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INPUT   DATA

Title

Liquid density		lbm/ft3
Gas gravity		air = 1
Surface tension		dynes/cm
Pressure		psia
Flow area of conduit		ft2
Temperature		°F
Gas compressibility factor
Gas viscosity (optional)		cp

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OUTPUT   VARIABLES   &   GRAPHS

	Gas Velocity (ft/sec)	Gas Critical Flow Rate (MMscf/D)
♦  Turner's Equation
♦  Coleman
♦  Nossier-I (Transition flow)
♦  Nossier-II (Highly turbulent)
♦  Li's Equation

Gas Well Liquid Loading

This phenomenon occurs when liquids (interstitial water and hydrocarbon condensates) entrained in the produced gas, accumulate in the wellbore to the extent that they can severely reduce production by backpressure and by reduced gas relative permeability in the surrounding formation. The accumulating fluid may eventually balance out the available gas reservoir energy and cause the well to die.

A critical velocity exists when gas can no longer transport liquid upwards through the well tubing. The critical gas rate is defined as the minimum gas flow rate that will ensure the continuous removal of liquids from the wellbore. The most widely used equation to estimate critical rate is Turner's equation derived from the spherical liquid droplet model, assuming a constant turbulent flow regime. A slight variation of this equation was proposed by Coleman. And more recently, an enhancement of the model was proposed by Nosseir who considered the prevailing flow regimes, and by Li who, to obtain a match to to the behavior of the wells he studied, considered the shape of entrained droplets to more like convex bean than spherical.

All the methods are essentially Turner's equation with different constant terms corresponding to different flow conditions.

The relevant equations are:

Turner's Equation:
     v_gc = 1.912[σ^1/4(ρ_l - ρ_g)^1/4] /[(ρ_g)^1/2];    ...assumed C_d=0.44

Coleman's Equation:
     v_gc = 1.593[σ^1/4(ρ_l - ρ_g)^1/4] /[(ρ_g)^1/2];    ...assumed C_d=0.44

Nosseir's Equation-I (Transition flow regime):
     v_gc = 0.5092[σ^0.35(ρ_l - ρ_g)^0.21] /[(μ_g)^0.134(ρ_g)^0.426];

Nosseir's Equation-II (Highly turbulent flow regime):
     v_gc = 1.938[σ^1/4(ρ_l - ρ_g)^1/4] /[(ρ_g)^1/2];    ...assumed C_d=0.2

Li's Equation:
     v_gc = 0.724[σ^1/4(ρ_l - ρ_g)^1/4] /[(ρ_g)^1/2];    ...assumed C_d=1.0

Gas density can be related to gas gravity (Dake) by: ρ_g = 2.699*γ_g*p/[Tz]

Finally, the critical flow rate can be determined from critical velocity by the expression:
     q_c = 3.06pv_gcA/Tz

Where:

   v_gc = critical gas velocity, ft/sec.
   q_c = critical gas flow rate, MMscf/day
   ρ_l = density of liquid, lbm/ft³
   ρ_g = density of gas, lbm/ft³
   γ_g = gas gravity (air = 1)
   σ = surface tension of liquid to gas, dynes/cm
   μ_g = viscosity of gas, lbm/ft/sec
   C_d = drag coefficient (dimensionless)
   p = pressure, psia
   A = cross-sectional area of flow, ft²
   T = temperature, °R
   z = gas compressibility factor, dimensionless

BIBLIOGRAPHY

• Lea J.F. & Nickens H.V.; Solving gas-well liquid-loading problems; J Petroleum Tech, April, 2004, p. 30-36.
• Li M, Li S.L. & Sun L.T.; New view on continuous removal of liquids from gas wells; SPE J Production & Facilities, Feb. 2002, p. 42-46.
• Nosseir M.A., Darwish T.A., Sayyouh M.H. & El Sallaly M.; A new approach for accurate prediction of loading in gas wells under different flowing conditions; SPE J Production & Facilities, Nov., 2000, p. 241-246.
• Coleman S.B., Clay H.B., McCurdy D.G. & Norris III H.L.; A new look at predicting gas well load-up; J Petroleum Tech, Mar., 1991, p. 329-333.
• Turner R.G., Hubbard M.G. & Dukler A.E.; Analysis and prediction of minimum flow rate for the continuous removal of liquids from gas wells; J Petroleum Tech, Nov., 1969, p. 1475-1480.
• Dake L.P.; Fundamentals Of Reservoir Engineering; Elsevier Scientific Publ. Co., Amsterdam, Netherlands, 1978, chap. 1.