drilling · hydraulics
Cuttings Slip Velocity (Chien/Moore)
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Inputs
in
lb/ft³
lb/gal
cP
lbf/100ft²
—
—
Description
Computes the terminal settling (slip) velocity of a drilled cuttings particle relative to the drilling fluid, via a selectable correlation — Chien (1994, the form API RP 13D adopted) or Moore (1974). Slip velocity is the other half of the hole-cleaning comparison against Annular Velocity: a particle is carried out of the hole only if the fluid moves up faster than the particle falls through it.
Variables
| Symbol | Unit | Description |
|---|---|---|
| Vs | ft/s | Cuttings Slip Velocity |
| Dp | in | Representative equivalent diameter of a drilled cuttings particle — commonly 3/16 to 1 in (4.8-25.4 mm) depending on bit type and formation. |
| ρp | lb/ft³ | Density of the drilled rock cuttings — typically 2,300-2,700 kg/m³ for shale/limestone, higher for denser formations. |
| ρl | lb/gal | Drilling fluid density. |
| PV | cP | Plastic viscosity from a Fann viscometer test. |
| YP | lbf/100ft² | Yield point from a Fann viscometer test. Used only by Chien's method (Moore's implementation here uses plastic viscosity alone as the apparent viscosity, the same simplification Reynolds Number already makes). |
| ψ | — | Sphericity of drilled cuttings (1.0 = perfect sphere; real cuttings fragments are typically 0.7-0.9). Used only by Chien's method. |
| Method | — | 1 = Chien (1994) — single continuous equation across all flow regimes, the form API RP 13D adopted as its recommended procedure; 2 = Moore (1974) — regime-branched (laminar/transitional/turbulent), found to have the lowest average error in Sample & Bourgoyne's (1977) experimental evaluation. The two can diverge substantially — see limitations. |
Assumptions
- Cuttings are approximately spherical with the sphericity correction folded into Chien's drag coefficient — Moore's implementation here does not apply a separate sphericity correction
- A single representative particle diameter and density stand in for the real distribution of cuttings sizes actually generated at the bit
- Moore's apparent viscosity is taken as plastic viscosity alone (μa ≈ PV), the same simplification this discipline's Reynolds Number already makes for the Bingham-plastic apparent viscosity — not the power-law apparent-viscosity route Moore's own original paper also presents as an alternative
Limitations
- Chien and Moore are genuinely competing, not complementary, correlations — they can diverge substantially on the same inputs (this platform's own cross-check found roughly a 2-3x difference on a representative case), and neither should be read as simply "correct." Sample & Bourgoyne's (1977) experimental evaluation found Moore's method had the lowest average error among the correlations they tested; a separate later analysis found Chien's 1994/API form over-predicting measured settling velocity by roughly 26-48% depending on how the fluid's rheological parameters were derived. Which method runs higher is not universal — it depends on fluid rheology and particle size, not a fixed direction.
- Both methods assume a single spherical (or sphericity-corrected) particle settling in an otherwise still or uniformly-moving fluid — real cuttings transport in an annulus also involves particle-particle interference at high cuttings concentration and pipe eccentricity effects, neither modeled here
- Chien's method as implemented here uses the Bingham-plastic (PV/YP) effective-viscosity route rather than the power-law (K, n) apparent-viscosity route Chien's and Moore's own source literature also present — consistent with this whole discipline's established Bingham-plastic convention (pv_yp_fann, pressure_loss, reynolds_number), but a genuinely different fluid characterization than a power-law-based implementation would use
Use Cases
- → Cuttings transport ratio input: Provide slip velocity to Cuttings Transport Ratio, alongside Annular Velocity, to evaluate whether current circulating parameters adequately clean the hole.
- → Minimum flow rate planning: Estimate the annular velocity a hydraulics program must exceed to keep cuttings moving toward surface rather than accumulating in the annulus.
- → Mud rheology sensitivity screening: Compare how raising plastic viscosity or yield point lowers slip velocity (improving hole cleaning) against the cost in circulating pressure loss.
Related Calculations
Region Notes
Global
Run both methods on the same inputs when a hole-cleaning decision is marginal — if Chien and Moore agree the well is comfortably above or below the minimum transport ratio, the method choice doesn't matter; if they disagree, treat the result as uncertain rather than trusting either number alone.
References
Primary source
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