Exercise set

Distillation Column VLE, Reflux, Tray, and Flooding Exercises

Worked distillation exercises for product balances, recovery, reflux, VLE, minimum stages, tray efficiency, flooding and packed height.

Branch: Chemical Engineering
Content: Exercise set
Updated: Jul 03, 2026
Revision: v1.1.0 · reviewed

These exercises focus on distillation-column calculations: product balances, light-component recovery, reflux and condenser flow, reboiler duty, relative volatility, minimum stages, feed quality, tray efficiency, vapor traffic, flooding margin, packed height and release gates.

Absorption, extraction, membrane concentration, filtration, crystallization, drying and recycle/purge governance are handled in the companion specialist exercise set.

How to use these exercises

Use the set as a distillation rate-release review. Exercises 1 to 5 establish material balance, recovery, reflux flow, condenser duty and reboiler duty. Exercises 6 to 10 check VLE assumptions, minimum stages, reflux margin, feed quality and tray count. Exercises 11 to 15 add flooding, pressure drop, tray efficiency, packed height and packing pressure drop. Exercises 16 to 18 connect utility margin, specific energy and the final release gate.

Before calculating, state the feed basis, pressure, thermodynamic model, composition specification, reflux mode, feed thermal condition, tray or packing condition and hydraulic limit. A column can meet product purity and still fail release because flooding, pressure drop, utility duty or analyzer timing is outside the accepted operating envelope. The engineering comment below each exercise identifies which release boundary the number informs.

Release Evidence Notes

Distillation evidence should state feed composition basis, pressure, thermodynamic model, sampling method, condenser and reboiler utilities, tray or packing condition, hydraulic margin, pressure drop, reflux mode, feed quality and product acceptance rule. A purity calculation is weak evidence if flooding margin or utility duty is unavailable.

The evidence package should separate separation evidence, utility evidence and hydraulic evidence. Separation evidence covers VLE, relative volatility, stages, reflux and product sampling. Utility evidence covers condenser duty, reboiler duty, cooling-water or steam availability and control-valve authority. Hydraulic evidence covers vapor traffic, flooding, entrainment, weeping, pressure drop, foaming and tray or packing condition.

Release evidence should also identify whether the calculation supports design, troubleshooting, debottlenecking or rate increase. A shortcut stage estimate may guide design, but a rate release needs reconciled plant data and current column condition.

Engineering Boundary Notes

These examples are first-pass calculations. Real column work should also check VLE data, nonideal mixtures, side draws, pressure profile, entrainment, weeping, foaming, heat integration, analyzer timing, relief basis, materials compatibility and operating procedures.

The main boundary is operating range. Relative volatility, tray efficiency, HETP and flooding correlations are valid only for the mixture, pressure, loading and hardware condition they represent. The second boundary is coupled constraints: increasing reflux may help separation while worsening flooding, condenser duty and reboiler duty.

Common Release Mistakes

optimizing purity while recovery or flooding margin fails;
using relative volatility outside its valid composition and pressure range;
treating minimum stages as actual trays;
ignoring feed thermal condition when estimating internal traffic;
accepting tray count without efficiency evidence;
releasing a higher rate before condenser, reboiler and pressure-drop evidence agree.

Another common mistake is treating column symptoms independently. A pressure-drop increase, purity drift, reboiler duty limit and rising reflux may be the same hydraulic bottleneck. The release record should show how composition, energy and hydraulics were reconciled.

Do not use a single product sample to release a new rate. Sampling method, analyzer timing, reflux state, feed disturbance and inventory lag can make a transient pass look like stable operation.

Scenario Map

Scenario	Exercises	Main calculation	Release decision
Product and recovery	1, 2, 17	Distillate flow, recovery and product energy	Accept target or change specification.
VLE and stages	6, 7, 8, 10, 13	Equilibrium, Fenske stages, reflux screen, tray efficiency and Murphree step	Estimate stage requirement and test basis.
Hydraulics and packing	9, 11, 12, 14, 15	Feed quality, vapor traffic, flooding, tray pressure drop and packed height	Derate, debottleneck or reject rate increase.
Release evidence	3, 4, 5, 16, 18	Reflux flow, condenser duty, reboiler duty, utility margin and final gate	Release only when quality, duty and hydraulics pass.

Validation Package Checklist

feed, product and bottoms composition basis;
pressure, VLE model and relative-volatility range;
reflux mode, condenser duty and reboiler duty;
tray or packing condition, efficiency and pressure drop;
flooding margin, entrainment and weeping evidence;
release action when purity, recovery, duty or hydraulics fail.
analyzer timing, sampling method and steady-state duration;
utility availability, control-valve authority and fouling assumption;
rate-release boundary states accept, derate, retest, refit or hold.

