reservoir · inflow performance
Darcy Flow (Linear)
q = 0.001127 × k × A × ΔP / (μ × L)
click formula to derive ↑
Inputs
mD
ft²
psi
cp
ft
Description
Computes linear (one-dimensional) flow rate through a porous medium using Darcy's law — the foundational relationship underlying nearly all reservoir flow equations, from core flow tests to well inflow performance.
Variables
| Symbol | Unit | Description |
|---|---|---|
| q | STB/d | Flow Rate |
| k | mD | Permeability of the linear flow path, from core analysis or a permeability log. |
| A | ft² | Cross-sectional area perpendicular to the direction of flow. |
| ΔP | psi | Pressure difference driving flow across the length L. |
| μ | cp | Viscosity of the flowing fluid at reservoir conditions. Water/light oil ≈ 0.5-2 cp; heavy oil can exceed 100 cp. |
| L | ft | Length of the flow path over which the pressure drop ΔP is measured. |
Assumptions
- Flow is laminar (Darcy, non-turbulent) — valid for most reservoir-scale flow but breaks down near high-rate wellbores
- The porous medium is homogeneous and isotropic over the flow length L, with a single representative permeability k
- Single-phase flow of an incompressible fluid (no significant compressibility or multiphase relative permeability effects)
Limitations
- Does not account for non-Darcy (turbulent) flow effects that become significant at high velocity near wellbores, particularly in gas wells
- Assumes single-phase flow — multiphase systems require relative permeability terms not included in this basic form
- A single k and L oversimplifies heterogeneous reservoirs; use a flow-capacity (k·h) weighted approach for layered systems
Use Cases
- → Core flow test interpretation: Compute or back-calculate permeability from a linear core flood experiment using measured rate, pressure drop, and core dimensions.
- → Foundational teaching example: Illustrate the basic Darcy relationship before extending to radial (wellbore) flow geometry in the productivity index and IPR calculators.
- → Flow capacity sanity check: Sanity-check a computed productivity index or IPR result against a simple linear-flow estimate using representative reservoir dimensions.
Related Calculations
Region Notes
Permian Basin
Wolfcamp matrix permeability is typically 0.001-0.1 mD — at these very low k values, linear flow through the matrix is extremely slow and most production comes from the induced fracture network rather than matrix Darcy flow.
Gulf of Mexico
Unconsolidated Miocene/Pliocene sandstones with k of 100-1000+ mD allow this linear form to approximate near-wellbore flow reasonably well at moderate rates.
Global
Always check the calculated flow velocity against a non-Darcy flow criterion (e.g., Reynolds number or turbulence factor) before trusting this equation at high rates, especially for gas.
References
Primary source
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