A new model for predicting the critical liquid-carrying velocity in inclined gas wells

WANG Wujie,CUI Guomin,WEI Yaoqi,PAN Jie

Table 3 Correction factors of interfacial friction factors under the different experimental conditions.

Experiment Inner diameter/ mm Data type Experimental media f(α) Pearson correlation coefficient R2 Average relative error/% Birvalski et al.[16] 50.8 Critical liquid- carrying velocity Critical pressure gradient Critical liquid holdup Air/water $f\left( \alpha \right)=0.028\ 7\alpha +0.718\ 79$ 0.733 0.074 3.37 Air/glycerol-water solution (glycerol mass fraction of 60%) $f\left( \alpha \right)\text{=}0.091\ 2\alpha \text{+}0.527\ 88$ 0.927 0.720 3.05 current study 40.0 Critical liquid- carrying velocity Critical pressure gradient Air/water $f\left( \alpha \right)=0.162\ 9\alpha +0.246\ 8$ 0.999 0.998 2.37 Air/glycerol-water solution (both mass fraction of 50%) $f\left( \alpha \right)=0.086\ 5\alpha +0.432\ 67$ 0.995 0.989 4.01 60.0 Critical liquid- carrying velocity Critical pressure gradient Air/water $f\left( \alpha \right)=0.164\ 4\alpha +0.765\ 67$ 0.992 0.969 2.46 Air/glycerol-water solution (both mass fraction of 50%) $f\left( \alpha \right)=0.175\ 9\alpha +0.574$ 0.956 0.829 3.14