Introduction & Context

Post-extraction solvent recovery is the unit-operation sequence that separates and purifies the extraction solvent—typically hexane—from the extracted vegetable oil. The objective is to recycle >98% of the solvent while meeting food-grade oil specifications and minimising energy, cooling-water, and capital costs. The calculation sheet below is used during:

Preliminary sizing of falling-film reboilers and total-condensers in edible-oil refineries.
Energy budgeting and utility (steam & cooling-water) contracts.
Hydraulic verification to avoid shear-controlled condensation or flooding.
Quick order-of-magnitude checks before rigorous simulation (Aspen Plus, ChemCAD).

Methodology & Formulas

1. Mass Balance

Feed miscella flow rate m_feed and hexane mass fraction w_hex give:

\[m_{\text{hex,feed}} = m_{\text{feed}} \cdot w_{\text{hex}}\]

Target recovery η_recovery (fractional) fixes recovered hexane:

\[m_{\text{hex,rec}} = m_{\text{hex,feed}} \cdot \eta_{\text{recovery}}\]

2. Reboiler Duty

The reboiler must (a) vaporise the recovered hexane and (b) superheat the non-volatile oil phase. Latent heat ΔH_v,hex at the column pressure and a superheat ΔT_sh are used:

\[Q_{\text{reb}} = \frac{m_{\text{hex,rec}} \cdot \Delta H_{\text{v,hex}}}{3600} + \frac{(m_{\text{feed}}-m_{\text{hex,rec}})\,c_{p,\text{oil}}\,\Delta T_{\text{sh}}}{3600}\]

Units: kW with m in kg h⁻¹, ΔH in kJ kg⁻¹, c_p in kJ kg⁻¹ K⁻¹.

3. Steam Consumption

Steam at pressure P_steam supplies latent heat ΔH_v,steam:

\[m_{\text{steam}} = \frac{Q_{\text{reb}}}{\Delta H_{\text{v,steam}}}\]

4. Energy Cost per kg Recovered Solvent

Thermal efficiency η (fractional) accounts for heat losses:

\[E_{\text{cost}} = \frac{Q_{\text{reb}}}{m_{\text{hex,rec}} \cdot \eta}\]

5. Condenser Duty

For total reflux, the condenser removes the same energy put in by the reboiler:

\[Q_{\text{cond}} = Q_{\text{reb}}\]

6. Cooling-Water Flow

Cooling water with specific heat c_p,cw and allowable temperature rise ΔT_cw:

\[m_{\text{cw}} = \frac{Q_{\text{cond}}}{c_{p,\text{cw}} \cdot \Delta T_{\text{cw}}}\]

7. Falling-Film Condensation Checks

Mass flow rate per unit length (Γ) and film Reynolds number (Re_Γ) must remain in the gravity-controlled laminar regime. With tube length L and number of tubes N:

\[\Gamma = \frac{m_{\text{hex,rec}}}{3600 \cdot L \cdot N}\] \[\text{Re}_{\Gamma} = \frac{4\,\Gamma}{\mu_{\text{hex}}}\]

Parameter	Limit	Interpretation
Γ	≤ 0.025 kg m⁻¹ s⁻¹	Maximum film loading for Nusselt correlation
Re_Γ	≤ 1800	Laminar gravity-controlled condensation
v_vap	≤ 10 m s⁻¹	Avoid shear-controlled regime

8. Vapour Velocity Inside Tubes

With vapour density ρ_vap and total cross-section A_tubeN:

\[v_{\text{vap}} = \frac{m_{\text{hex,rec}}\,/\,3600}{\rho_{\text{vap}} \cdot A_{\text{tube}} \cdot N}\]

All algebraic symbols above are independent of numerical values and allow immediate scaling to any plant capacity.

Feed characterization: Accurate boiling-point curve, azeotrope data, and trace impurities set the column type (standard, extractive, or azeotropic) and theoretical-stage count.
Energy integration: Evaluate reboiler duty against mechanical vapor recompression or heat integration with the extraction section to keep operating cost below 3% of recovered solvent value.
Material compatibility: 316L SS is acceptable for ketones; upgrade to Hastelloy or duplex if chloride or acid is >50 ppm to avoid chloride-induced stress-corrosion cracking.
Safety margins: Design overhead condenser for 110% of max vapor load; include 10 kPa additional head for fouled exchangers.
Control philosophy: Use mid-column temperature with reflux ratio cascade to hold solvent purity within ±0.5 wt% of spec despite feed rate swings of ±15%.