A complete validation package should make the column decision reproducible. Another engineer should be able to see which split was targeted, which thermodynamics were used, which utilities and hydraulics were limiting, and what operating restriction follows when a gate fails.

Exercise 1: Binary Distillation Product Flow Rates

A binary feed enters at $F=100\ \text{kmol/h}$ with light-component mole fraction $z_F=0.40$ . Distillate composition is $x_D=0.95$ and bottoms composition is $x_B=0.05$ . Estimate distillate flow.

Solution

D=\dfrac{F(z_F-x_B)}{x_D-x_B}=\dfrac{100(0.40-0.05)}{0.95-0.05}=38.9\ \text{kmol/h}

Engineering Comment

The result is a material-balance target, not proof that the column can hydraulically or thermodynamically achieve the split.

Plausibility Check

The feed is closer to bottoms composition than distillate composition, so distillate is less than half the feed.

Exercise 2: Light-Component Recovery

Using $F=100\ \text{kmol/h}$ , $z_F=0.40$ , $D=38.9\ \text{kmol/h}$ and $x_D=0.95$ , compute light-component recovery in distillate.

Solution

R=\dfrac{Dx_D}{Fz_F}=\dfrac{38.9(0.95)}{100(0.40)}=92.4\%

Engineering Comment

High recovery should be reviewed with bottoms loss, energy use, reflux, pressure drop and product purity.

Plausibility Check

Most light component leaves in the distillate because distillate is very rich in the light component.

Exercise 3: Reflux and Condenser Internal Flow

Distillate flow is $40\ \text{kmol/h}$ and reflux ratio is $R=2.5$ . Find reflux flow and total condenser liquid flow.

Solution

L=RD=2.5(40)=100\ \text{kmol/h}

L+D=100+40=140\ \text{kmol/h}

Engineering Comment

Higher reflux improves separation but increases condenser and reboiler duty and internal traffic.

Plausibility Check

With reflux ratio above two, reflux flow is larger than product flow.

Exercise 4: Condenser Duty

Overhead vapor condensation load is $130\ \text{kmol/h}$ and latent heat is $31\ \text{MJ/kmol}$ . Compute condenser duty.

Solution

\dot{Q}=\dfrac{130(31)}{3.6}=1119\ \text{kW}

Engineering Comment

Condenser duty must be checked against cooling-water return limit, pressure control and noncondensable handling.

Plausibility Check

Thousands of megajoules per hour convert to about one megawatt.

Exercise 5: Reboiler Duty from Vaporization Load

Boilup is $120\ \text{kmol/h}$ and latent heat is $34\ \text{MJ/kmol}$ . Compute reboiler duty.

Solution

\dot{Q}=\dfrac{120(34)}{3.6}=1133\ \text{kW}

Engineering Comment

Reboiler duty also needs steam pressure, condensate drainage, tube-wall temperature and relief review.

Plausibility Check

The duty is similar to condenser duty because vapor traffic is similar.

Exercise 6: Equilibrium Vapor Composition from Relative Volatility

For relative volatility $\alpha=2.4$ and liquid mole fraction $x=0.35$ , estimate vapor mole fraction:

y=\dfrac{\alpha x}{1+(\alpha-1)x}

Solution

y=\dfrac{2.4(0.35)}{1+(2.4-1)(0.35)}=0.564

Engineering Comment

Relative volatility is a simplified VLE model. Nonideal mixtures require validated thermodynamics.

Plausibility Check

For $\alpha>1$ , vapor is richer in the light component than liquid.

Exercise 7: Minimum Stages from Fenske Equation

Use $x_D=0.95$ , $x_B=0.05$ and $\alpha=2.4$ to estimate minimum stages:

N_{min}=\dfrac{\ln\left[\dfrac{x_D}{1-x_D}\dfrac{1-x_B}{x_B}\right]}{\ln(\alpha)}

Solution

N_{min}=\dfrac{\ln[(0.95/0.05)(0.95/0.05)]}{\ln(2.4)}=6.73

Engineering Comment

Minimum stages assume total reflux. Actual operation needs more stages and finite reflux.

Plausibility Check

A demanding split with moderate relative volatility requires several ideal stages.

Exercise 8: Minimum Reflux Margin

A shortcut calculation gives minimum reflux $R_{min}=1.4$ . Planned reflux is $R=2.1$ . Compute reflux margin ratio.

Solution

M_R=\dfrac{2.1-1.4}{1.4}=50.0\%

Engineering Comment

Reflux margin helps separation but raises internal traffic. It should be checked against flooding and utility duty.

Plausibility Check

The planned reflux is one and a half times the minimum.

Exercise 9: Feed Quality and Internal Traffic

A feed is $60\%$ liquid, so $q=0.60$ . Feed flow is $80\ \text{kmol/h}$ . Estimate liquid and vapor traffic added by feed.

