Chemical, Process & Catalysis Engineering
Onda (1968) Packed-Column Wetted Surface Area (a_w) Formula: Surface Tension & HTU
Calculate effective liquid-wetted interfacial area a_w (m^2/m^3) in random-packed gas absorbers and air strippers using Kakusaburo Onda, Hiroshi Takeuchi & Yoshio Okumoto’s (1968) dimensionless Reynolds-Froude-Weber-Capillary correlation.
Why plastic packing wets poorly in water — and how Onda’s sigma_c / sigma term predicts active mass-transfer area!
Dry geometric specific surface area a_t (e.g., 205 m^2/m^3 for 25-mm Pall rings) is NEVER 100% covered by flowing liquid film, especially on low-energy polypropylene packing (critical surface tension sigma_c ~= 0.033 N/m) irrigated by high-surface-tension water (sigma ~= 0.072 N/m) versus wettable ceramic (sigma_c ~= 0.061 N/m) or stainless steel (sigma_c ~= 0.075 N/m)!
Validated across thousands of VOC air-stripping and acid-gas scrubbing towers (and recommended by US EPA drinking-water air-stripping design manuals), Kakusaburo Onda, Hiroshi Takeuchi, and Yoshio Okumoto (1968, Journal of Chemical Engineering of Japan) expressed Fractional Wetted Area a_w / a_t in terms of Liquid Reynolds Number Re_L = L_m / (a_t * mu_L), Liquid Froude Number Fr_L = (L_m^2 * a_t) / (rho_L^2 * g), Liquid Weber Number We_L = (L_m^2) / (rho_L * sigma * a_t), and Packing Critical-to-Liquid Surface-Tension Ratio (sigma_c / sigma): a_w / a_t = 1 - EXP(-1.45 * ((sigma_c / sigma)^0.75) * (Re_L^0.10) * (Fr_L^-0.05) * (We_L^0.20))!
| Packing Material (a_t = 205 m^2/m^3, Water L_m = 12 kg/(m^2·s), sigma = 0.072 N/m) | Critical Surface Tension sigma_c | Wetted Fraction a_w / a_t | Effective Wetted Area a_w |
|---|---|---|---|
| Polypropylene Plastic Pall Rings | 0.033 N/m (Hydrophobic) | 0.4741 (47.4% Wetted) | 97.2 m^2/m^3 |
| Glazed Ceramic Saddles | 0.061 N/m (Hydrophilic) | 0.6380 (63.8% Wetted) | 130.8 m^2/m^3 |
| 316 Stainless Steel Rings | 0.075 N/m (High Energy) | 0.6957 (69.6% Wetted) | 142.6 m^2/m^3 (+47% more area!) |
Onda (1968) Fractional Wetted Packing Surface Area a_w / a_t (0 to 1)
Evaluates 1 - EXP(-1.45 * ((sigma_c / sigma)^0.75) * (Re_L^0.1) * (Fr_L^-0.05) * (We_L^0.2)) across dry packing area a_t (B2 m^2/m^3), liquid mass flux L_m (B3 kg/(m^2·s)), liquid density rho_L (B4 kg/m^3), dynamic viscosity mu_L (B5 Pa·s), liquid surface tension sigma (B6 N/m), and packing critical surface tension sigma_c (B7 N/m).
=IF(OR(B2 <= 0, B3 <= 0, B4 <= 0, B5 <= 0, B6 <= 0, B7 <= 0), "Invalid Onda Packing or Liquid Property Inputs", ROUND(1 - EXP(-1.45 * ((B7 / B6) ^ 0.75) * ((B3 / (B2 * B5)) ^ 0.1) * ((((B3 ^ 2) * B2) / ((B4 ^ 2) * 9.80665)) ^ -0.05) * (((B3 ^ 2) / (B4 * B6 * B2)) ^ 0.2)), 4))Effective Interfacial Mass-Transfer Area a_w (m^2 / m^3)
Multiplies dry geometric packing area a_t (B2) by unrounded Onda wetted fraction to output active interfacial area a_w (m^2/m^3) for k_L*a_w and HTU calculations.
=IF(OR(B2 <= 0, B3 <= 0, B4 <= 0, B5 <= 0, B6 <= 0, B7 <= 0), "Invalid Onda Packing or Liquid Property Inputs", ROUND(B2 * (1 - EXP(-1.45 * ((B7 / B6) ^ 0.75) * ((B3 / (B2 * B5)) ^ 0.1) * ((((B3 ^ 2) * B2) / ((B4 ^ 2) * 9.80665)) ^ -0.05) * (((B3 ^ 2) / (B4 * B6 * B2)) ^ 0.2))), 2))Try the example
Use the original values or change them to test your understanding.