Chemical engineering transport & equilibrium foundations of Tubular Evaporator Steam Economy.
Evaporation is a major thermal separation unit operation in chemical processing, pulp and paper, desalination, and sugar manufacturing, responsible for concentrating dilute aqueous solutions by boiling off volatile water solvent. A single-effect tubular evaporator comprises a vertical shell-and-tube calandria where condensing utility steam outside the tubes transfers latent heat across the metal wall into the process liquid boiling inside the tubes. As vapor is generated, rising vapor bubbles expand rapidly, accelerating the liquid upward in climbing-film annular flow or descending as a thin turbulent falling film. Key performance metrics include the water evaporation mass rate m_dot_v, the overall heat transfer coefficient U_evap, and the dimensionless steam economy SE, defined as kilograms of water evaporated per kilogram of heating steam consumed: SE = m_dot_v / m_dot_s. For a single-effect unit without vapor recompression, steam economy is fundamentally limited to less than 1.0 (typically 0.80 to 0.95) due to radiation losses, feed preheating, and boiling point elevation (BPE) caused by non-volatile solutes. Increasing steam jacket pressure P_s elevates steam saturation temperature T_s, widening the thermal driving force (T_s - T_boil) and proportionally accelerating the evaporation rate: m_dot_v = S · P_s. In this experiment, a pilot climbing-film evaporator concentrating a 10 wt% sucrose feed is operated across steam pressures from 0.5 to 3.0 bar to evaluate evaporation rate sensitivity S and measure steam economy.
1. Principles of Industrial Evaporation
Evaporation concentrates non-volatile solutes (e.g., sucrose, caustic soda, inorganic salts) by vaporizing water solvent through thermal heat exchange. The unit operation differs from distillation in that the vapor product is pure solvent, and no attempt is made to fractionate multiple volatile components.
2. Heat Transfer & Energy Balance in a Calandria
In a single-effect vertical tubular calandria, saturated steam at pressure $P_s$ and saturation temperature $T_s$ condenses on the outer tube surfaces, releasing latent heat $\lambda_s$. Heat conducts across the tube wall into boiling process liquid inside the tubes at boiling temperature $T_1$:
\[ q = U_{evap} A (T_s - T_1) = \dot{m}_s \lambda_s \]where $U_{evap}$ is the overall boiling heat transfer coefficient, $A = \pi D L$ is calandria surface area, and $\dot{m}_s$ is heating steam mass consumption rate. The heat transferred preheats incoming feed from $T_f$ to $T_1$ and vaporizes solvent at evaporation rate $\dot{m}_v$:
\[ q = \dot{m}_f c_{p,f} (T_1 - T_f) + \dot{m}_v \lambda_v \]where $\lambda_v$ is the latent heat of vaporization of water at boiling pressure.
3. Steam Economy & Pressure Driving Force Scaling
The thermal efficiency of an evaporator is quantified by the dimensionless Steam Economy ($SE$):
\[ SE = \frac{\dot{m}_v}{\dot{m}_s} = \frac{\text{kg water evaporated}}{\text{kg steam consumed}} \]For saturated steam, saturation temperature $T_s$ increases monotonically with gauge pressure $P_s$. Over the operating window $0.5$ to $3.0\text{ bar}$, the effective temperature difference $(T_s - T_1)$ scales approximately linearly with steam gauge pressure $P_s$. Consequently, the water evaporation mass rate $\dot{m}_v$ follows the linear calibration model:
\[ \dot{m}_v = S \cdot P_s \]where $S$ is the evaporation rate sensitivity slope in $\text{kg/(h}\cdot\text{bar)}$.
Viva voce questions & analytical theory
What is Steam Economy and why can a single-effect evaporator never exceed SE = 1.0?
Steam economy is the ratio of kilograms of water evaporated to kilograms of heating steam consumed; in a single-effect unit, one kilogram of condensing steam supplies approximately one latent heat unit, which can vaporize at most one kilogram of water (SE < 1.0 due to radiation losses and feed sensible heating).
How do multiple-effect evaporator systems achieve steam economies far greater than 1.0?
Vapor evaporated in Effect 1 is used as heating steam in Effect 2 (operating at a lower pressure/boiling point), cascading across N effects so that 1 kg of primary steam evaporates approximately 0.8 × N kg of water.
What is Boiling Point Elevation (BPE) and Dühring's rule?
BPE is the elevation in solution boiling point above pure water at the same pressure due to dissolved non-volatile solute (Raoult's law); Dühring's rule states that the boiling point of a solution is a linear function of the boiling point of pure water at the same pressure.
How does the climbing-film (rising-film) mechanism operate inside vertical evaporator tubes?
Liquid enters at the bottom; as boiling initiates, vapor bubbles expand rapidly and coalesce into a high-velocity central vapor core that drags a thin liquid film upward along the tube wall by interfacial shear.
What is the function of the vapor-liquid cyclone separator?
The high-velocity two-phase mixture exiting the calandria enters tangential cyclone separators where centrifugal force flings dense liquid droplets to the wall, preventing product entrainment into the overhead condenser.
What is mechanical vapor recompression (MVR) in modern industrial evaporation?
MVR uses an electrically driven mechanical compressor to compress evaporated overhead vapor, elevating its saturation temperature and pressure so it can be recycled back to heat its own boiling calandria, slashing energy consumption by up to 90%.
Experimental precautions and process safety
- Bleed non-condensable gases from the steam jacket; air accumulation creates an insulating gas barrier that collapses heat transfer.
- Maintain uniform liquid feed rate to prevent tube dryout and product burning (caramelization) on tube walls.
- Wear heat-resistant face shields, thermal gloves, and lab coats when working around pressurized steam lines.
- Ensure vacuum relief valves and rupture discs are certified and unblocked.
Theoretical assumptions & boundary condition limits
- The transport and thermodynamic models apply within the specified calibrated operating window (0.5 to 3.0 bar).
- Assumes ideal continuum flow and homogeneous phase mixing without unmodeled parasitic wall losses.
- Continuous sensor readings reflect ordinary least-squares regression across successive observations.
- High-temperature or extreme concentration excursions require non-ideal equation-of-state corrections.