Woldesemayat and Ghajar

General Description

The correlation for two-phase flow by Woldesemayat and Ghajar (2007)¹ is based on an extensive review of void fraction/liquid hold up correlations with associated data sets. 68 correlations with a total of 2845 underlying data points were used in the study. The authors arrived at six correlations having the best accuracy, in which one of them is selected and modified to make its predictions the most accurate overall of those reviewed.

The modified correlation is

$$\begin{equation} H_L=1-\frac{v_{sg}}{v_{sg}A + B} \end{equation}$$ where $$\begin{align} &A=1+\big(\frac{v_{sL}}{v_{sg}}\big)^{\big(\frac{\rho_g}{\rho_L}\big)^{0.1}}\\ &B=2.9\bigg[\frac{g\sigma (1+\cos(\phi))(\rho_L-\rho_g)}{\rho_L^2}\bigg]^{\frac{1}{4}}\big(1.22+1.22\sin(\phi)\big)^{\frac{p_{sc}}{p}} \end{align}$$

Pressure Gradient Calculations

The authors are only reviewing liquid-hold-up correlations, and do not discuss pressure-drop calculations. Therefore, it is up to the reader to decide which properties to use for pressure-gradient calculations. The following properties are suggested here

Density in the gravity gradient \(\rho_g=\rho_s\)

Density in the friction gradient \(\rho_f=\rho_s\)

Density in the acceleration gradient \(\rho_a=\rho_s\)

Friction factor \(f_D\) is calculated with \(N_{Re}=\rho_sv_md_h/\mu_s\)

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1. Melkamu A. Woldesemayat and Afshin J. Ghajar. Comparison of void fraction correlations for different flow patterns in horizontal and upward inclined pipes. International Journal of Multiphase Flow, 33$4$:347–370, 2007. doi:10.1016/j.ijmultiphaseflow.2006.09.004. ↩