Reference ID: MET-40A3 | Process Engineering Reference Sheets Calculation Guide
Introduction & Context
Evaporative concentration is a unit operation in which solvent is removed as vapor from a dilute feed, thereby increasing the concentration of non-volatile solutes. The calculation is central to the design and rating of single-effect and multiple-effect evaporators, flash crystallisers, and re-boilers in the food, pharmaceutical, water-treatment, and chemical-process industries. Accurate prediction of vapor flow and heat duty sets exchanger area, steam economy, and product quality.
Methodology & Formulas
Overall mass balance
Feed mass flow rate \( \dot{m}_{\text{feed}} \) is split into concentrate and vapor streams. Solids are conserved:
\[
\dot{m}_{\text{feed}}\,x_{\text{feed}} = \dot{m}_{\text{conc}}\,x_{\text{conc}}
\quad\Rightarrow\quad
\dot{m}_{\text{conc}} = \dot{m}_{\text{feed}}\,\frac{x_{\text{feed}}}{x_{\text{conc}}}
\]
Vapor mass flow is the difference:
\[
\dot{m}_{\text{vap}} = \dot{m}_{\text{feed}} - \dot{m}_{\text{conc}}
= \dot{m}_{\text{feed}}\left(1-\frac{x_{\text{feed}}}{x_{\text{conc}}}\right)
\]
Energy duty
Latent heat of vaporisation \( h_{\text{fg}} \) at the saturation pressure determines the heat load:
\[
Q = \dot{m}_{\text{vap}}\,h_{\text{fg}}
\]
Convert to kilowatts with the factor 1 kW = 3600 kJ h-1.
Jakob number
The Jakob number compares sensible heat in the liquid boundary layer to the latent heat of phase change:
\[
Ja = \frac{c_{p,\ell}\,\Delta T_{\text{wall}}}{h_{\text{fg}}}
\]
where \( \Delta T_{\text{wall}} \) is the superheat of the heating surface above saturation.
Boiling-regime criteria for gentle nucleate boiling
Use the mass-balance equation: C₂ = C₁ × (V₁ / V₂), where C₁ and V₁ are the initial concentration and volume, and V₂ is the final volume after evaporation. Ensure temperature is constant so density changes do not skew the volume measurement. If solids precipitate, filter and weigh the dry cake to confirm the calculated concentration.
Temperature: Every 10 °C rise can double degradation rates; keep wall temperature < 90 °C for botanicals.
Residence time: Short-path or wiped-film units cut contact time to seconds instead of hours.
Pressure: Vacuum at 50–100 mbar lowers boiling point by 30–40 °C, preserving actives.
Surface renewal: High agitation minimizes hot spots and fouling that amplify local degradation.
Track the overall heat-transfer coefficient (U) in real time; a 15–20 % drop from baseline signals imminent fouling. Couple this with differential pressure across the evaporator—an increase > 0.3 bar indicates deposit buildup. For sticky extracts, plot these parameters against run hours; the knee in the curve gives the optimal cleaning interval.
Viscosity < 200 cP and low fouling: Falling-film offers high heat flux at low holdup.
Viscosity > 200 cP or tendency to salt out: Forced-circulation with external heat exchanger maintains turbulent flow and prevents tube blockage.
Boiling-point rise > 15 °C: Forced-circulation handles the greater temperature driving force without dry-out.
Worked Example: Concentrating an Antibiotic Broth by Single-Effect Evaporation
A pharmaceutical plant must concentrate 1 t h-1 of an antibiotic fermentation broth from 5 wt % solids to 50 wt % solids. A single-effect evaporator operating at 0.2 bar absolute (≈ 60 °C saturation temperature) will be used. Estimate the required heat-transfer duty and check that nucleate-boiling conditions are maintained.
Knowns
Feed mass flow rate, \( \dot{m}_{\text{feed}} \) = 1000 kg h-1
Feed solids mass fraction, \( x_{\text{feed}} \) = 0.05
Product solids mass fraction, \( x_{\text{conc}} \) = 0.50
Evaporator pressure, \( P_{\text{abs}} \) = 0.2 bar
Saturation temperature at 0.2 bar, \( T_{\text{sat}} \) = 60 °C
Latent heat of vaporisation at 60 °C, \( h_{\text{fg}} \) = 2358 kJ kg-1
Maximum allowable Jakob number for stable boiling, \( Ja_{\text{max}} \) = 0.1
Assumed temperature difference across the heating wall, \( \Delta T_{\text{wall}} \) = 2 K
Step-by-step calculation
Water evaporated
Overall mass balance on solids gives
\[ \dot{m}_{\text{conc}} = \frac{x_{\text{feed}}}{x_{\text{conc}}} \dot{m}_{\text{feed}} = \frac{0.05}{0.50} \times 1000 = 100 \text{ kg h}^{-1} \]
Water evaporated, \( \dot{m}_{\text{vap}} = \dot{m}_{\text{feed}} - \dot{m}_{\text{conc}} = 1000 - 100 = 900 \text{ kg h}^{-1} \)
Energy required
Neglecting sensible heat of concentration and assuming feed enters at saturation temperature, the heat duty is essentially the latent heat load:
\[ Q = \dot{m}_{\text{vap}} \cdot h_{\text{fg}} = 900 \times 2358 = 2\,122\,200 \text{ kJ h}^{-1} \]
Convert to kilowatts:
\[ Q = \frac{2\,122\,200}{3600} = 589.5 \text{ kW} \]
Jakob number check
The Jakob number quantifies the ratio of sensible heat to latent heat in the boundary layer:
\[ Ja = \frac{c_{p,l} \, \Delta T_{\text{wall}}}{h_{\text{fg}}} = \frac{4.0 \times 2}{2358} = 0.0034 \]
Because \( Ja = 0.0034 < Ja_{\text{max}} = 0.1 \), nucleate-boiling regime is preserved and excessive superheating or film boiling is avoided.
Final Answer
The evaporator must supply 589 kW of heat to concentrate the broth as specified, while the low Jakob number (0.003) confirms operation in the desirable nucleate-boiling regime.
"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
