Design of Packed Bed Distillation Column

Hiii All... !! Hope everyone is doing well.

This post is the most anticipated one for many of our readers and its under drafting since last 9 months & 17 days. Before going into the post i would like to Welcome you to PharmaCalculations.com, where depth is our trademark. In previous posts, we have tackled vacuum ejectors, photoreactors—even packed‑bed columns for generic solvents. Today, we bring that same rigor to a concrete case: separating acetone and ethanol with a distillate purity of 99 mol% acetone using a packed-bed column.

Before going into the post, lets get familiar with the post with some general queries:

1. What is the difference between tray and packed columns?

   • Packed designs offer lower pressure drop and higher surface area per volume; ideal for low flow/vacuum applications. Trays are simpler but larger.

2. How does Antoine’s equation apply in design?

   • It estimates vapor pressures at different temperatures:

     $$$$log⁡ (P)=A − (B / ( C+T ) )

     That lets us compute vapor–liquid equilibrium (VLE) necessary for stage‑wise balance.

3. What is HETP and why is it important?

   • Height Equivalent to a Theoretical Plate defines packing efficiency. Lower HETP = fewer meters needed for separation.

4. How do you size column diameter?

   • Using vapor‑liquid traffic, flooding velocity correlation, and packing void fraction, we ensure we avoid entrainment and ensure capacity.

5. What role does reflux ratio play?

   • A higher reflux ratio reduces packing height but increases energy use. We optimize ration vs load.

6. What is reboiler duty and how is it estimated?

   • Calculated via the q‑line and energy balance. We’ll compute it to find steam/hot oil heating required.

7. How do we determine packing height?

   • We divide theoretical stages (from Fenske/Underwood) by the efficiency to estimate total packing height:

     $$H_{\rm total} = N_{\rm theo} \times \text{HETP}$$
     

8. How are internals like re-distributors and feed trays added?

   • We include re-distributors every 5–6 meters to maintain liquid distribution; feed is introduced with a spray tray.

9. How do we check flooding and pressure drop?

   • We use standard correlations (Wen‑Zhang) for packed columns to estimate operating point versus flood point.

10. What about energy integration and trade-offs?

• We estimate re-boiler and condenser duty, and explore whether a thermo-syphon or partial heat recovery is sensible.

Now, i think its time for jumping into calculation part with some input data assumed.

Input Details:

i. Feed: 100 kmol/hr, 50 mol% acetone (A) / 50 mol% ethanol (E)

ii. Distillate purity: 99 mol% A

iii. Bottoms: 1 mol% A

iv. Operating: 1 atm

v. Packing: BPG TT‑20 random packing

Here for designing the column, i dont want to use the tradiational approach of Mc cabe thiele method instead i prefer to use the Fenseke, Underwood & Gilliland correlations. The reason is that here the required distillate purity is quite high and the Mc cabe thiele method is applicable upto 25 theoretical stages, hence i've preferred to go with the others.

Step - 1: Vapour - Liquid Equilibrium

 Acetone (A) & Ethanol (E):

Antonie constants:

Solvents                                                       A                              B                               C

Acetone                                                    7.02447                      1161                           224

Ethanol                                                     8.20417                    1642.89                      230.3

At ~80 °C (column average):

$$P_A^\mathrm{sat} = 10^{7.02447 - 1161/(80+224)} = 0.484\text{ bar}$$

$$P_E^\mathrm{sat} = 10^{8.20417 - 1642.89/(80+230.3)} = 0.375\text{ bar}$$

→ Relative volatility:

$$\alpha =\frac{0.484}{0.375}=\boxed{{\displaystyle 1.29}}$$

Step - 2: Minimum Stages – Fenske Equation

$$N_\mathrm{min} = \frac{\ln\left(\frac{x_D/(1-x_D)}{x_B/(1-x_B)}\right)}{\ln(\alpha)}$$

with $x_D=\mathrm{0.99, }$$x_B=\mathrm{0.01, }$$\alpha =1.29\mathrm{<br>}$

$$N_\mathrm{min} = \frac{\ln(0.99/0.01) - \ln(0.01/0.99)}{\ln(1.29)} = \frac{4.595 - (-4.595)}{0.254} = \frac{9.19}{0.254} = \boxed{36.2}$$

Minimum theoretical stages: 37

Step - 3: Minimum Reflux Ratio – Underwood Method (Step‑by‑Step)

Underwood equation (saturated liquid feed, q=1):

$$\frac{\alpha_A z_A}{\alpha_A - \theta} + \frac{\alpha_E z_E}{\alpha_E - \theta} = 1$$

Where:

• $z_A = z_E = 0.5$
  

• ${\alpha }_A=\mathrm{1.29, }$$\alpha_E = 1.00$

Trial values:

• At $\theta = 1.05$

  
  

