Gray correlation
Contents
Brief
Gray is an empirical two-phase flow correlation published in 1974 ^{[1]}.
Gray is the default VLP correlation for the gas wells in the PQplot.
Math & Physics
Following the law of conservation of energy the basic steady state flow equation is:
where
- , slip mixture density ^{[1]}.
- , no-slip mixture density ^{[1]}.
Colebrook–White ^{[2]} equation for the Darcy's friction factor:
- ^{[3]}
The pseudo wall roughness:
- , with the limit ^{[1]}
Reynolds two phase number:
- ^{[4]}
Discussion
Why Gray correlation?
The Gray correlation was found to be the best of several initially tested ...— Nitesh Kumar l^{[5]}
Workflow H_{g} & C_{L}
- ^{[4]}
- ^{[6]}
- ^{[6]}
- ^{[6]}
- ^{[1]}
- ^{[1]}
- ^{[1]}
- ^{[1]}
- ^{[1]}
- ^{[1]}
- ^{[1]}
Modifications
1. Use Fanning correlation for the dry gas (WGR=0 and OGR=0 case).
2. Use watercut instead of WOR to account for the OGR=0 case.
3. If the relative roughness: use 0.05 in the Moody Diagram ^{[3]}.
4. If H_{L} can't be calculated then H_{L} = C_{L}.
Nomenclature
- = correlation group, dimensionless
- = flow area, ft2
- = correlation group, dimensionless
- = formation factor, bbl/stb
- = no-slip holdup factor, dimensionless
- = pipe diameter, ft
- = depth, ft
- = 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, lb_{m}/bbl
- = pipe diameter number, dimensionless
- = velocity number, dimensionless
- = pressure, psia
- = conversion constant equal to 32.174049, lb_{m}ft / lb_{f}sec^{2}
- = production rate, bbl/d
- = superficial liquid to gas ratio, dimensionless
- = Reynolds number, dimensionless
- = 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
- = pseudo wall roughness, ft
- = viscosity, cp
- = density, lb_{m}/ft^{3}
- = slip density, lb_{m}/ft^{2}
- = surface tension of liquid-air interface, dynes/cm
Subscripts
g = gas
K = °K
L = liquid
m = gas/liquid mixture
o = oil
R = °R
SL = superficial liquid
SG = superficial gas
w = water
References
- ↑ ^{1.00} ^{1.01} ^{1.02} ^{1.03} ^{1.04} ^{1.05} ^{1.06} ^{1.07} ^{1.08} ^{1.09} ^{1.10} 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.
- ↑ ^{3.0} ^{3.1} Moody, L. F. (1944). "Friction factors for pipe flow". Transactions of the ASME. 66 (8): 671–684.
- ↑ ^{4.0} ^{4.1} 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.
- ↑ Kumar, N.; Lea, J. F. (January 1, 2005). "Improvements for Flow Correlations for Gas Wells Experiencing Liquid Loading" (SPE-92049-MS).
- ↑ ^{6.0} ^{6.1} ^{6.2} Lyons, W.C. (1996). Standard handbook of petroleum and natural gas engineering. 2. Houston, TX: Gulf Professional Publishing. ISBN 0-88415-643-5.