Critical gas rate to unload liquids (Turner)
The critical gas velocity that lifts water or condensate droplets out of the well, and the matching minimum gas rate for a given tubing size — after Turner (with the +20 % adjustment) or Coleman (without it). Below this rate liquid accumulates at the bottom and loads the well up.
v_c = k · [σ · g · (ρ_l − ρ_g)]^(1/4) / √ρ_g; k = (40 / 0.44)^(1/4) = 3.09 (Coleman), × 1.2 (Turner)ρ_g = M_air · γ_g · P / (Z · R · T)q_c = (π · d² / 4) · v_c · (P / P_st) · (T_st / T) / ZTurner's model: the gas holds up the largest stable droplet (critical Weber number 30, drag coefficient 0.44). Turner raised the velocity by 20 % to match field data; Coleman showed that wells with wellhead pressures below about 500 psi need no adjustment. If the well makes water, use water. If the actual rate is below q_c, liquid builds up at the bottom.
Source: 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, JPT, 1969; Coleman S.B. et al., A New Look at Predicting Gas-Well Load-Up, JPT, 1991
Inputs
You can change a field's unit: the value is converted to the formula's units automatically.
2-3/8 in — 50.3 mm; 2-7/8 in — 62.0 mm; 3-1/2 in — 76.0 mm; 4-1/2 in — 100.3 mm.
Usually the flowing wellhead pressure (as Turner did); with a large pressure change along the tubing check its shoe too.
Dry gas 0.56–0.65, rich gas up to 0.8 and above.
Turner used 60 mN/m for water and 20 mN/m for condensate.
Unit converter for this formulaLength · Pressure · Temperature · Density and °API · Gas rate · Velocity
- m1
- cm100
- mm1,000
- km0.001
- ft3.28084
- in39.3701
- 1/32 in1,259.84
- 1/64 in2,519.69
- mile0.000621371
- v_c — Critical gas velocity–
- ρ_g — Gas density at P and T–
More in Gas and chokes
Gas volume at 20 °C and 101.325 kPa (GOST 2939) from the volume at operating pressure and temperature, with the deviation factor; the gas formation volume factor. The same works for a flow rate: actual m³/h give standard m³/h.
Liquid rate of a flowing well at critical two-phase flow through the choke, from the tubing head pressure, the gas-liquid ratio and the choke size: the Gilbert, Ros, Baxendell and Achong correlations.
The choke size that gives a target liquid rate of a flowing well at a known tubing head pressure and gas-liquid ratio (critical flow).
Results are engineering estimates from standard formulas; for design decisions check them against the codes, project documents and specialists' calculations. The formulas carried over from the original set are unchanged, and their errors are described in the notes.