Exercise set

Liquid-Liquid Extraction, Leaching, and Solvent Recovery Exercises

Solved extraction and leaching exercises for solute recovery, raffinate loss, distribution ratio, solvent loss, wash stages, purge and release gates.

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

These exercises focus on liquid-liquid extraction, leaching and solvent recovery. They cover solute recovery, raffinate loss, distribution ratio, stage recovery, solvent-to-feed ratio, solvent entrainment, wash water, solvent recovery, purge control, impurity buildup, recycle risk and release gates.

Assume simplified screening calculations unless an exercise states otherwise. Real extraction and leaching design must check phase equilibrium, selectivity, solvent compatibility, emulsion formation, density difference, viscosity, residence time, phase disengagement, solvent emissions, wastewater load and product assay.

How to use these exercises

Use the set as a solvent-loop release review. Exercises 1 to 6 establish the extraction mass balance, distribution basis and staged recovery. Exercises 7 to 12 test whether solvent ratio, entrainment, wash water, recovery capacity and storage make the process operable. Exercises 13 to 17 extend the same thinking to leaching, retained liquid, recycle impurity, purge and evidence completion. Exercise 18 then applies the all-of release gate.

Track every stream explicitly: feed, extract, raffinate, wash, purge, recycle, recovered solvent and spent solids. Extraction performance is not mature evidence unless solute recovery, solvent loss, impurity buildup and waste or purge routing are all tied to the same operating case.

Release Evidence Notes

Extraction evidence should state feed basis, solute mass, solvent rate, distribution data, phase split, raffinate quality, extract quality, entrained solvent, wash conditions and recovery system status.

Leaching evidence should preserve solid mass, liquid rate, retained moisture, solute recovery and spent-solid route. A high recovery can still fail release if solvent or contaminant leaves in the wrong stream.

Solvent recovery evidence should include solvent loss, purge, recycle impurity, distillation or stripping availability, storage limits and environmental release route.

The release package should also identify the controlling limit. The constraint may be product recovery, raffinate discharge, solvent emissions, emulsion carryover, storage capacity, recovery-unit duty, fire or toxicity controls, purge treatment or spent-solid classification. A release record that names only percent recovery is incomplete.

Engineering Boundary Notes

These calculations do not replace laboratory distribution studies, mixer-settler hydraulics, extraction column design, solvent hazard review, emissions permitting or waste classification. They are screening exercises for separation decisions.

Real extraction and leaching systems depend on phase equilibrium, residence time, phase disengagement, interfacial tension, density difference, viscosity, emulsion stability, solvent degradation, corrosion, temperature, solids retention, entrainment separators, vent treatment and wastewater compatibility. Use the exercises to identify when a solvent or recycle constraint controls release before scaling or changing operation.

Common Release Mistakes

using percent extraction without raffinate load or solvent loss;
ignoring entrainment and emulsion carryover;
counting recovered solute while hiding contaminated wash or purge;
recycling solvent without impurity control;
releasing product from one clean assay while phase disengagement evidence is weak;
increasing solvent rate without checking recovery capacity, storage and emissions;
treating a wash step as removal without routing the contaminated wash stream;
reporting leaching recovery while ignoring retained liquid in spent solids;
closing recycle by purge math while leaving the purge route unapproved.

Scenario Map

Scenario	Exercises	Primary check	Engineering decision
Extraction recovery	1, 2, 3, 4, 5, 6	solute recovery, raffinate load, distribution and stage recovery	Decide whether the extraction target is credible.
Solvent and wash	7, 8, 9, 10, 11, 12	solvent-to-feed, entrainment, wash, solvent recovery and loss	Decide whether solvent handling is controlled.
Leaching and recycle	13, 14, 15, 16, 17	leach recovery, retained liquid, purge, impurity buildup and evidence	Decide whether solids and recycle can be released.
Release gate	18	all-of extraction release	Decide whether the extraction package can close.

Exercise 1: Extraction Solute Recovery

A feed contains $50\ \text{kg/h}$ of solute. Extraction recovers $82\%$ to the solvent phase. Compute extracted solute.

Solution

\dot{m}_E=50(0.82)=41.0\ \text{kg/h}

Engineering Comment

Recovery should be paired with raffinate concentration and solvent loss before release.

Plausibility Check

Eighty-two percent of fifty kilograms per hour is a little above forty.

Exercise 2: Raffinate Solute Loss

Using the feed solute load of $50\ \text{kg/h}$ and extracted solute of $41.0\ \text{kg/h}$ , compute raffinate solute loss.

Solution

\dot{m}_R=50-41.0=9.0\ \text{kg/h}

Engineering Comment

The raffinate loss may govern wastewater treatment or product yield even when extract recovery looks acceptable.