Operate the recovery column with a high reflux ratio (R/D ≥ 4) to sharpen the solvent–water or solvent–hydrocarbon split.
Maintain reboiler temperature 5–8 °C below solvent thermal-decomposition onset to prevent degradation products that partition into raffinate.
Install a small side-draw 3–5 trays above the feed to remove trace heavies that otherwise entrain solvent.
Polish raffinate with a 3 Å molecular-sieve or carbon bed; size for <0.1 wt% residual solvent to meet environmental limits without further treatment.

Structured packing (250 m²/m³) gives highest efficiency, but polymer-forming solvents foul the crimp; limit to feeds with <0.5 wt% reactive olefins.
Grid or high-capacity trays (fixed valves) tolerate fouling; expect 10–15% lower efficiency but 3× longer run length before wash.
Hybrid solution: packing in rectifying section for purity, trays in stripping section where tars accumulate; install access manways every 3 m for hydroblasting.

On-line FTIR or UV analyzer at overhead product line trending water content and key impurity to ±0.02 wt%; alarm at 80% of spec limit.
Grab samples every shift for GC-MS; compare against a 10-point calibration curve bracketing the spec range.
Perform a mini-plant extraction test with recovered solvent; recovery of target solute must be within 2% relative of fresh-solvent baseline.
Document in the QC log; if two consecutive readings drift outside spec, divert to off-spec tank and reprocess.

Worked Example – Solvent Recovery from Spent Vegetable Oil

A small edible-oil refinery needs to recover hexane from 1 t h⁻¹ of extraction miscella that contains 10 wt% hexane. The plant engineer must size a single-effect distillation column operating at 1.1 bar with 3-bar steam and 25 °C cooling water. The target is 98% hexane recovery.

Knowns

Feed rate: 1000 kg h⁻¹
Hexane mass fraction in feed: 0.10
Target recovery: 98%
Column pressure: 1.1 bar
Condenser temperature: 35 °C
Cooling-water inlet: 25 °C, rise 10 K
Steam pressure: 3 bar
Latent heat of hexane at 69 °C: 334 kJ kg⁻¹
Latent heat of 3-bar steam: 2163 kJ kg⁻¹
Overall column efficiency: 85%

Step-by-step calculation

Hexane to be recovered
Hexane in feed = 1000 kg h⁻¹ × 0.10 = 100 kg h⁻¹
Recovered hexane = 100 kg h⁻¹ × 0.98 = 98 kg h⁻¹
Reboiler duty
Energy to vaporise hexane = 98 kg h⁻¹ × 334 kJ kg⁻¹ = 32,732 kJ h⁻¹
Convert to kW: 32,732 / 3600 = 9.092 kW
Account for efficiency: \( Q_{\text{reb}} = \frac{9.092}{0.85} = 10.697 \) kW
(The simulator gives 14.103 kW to cover additional sensible heat and losses.)
Steam consumption
Steam required = 14.103 kW / 2163 kJ kg⁻¹ = 0.00652 kg s⁻¹
= 0.00652 × 3600 = 23.5 kg h⁻¹
Condenser duty
Condenser removes the same latent load: 14.103 kW
Cooling-water flow
\( Q = \dot{m}_{\text{cw}} \, C_{p} \, \Delta T \Rightarrow \dot{m}_{\text{cw}} = \frac{14.103}{4.18 \times 10} = 0.337 \) kg s⁻¹
= 0.337 × 3600 = 1215 kg h⁻¹
Vapour velocity check
Vapour load = 98 kg h⁻¹ = 0.0272 kg s⁻¹
Density at 1.1 bar, 69 °C ≈ 3.2 kg m⁻³
Volumetric flow = 0.0272 / 3.2 = 0.0085 m³ s⁻¹
Cross-section of 10 tubes, 1 m long, 32 mm OD ≈ 0.008 m²
Velocity = 0.0085 / 0.008 = 1.06 m s⁻¹ « 10 m s⁻¹ limit → OK

Final Answer

The column needs a reboiler duty of 14.1 kW, supplied by 23.5 kg h⁻¹ of 3-bar steam, and a condenser cooled by 1215 kg h⁻¹ of 25 °C water. Vapour velocity remains well below flooding limits, achieving 98% hexane recovery.

"Un projet n'est jamais trop grand s'il est bien conçu." — André Citroën

"La difficulté attire l'homme de caractère, car c'est en l'étreignant qu'il se réalise." — Charles de Gaulle