Solvent Recovery Calculation: Boiling Point Under Vacuum, Heat Load and Time
Batch solvent recovery under vacuum comes down to one question repeated at every step: at what temperature does this solvent boil at this pressure, and how much heat does it take to get there and keep it boiling? Everything else (condenser sizing, vacuum pump capacity, recovery time) follows from that.
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Boiling Point at Vacuum: the Antoine Equation
⇒ Tb = B / (A − log₁₀P) − C
Where P is pressure in mmHg, T is temperature in °C, and A, B, C are compound-specific Antoine coefficients fitted from experimental vapor-pressure data. At standard atmospheric pressure (760 mmHg), this reduces to the solvent's normal boiling point, which is a handy sanity check on any Antoine coefficient set before trusting it at vacuum.
Worked Example: Toluene Under Vacuum
Toluene's Antoine coefficients (in this form) are A = 6.95087, B = 1342.31, C = 219.187. At 100 mmHg vacuum:
= 1342.31 / (6.95087 − 2.0) − 219.187
≈ 271.2 − 219.187 ≈ 52.0°C
Compare that to toluene's normal boiling point of 110.6°C at 760 mmHg (the same equation with P = 760). Pulling vacuum drops the boiling point by nearly 60°C. That is the whole reason batch recovery runs under vacuum: it lets you strip solvent at a temperature the batch (and the jacket steam pressure available) can actually sustain.
Heat Load & Recovery Time
Once you know the boiling temperature, the heat duty to sustain boiling is governed by the solvent's latent heat of vaporization and the target vapor rate: Duty (kW) = mass vaporization rate (kg/s) × latent heat (kJ/kg). Recovery time then follows from total solvent mass to be recovered divided by that vaporization rate, adjusted for the available heating duty from the jacket or coil.
Worked Example: Heat Load and Recovery Time
Continuing with toluene: say 2,000 kg has to be stripped at a steady 500 kg/hr. Toluene's latent heat is about 360 kJ/kg near its normal boiling point (use the value at your actual recovery temperature for design).
Heat duty = 0.139 × 360 ≈ 50 kW
Recovery time = 2,000 / 500 = 4 hours
This is the boiling duty alone. Add the sensible heat to bring the batch up to 52°C and an allowance for heat losses. If the jacket can only supply, say, 35 kW, the vapor rate drops in proportion and the recovery takes longer than 4 hours. The condenser has to remove the same ~50 kW, which is the starting point for sizing it.
In the Plant
Antoine coefficients are only valid over the temperature/pressure range they were fitted to. Extrapolating far outside that range (very deep vacuum, or temperatures near a solvent's critical point) can give a boiling point that looks plausible but is wrong. Always check the returned value against a known reference point (like the normal boiling point) before using it to size equipment.
Common Mistakes
Mixing up mmHg and mbar (a factor of ~1.33 apart) when entering the vacuum level; using latent heat measured at atmospheric pressure without adjusting for the actual recovery temperature; and forgetting that mixed-solvent systems don't follow a single Antoine curve at all. A binary or multi-component mix needs a real VLE calculation, not this single-compound shortcut.
Frequently Asked Questions
How do you calculate the boiling point of a solvent under vacuum?
Rearrange the Antoine equation: Tb = B / (A − log₁₀P) − C, with P in mmHg and the A, B, C coefficients for that solvent. For toluene at 100 mmHg this gives about 52°C.
How do you calculate heat load for solvent recovery?
Heat duty (kW) = vaporisation rate (kg/s) × latent heat (kJ/kg). In the example above, 500 kg/hr of toluene needs roughly 50 kW before sensible heat and losses.
Is mmHg the same as mbar?
No. 1 mmHg ≈ 1.333 mbar. Check which unit your Antoine coefficients were fitted in before entering the vacuum level.