Gas well deliverability: two-term (Forchheimer) equation
The flow coefficients a and b of the two-term equation P̄² − P_wf² = a · q + b · q² from two stabilized rates, and the absolute open flow — the standard way of interpreting gas well tests in Russian and Kazakh practice.
Δ = P̄² − P_wf² = a · q + b · q²b = (Δ₂ / q₂ − Δ₁ / q₁) / (q₂ − q₁), a = Δ₁ / q₁ − b · q₁AOF = (√(a² + 4 · b · (P̄² − P_a²)) − a) / (2 · b), P_a = 0.101325 MPaAbsolute pressures, stabilized rates. Two rates fix a and b exactly, but 4–5 rates on a plot of Δ/q against q (a straight line with intercept a and slope b) are more reliable. b ≤ 0 or a < 0 means the rates were not stabilized or the gauges are wrong. Rates are in 10³ Sm³/d at 20 °C.
Source: Houpeurt (1959); Instructions for the comprehensive testing of gas and gas-condensate reservoirs and wells, ed. G. A. Zotov and Z. S. Aliev (1980)
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.
- a — Coefficient a (Darcy flow)–MPa²·d/10³ m³
- b — Coefficient b (non-Darcy flow)–MPa²·(d/10³ m³)²
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.