Plausibility Check

The loss is the complement of $82\%$ recovery, or $18\%$ of feed solute.

Exercise 3: Raffinate Concentration

Raffinate flow is $18\ \text{m}^3/\text{h}$ and raffinate solute loss is $9.0\ \text{kg/h}$ . Compute raffinate concentration.

Solution

C_R=\dfrac{9.0}{18}=0.50\ \text{kg/m}^3

Engineering Comment

Raffinate concentration is the number usually seen by downstream wastewater, recycle or product-quality systems.

Plausibility Check

Nine kilograms spread through eighteen cubic meters gives half a kilogram per cubic meter.

Exercise 4: Distribution Ratio

At equilibrium, extract concentration is $2.4\ \text{kg/m}^3$ and raffinate concentration is $0.50\ \text{kg/m}^3$ . Compute distribution ratio.

Solution

D=\dfrac{2.4}{0.50}=4.8

Engineering Comment

A high distribution ratio supports extraction, but phase ratio and stage efficiency still control actual recovery.

Plausibility Check

The extract concentration is nearly five times the raffinate concentration.

Exercise 5: Single-Stage Extraction Fraction

Use the screening relation:

E=\dfrac{DS}{F+DS}

where $D=4.8$ , solvent phase flow $S=6\ \text{m}^3/\text{h}$ and feed phase flow $F=18\ \text{m}^3/\text{h}$ . Compute extraction fraction.

Solution

E=\dfrac{4.8(6)}{18+4.8(6)}=\dfrac{28.8}{46.8}=0.615

Engineering Comment

One ideal stage would recover about $61.5\%$ under this simplified equilibrium basis.

Plausibility Check

The solvent-equilibrium term is larger than feed flow but not dominant, so recovery above half is plausible.

Exercise 6: Two-Stage Recovery

If each ideal stage recovers $61.5\%$ of the solute remaining in raffinate, estimate two-stage recovery.

Solution

Fraction remaining after two stages:

f_R=(1-0.615)^2=0.148

Recovery:

R=1-0.148=85.2\%

Engineering Comment

Countercurrent staging and nonideal phase behavior can change this result, but the screen shows why staging matters.

Plausibility Check

Two stages should recover more than one stage, but not reach one hundred percent.

Exercise 7: Solvent-to-Feed Ratio

Solvent flow is $6\ \text{m}^3/\text{h}$ and feed flow is $18\ \text{m}^3/\text{h}$ . Compute solvent-to-feed ratio.

Solution

\dfrac{S}{F}=\dfrac{6}{18}=0.333

Engineering Comment

Increasing solvent ratio can improve recovery but raises solvent inventory, recovery duty and loss risk.

Plausibility Check

The solvent flow is one third of feed flow.

Exercise 8: Solvent Entrainment Loss

Raffinate entrains $3.5\ \text{kg}$ solvent per $\text{m}^3$ raffinate. Raffinate flow is $18\ \text{m}^3/\text{h}$ . Compute solvent loss.

Solution

\dot{m}_{loss}=3.5(18)=63\ \text{kg/h}

Engineering Comment

Solvent loss can govern safety, environmental load and economics even when solute recovery passes.

Plausibility Check

A few kilograms per cubic meter over tens of cubic meters per hour gives tens of kilograms per hour.

Exercise 9: Solvent-Loss Cost

Solvent loss is $63\ \text{kg/h}$ and solvent cost is $2.80/\text{kg}$ . Compute hourly solvent-loss cost.

Solution

C=63(2.80)=176.4\ \text{/h}

Engineering Comment

This direct cost does not include emissions control, wastewater treatment or fire-risk burden.

Plausibility Check

Sixty kilograms per hour at a few currency units per kilogram is hundreds per hour.

Exercise 10: Wash Water Dilution

Entrained solvent concentration in raffinate is $3.5\ \text{kg/m}^3$ . A wash reduces concentration by $70\%$ . Compute post-wash concentration.

Solution

C_w=3.5(1-0.70)=1.05\ \text{kg/m}^3

Engineering Comment

The solvent removed by wash becomes a contaminated wash stream and must be routed.

Plausibility Check

Thirty percent of $3.5$ is a little above one.

Exercise 11: Solvent Recovery Unit Capacity

Solvent recovery unit capacity is $58\ \text{kg/h}$ and solvent loss entering recovery is $63\ \text{kg/h}$ . Compute capacity shortfall.

Solution

\Delta=63-58=5\ \text{kg/h}

Engineering Comment

A small capacity shortfall can accumulate in wastewater, vents or storage over a long campaign.

