Well circulation: cycle time and flow velocity
Full circulation time through the tubing, the time for fluid to rise from the tubing shoe to surface in direct and reverse circulation, and the upward velocities in the annulus and in the tubing.
V_t = π/4 · d_i² · L; V_a = π/4 · (D² − d_o²) · Lt_c = (V_t + V_a) / Qt_dir = V_a / Q; t_rev = V_t / Qv_a = Q / (π/4 · (D² − d_o²)); v_t = Q / (π/4 · d_i²)In reverse circulation the fluid rises in the tubing several times faster than in the annulus in direct circulation — that is why sand fill and debris are washed out by reverse circulation. To lift particles, the upward velocity must exceed their settling velocity. Surface lines and the hole below the tubing shoe are not included.
Source: Volume balance and the continuity equation
Inputs
You can change a field's unit: the value is converted to the formula's units automatically.
Rate of the pump unit in the selected gear.
Unit converter for this formulaLength · Liquid rate · Time · Velocity
- m1
- cm100
- mm1,000
- km0.001
- ft3.28084
- in39.3701
- 1/32 in1,259.84
- 1/64 in2,519.69
- mile0.000621371
- t_dir — Direct circulation: tubing shoe to surface–
- t_rev — Reverse circulation: tubing shoe to surface–
- v_a — Upward velocity in the annulus (direct)–
- v_t — Upward velocity in the tubing (reverse)–
More in Volumes and circulation
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.