Chemical, Process & Catalysis Engineering
Beggs-Brill Two-Phase Flow Formula: Mixture Froude Number & Horizontal Liquid Holdup H_L(0)
Determine horizontal gas-liquid pipeline Mixture Froude Number N_Fr = v_m^2 / (g * D), Input No-Slip Liquid Fraction lambda_L, and Segregated/Intermittent/Distributed Liquid Holdup H_L(0) via H. Dale Beggs and James P. Brill (1973).
Predict pipeline liquid inventory from superficial gas & liquid velocities!
Published by H. Dale Beggs and James P. Brill (1973, Journal of Petroleum Technology), the Beggs-Brill multiphase pipeline model begins with Superficial Liquid Velocity v_sL = Q_L / A, Superficial Gas Velocity v_sG = Q_G / A, Mixture Velocity v_m = v_sL + v_sG (m/s), No-Slip Input Liquid Volume Fraction lambda_L = v_sL / v_m, and Mixture Froude Number N_Fr = (v_m^2) / (9.80665 * D_m)!
Across horizontal pipe flow regimes, Beggs & Brill’s horizontal holdup power law takes the universal form H_L(0) = (a * (lambda_L^b)) / (N_Fr^c) (subject to physical constraint H_L(0) >= lambda_L): Segregated Flow uses (a = 0.980, b = 0.4846, c = 0.0868), Intermittent (Plug/Slug) Flow uses (a = 0.845, b = 0.5351, c = 0.0173), and Distributed (Bubble/Mist) Flow uses (a = 1.065, b = 0.5824, c = 0.0609)!
| Beggs-Brill Horizontal Flow Regime | Power-Law Constants (a, b, c) | Evaluated H_L(0) at lambda_L = 0.25, N_Fr = 12.0 |
|---|---|---|
| Segregated (Stratified / Wavy / Annular) | a = 0.980, b = 0.4846, c = 0.0868 | H_L(0) = 0.4032 |
| Intermittent (Plug / Elongated Slug) | a = 0.845, b = 0.5351, c = 0.0173 | H_L(0) = 0.3855 |
| Distributed (Dispersed Bubble / Mist) | a = 1.065, b = 0.5824, c = 0.0609 | H_L(0) = 0.4080 |
Beggs-Brill Mixture Froude Number N_Fr = (v_sL + v_sG)^2 / (g * D)
Evaluates ((v_sL + v_sG)^2) / (9.80665 * D) from superficial liquid velocity B2 (m/s), superficial gas velocity B3 (m/s), and inner pipe diameter B4 (m).
=IF(OR(B2 <= 0, B3 <= 0, B4 <= 0), "Requires Positive v_sL, v_sG, and Pipe Diameter D", ROUND(((B2 + B3) ^ 2) / (9.80665 * B4), 4))Beggs-Brill Intermittent-Slug Horizontal Liquid Holdup H_L(0)
Computes MAX(lambda_L, 0.845 * (lambda_L^0.5351) / (N_Fr^0.0173)) enforcing Beggs & Brill’s physical no-slip floor H_L(0) >= lambda_L.
=IF(OR(B2 <= 0, B3 <= 0, B4 <= 0), "Requires Positive v_sL, v_sG, and Pipe Diameter D", ROUND(MAX(B2 / (B2 + B3), (0.845 * ((B2 / (B2 + B3)) ^ 0.5351)) / ((((B2 + B3) ^ 2) / (9.80665 * B4)) ^ 0.0173)), 4))Try the example
Use the original values or change them to test your understanding.