Plausibility Check

The unit is slightly undersized relative to the loss load.

Exercise 12: Solvent Storage Accumulation

Unrecovered solvent accumulates at $5\ \text{kg/h}$ . Available off-spec solvent storage is $220\ \text{kg}$ . Estimate time to fill.

Solution

t=\dfrac{220}{5}=44\ \text{h}

Engineering Comment

Storage time defines the operating window before rate reduction or shutdown is needed.

Plausibility Check

At five kilograms per hour, a few hundred kilograms lasts a few dozen hours.

Exercise 13: Leaching Recovery

A solid feed contains $320\ \text{kg}$ soluble product. Leaching removes $74\%$ . Compute product recovered and product remaining in spent solids.

Solution

Recovered:

M_R=320(0.74)=236.8\ \text{kg}

Remaining:

M_S=320-236.8=83.2\ \text{kg}

Engineering Comment

Spent solids may still be valuable product loss or regulated waste, depending on the solute.

Plausibility Check

Three quarters of $320$ kilograms is about $240$ kilograms.

Exercise 14: Retained Liquid in Leached Solids

Spent solids mass is $1400\ \text{kg}$ and retained liquid is $18\%$ of wet solids. Estimate retained liquid mass.

Solution

M_L=0.18(1400)=252\ \text{kg}

Engineering Comment

Retained liquid can carry solvent, product and contaminants to drying or disposal.

Plausibility Check

Eighteen percent of $1400$ is a few hundred kilograms.

Exercise 15: Recycle Impurity Buildup

Recycle solvent contains $0.8\%$ impurity by mass. The release limit is $1.2\%$ . Compute remaining impurity margin.

Solution

\text{margin}=\dfrac{1.2-0.8}{1.2}=0.333=33.3\%

Engineering Comment

Recycle is acceptable only if the impurity trend is stable or purge capacity can hold the limit.

Plausibility Check

The solvent is two thirds of the way to the limit, leaving one third margin.

Exercise 16: Purge Rate for Impurity Control

Impurity enters the solvent loop at $4.5\ \text{kg/h}$ . Recycle solvent impurity concentration is $0.009\ \text{kg/kg}$ . Compute purge mass flow required to remove the impurity at steady state.

Solution

\dot{m}_P=\dfrac{4.5}{0.009}=500\ \text{kg/h}

Engineering Comment

Purge must have a treatment or recovery route; otherwise impurity control simply moves the problem.

Plausibility Check

Removing a few kilograms per hour at a concentration below one percent requires hundreds of kilograms per hour of purge.

Exercise 17: Extraction Evidence Completion

The release package requires feed assay, solvent assay, raffinate assay, extract assay, phase split, solvent loss, wash stream, recovery-unit status, purge route and storage inventory. Eight of ten records are complete. Compute completion.

Solution

C=\dfrac{8}{10}=80\%

Engineering Comment

Missing solvent-loss or purge-route evidence should hold release even if extraction recovery is high.

Plausibility Check

Eight of ten is exactly eighty percent.

Exercise 18: Extraction Release Gate

A release gate requires recovery above $85\%$ , solvent recovery capacity above solvent loss, impurity below $1.2\%$ , no unassigned purge and evidence completion above $90\%$ . Current values are recovery $85.2\%$ , recovery capacity $58\ \text{kg/h}$ versus loss $63\ \text{kg/h}$ , impurity $0.8\%$ , purge route assigned and evidence completion $80\%$ . Decide release status.

Solution

Recovery and impurity pass, and purge route is assigned. Solvent recovery capacity fails and evidence completion fails:

58<63

80\%<90\%

Release status:

\text{hold}

Engineering Comment

The extraction chemistry is acceptable, but solvent handling and evidence are not release-ready.

Plausibility Check

An all-of release gate fails when solvent recovery and records do not meet threshold.

Validation Package Checklist

Feed, extract, raffinate, wash, purge and recycle streams have stated flow and composition basis.
Recovery is checked alongside raffinate loss, solvent entrainment and recovery capacity.
Leached solids retain product and solvent mass in the balance.
Purge and off-spec solvent routes are documented before recycle is released.
Phase split, emulsion tendency, density difference and residence time match the release condition.
Solvent storage, recovery-unit duty, vent treatment and wastewater limits are checked together.
Recycle impurity trends and purge controls are assigned to an operating owner.
Product, raffinate, spent solids and contaminated wash each have a release or hold decision.

The final acceptance question is whether the process can keep recovering solute without moving risk into solvent loss, recycle impurity, spent solids or wastewater. If the answer is not documented on the same mass balance, the extraction package should remain on hold.

REF