Difference between revisions of "Gray correlation"
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:<math> \sigma_L = \frac{\sigma_o\ q_o + 0.617\ \sigma_w\ q_w}{q_o + 0.617\ q_w}</math> <ref name= Gray/> | :<math> \sigma_L = \frac{\sigma_o\ q_o + 0.617\ \sigma_w\ q_w}{q_o + 0.617\ q_w}</math> <ref name= Gray/> | ||
− | :<math> N_V = 453.592\ \frac{{\rho_m}^2 {v_m}^4}{g_c \sigma_L (\rho_L - \rho_g)} </math> | + | :<math> N_V = 453.592\ \frac{{\rho_m}^2 {v_m}^4}{g_c \sigma_L (\rho_L - \rho_g)} </math><ref name= Gray/> |
− | :<math> N_D = 453.592\ \frac{g_c (\rho_L - \rho_g) D^2}{\sigma_L } </math> | + | :<math> N_D = 453.592\ \frac{g_c (\rho_L - \rho_g) D^2}{\sigma_L } </math><ref name= Gray/> |
− | :<math> R = \frac{v_{SL}}{v_{SG}} </math> | + | :<math> R = \frac{v_{SL}}{v_{SG}} </math><ref name= Gray/> |
− | :<math> B = 0.0814 \left ( 1 - 0.554\ \ln \left (1 + \frac{730 R}{R+1} \right ) \right ) </math> | + | :<math> B = 0.0814 \left ( 1 - 0.554\ \ln \left (1 + \frac{730 R}{R+1} \right ) \right ) </math><ref name= Gray/> |
− | :<math> A = -2.2314 \left ( N_V \left (1 + \frac{205}{N_D} \right ) \right )^B </math> | + | :<math> A = -2.2314 \left ( N_V \left (1 + \frac{205}{N_D} \right ) \right )^B </math><ref name= Gray/> |
− | :<math> H_g = \frac{1-e^A}{R+1}</math> | + | :<math> H_g = \frac{1-e^A}{R+1}</math><ref name= Gray/> |
:<math> C_L = \frac{v_{SL}}{v_{SG}+v_{SL}}</math> | :<math> C_L = \frac{v_{SL}}{v_{SG}+v_{SL}}</math> |
Revision as of 19:15, 4 April 2017
Brief
Math & Physics
Following the law of conservation of energy the basic steady state flow equation is:
where
- , slip mixture density
- , no-slip mixture density
Colebrook–White [2] equation for the Darcy's friction factor:
The pseudo wall roughness [1]:
- , with the limit
Reynolds two phase number:
Discussion
Workflow Hg
Nomenclature
NV velocity number
References
- ↑ 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 Gray, H. E. (1974). "Vertical Flow Correlation in Gas Wells". User manual for API 14B, Subsurface controlled safety valve sizing computer program. API.
- ↑ Colebrook, C. F. (1938–1939). "Turbulent Flow in Pipes, With Particular Reference to the Transition Region Between the Smooth and Rough Pipe Laws". Journal of the Institution of Civil Engineers. London, England. 11: 133–156.
- ↑ Moody, L. F. (1944). "Friction factors for pipe flow". Transactions of the ASME. 66 (8): 671–684.
- ↑ Hagedorn, A. R.; Brown, K. E. (1965). "Experimental study of pressure gradients occurring during continuous two-phase flow in small-diameter vertical conduits". Journal of Petroleum Technology. 17(04): 475–484.
- ↑ 5.0 5.1 Lyons, W.C. (1996). Standard handbook of petroleum and natural gas engineering. 2. Houston, TX: Gulf Professional Publishing. ISBN 0-88415-643-5.