reservoir · inflow performance
Gas Well Deliverability (Backpressure Equation)
q = C × (Pres² − Pwf²)^n
click formula to derive ↑
Inputs
psi
—
Mscf/d
psi
psi
Description
Computes gas well deliverable rate at a target flowing bottomhole pressure using the empirical backpressure (deliverability) equation, and estimates the absolute open flow (AOF) potential of the well. C and n are determined from a single test point plus reservoir pressure; n controls how turbulence affects deliverability relative to the ideal Darcy case.
Variables
| Symbol | Unit | Description |
|---|---|---|
| q | Mscf/d | Gas Rate at Pwf |
| AOF | Mscf/d | Absolute Open Flow |
| Pres | psi | Average reservoir (static) pressure. For gas deliverability, this is the static bottomhole pressure or the average reservoir pressure from a pressure buildup test. |
| n | — | Empirical exponent from a multi-rate (isochronal or flow-after-flow) well test. n = 1.0 is pure Darcy (laminar) flow; n = 0.5 is fully turbulent (non-Darcy) flow; most real wells show n = 0.6–0.9. |
| q_test | Mscf/d | Stabilized gas production rate from a backpressure test point, at which Pwf_test was measured. |
| Pwf_test | psi | Flowing bottomhole pressure measured at the test rate q_test. Used with Pres and q_test to back-calculate the deliverability coefficient C. |
| Pwf | psi | Flowing bottomhole pressure at which to evaluate the deliverable gas rate q — the design operating point. |
Assumptions
- The test rate q_test and pressure Pwf_test represent stabilized (pseudo-steady-state) conditions, not transient flow — unstabilized tests give optimistic C values
- Reservoir pressure Pres is the current average static pressure, not an initial or extrapolated value
- The n exponent is constant across all drawdown levels — in practice, n may vary slightly with rate if the turbulence regime changes significantly
Limitations
- The P² approximation loses accuracy below ~2,000 psi reservoir pressure — use the real-gas pseudo-pressure m(P) formulation for low-pressure or tight-gas wells to capture Z-factor and viscosity variation across the full pressure range
- C changes as reservoir pressure depletes — a deliverability test performed at one stage of reservoir life does not reliably predict AOF at a significantly lower Pres
- A single-point C determination (one test rate) is less accurate than a multi-rate isochronal test, which fits both n and C simultaneously with less uncertainty
Use Cases
- → Gas well AOF certification: Establish the absolute open flow potential for regulatory reserve reporting or field development planning, from a backpressure test.
- → Artificial lift or compression evaluation: Determine what gas rate a well can sustain at the minimum Pwf achievable with a given compressor suction pressure, to evaluate compression economics.
- → Nodal analysis inflow for gas wells: Provide the reservoir-inflow (IPR) curve — q vs. Pwf — for pairing with tubing performance curves in nodal analysis of gas wells, analogous to Vogel's IPR for oil.
Related Calculations
Region Notes
Permian Basin
Wolfcamp/Bone Spring gas-condensate: n typically 0.6–0.8 for hydraulically fractured wells; high-velocity near-fracture flow drives turbulence. AOF should be re-established after each major pressure depletion stage (e.g., every 500–1,000 psi of average reservoir pressure decline).
Haynesville
High-rate Haynesville shale gas wells commonly show n = 0.55–0.75 due to non-Darcy effects at the high flow velocities near hydraulic fractures; pseudo-pressure formulation is preferred given formation pressures > 8,000 psi.
Appalachian Basin
Low-permeability Marcellus wells often approach n = 1.0 (near-Darcy behavior) at the relatively low production rates achievable through tight matrix; turbulence is less of a factor than in high-rate plays.
Gulf of Mexico
Conventional GOM shelf gas wells in high-permeability sands commonly produce at rates where non-Darcy effects are significant (n = 0.65–0.80). Flow-after-flow tests are standard for initial deliverability assessment.
References
Primary source
Need geoscience support? BauerCalc is just one of the tools we build. If you're looking for independent expertise in well planning, geosteering, reservoir characterization, or opportunity evaluation, visit BauerSubsurface.com.