Wellbore storage coefficient and its duration
Wellbore storage coefficient from a moving liquid level and from fluid compression in a closed wellbore, and the time after which the build-up or drawdown reaches the semilog straight line of radial flow.
C = V_u / (ρ · g) + V_w · c_wt_wbs = (60 + 3.5 · s) · C · μ / (2π · k · h)With a free liquid level (build-ups of pumping wells) fluid compression is negligible: storage is tens to hundreds of times stronger than in a closed flowing well and lasts for days. t_wbs is the start of radial flow, about 1.5 log cycles after the unit slope; in field units (C in bbl/psi, μ in cP, k in mD, h in ft) t ≈ (200 000 + 12 000 · s) · C · μ / (k · h) h. A downhole shut-in cuts C sharply.
Source: Earlougher, SPE Monograph 5 (1977), ch. 2: t_D = (60 + 3.5 · s) · C_D; Lee, Well Testing (1982): C = 25.65 · A / ρ
Inputs
You can change a field's unit: the value is converted to the formula's units automatically.
The annulus of a pumping well or the tubing; 0 if the wellbore is full and shut at surface. 5½″ casing with 2⅞″ tubing: about 0.009 m³/m.
For fluid compression with the well shut at surface; with a downhole shut-in only the volume below the valve.
Oil (1–2)·10⁻³, water about 4.5·10⁻⁴ MPa⁻¹; gas about 1/p.
Unit converter for this formulaVolume per length (capacity) · Density and °API · Liquid volume · Compressibility · Permeability · Length · Viscosity · Wellbore storage · Time
- L/m1
- m³/m0.001
- bbl/ft0.00191713
- gal/ft0.0805196
- ft³/ft0.0107639
- t_wbs — End of wellbore storage (start of radial flow)–
More in Test design
How far from the well the pressure transient has travelled during the test, and the hydraulic diffusivity: to choose the test duration and to judge whether the test will see the boundaries.
How many hours after a well starts at a constant rate the pressure begins to fall at the same rate throughout the drainage area: to plan drawdowns that reach the boundaries and reservoir limit tests.
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.