drilling · hydraulics
Reynolds Number (Pipe & Annulus)
click formula to derive ↑
Inputs
lb/gal
gpm
cP
in
in
in
Description
Computes the generalized (Bingham plastic) Reynolds number for both pipe flow and annular flow, using plastic viscosity as the apparent viscosity — the drilling-specific formulation, not a generic Newtonian Reynolds number. NRe determines whether flow is laminar or turbulent, which in turn determines which pressure-loss model applies (Pressure Loss in this cluster covers the laminar case).
Variables
| Symbol | Unit | Description |
|---|---|---|
| NRe,pipe | — | Reynolds Number — Pipe |
| NRe,ann | — | Reynolds Number — Annulus |
| ρ | lb/gal | Drilling fluid density. |
| Q | gpm | Circulating flow rate, from Pump Output or a measured pump rate. |
| μp | cP | Plastic viscosity from a Fann viscometer test, used as the apparent viscosity in the Bingham plastic Reynolds number formulation. |
| d | in | Drillpipe internal diameter, for the pipe-flow Reynolds number. |
| d1 | in | Drillpipe outer diameter, for the annular-flow Reynolds number. |
| d2 | in | Open hole or casing internal diameter, for the annular-flow Reynolds number. |
Assumptions
- Drilling fluid rheology is reasonably approximated by the Bingham plastic model (see pv_yp_fann's own assumptions)
- Velocity is the average (bulk) flow velocity, computed here from flow rate and cross-sectional area — not a local or wall velocity
- Pipe and annular geometries are each treated as a simple circular pipe / concentric annulus — tool joints, stabilizers, and non-concentric (eccentric) annular clearance are not modeled
Limitations
- The 2100 laminar/turbulent threshold is the same criterion used for Newtonian fluids applied by convention to Bingham plastics — a more rigorous treatment uses the Hedstrom number to adjust the critical Reynolds number for yield-stress fluids, not implemented here
- Does not account for pipe eccentricity in the annulus (drillpipe resting against the low side of the hole), which measurably changes the true annular velocity distribution
- A single flow-regime screening tool, not a full hydraulics model — use Pressure Loss for the laminar-flow pressure result once flow regime is confirmed
Use Cases
- → Flow regime screening: Determine whether drillpipe and annular flow are laminar or turbulent before selecting the appropriate pressure-loss model.
- → Hole cleaning assessment: Screen annular flow regime as part of evaluating whether current circulating parameters provide adequate cuttings transport.
- → Hydraulics program design: Check flow regime across a range of candidate flow rates and mud properties when designing a well's circulating hydraulics program.
Related Calculations
Region Notes
Global
Drillpipe interior flow is almost always turbulent at normal circulating rates; annular flow is far more often laminar due to the much larger flow area — both regimes should be checked independently rather than assumed.
References
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.