Hydraulics · hole cleaning · field units

Hole cleaning: minimum annular velocity, slip velocity and cuttings transport ratio

Good hole cleaning means the mud lifts cuttings out of the well faster than the bit makes them. In a near-vertical well, check it with three numbers: the annular velocity Va = 24.5 × Q ÷ (Dh² − Dp²) ft/min, the cuttings slip velocity Vs (for example from Moore's correlation), and the transport ratio Rt = 1 − Vs ÷ Va, which should stay above about 0.5. The cuttings concentration in the annulus, ROP × Dh² ÷ (1471 × Q × Rt), should stay below about 5%. Above roughly 35° inclination cuttings settle into beds on the low side, and flow rate, pipe rotation and mud properties matter more than any single velocity rule. This page explains each formula and works one 12¼ in section through at two flow rates.

Reference material only. Flow rate, mud properties, rotation and hole-cleaning practices for a well come from the drilling programme and the mud engineer. Worked examples are illustrative arithmetic, not a hydraulics design.

1. The hole cleaning formulas

Q is the flow rate in gpm, Dh the hole (or casing) inside diameter and Dp the pipe outside diameter in inches, ROP the rate of penetration in ft/h, ds the cuttings size in inches, ρs and ρm the cuttings and mud densities in ppg, and μa the mud's apparent viscosity in the annulus in cP. The 24.5 constant is explained on the annular velocity formula page. The 1471 constant converts a hole drilled at ROP ft/h into gallons of rock per minute: (π ÷ 4) × (Dh ÷ 12)² × ROP ÷ 60 ft³/min × 7.4805 gal/ft³ = ROP × Dh² ÷ 1471.

2. Minimum annular velocity: what the rules of thumb mean

Annular velocity is the easiest number to check, which is why it is quoted so often. The history behind the usual figures, as summarised in SPE's PetroWiki article on cuttings transport:

• About 100 ft/min became the widely accepted figure for vertical wells after Williams and Bruce's 1951 work on the carrying capacity of drilling muds. Before that, about 200 ft/min was common practice.
• About 50 ft/min was found by Sifferman and Becker to give satisfactory transport for a typical viscous drilling mud, while water needed about 100 ft/min.
• About 3 to 4 ft/s (180 to 240 ft/min) was the critical average velocity Larsen found, in more than 700 flow-loop tests, to stop a cuttings bed growing in inclined hole. The exact value depended on rheology, drilling rate, pipe eccentricity and rotation.

The lowest annular velocity in the well is around the drill pipe in the largest hole or riser section, not around the collars, so check every section. A fixed velocity rule ignores mud rheology, cuttings size and ROP; the slip velocity and transport ratio below take those into account.

3. Slip velocity and transport ratio

Cuttings fall through the mud at their slip velocity while the mud carries them up at the annular velocity. Their net upward speed is the transport velocity, Va − Vs, and the transport ratio Rt = (Va − Vs) ÷ Va says what fraction of the mud's speed the cuttings keep. Rt = 1 means the cuttings move with the mud; Rt = 0 means they hang in place. A transport ratio above about 0.5 is a common minimum for vertical wells.

Moore's correlation (1974), set out in Applied Drilling Engineering and Lapeyrouse's field formula book, estimates slip velocity in four steps:

• Power-law constants from the viscometer: n = 3.32 × log(θ600 ÷ θ300) and K = θ300 ÷ 511ⁿ.
• Apparent viscosity in the annulus: μa = [ (2.4 × Va ÷ (Dh − Dp)) × (2n + 1) ÷ (3n) ]ⁿ × 200 × K × (Dh − Dp) ÷ Va, with Va in ft/min.
• Slip velocity for the intermediate regime, the usual case for drilled cuttings: Vs = 2.90 × ds × (ρs − ρm)^0.667 ÷ (ρm^0.333 × μa^0.333) ft/s. Multiply by 60 for ft/min.
• Check the regime with the particle Reynolds number, NRe = 928 × ρm × Vs × ds ÷ μa (Vs in ft/s). Between 3 and 300 the intermediate equation applies. Below 3 use Moore's laminar form, Vs = 82.87 × ds² × (ρs − ρm) ÷ μa; above 300 use the turbulent form, Vs = 1.54 × √(ds × (ρs − ρm) ÷ ρm).

Slip velocity depends most on cuttings size and on the mud's viscosity at the low shear rates found in the annulus. That is why muds with the same funnel viscosity can clean the hole very differently, and why Becker, Azar and Okrajni (1991) found transport correlated best with the 6 rpm viscometer reading.

4. Worked example: 12¼ in hole at 750 gpm and 400 gpm

A near-vertical 12¼ in section is drilled with 5 in drill pipe and 10.0 ppg water-based mud with viscometer readings θ600 = 55 and θ300 = 35 (PV 20 cP, YP 15 lb/100 ft²). Cuttings are taken as 0.25 in across with a density of 21.5 ppg (specific gravity about 2.58). ROP is 60 ft/h. All figures are illustrative.

