Griffith correlation

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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). "Two-Phase Slug Flow"Paid subscription required. Journal of Heat Transfer. ASME. 83: 307–320. 
  2. 2.0 2.1 2.2 2.3 Orkiszewski, J. (June 1967). "Predicting Two-Phase Pressure Drops in Vertical Pipe"Paid subscription required. 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.