamic data, mass-transfer correlations, equipment hydraulics, fouling behaviour, solvent compatibility, heat-transfer limits, process control, safety review, environmental disposition, and validation with representative feed variability.

How to Use These Exercises

For each problem:

1. define the feed, product, reject, recycle, purge, or waste streams;
2. state whether composition is mass fraction, mole fraction, concentration, or ppm;
3. keep total balance and component balance separate;
4. identify which measurement validates purity, recovery, solvent loss, or waste loading;
5. check whether the separation creates a downstream utility, safety, or environmental burden.

The most common mistake is optimizing purity alone. A useful separation must satisfy purity, recovery, capacity, energy, safety, operability, and waste handling at the same time.

For each result, state whether it supports a separation specification, utility estimate, recovery target, waste-loading decision, recycle limit, fouling response, or off-spec hold point. Separation calculations are useful only when they connect product quality to capacity, energy, and downstream consequences.

Exercise 1: Binary Distillation Product Flow Rates

A binary feed enters a distillation column at F=100\ \text{kmol/h} with mole fraction of light component z_F=0.40. Distillate composition is x_D=0.95 light component and bottoms composition is x_B=0.05 light component.

Estimate distillate and bottoms flow rates.

Solution

Total balance:

Component balance on light component:

Substitute B=F-D:

Solve for distillate:

Bottoms:

Engineering Comment

The balance shows that the requested purities and product rates are physically consistent. It does not prove the column has enough stages, reflux, heat duty, pressure margin, or hydraulic capacity.

Exercise 2: Light-Component Recovery

Use the distillation result from Exercise 1. Estimate recovery of the light component to the distillate.

Solution

Light component in feed:

Light component in distillate:

Recovery:

Engineering Comment

Recovery and purity must be reported together. A very pure distillate may still be poor design if too much valuable light component is lost to bottoms or recycle.

Exercise 3: Reflux and Condenser Internal Flow

The column in Exercise 1 operates with reflux ratio R=L/D=2.0. Assume a total condenser and constant molar overflow for a first-pass estimate.

Estimate reflux flow and overhead vapor condensed.

Solution

Reflux flow:

For a total condenser:

Engineering Comment

Higher reflux can improve separation but increases condenser and reboiler duty, column vapor traffic, flooding risk, cooling utility demand, and operating cost.

Exercise 4: Reboiler Duty from Vaporization Load

Using the overhead vapor estimate V=116.7\ \text{kmol/h}, assume latent heat is 31\ \text{kJ/mol}.

Estimate approximate vaporization duty.

Solution

Convert vapor flow:

Heat duty:

Convert to kW:

Engineering Comment

This simple duty links separation specification to utilities. A column design is incomplete without condenser duty, reboiler duty, pressure drop, turndown, fouling, relief scenarios, and energy-integration review.

Exercise 5: Absorber Contaminant Removal

A gas absorber treats 5000\ \text{Nm}^3/\text{h} of gas. Contaminant concentration decreases from 1200\ \text{ppm} to 80\ \text{ppm} by volume.

Estimate removal efficiency and contaminant volume removed on a normal-volume basis.

Solution

Removal efficiency:

Contaminant removed:

Engineering Comment

Removal efficiency is not enough. The solvent or scrubbing liquid must handle the absorbed load, regeneration or disposal, heat effects, pressure drop, corrosion, mist carryover, and emissions during upset conditions.

Exercise 6: Liquid-Liquid Extraction Solute Balance

An extraction step receives 80\ \text{kg/h} of solute in the feed. Raffinate contains 22\ \text{kg/h} of solute and extract contains 56\ \text{kg/h} of solute.

Estimate solute recovery to extract and unaccounted solute.

Solution

Recovery to extract:

Unaccounted solute:

Unaccounted fraction:

Engineering Comment

The unaccounted solute may be sampling error, holdup, entrainment, solvent loss, degradation, or an unmeasured phase. Solvent and solute balances should be reconciled before changing solvent ratio or declaring recovery improvement.

Exercise 7: Membrane Concentration Balance

A membrane unit treats 25\ \text{m}^3/\text{h} of feed containing solute at 2.0\ \text{g/L}. Permeate flow is 18\ \text{m}^3/\text{h} with solute concentration 0.15\ \text{g/L}. Assume no solute loss other than permeate and retentate.

Estimate retentate solute concentration.

Solution

Feed solute:

Permeate solute:

Retentate flow:

Retentate solute:

Retentate concentration:

Engineering Comment

The retentate is concentrated by more than three times. Membrane design should check osmotic pressure, fouling, scaling, cleaning, recovery limit, reject handling, and whether permeate quality remains stable as concentration increases.

Exercise 8: Filtration Flux Decline

A filter produces 6.0\ \text{m}^3 of filtrate in 45 minutes through 12\ \text{m}^2 of filter area. Clean reference flux is 1.0\ \text{m}^3/(\text{m}^2\text{h}).

Estimate operating flux and percent decline from clean reference.

Solution

Convert time:

Flux:

Flux decline:

Engineering Comment

The flux decline may indicate cake resistance, blinding, viscosity change, particle-size shift, poor precoat, or insufficient cleaning. The response should be based on pressure drop, solids properties, and product-quality evidence.

Exercise 9: Dryer Solvent Removal

A wet cake feed to a dryer is 1200\ \text{kg} and contains 18\% solvent by mass. The target dried product contains 2\% solvent by mass. Assume dry solids are conserved.

Estimate solvent removed.

Solution

Initial solvent:

Dry solids:

Final product mass:

Final solvent:

Solvent removed:

Engineering Comment

Drying calculations must also check vapor handling, lower explosive limit margin, product temperature, residual solvent specification, dust control, heat-transfer limits, and solvent recovery or abatement.

Exercise 10: Off-Spec Recycle Risk Ranking

A separation system can recycle off-spec intermediate material and accumulate impurity in the feed tank. Initial rankings are severity S=8, occurrence O=4, and detection D=5.

After online analyzer validation, off-spec quarantine, and solvent-balance review are introduced, occurrence is estimated at O=2 and detection at D=2. Compare traditional risk priority numbers.

Solution

Initial risk priority number:

Revised risk priority number:

Reduction:

Engineering Comment

The revised ranking is lower, but the operating window still needs evidence: analyzer calibration, tank composition, recycle volume, purge route, product disposition, waste handling, alarm response, and authority to stop recycle when impurity accumulates.

Separation Review Checklist

Before using these calculations in design, troubleshooting, or operating-window review, check:

• Are compositions reported on a clear mass, mole, volume, concentration, or ppm basis?
• Are purity, recovery, throughput, energy, waste, and recycle limits evaluated together?
• Are vapor-liquid, liquid-liquid, membrane, filtration, and drying assumptions validated with representative feed variability?
• Are utility duties linked to condenser, reboiler, dryer, regeneration, or heat-recovery constraints?
• Are solvent, entrainment, unaccounted mass, and purge terms reconciled before changing operating targets?
• Are fouling, scaling, blinding, viscosity, pressure drop, and cleaning limits considered for sustained operation?
• Are product-release decisions backed by analyzer validation, sampling alignment, laboratory checks, and off-spec quarantine?
• Are recycle and waste-handling decisions tied to impurity accumulation, environmental disposition, alarms, and operator authority?

Strong separation engineering does not optimize one number in isolation. It shows which trade-off controls the plant: purity, recovery, capacity, energy, safety, or waste handling.