Productivity index in pseudo-steady-state flow
Theoretical productivity index of a vertical well in a bounded drainage area (circle, square, rectangle) from permeability, thickness, fluid properties and skin, and the same without skin. The drainage radius comes from the area per well.
J = 2π · k · h / (μ · B · (½ · ln(4A / (γ · C_A · r_w²)) + s)), γ = 1.781C_A = 31.62: ½ · ln(4A / (γ · C_A · r_w²)) = ln(r_e / r_w) − 0.75, r_e = √(A / π)Pseudo-steady state: no flow across the drainage boundary, the pressure falls at the same rate everywhere. J refers to the average reservoir pressure: q = J · (P̄ − P_wf). Single-phase oil inflow (bottomhole pressure above the bubble point), homogeneous reservoir, the well penetrates the whole pay. For a constant pressure at the boundary, use the radial flow calculator.
Source: Dake, Fundamentals of Reservoir Engineering (1978), ch. 6; shape factors: Dietz (1965), Earlougher, SPE Monograph 5 (1977), app. C
Inputs
You can change a field's unit: the value is converted to the formula's units automatically.
Area per well: 16 ha for a 400 × 400 m pattern (about 40 acres).
From the bit: 0.108 m for 8½″ (215.9 mm), 0.078 m for 6⅛″ (155.6 mm).
Unit converter for this formulaPermeability · Length · Viscosity · Oil formation volume factor · Area · Productivity index · Fraction and percent
- mD1
- D0.001
- µm²0.000986923
- 10⁻³ µm²0.986923
1 D = 0.9869 µm². Russian-language reports often give permeability in 10⁻³ µm², which is almost mD (1 mD = 0.9869 · 10⁻³ µm²).
- J₀ — Productivity index without skin (s = 0)–
- J/J₀ — Flow efficiency–
- r_e — Drainage radius (circle of the same area)–
More in Inflow and flow in porous media
Liquid flow rate in linear flow by Darcy's law, in barrels per day.
Well flow rate for radial liquid flow by Darcy's law, in barrels per day.
Well flow rate for radial flow by Darcy's law, corrected by the oil formation volume factor, in cubic metres per day.
Steady-state productivity index of a horizontal well by Joshi's equation with permeability anisotropy, compared with a vertical well in the same drainage area.
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.