Hagedorn and Brown correlation

Info

Hagedorn and Brown is an empirical two-phase flow correlation published in 1965.

It doesn't distinguish between the flow regimes.

The heart of the Hagedorn and Brown method is a correlation for the liquid holdup :$H_L$.

Math & Physics

The basic steady state flow equation is:

$144 \frac{\Delta p}{\Delta h} = \bar \rho_m + \frac{f q_L^2 M^2}{2.9652 \times 10^{11} D^5 \bar \rho_m} + \bar \rho_m \frac{\Delta{(\frac{v_m^2}{2g_c}})}{\Delta h}$

where

$\bar \rho_m = \bar \rho_L H_L + \bar \rho_g (1 - H_L)$

friction factor the Colebrook–White equation:

$\frac{1}{\sqrt{f}}= -2 \log \left( \frac { \varepsilon} {3.7 D} + \frac {2.51} {\mathrm{Re} \sqrt{f}} \right)$

Reynolds two phase number:

$Re = 2.2 \times 10^-2 \frac {q_L M}{D \mu^H_L \mu^{(1-H_L)}}$

Workflow

For each pipe segment find: