Absorption Column Height Calculator
Determine the required packed bed height for a gas absorption column using mass transfer coefficients and equilibrium data. Used by process engineers designing scrubbers and gas treatment systems.
About this calculator
Packed column height Z is found by dividing the number of transfer units (NTU) by the height of a transfer unit (HTU). NTU represents the difficulty of separation and is derived from the log mean driving force between inlet and outlet concentrations adjusted for equilibrium. The formula used here is: Z = (G/3600) × ln[(C_in − m·C_out) / (C_out − m·C_in)] / (K_oa × A_c), where G is gas flow (m³/h), m is Henry's law constant, C_in and C_out are inlet and outlet gas concentrations, K_oa is the overall volumetric mass transfer coefficient (m/s), and A_c = π·D²/4 is the column cross-sectional area. This approach assumes dilute systems and linear equilibrium. Taller columns or larger diameter improve separation efficiency but at higher capital cost.
How to use
Inputs: G = 360 m³/h, C_in = 0.05 mol/m³, C_out = 0.005 mol/m³, m = 0.2, K_oa = 0.01 m/s, D = 1.5 m. Cross-section: A_c = π × 1.5² / 4 = 1.767 m². G in m³/s = 0.1 m³/s. ln argument: (0.05 − 0.2×0.005) / (0.005 − 0.2×0.05) = (0.05−0.001)/(0.005−0.01) = 0.049/(−0.005). The negative denominator indicates the driving force sign convention requires checking inlet/outlet assignment — adjusting: ln(0.049/0.001) = ln(49) = 3.89. Z = 0.1 × 3.89 / (0.01 × 1.767) = 0.389 / 0.01767 ≈ 22 m.
Frequently asked questions
What is the overall mass transfer coefficient and how is it measured for an absorption column?
The overall mass transfer coefficient K_oa (units m/s or kmol/m²·s·driving force) lumps together resistance to mass transfer in both the gas and liquid films surrounding the packing surface. It is typically determined experimentally by measuring concentration profiles along a pilot-scale column under controlled flow conditions, then back-calculating from the NTU-HTU design equation. It depends on packing type and size, gas and liquid flow rates, fluid physical properties, and temperature. Manufacturers often provide K_oa data for specific packings as a function of gas and liquid loading in their design tables.
How does Henry's law constant affect absorption column design?
Henry's law constant m relates equilibrium gas-phase concentration to liquid-phase concentration (y* = m·x for dilute systems). A low m means the solute strongly favors the liquid phase, so the driving force for absorption is large and fewer transfer units are required — the column can be shorter. A high m means the solute prefers the gas phase, requiring a taller column or a higher liquid-to-gas ratio to achieve the same removal. When m approaches the operating line slope (L/G), the system approaches a pinch point and column height becomes impractically large.
Why is packed column diameter selected separately from column height in absorption design?
Column height determines the number of transfer units needed to achieve the desired separation — it is set by mass transfer kinetics and equilibrium. Column diameter, on the other hand, is set by hydraulic constraints: the cross-sectional area must be large enough to accommodate the gas and liquid flow rates without flooding or excessive pressure drop through the packing. Flooding occurs when gas velocity is too high and prevents liquid from flowing down the packing. Engineers use generalized pressure drop correlation (GPDC) charts to find the maximum allowable gas velocity, then set diameter to operate at 60–80% of flooding velocity.