Estimations of Large Bubble Length, Liquid Slug Length, Slug Unit Length and Slug Period of Gas-Liquid Two-Phase Slug Flow in Vertical Pipes

Abstract

Fundamental forms of correlations are proposed for large bubble lengths, liquid slug lengths and slug unit lengths, and slug periods of gas-liquid two-phase slug flow in vertical pipes. The empirical correlations for each length are derived using 337 experimental data obtained from water-air, water solution containing NaOH, K₃Fe(CN)₆ and K₄Fe(CN)₆- air and water-carbon dioxide two-phase slug flows in pipes of their diameter 8-50.8mm, and volumetric fluxes J_G=0.0256−3.42m/s, J_L=0.0390−1.50m/s, J_T=0.0847−4.40 m/s. They are shown below. For large bubble length L_LB: L_LB=0.121D(J_G/J_T)^1.70(J_L/J_T)^-0.408(J_T/(gD)^0.5)^0.582(ρ_LDJ_T/μ_L)^0.149(ρ_LDJ_T²/σ)^-0.207(μ_G/μ_L)^0.291(ρ_G/ρ_L)^-0.831+0.00186. For liquid slug length L_LS: L_LS=534000D(J_G/J_T)^0.415(J_L/J_T)^0.143(J_T/(gD)^0.5)^0.143(ρ_LDJ_T/μ_L)^0.0983(ρ_LDJ_T²/σ)^-0.119(μ_G/μ_L)^1.34(ρ_G/ρ_L)^0.753−0.124. For slug unit length L_SU: L_SU=19700D(J_G/J_T)^0.305(J_L/J_T)^-0.340(J_T/(gD)^0.5)^0.393(ρ_LDJ_T/μ_L)^0.0275(ρ_LDJ_T²/σ)^-0.154(μ_G/μ_L)^0.944(ρ_G/ρ_L)^0.346−0.291. The similar method is applied to derive the correlation for the slug period. The following correlation is obtained using 205 experimental data. T_B=16100(D/J_T)(J_G/J_T)^1.38(J_L/J_T)^-0.166(J_T(gD)^0.5)^-0.317(ρ_LDJ_T/μ_L)^1.61(ρ_LDJ_T²/σ)^-0.564(μ_G/μ_L)^0.333(ρ_G/ρ_L)^3.04+0.0870. These empirical correlations are applicable for gas-liquid two-phase slug flow under nearly room temperature and at atmospheric pressure.