Hagedorn and Brown correlation
Contents
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 HL [2].
Hagedorn and Brown is a default correlation for oil well in the.
Math & Physics
Following the law of conservation of energy the basic steady state flow equation is:
where
Colebrook–White [3] equation for the Darcy's friction factor:
Reynolds two phase number:
Discussion
Why Hagedorn and Brown?
One of the consistently best correlations ...— Michael Economides et al[2]
Flow Diagram
Workflow HL
Modifications
1. Use the no-slip holdup when the original empirical correlation predicts a liquid holdup HL less than the no-slip holdup [2].
2. Use the Griffith correlation to define the bubble flow regime[2] and calculate HL.
3. Use watercut instead of WOR to account for the watercut = 100%.
Nomenclature
- = correlation group, dimensionless
- = formation factor, bbl/stb
- = coefficient for liquid viscosity number, dimensionless
- = pipe diameter, ft
- = depth, ft
- = correlation group, dimensionless
- = liquid holdup factor, dimensionless
- = friction factor, dimensionless
- = gas-liquid ratio, scf/bbl
- = total mass of oil, water and gas associated with 1 bbl of liquid flowing into and out of the flow string, lbm/bbl
- = pipe diameter number number, dimensionless
- = gas velocity number, dimensionless
- = liquid viscosity number, dimensionless
- = liquid velocity number, dimensionless
- = pressure, psia
- = conversion constant equal to 32.174, lbmft / lbfsec2
- = total liquid production rate, bbl/d
- = Reynolds number, dimensionless
- = solution gas-oil ratio, scf/stb
- = specific gravity, dimensionless
- = temperature, °R or °K, follow the subscript
- = velocity, ft/sec
- = water-oil ratio, bbl/bbl
- = gas compressibility factor, dimensionless
Greek symbols
- = absolute roughness, ft
- = oil viscosity, cp
- = density, lbm/ft3
- = integrated average density at flowing conditions, lbm/ft2
- = surface tension of liquid-air interface, dynes/cm (ref. values: 72 - water, 35 - oil)
- = secondary correlation factor, dimensionless
Subscripts
g = gas
K = °K
L = liquid
m = gas/liquid mixture
o = oil
R = °R
SL = superficial liquid
SG = superficial gas
w = water
References
- ↑ 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 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.
- ↑ 2.0 2.1 2.2 2.3 2.4 2.5 2.6 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.
- ↑ 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.
- ↑ 5.0 5.1 5.2 5.3 5.4 5.5 Lyons, W.C. (1996). Standard handbook of petroleum and natural gas engineering. 2. Houston, TX: Gulf Professional Publishing. ISBN 0-88415-643-5.
- ↑ 6.0 6.1 Trina, S. (2010). An integrated horizontal and vertical flow simulation with application to wax precipitation (Master of Engineering Thesis). Canada: Memorial University of Newfoundland.