# Griffith correlation

## Brief

The Griffith correlation [1] is an empirical correlation which defines:

• The boundary between the bubble and slug flow[2]
• The void fraction of gas in bubble flow - gas hold up Hg[2]

## Math & Physics

The bubble flow exist when:

$\frac{v_g}{v_g + v_L} < L_B$[3]
$L_B = 1.071 - 0.2218 \frac{(v_g+v_L)^2}{D}$, with the limit $L_B \geqslant 0.13$[2]

The gas holdup:

$H_g = \frac{1}{2}\ \left ( 1 + \frac{v_g+v_L}{v_s} - \sqrt{ \left ( 1 + \frac{v_g+v_L}{v_s} \right )^2 - 4 \frac{v_g}{v_s}} \right )$[2]

## Discussion

Griffith correlation adds a hook to the originally straight Hagedorn and Brown VLP curve.

## Nomenclature

$D$ = pipe diameter, ft
$H_g$ = gas holdup factor, dimensionless
$L_B$ = bubble-slug boundary, dimensionless
$v_g$ = gas velocity, ft/sec
$v_L$ = liquid velocity, ft/sec
$v_s$ = 0.8, slip velocity (difference between average gas and liquid velocities), ft/sec

## References

1. Griffith, P.; Wallis, G. B. (August 1961). . Journal of Heat Transfer. ASME. 83: 307–320.
2. Orkiszewski, J. (June 1967). . Journal of Petroleum Technology. SPE. 19 (SPE-1546-PA).
3. Economides, M.J.; Hill, A.D.; Economides, C.E.; Zhu, D. (2013). Petroleum Production Systems (2 ed.). Westford, Massachusetts: Prentice Hall. ISBN 978-0-13-703158-0.