Gas well deliverability: backpressure equation (Rawlins–Schellhardt)
Coefficients C and n of the gas deliverability equation q = C · (P̄² − P_wf²)ⁿ from two stabilized rates, and the absolute open flow, the rate at atmospheric bottomhole pressure.
q = C · (P̄² − P_wf²)ⁿn = log₁₀(q₂ / q₁) / log₁₀((P̄² − P_wf2²) / (P̄² − P_wf1²))AOF = C · (P̄² − P_a²)ⁿ, P_a = 0.101325 MPaAbsolute pressures, stabilized (or isochronal) rates. n = 1 is laminar flow, n → 0.5 strong non-Darcy flow; n outside 0.5–1 points to unstabilized rates or bad gauges. The AOF is an extrapolation far beyond the measured points, i.e. an estimate. Russian and Kazakh practice uses the two-term equation — see the next calculator.
Source: Rawlins & Schellhardt, Backpressure Data on Natural Gas Wells and Their Application to Production Practices, U.S. Bureau of Mines Monograph 7 (1935)
Inputs
You can change a field's unit: the value is converted to the formula's units automatically.
Absolute, after full build-up; enter a gauge value in MPa(g).
The two rates should differ markedly.
Unit converter for this formulaPressure · Gas rate
- MPa1
- kPa1,000
- bar10
- atm9.86923
- kgf/cm²10.1972
- mmHg7,500.62
- MPa(g)0.898675
- barg8.98675
- psi145.038
- psia145.038
- psig130.342
- ksi0.145038
psi and psia are absolute pressure; gauge units (barg, MPa(g), psig) are above atmospheric (101.325 kPa = 14.696 psi). Pressure differences in the formulas do not depend on this.
- n — Backpressure exponent–
- C — Coefficient C–10³ m³/(d·MPa²ⁿ)
More in Gas wells
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.