Difference between revisions of "Hagedorn and Brown correlation"

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Why [[Hagedorn and Brown]]?
 
Why [[Hagedorn and Brown]]?
  
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''One of the consistently best correlations was found to be the empirical Hagedorn and Brown correlation.'' <ref = Economides/>
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''One of the consistently best correlations was found to be the empirical Hagedorn and Brown correlation.'' <ref = Economides\>
  
 
== Flow Diagram ==
 
== Flow Diagram ==

Revision as of 12:04, 24 March 2017

Brief

Hagedorn and Brown is an empirical two-phase flow correlation published in 1965 [1].

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[2].

Math & Physics

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}[1]

where

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

Colebrook–White [3] 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)[4]

Reynolds two phase number:

Re = 2.2 \times 10^{-2} \frac {q_L M}{D \mu_L^{H_L} \mu_g^{(1-H_L)}}[1]

Discussion

Why Hagedorn and Brown?

One of the consistently best correlations was found to be the empirical Hagedorn and Brown correlation. Cite error: Closing </ref> missing for <ref> tag

[2]

[3]

[4]

[5]

[6]

</references>
  1. ↑ 1.0 1.1 1.2 1.3 Cite error: Invalid <ref> tag; no text was provided for refs named HB
  2. ↑ 2.0 2.1 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. 
  3. ↑ 3.0 3.1 Colebrook, C. F. (1938–1939). "Turbulent Flow in Pipes, With Particular Reference to the Transition Region Between the Smooth and Rough Pipe Laws"Paid subscription required. Journal of the Institution of Civil Engineers. London, England. 11: 133–156. 
  4. ↑ 4.0 4.1 Moody, L. F. (1944). "Friction factors for pipe flow"Paid subscription required. Transactions of the ASME. 66 (8): 671–684. 
  5. ↑ Lyons, W.C. (1996). Standard handbook of petroleum and natural gas engineering. 2. Houston, TX: Gulf Professional Publishing. ISBN 0-88415-643-5. 
  6. ↑ Trina, S. (2010). An integrated horizontal and vertical flow simulation with application to wax precipitation (Master of Engineering Thesis). Canada: Memorial University of Newfoundland. 
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