reservoir · inflow performance
Radial Flow (Steady-State Darcy)
click formula to derive ↑
Inputs
mD
ft
psi
psi
cp
RB/STB
ft
ft
Description
Computes steady-state oil inflow rate using the radial form of Darcy's law — flow converging cylindrically from a constant-pressure drainage boundary re to a wellbore of radius rw. This is the theoretical, skin-free counterpart to the empirically-measured productivity index, and the direct radial generalization of the linear Darcy flow equation. Oil (liquid) form only in this session — a gas pseudo-pressure/real-gas-deviation-factor form was deferred, not built.
Variables
| Symbol | Unit | Description |
|---|---|---|
| q | STB/d | Flow Rate |
| k | mD | Effective permeability to oil between the wellbore and the drainage boundary, from core analysis or well test interpretation. |
| h | ft | Net (flowing) reservoir thickness open to the wellbore. |
| Pe | psi | Pressure at the outer (constant-pressure) drainage boundary re — the steady-state analog of average reservoir pressure. |
| Pwf | psi | Flowing bottomhole pressure at the wellbore radius rw. |
| μ | cp | Viscosity of the flowing oil at reservoir conditions. |
| Bo | RB/STB | Oil formation volume factor at reservoir conditions. |
| re | ft | Radius of the (assumed circular) drainage boundary — from the Well Spacing calculator or an assumed spacing pattern. |
| rw | ft | Radius of the wellbore (typically the drilled hole radius). 0.107 m ≈ 8.5 in diameter hole. |
Assumptions
- Steady-state flow with a constant-pressure outer boundary (Pe) — typically an aquifer- or gas-cap-supported reservoir, not a depleting closed volume
- Single-phase, incompressible oil flow with no skin (S=0) and a homogeneous, isotropic reservoir between rw and re
- Idealized circular (radially symmetric) drainage geometry centered on a single vertical wellbore
Limitations
- Oil (liquid) form only — a gas radial-flow variant requires a pseudo-pressure/real-gas deviation factor formulation not built in this session
- Assumes zero skin; real wells commonly have S≠0 — pair with the Skin Factor calculator, or use Productivity Index for an empirically-measured (skin-inclusive) alternative
- The steady-state, constant-Pe assumption does not apply to a depleting closed reservoir, which instead follows pseudo-steady-state behavior (not covered by this equation)
Use Cases
- → Theoretical inflow-rate estimate: Predict expected oil rate for a well flowing from a pressure-supported circular drainage area, given reservoir rock/fluid properties and well geometry.
- → Productivity index sanity check: Compare a measured productivity index against this theoretical Darcy radial-flow prediction to flag unexplained deliverability shortfalls (often indicating skin damage).
- → Spacing-pattern rate screening: Pair with the Well Spacing calculator's drainage radius output to estimate the rate a candidate spacing pattern could support.
Related Calculations
Region Notes
Permian Basin
Wolfcamp/Bone Spring matrix permeability (0.001-0.1 mD) makes this steady-state matrix-flow form a poor predictor of actual well rates, which are dominated by the induced fracture network rather than radial matrix flow.
Gulf of Mexico
Aquifer-supported Miocene/Pliocene sandstone reservoirs are among the better real-world matches to this equation's constant-boundary-pressure assumption.
North Sea
Water-injection-supported Brent Group reservoirs can approximate steady-state behavior once injection has stabilized the pressure at the drainage boundary.
Global
Always check whether the reservoir is genuinely pressure-supported (steady-state) or depleting (pseudo-steady-state) before applying this equation — using it on a depleting closed reservoir overstates the sustainable rate.
References
Primary source
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