Solution

L_{add}=qF=0.60(80)=48\ \text{kmol/h}

V_{add}=(1-q)F=0.40(80)=32\ \text{kmol/h}

Engineering Comment

Feed thermal condition changes traffic above and below the feed stage and can move the flooding bottleneck.

Plausibility Check

The liquid addition is larger because the feed is mostly liquid.

Exercise 10: Actual Tray Count from Efficiency

An ideal-stage estimate requires $14$ stages. Overall tray efficiency is $70\%$ . Estimate actual tray count.

Solution

N_{actual}=\dfrac{14}{0.70}=20

Engineering Comment

Tray efficiency depends on system, hydraulics, weeping, entrainment, foaming and tray condition.

Plausibility Check

Efficiency below one requires more actual trays than ideal stages.

Exercise 11: Column Vapor Traffic and Flooding Margin

Current vapor traffic is $72\%$ of flooding. A rate increase raises vapor traffic by $18\%$ . Estimate new flooding fraction.

Solution

f_{new}=0.72(1+0.18)=0.850=85.0\%

Engineering Comment

The new traffic is near typical operating limits. Confirm pressure drop, entrainment and tray condition before release.

Plausibility Check

An eighteen percent increase on seventy-two percent adds about thirteen percentage points.

Exercise 12: Tray Pressure-Drop Rise

Tray pressure drop is $0.62\ \text{kPa/tray}$ over $28$ active trays. Estimate column tray-section pressure drop.

Solution

\Delta P=0.62(28)=17.4\ \text{kPa}

Engineering Comment

Pressure drop affects boiling point, condenser pressure, reboiler load and relief basis.

Plausibility Check

Less than one kilopascal per tray over dozens of trays gives tens of kilopascals.

Exercise 13: Murphree Step Efficiency

For one tray, vapor enters with $y_{in}=0.42$ , equilibrium vapor at leaving liquid is $y^*=0.62$ and actual outlet is $y_{out}=0.54$ . Estimate Murphree efficiency.

Solution

E_M=\dfrac{y_{out}-y_{in}}{y^*-y_{in}}=\dfrac{0.54-0.42}{0.62-0.42}=60.0\%

Engineering Comment

Tray efficiency should be based on representative sampling and correct phase equilibrium.

Plausibility Check

The actual outlet moves a little over halfway toward equilibrium.

Exercise 14: Packed-Column HETP Height

A packed section needs $10$ theoretical stages and the packing has $HETP=0.55\ \text{m/stage}$ . Compute packed height.

Solution

Z=10(0.55)=5.5\ \text{m}

Engineering Comment

Packed height also needs liquid distribution, pressure drop, fouling, turndown and flooding checks.

Plausibility Check

Half a meter per stage over ten stages gives a few meters.

Exercise 15: Packed-Column Pressure Drop

Packed pressure drop is $0.35\ \text{kPa/m}$ and packed height is $5.5\ \text{m}$ . Compute pressure drop.

Solution

\Delta P=0.35(5.5)=1.93\ \text{kPa}

Engineering Comment

Low clean pressure drop can rise with fouling, maldistribution or foaming. Use monitored evidence for release.

Plausibility Check

A fraction of a kilopascal per meter over several meters gives about two kilopascals.

Exercise 16: Reboiler Utility Margin

Required reboiler duty is $1.13\ \text{MW}$ and available steam duty is $1.30\ \text{MW}$ . Compute margin.

Solution

M=1.30-1.13=0.17\ \text{MW}

Engineering Comment

The margin should cover fouling, pressure changes, condensate drainage and control-valve position.

Plausibility Check

Available duty is only slightly above required duty.

Exercise 17: Specific Energy per Distillate

Reboiler duty is $1.13\ \text{MW}$ and distillate production is $40\ \text{kmol/h}$ . Compute energy per kmol distillate.

Solution

E=\dfrac{1.13(3600)}{40}=101.7\ \text{MJ/kmol}

Engineering Comment

Specific energy helps compare reflux policies, but purity and recovery constraints still govern release.

Plausibility Check

One megawatt over one hour is thousands of megajoules, divided by tens of kmol.

Exercise 18: Distillation Release Gate

A column rate increase requires recovery above $90\%$ , flooding below $85\%$ , reboiler margin positive and no unresolved pressure-drop alarm. Results are $92.4\%$ , $85.0\%$ , positive and no alarm. The flooding limit is strict: less than $85\%$ . Does it release?

Solution

The flooding gate fails because:

85.0\%\not<85.0\%

The release fails.

Engineering Comment

A column can meet composition while losing hydraulic margin. Rate release should respect the limiting gate.

Plausibility Check

The result is exactly at the limit, and the rule requires less than the limit.

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