Reflux Column Design and Calculations
Knowing the wash and column, we can calculate:
- Recommended minimum and maximum column diameters
- Expected purity off the top of the column
- Heat-up time
Then we can evaluate column performance over time:
- How much is collected
- How purity changes
- How performance evolves during the run
I have collated all required physical constants for water and ethanol on a date page.
Min & Max Diameter
Calculate the flooding diameter based on Figure 18-38 in Perry.
(call this “y”) vs
(call this “x”)
Plotting the flooding line:
y = 1.4427 x² − 1.0271 x + 0.2312
Where:
- U_t = superficial gas velocity (m/s)
- a_p = packing surface area (m²/m³)
- e = fractional voids in packing
- g = gravitational constant (9.8067 m/s²)
- G' = gas mass flux (kg/s·m²)
- L' = liquid mass flux (kg/s·m²)
- ρ_g, ρ_l = gas and liquid densities (kg/m³)
- μ_l = liquid viscosity (mPa·s)
Through the top section:
- V = vapor flowrate (kg/s)
- D = distillate flowrate (kg/s)
- L = liquid flowrate (kg/s)
Heat balance:
Q_distill = (V × %ethanol × H_vap_ethanol) + (V × %water × H_vap_water)
Gas flux:
G' = V / column area
Reflux Relationship
Then:
L' = L / column area
Note: vapor composition changes along the column, so a mass balance estimate is needed.
Solve for x and y, then calculate U_t and flooding diameter.
This gives the minimum column diameter.
Recommended operating diameter (~65% flooding):
Maximum usable diameter (~25% flooding):
HETP (Height Equivalent to a Theoretical Plate)
Estimated using Onda’s method.
Effective Area
Where:
- a_w = effective interfacial area (m²/m³)
- a = packing surface area (m²/m³)
- σ_c = critical surface tension
- σ_L = liquid surface tension
- L* = liquid mass flux
Critical Surface Tension
| Material | σ_c (mN/m) |
|---|---|
| Ceramic | 61 |
| Steel | 75 |
| Plastic | 33 |
| Carbon | 56 |
Mass Transfer Coefficients
Film Transfer Heights
Overall Transfer Unit Height
Stage / Transfer Unit Relations
Relationship between number of theoretical stages and transfer units.
Packed height expressed in terms of transfer units and HETP.
Mass Balance
Estimate top purity from the equilibrium diagram:
This diagram shows the stepping method used to estimate distillate composition from theoretical stages.
Approximate Equilibrium Correlation
y = −31.065x⁶ + 116.08x⁵ − 169.95x⁴ + 123.99x³ − 47.195x² + 9.1398x
(x and y expressed as fractions, not percent)
Procedure
- Choose a timestep
- Calculate volume removed = flowrate × time
- Determine distillate purity
- Update:
* total collected * average collected purity * remaining wash composition
Repeat per timestep.
HETP variation during the run is typically small and often ignored.
Important
Maintain consistent units:
- moles vs mass
- kg vs g
- SI vs Imperial
Attribution
Original calculations and explanation by Tony Ackland (HomeDistiller.org)
3 June 2000