Calculator Inputs
Example Data Table
| Scenario | Hole / Pipe (in) | Flow (gpm) | Mud (ppg) | PV / YP | Incl (deg) | Annular Velocity (ft/min) | Transport Ratio (%) |
|---|---|---|---|---|---|---|---|
| Baseline | 8.5 / 5.0 | 500 | 10.5 | 18 / 22 | 20 | ~167 | ~70–90 |
| Low Flow | 8.5 / 5.0 | 350 | 10.5 | 18 / 22 | 20 | ~117 | Lower |
| High Inclination | 8.5 / 5.0 | 500 | 10.5 | 18 / 22 | 70 | ~167 | Typically higher |
Formula Used
- Annular area:
A = (π/4) · (Dh2 − Dp2) - Annular velocity:
V = Q / A - Hydraulic diameter (concentric annulus):
Dhyd = Dh − Dp - Shear rate (estimate):
γ̇ ≈ 8V / Dhyd - Apparent viscosity (Bingham estimate):
μapp = PV + YP/γ̇ - Reynolds number:
Re = ρ V Dhyd / μapp - Slip velocity: iterative drag model using
Vs = √(4gd(ρs−ρ)/[3Cdρ]) - Effective slip vs inclination:
Vs,eff = Vs · cos(θ) - Transport ratio:
TR = (V − Vs,eff)/V · 100% - Pressure loss (estimate): Darcy–Weisbach with
ΔP = f(L/Dhyd)(ρV²/2)
How to Use This Calculator
- Enter hole and pipe dimensions to define the annulus.
- Provide flow rate and fluid properties (mud weight, PV, YP).
- Set inclination, cuttings size and density, plus ROP.
- Click Calculate to view results above the form.
- Use CSV/PDF buttons to export the last calculation.
Annular Velocity Benchmarks
For vertical and low-angle intervals, many programs target 120–180 ft/min annular velocity, while high-angle sections often need 150–250 ft/min to limit bed formation. With an 8.5 in hole and 5.0 in pipe, 500 gpm often yields about 165 ft/min. Use the calculator to test pump-rate steps and find the minimum velocity that keeps net transport positive.
Transport Ratio Interpretation
Transport ratio compares upward fluid velocity to effective slip along the well axis. A planning target near 70% is common for steady cleaning, but tolerance varies by cuttings size, rheology, and connection time. Values below 50% suggest settling during pumps-off periods, while values above 80% provide margin when ROP increases. The inclination adjustment is idealized and does not model eccentricity beds.
Rheology and Apparent Viscosity
PV and YP influence apparent viscosity through μapp = PV + YP/γ̇. Higher velocity increases shear rate, reducing the YP/γ̇ term and lowering μapp, which raises Reynolds number and can shift the regime toward turbulent. Typical field ranges are PV 10–30 cP and YP 15–35 lbf/100 ft². For PV 18 and YP 22, μapp is roughly 29 cP at ~200 1/s.
Cuttings Loading and Concentration
The tool estimates cuttings generation from ROP and hole area, then compares it with mud flow and net annular capacity. A cuttings loading of 0.5–2.0% of flow is common; higher values quickly elevate annular concentration when Vnet is low. Larger cuttings increase slip, so a rise from 0.25 in to 0.38 in can noticeably reduce transport ratio. Keeping estimated concentration under 2–3% helps reduce torque/drag and packoff risk.
Pressure Loss and Operational Limits
Pressure loss is estimated with Darcy–Weisbach using hydraulic diameter and interval length. Use the result to sanity-check standpipe pressure margin, ECD sensitivity, and motor limits. If ΔP rises sharply with rate, evaluate nozzle sizing, fluid density, and rheology control. Combining higher RPM with modest rate increases can improve cleaning without excessive pressure. Run sensitivity cases for RPM and inclination, then document chosen rates as operating envelopes for drills, connections, and planned sweep volumes in each section.
FAQs
1) What does transport ratio indicate?
It estimates how much of the annular fluid velocity remains after subtracting effective cuttings slip. Higher values generally mean better upward transport, but real cleaning also depends on eccentricity, beds, and pumps-off time.
2) Why does inclination affect slip in the calculator?
Slip is projected along the well axis using cos(θ). This shows how gravity-driven settling aligns with the hole direction. In practice, high-angle wells may still build beds, so treat the value as optimistic.
3) Which inputs change annular velocity the most?
Flow rate and annular area dominate. Increasing pump rate raises velocity linearly, while larger hole diameter or larger pipe OD changes area and can increase or reduce velocity depending on the combination.
4) How should I pick a cuttings diameter?
Use a representative size from shakers or lithology expectations. If unknown, run sensitivity cases (for example 0.20–0.40 in) and design for the larger value, because slip increases with size and reduces transport margin.
5) Can this be used with non-Newtonian fluids?
Yes, it uses a Bingham-style apparent viscosity from PV and YP, which is common for field planning. For power-law or Herschel–Bulkley models, treat results as screening estimates and calibrate with hydraulics software.
6) Why is the pressure-loss result only an estimate?
The model applies a hydraulic-diameter approach and simple friction-factor correlations. Real pressure loss depends on eccentricity, tool joints, temperature, and rheology changes downhole. Use it for comparisons and verify with measured pressures.