Chemical, Process & Catalysis Engineering
Eckert GPDC Packed-Column Flooding Formula: Flow Parameter F_LV & Tower Diameter
Size random and structured packed absorption, stripping, and distillation towers using Sherwood-Eckert Generalized Pressure Drop Correlation (GPDC) Flow Parameter F_LV = (L / G) * SQRT(rho_G / rho_L), Flooding Gas Velocity u_flood, and Column Diameter.
Prevent packed-tower liquid backup (flooding) by balancing gas kinetic head against liquid drainage!
In countercurrent packed gas scrubbers, strippers, and distillation columns, rising gas (mass flow G kg/s, density rho_G kg/m^3) shears against trickling liquid film (mass flow L kg/s, density rho_L kg/m^3, kinematic viscosity nu_L in centistokes cSt)! Pioneered by Sherwood, Shipley & Holloway (1938) and generalized across Pall rings, Raschig rings, Intalox saddles, and structured packings via Packing Factor F_p (ft^-1 or m^-1) by John S. Eckert (1970, Chemical Engineering Progress) and Kister, the Generalized Pressure Drop Correlation (GPDC) plots abscissa Flow Parameter F_LV:
F_LV = (L / G) * SQRT(rho_G / rho_L)! At incipient flooding, Kessler-ankored analytical fit of Eckert’s GPDC flooding curve gives Capacity Parameter Y_flood = EXP(-3.5021 - 1.028 * LN(F_LV) - 0.11093 * ((LN(F_LV))^2))! Solving Eckert’s ordinate Y_flood = ((u_G,flood^2) * F_p_imperial * (nu_cSt^0.1)) * (rho_G / (rho_L - rho_G)) / 32.174 (with standard F_p in ft^-1 and u_G,flood in ft/s, or metric 0.3048 * u_ft_s) yields Superficial Flooding Gas Velocity u_G,flood and Safe Design Tower Diameter D_col = SQRT((4 * Q_G) / (PI() * f_flood * u_G,flood)) at 70%–80% of flood!
| Packed Scrubber Sizing Quantity (2-in Pall Rings F_p = 24 ft^-1, L = 8 kg/s, G = 4 kg/s) | Formula | Evaluated Result |
|---|---|---|
| Sherwood-Eckert Flow Parameter F_LV (rho_G = 2.0, rho_L = 998 kg/m^3) | (L / G) * SQRT(rho_G / rho_L) | 0.0895 |
| GPDC Flooding Ordinate Y_flood | EXP(-3.5021 - 1.028*LN(F_LV) - 0.11093*LN(F_LV)^2) | 0.1895 |
| Superficial Flooding Gas Velocity u_G,flood (nu = 1.0 cSt) | 0.3048 * SQRT(32.174 * Y_flood * (rho_L - rho_G) / (F_p * rho_G * nu^0.1)) | 3.421 m/s (11.22 ft/s) |
| Design Column Inner Diameter at 75% Flood (Q_G = G/rho_G = 2.0 m^3/s) | SQRT(4 * Q_G / (PI() * 0.75 * u_flood)) | 0.995 m (~1.00 m ID) |
Sherwood-Eckert Packed-Tower Flow Parameter F_LV = (L / G) * SQRT(rho_G / rho_L)
Evaluates dimensionless liquid-to-gas kinetic ratio across liquid mass rate L (B2 kg/s), gas mass rate G (B3 kg/s), gas density rho_G (B4 kg/m^3), and liquid density rho_L > rho_G (B5 kg/m^3).
=IF(OR(B2 <= 0, B3 <= 0, B4 <= 0, B5 <= B4), "Requires Positive L, G, and 0 < rho_G < rho_L", ROUND((B2 / B3) * SQRT(B4 / B5), 4))Eckert GPDC Superficial Flooding Gas Velocity u_G,flood (m/s)
Evaluates Kessler-Eckert Y_flood from F_LV and returns metric superficial flooding gas velocity (m/s) given standard Imperial Packing Factor F_p (B6 ft^-1) and liquid kinematic viscosity nu_L (B7 cSt).
=IF(OR(B2 <= 0, B3 <= 0, B4 <= 0, B5 <= B4, B6 <= 0, B7 <= 0), "Invalid Packed-Column Flooding Inputs", ROUND(0.3048 * SQRT((32.174 * EXP(-3.5021 - 1.028 * LN((B2 / B3) * SQRT(B4 / B5)) - 0.11093 * ((LN((B2 / B3) * SQRT(B4 / B5))) ^ 2)) * (B5 - B4)) / (B6 * B4 * (B7 ^ 0.1))), 3))Try the example
Use the original values or change them to test your understanding.