Pressure Loss Correlations

21/1/2014

Pressure Loss Correlations incorporates the Flanigan correction of the Flow Efficiency for multiphase flow and a calculation of hydrostatic pressure difference to account for uphill flow. There is no hydrostatic pressure recovery for downhill flow. In this software, the Flanigan correlation is also applied to the Panhandle and Modified Panhandle correlations. It is recommended that this correlation not be used beyond +/- 10 degrees from the horizontal.

Each of these correlations was developed for it’s own unique set of experimental conditions, and accordingly, results will vary between them.

Single Phase Gas In the case of single-phase gas, the available correlations are the Panhandle, Modified Panhandle, Weymouth and Fanning Gas. These correlations were developed for horizontal pipes, but have been adapted to vertical and inclined flow by including the hydrostatic pressure component. In vertical flow situations, the Fanning Gas is equivalent to a multi-step Cullender and Smith calculation.

Single Phase Liquid In the case of single-phase liquid, the available correlation is the Fanning Liquid. It has been implemented to apply to horizontal, inclined and vertical wells. For multiphase flow in essentially horizontal pipes, the available correlations are Beggs and Brill, Gray, Hagedorn and Brown, Flanigan, Modified-Flanigan and Weymouth (Multiphase). All of these correlations are accessible on the Pipe page and the Comparison page.

Multiphase Flow For multiphase flow in essentially vertical wells, the available correlations are Beggs and Brill, Gray, and Hagedorn and Brown. If used for single-phase flow, these three correlations devolve to the Fanning Gas or Fanning Liquid correlation. When switching from multiphase flow to single-phase flow, the correlation will default to the Fanning. When switching from singlephase flow to multiphase flow, the correlation will default to the Beggs and Brill. Important Notes The Flanigan, Modified-Flanigan and Weymouth (Multiphase) correlations can give erroneous results if the pipe described deviates substantially (more than 10 degrees) from the horizontal. The Gray and Hagedorn and Brown correlations were derived for vertical wells and may not apply to horizontal pipes. In our software, the Gray, the Hagedorn and Brown and the Beggs and Brill correlations revert to the appropriate single-phase Fanning correlation (Fanning Liquid or Fanning Gas. The Flanigan, Modified-Flanigan and Weymouth (Multiphase) revert to the Panhandle, Modified Panhandle and Weymouth respectively. However, they may not be used for single-phase liquid flow.

Single Phase & Multiphase Correlations Multiphase Gas Correlations

Vertical

Liquid Horizontal

Vertical

Horizontal

Fanning-Gas *

Fanning-Liquid Panhandle Modified Panhandle Weymouth Beggs & Brill Gray

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Hagedorn & Brown *

Flanigan

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Modified-Flanigan

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Weymouth (Multiphase) Mechanistic Model

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http://www.fekete.com/SAN/WebHelp/virtuwell/webhelp/c-te-pressdrop.htm

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Pressure Loss Correlations

5.

, where: D (ft),

(lb/ft3),

G

(lb/ft3),

L

(dyn/cm)

6.

, where:

L

(lb/ft3),

G

(lb/ft3),

(dyn/cm)

Nomenclature A = cross sectional area C0 = velocity distribution coefficient D = pipe internal diameter E = in situ volume fraction FE = liquid fraction entrained g = acceleration due to gravity hL = height of liquid (stratified flow) L = length P = pressure Re = Reynolds number S = contact perimeter VSG = superficial gas velocity VSL = superficial liquid velocity = liquid film thickness = pipe roughness = pressure gradient weighting factor (intermittent flow) = Angle of inclination = viscosity = density = interfacial (surface) tension = shear stress = dimensionless quantity

Subscripts b = relating to the gas bubble c = relating to the gas core F = relating to the liquid film db = relating to dispersed bubbles G = relating to gas phase i = relating to interface L = relating to liquid phase m = relating to mixture SG = based on superficial gas velocity s = relating to liquid slug SL = based on superficial liquid velocity wL = relating to wall-liquid interface wG = relating to wall-gas interface C0 = velocity distribution coefficient

References Petalas, N., Aziz, K.: "A Mechanistic Model for Multiphase Flow in Pipes," J. Pet. Tech. (June 2000), 43-55. Petalas, N., Aziz, K.: "Development and Testing of a New Mechanistic Model for Multiphase Flow in Pipes," ASME 1996 Fluids Engineering Division Conference (1996), FED-Vol 236, 153-159. Gomez, L.E. et al.: "Unified Mechanistic Model for Steady-State Two-Phase Flow," Petalas, N., Aziz, K.: "A Mechanistic Model for Multiphase Flow in Pipes," SPE Journal (September 2000), 339-350.

Beggs And Brill Correlation For multiphase flow, many of the published correlations are applicable for "vertical flow" only, while others apply for "horizontal flow" only. Not many correlations apply to the whole spectrum of flow situations that may be encountered in oil and gas operations, namely uphill, downhill, horizontal, inclined and vertical flow. The Beggs and Brill (1973) correlation, is one of the few published correlations capable of handling all these flow directions. It was developed using 1" and 1-1/2" sections of pipe that could be inclined at any angle from the horizontal. The Beggs and Brill multiphase correlation deals with both the friction pressure loss and the hydrostatic pressure difference. First the appropriate flow regime for the particular combination of gas and liquid rates (Segregated, Intermittent or Distributed) is determined. The liquid holdup, and hence, the in-situ density of the gas-liquid mixture is then calculated according to the appropriate flow regime, to obtain the hydrostatic pressure difference. A two-phase friction factor is calculated based on the "input" gas-liquid ratio and the http://www.fekete.com/SAN/WebHelp/virtuwell/webhelp/c-te-pressdrop.htm

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