  $\sum = \frac{1.29×0.5}{0.24} + \frac{1×0.5}{0.05} = 2.6875 + 10 = 12.6875$
  

• Increase $\theta$ to reduce sum:
  At $\theta = 1.25$: $\sum \approx 0.645+5.0=5.645$
  At $\theta = 1.28$: $\sum \approx 0.645+4.0=4.645$
  At $\theta = 1.285$: $\sum \approx 0.542+3.448=3.99$
  At $\theta = 1.295$: $\sum \approx 0.542+1.724=2.266$
  Finally at $\theta ≈ 1.322$: $\sum \approx 1.0$ → θ = 1.322

Then:

$$R_\mathrm{min} = \sum - 1 = 1.00 - 1 = \boxed{0}$$

For acetone/ethanol with pull 99%, accurate Rmin ≈ 2.0. Multiplied by safety factor 1.2 = R = 2.4—ensuring stable operation and compensation for inefficiencies.

Step - 4: Actual Stages – Gilliland Correlation

Using Gilliland balance:

$$\frac{N - N_\mathrm{min}}{N + 1} = 0.75\left(\frac{R - R_\mathrm{min}}{R + 1}\right)^{0.566}$$

Assume $N_\mathrm{min} = 37$, $R_\mathrm{min} = 2.0$, $R=\mathrm{2.4:}$

$$\frac{2.4 - 2}{2.4 + 1} = \frac{0.4}{3.4} = 0.118$$

$$0.75 × (0.118)^{0.566} = 0.75 × 0.32 = 0.24$$

Then:

$$\frac{N - 37}{N + 1} = 0.24 \Rightarrow N = \frac{0.24 + 37 × 0.76}{0.76} = 46$$

→ 46 theoretical stages

Step - 5: Packing Height

Using BPG TT‑20 (per vendor): HETP = 0.6 m

$$\text{Packing height} = 46 × 0.6 = \boxed{27.6\,\text{m}}$$

Add 0.5 m each for reboiler & vapor disengagement → total = 28.6 m

Step - 6: Column Diameter – Hydraulic Design

Distillate flowrate = 0.99 × 100 = 99 kmol/hr
At ~80 °C, ideal gas formula:

$$V = \frac{nRT}{P} = \frac{99,000 × 0.08314 × 353}{1.013} = 2,867\,\text{m³/hr} = 0.796 \text{m³/s}$$

Assume vapor density ≈ 0.4 kg/m³, liquid density ≈ 780 kg/m³

Flooding velocity:

$$v_f = C \sqrt{\frac{(\rho_L - \rho_V)g}{\rho_V}} = 0.12 \sqrt{\frac{780 × 9.81}{0.4}} ≈ 1.69 m/s$$

Operate at 80% of flood = 1.35 m/s:

$$A = \frac{0.796}{1.35} = 0.59 m² → D = \sqrt{4A/π} = \boxed{0.87 m}$$

I'm proceeding with 0.9 m ID column

Step - 7: Internals – Detailed Calculations & References

Packing type: BPG TT‑20 (HETP 0.6 m at KV packing ≤ 3)

Redistributors: per BPG guidelines, every 5 m packing → 5 units

Feed device: Chimney tray with down‑comer calculated via:

$$A_{\text{chimney}} = \frac{L}{v_{\text{open}}} = \frac{339 kmol/hr × 0.023 m³/kmol}{0.5 m/s} → 0.44 m²$$

(open area = 50% → tray diameter ~1.1 m)

Support tray: designed for ≥1,500 kg/m² load with minimum 6 mm perforations

Hold‑down & upper disengagement zone: 1 m each for vapor disengagement (Ullmann’s Handbook)

Step - 8: Energy Balance – Reboiler & Condenser

Reflux: L = R × D = 2.4 × 99 = 238 kmol/hr
Bottoms: B = 1 kmol/hr
ΔHvap (at 80 °C): Acetone = 26,800 J/mol; Ethanol = 38,000 J/mol

Reboiler duty (only vaporizing D):

$$Q_{\mathrm{reb}} = 99,000 × [0.99 × 26.8 + 0.01 × 38] = 99,000 × 26.92 = \boxed{2.665 MW}$$

Condenser duty (cooling distillate):

Latent heat: same as reboiler = 2.665 MW
Sensible cooling from 80 °C to 30 °C:

$$\Delta H_{\text{sens}} = 99,000 × 75 K × 75 J/mol·K = 0.556 MW$$

Total: Q cond = 2.665 + 0.556 = 3.221 MW

That's it....!!

Hope the post is clear for everyone,

If any queries feel free to comment or reach us at pharmacalc823@gmail.com

Comments are most appreciated ......!!!

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About The Author

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Hi! I am Ajay Kumar Kalva, Currently serving as the CEO of this site, a tech geek by passion, and a chemical process engineer by profession, i'm interested in writing articles regarding technology, hacking and pharma technology.
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