At 750 gpm every check passes with margin. At 400 gpm the transport ratio still looks acceptable at 0.72, but the CCI drops to 0.6 and, if the bit speeds up to 150 ft/h, cuttings concentration passes the 5% guideline. The fix is more flow, a slower controlled ROP, or better low-shear-rate mud properties. More flow also raises annular pressure loss and ECD, so check both against the fracture gradient and MAASP; the extra cuttings load also adds to ECD.

For the CCI, K is Robinson's consistency in effective cP: n = 3.322 × log((2PV + YP) ÷ (PV + YP)) and K = (PV + YP) × 511^(1 − n), which gives K = 306 for this mud. It is a different unit from the K used in Moore's apparent viscosity.

5. Cuttings concentration and the carrying capacity index

At 60 ft/h a 12¼ in bit makes 12.25² ÷ 1029.4 = 0.146 bbl of rock per foot, or about 8.7 bbl (roughly 7,900 lb at 21.5 ppg) every hour. That rock is spread through the annular mud. The concentration estimate above divides the cuttings volume rate by the effective mud flow carrying it (Q × Rt). Pigott's 1941 guideline of keeping it below about 5% by volume is still the figure most often quoted. High concentrations raise mud weight in the annulus, add to ECD and increase the risk of pack-off when circulation stops.

The carrying capacity index combines mud consistency, velocity and weight in one number. In Robinson and Morgan's AADE paper on hole cleaning and drilling rate, a CCI of about 1 goes with sharp-edged cuttings that show little grinding, while rounded cuttings point to poor carrying capacity: cuttings that spend a long time in the annulus get ground down. It is a vertical-well index; it does not account for beds in deviated hole.

6. Deviated and horizontal wells

In inclined hole a cutting only has to fall across the annulus, a few inches, before it reaches the low side, so beds form even when the transport ratio looks fine. Findings summarised in PetroWiki:

• Inclination. Tomren, Iyoho and Azar (1986) saw beds forming above about 35° from vertical. Between roughly 35° and 55° the bed can slide back down the hole (Larsen), the hardest range to clean. From about 55° to 90° bed height stayed roughly constant.
• Flow rate has the largest positive effect. Rates high enough for large, high-angle holes can exceed pump or pressure limits, especially in hole larger than 12¼ in.
• Pipe rotation helps significantly, more so in small annuli, with small cuttings and with more viscous mud, and more in inclined than vertical hole.
• Eccentric pipe lying on the low side diverts flow away from where the cuttings settle.
• Small cuttings are harder to remove from a bed than large ones, and higher ROP raises the hydraulics needed.

Cuttings beds are a common cause of pack-off and stuck pipe, and of high swab and surge pressures on trips.

7. Signs of poor hole cleaning on the rig

• Shaker returns lower than the rock volume being drilled (0.146 bbl/ft in 12¼ in hole), then a surge of cuttings after a sweep or a period of high flow and rotation.
• Cuttings shape: small, rounded, ground-up cuttings instead of sharp-edged ones.
• Torque and drag trending up, overpull or erratic torque on connections, and higher pick-up weights than the trend.
• ECD or standpipe pressure creeping up at constant flow rate and mud weight.
• Pack-off tendencies when circulation starts, or fill on bottom after trips.

Record circulating time, sweeps and any time lost to tight hole in the daily drilling report; repeated hole-cleaning problems show up as non-productive time.

8. In DrillX

DrillX brings daily drilling reports with IADC-style time logs, a rig fleet view, NPT insights and engineering calculators into one tool. The calculators cover hydrostatic pressure, ECD, annular pressure loss, triplex pump output, annular capacity and velocity, buoyancy and the kill sheet. This page explains the hole cleaning arithmetic; it does not describe a DrillX hole cleaning or cuttings transport calculator. DrillX is in final testing; email info@drillx.app for a demo or early access.

Sources and further reading

• SPE PetroWiki, Cuttings transport: history of annular velocity guidelines (Williams and Bruce 1951; Sifferman and Becker), Pigott's 5% concentration guideline, Larsen's critical velocity, inclination effects (Tomren et al. 1986) and the effect of flow rate, rotation, rheology and eccentricity.
• L. Robinson and M. Morgan, Effect of Hole Cleaning on Drilling Rate and Performance, AADE-04-DF-HO-42 (AADE Drilling Fluids Conference, Houston, 2004): carrying capacity index and cuttings shape.
• A. T. Bourgoyne Jr. et al., Applied Drilling Engineering, SPE Textbook Series Vol. 2 (1986), chapter 4: drilling hydraulics, power-law fluids and Moore's slip velocity correlation.
• N. J. Lapeyrouse, Formulas and Calculations for Drilling, Production and Workover, 2nd ed. (Gulf Professional Publishing, 2002): annular velocity, slip velocity and cuttings calculations in field units.
• API RP 13D, Rheology and Hydraulics of Oil-well Drilling Fluids: hole cleaning and hydraulics practice.

Reference summary only. Worked examples are illustrative arithmetic. Flow rates, mud properties and hole-cleaning practices are set by your operator's drilling programme and mud engineer.