Difference between revisions of "Hagedorn and Brown correlation"

Revision as of 16:28, 20 March 2017

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 : $H_L$ .

Following the law of conservation of energy 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)

Colebrook–White equation for the Darcy's friction factor:

\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_L^{H_L} \mu_g^{(1-H_L)}}

M =SG_o\ 350.52\ \frac{1}{1+WOR}+SG_w\ 350.52\ \frac{WOR}{1+WOR}+SG_g\ 0.0764\ GLR

\bar \rho_L= \frac{62.4\ SG_o + \frac{Rs\ 0.0764\ SG_g}{5.614}}{B_o} \frac{1}{1+WOR} + 62.4\ SG_w\ \frac{WOR}{1 + WOR}

\bar \rho_g = \frac{28.967\ SG_g\ p}{z\ 10.732\ T}

\mu_L = \mu_o \frac{1}{1 + WOR} + \mu_w \frac{WOR}{1 + WOR}

\sigma = \sigma_o \frac{1}{1 + WOR} + \sigma_w \frac{WOR}{1 + WOR}

N_L = 0.15726\ \mu_L \sqrt[4]{\frac{1}{\rho_L \sigma_L^3}}

CN_L = 0.061\ N_L^3 - 0.0929\ N_L^2 + 0.0505\ N_L + 0.0019

v_{SL}

v_{SG}

Failed to parse (syntax error): N_{LV} = 1.938 v_{SL} \sqrt[4]{\frac{\rho_L}{\sigma}

Failed to parse (syntax error): N_{GV} = 1.938 v_{SG} \sqrt[4]{\frac{\rho_L}{\sigma}

N_D

corr p1

\frac{H_L}{\psi}

corr p2

\psi

@@ Line 29: / Line 29: @@
 :<math> \mu_L = \mu_o \frac{1}{1 + WOR} + \mu_w \frac{WOR}{1 + WOR}</math>
-:<math> \sigma_L = \sigma_o \frac{1}{1 + WOR} + \sigma_w \frac{WOR}{1 + WOR}</math>
+:<math> \sigma = \sigma_o \frac{1}{1 + WOR} + \sigma_w \frac{WOR}{1 + WOR}</math>
 :<math> N_L = 0.15726\ \mu_L \sqrt[4]{\frac{1}{\rho_L \sigma_L^3}}</math>
@@ Line 39: / Line 39: @@
 :<math> v_{SG} </math>
-:<math> N_{LV} </math>
+:<math> N_{LV} = 1.938 v_{SL} \sqrt[4]{\frac{\rho_L}{\sigma} </math>
-:<math> N_{GV} </math>
+:<math> N_{GV} = 1.938 v_{SG} \sqrt[4]{\frac{\rho_L}{\sigma} </math>
 :<math> N_D </math>