Process design of packed columns: pressure drop and diameter

Why it matters

Packed columns carry out absorption, stripping, scrubbing and many distillations, especially in small diameters, under vacuum and with corrosive or foaming systems. Their capacity is limited by flooding and their energy cost by gas pressure drop, so the diameter is chosen from a pressure-drop correlation rather than from a simple velocity rule. Good internals — distributors, supports and redistributors — matter as much as the packing itself.

Key ideas

Packings.

• Random (dumped) packings: rings (Raschig, Pall, metal "high-performance" rings) and saddles (Berl, Intalox), in ceramic (corrosive service, high temperature), metal (strength, high capacity) or plastic (light, cheap, below about 100 °C). Modern rings and saddles with open walls give more capacity and lower pressure drop than old Raschig rings.
• Structured packings: corrugated sheets or gauze arranged in blocks. Very high surface area, low pressure drop per stage and high efficiency, ideal for vacuum distillation; more expensive and more sensitive to fouling and poor liquid distribution. Each packing has a packing factor F_p (m⁻¹), a characteristic of its hydraulic resistance, tabulated in data books; the lower F_p, the higher the capacity.

Hydraulic behaviour. Plot log(pressure drop) against log(gas rate) at constant liquid rate. At low gas rates the line is parallel to the dry-packing line. At the loading point the gas starts holding up liquid and the slope increases; at the flooding point liquid can no longer drain, the pressure drop rises almost vertically and liquid accumulates above the packing. Flooding is reached at lower gas rates when the liquid rate is higher, the liquid more viscous, or the packing denser (higher F_p).

Generalised pressure-drop correlation (GPDC). Sherwood, Eckert and later workers correlated flooding and constant-pressure-drop lines on a chart of a capacity parameter K4 against the flow parameter F_LV. Design steps:

1. Calculate F_LV from the liquid and gas mass flows and densities.
2. Choose a design pressure drop (as a rough guide: about 15–50 mm H₂O per metre of packing for absorbers and strippers, 40–80 mm H₂O/m for atmospheric and pressure distillation, lower under vacuum; follow your data book).
3. Read K4 at the design pressure drop (and at flooding) from the chart.
4. Solve K4 for the gas mass flux V*, then area A = V/V* and diameter D.
5. Round D up to a practical size and check the percentage of flooding, normally about 60–80 %.

Packing size and wetting. The packing must be small compared with the column, usually with D/d_p above about 10–15, or the gas bypasses along the wall. The liquid rate must be high enough to wet the packing; very low rates waste surface.

Height. Packed height = number of transfer units × height of a transfer unit (Z = N_OG·H_OG) for absorption, or number of theoretical stages × HETP for distillation. H_OG and HETP come from correlations (Onda, Cornell, Bravo–Fair) or vendor data; as a rough guide HETP grows with packing size (of the order of 0.4–0.5 m for 25 mm rings, up to about 1 m for 50 mm rings).

Internals. A liquid distributor at the top gives many uniformly spaced drip points; redistributors are fitted at intervals (for random packing every few column diameters and not more than about 6 m) because liquid migrates to the wall. A support plate with high open area (gas-injection type) carries the bed without causing premature flooding; a hold-down plate stops the bed lifting.

Packed or trayed? Packing suits small diameters (below about 0.6 m), vacuum (low pressure drop), corrosive (ceramic or plastic packing), foaming and heat-sensitive systems (low hold-up). Trays suit large diameters, high liquid rates, dirty or fouling services, side draws and intercoolers, and are easier to inspect.

Formulas

F_LV = (L* / V*)·√(ρ_V / ρ_L) (flow parameter; L*, V* liquid and gas mass fluxes or flows) K4 = 13.1·(V*)²·F_p·(μ_L / ρ_L)^0.1 / (ρ_V·(ρ_L − ρ_V)) (GPDC capacity parameter, Sinnott form)

• V* = gas mass flux (kg/m²·s); F_p = packing factor (m⁻¹, from data book); μ_L = liquid viscosity (Pa·s); ρ in kg/m³. V* = √(K4·ρ_V·(ρ_L − ρ_V) / (13.1·F_p·(μ_L/ρ_L)^0.1)) A = V / V*, D = √(4·A / π) % flooding = 100·√(K4 at design / K4 at flooding) Z = N_OG·H_OG or Z = N_stages·HETP

Worked examples

Example 1 (standard): diameter from the GPDC Given: gas 1.0 kg/s, ρ_V = 1.2 kg/m³; water-like liquid 3.0 kg/s, ρ_L = 1000 kg/m³, μ_L = 1.0 × 10⁻³ Pa·s; 38 mm plastic Pall rings, F_p = 130 m⁻¹ (data book); design pressure drop 20 mm H₂O/m, for which the chart gives K4 = 0.80; at flooding K4 = 2.4 (chart values given).

1. F_LV = (3.0/1.0) × √(1.2/1000) = 0.104.
2. (μ_L/ρ_L)^0.1 = (10⁻⁶)^0.1 = 0.251.
3. V* = √(0.80 × 1.2 × 998.8 / (13.1 × 130 × 0.251)) = √(958.8 / 427.8) = 1.497 kg/m²·s.
4. A = 1.0/1.497 = 0.668 m²; D = √(4 × 0.668/π) = 0.92 m.
5. At the design K4: % flooding = 100 × √(0.80/2.4) = 58 %.

Example 2 (GATE level): choosing the practical diameter and height Same duty. Compare 0.9 m and 1.0 m columns; N_OG = 6.5 and H_OG = 0.55 m (given).

1. D = 0.9 m: A = 0.636 m², V* = 1.572 kg/m²·s; K4 = 13.1 × 1.572² × 130 × 0.251 / (1.2 × 998.8) = 0.88, slightly above 0.80, so the pressure drop is a little over 20 mm H₂O/m; % flood = 100 × √(0.88/2.4) = 61 %.
2. D = 1.0 m: A = 0.785 m², V* = 1.273 kg/m²·s; K4 = 0.58, % flood = 49 % — under-loaded, poorer wetting and higher cost.
3. Choose D = 0.9 m (about 61 % of flood, pressure drop near the target). Check D/d_p = 900/38 = 24 > 10–15 ✓.
4. Packed height: Z = N_OG·H_OG = 6.5 × 0.55 = 3.6 m; one bed, with a distributor on top (a redistributor is not needed at this height).

Common mistakes

• Using a fixed "allowable velocity" instead of the GPDC with the packing factor.
• Using volumetric rather than mass flow ratios in F_LV.
• Forgetting the square root when converting a K4 ratio to percentage of flooding.
• Choosing packing too large for the column, giving wall channelling.
• Ignoring the distributor: poor distribution can halve the effective efficiency.
• Treating flooding as purely a liquid-rate effect; gas rate is the usual driver.

For GATE CH

Expect conceptual questions on loading and flooding points, packing factor, random versus structured packing, packed versus tray columns and the role of distributors, and numericals on diameter from a given gas mass flux, flow parameter, percentage flooding and packed height from N_OG and H_OG or HETP. Practise the K4 algebra carefully.

Quick check

1. What happens to the flooding gas rate if the liquid rate is increased?
2. Why are packed columns favoured for vacuum distillation?
3. A design K4 is 0.6 and the flooding K4 is 2.4. What is the percentage of flooding?
4. If N_OG = 8 and H_OG = 0.6 m, what packed height is needed?

Answers: 1. It falls. 2. Their pressure drop per theoretical stage is low. 3. 100 × √(0.25) = 50 %. 4. 4.8 m.