Chemical Engineering Principles: Drying, Distillation, and Evaporation

Posted on Jun 13, 2026 in Other university degrees and diplomas

Constant Rate Drying Equation Derivation

To derive the equation for constant-rate drying considering conduction, convection, and radiation, we perform an energy balance where the heat flux q” (W/m²) is the sum of all heat transfer modes.

Step 1: Moisture Flux

From drying theory, the drying rate N is defined as:

N = -(Ws/a)(dX/dt)

For constant-rate drying, N is constant, leading to:

t = (Ws/aN)(Xi – Xf)

Step 2: Energy Balance

The moisture evaporation rate is controlled by the heat supply:

N = q”/λ

Where λ is the latent heat of vaporization.

Step 3: Heat Transfer Modes

  • Conduction: q”cond = (k/L)(Ts – Ti)
  • Convection: q”conv = h(T∞ – Ts)
  • Radiation: q”rad = εσ(Tsur⁴ – Ts⁴)

Step 4: Final Equations

The total moisture flux is:

N = (1/λ)[(k/L)(Ts – Ti) + h(T∞ – Ts) + εσ(Tsur⁴ – Ts⁴)]

The total drying time is:

t = [Wsλ(Xi – Xf)] / {a[(k/L)(Ts – Ti) + h(T∞ – Ts) + εσ(Tsur⁴ – Ts⁴)]}

Distillation Column Temperature Calculation

To calculate the top and bottom temperatures of a multicomponent distillation column:

  1. Obtain operating pressures for the top and bottom.
  2. Determine product compositions.
  3. Assume an initial temperature.
  4. Calculate saturation pressures using VLE data or the Antoine equation.
  5. Apply Raoult’s Law: Σ(xiPi°) = P.
  6. Iterate until the calculated pressure matches the actual column pressure.

Batch Drying Time Calculation

Given a wet solid dried from 0.38 to 0.04 kg H₂O/kg dry solid, with Ws = 399 kg and a = 18.58 m², the drying time is calculated by integrating the inverse drying rate curve (1/R vs X) using the trapezium rule. The calculated drying time is 4.08 hours.

Triple Effect Evaporator Analysis

For a forward-feed evaporator concentrating NaOH, mass and energy balances are performed across each effect. By solving the heat balance equations simultaneously, we determine the steam consumption and surface area. For the provided parameters, the steam consumption is 5336 kg/h and the surface area per effect is approximately 72.6 m².

Chemical Engineering FAQs

Pinch Point

The pinch point is the location in a heat exchanger network where the temperature difference between hot and cold streams is at its minimum (ΔTmin).

Cooling Tower Terminology

  • Range: The difference between hot water inlet and cold water outlet temperatures.
  • Approach: The difference between cold water outlet temperature and entering air wet-bulb temperature.

Evaporator Feed Types

  • Forward Feed: Simple and cost-effective; ideal for heat-sensitive materials.
  • Backward Feed: Higher heat transfer rates due to lower viscosity of concentrated liquor; ideal for viscous solutions.