Hole Cleaning / Cuttings Transport Ratio Calculator

Hole cleaning is the ability of the drilling fluid to lift rock cuttings out of the annulus and up to the surface. If the mud flowing up the annulus moves slower than the cuttings settle, cuttings pile up into a bed on the low side of the hole. That bed can restrict flow, increase torque and drag, cause pack off, or lead to stuck pipe. This calculator estimates the annular velocity, the cutting slip velocity, and the resulting net rise velocity so you can judge whether a given flow rate is adequate before or during drilling.

The three quantities behind hole cleaning

Three velocities describe what happens to a rock cutting once it leaves the bit and enters the annulus.

• Annular velocity (AV), the upward speed of the drilling fluid in the annulus between the drill pipe and the hole wall.
• Cutting slip velocity (Vs), the speed at which a cutting falls through the mud under gravity, resisted by the fluid’s viscosity and the drag on the particle.
• Net rise velocity, simply AV minus Vs. If this number is positive, cuttings are carried upward faster than they settle. If it is negative, cuttings sink faster than the mud can lift them.

Formulas used

Annular velocity in field units (ft/min) is calculated from flow rate Q in gpm, hole diameter Dh in inches, and drill pipe OD Dp in inches:

AV = 24.51 x Q / (Dh^2 – Dp^2)

Cutting slip velocity is estimated with the standard turbulent flow relation, valid when the particle Reynolds number is above about 100, which covers the great majority of field cutting sizes and mud weights:

Vs = 175 x Dc x SQRT((DenC – MW) / MW)

Where Dc is the cutting diameter in inches, DenC is the cutting density in ppg, and MW is the mud weight in ppg. The calculator also checks the particle Reynolds number, NRE = 928 x MW x Vs x Dc / PV using the plastic viscosity PV in centipoise, and flags results that fall outside the turbulent range so you know when the simplified formula is being pushed past its comfort zone. Net rise velocity is then AV minus Vs, and the transport ratio expresses net rise velocity as a percentage of annular velocity.

Worked example

Using a flow rate of 300 gpm, a 6.3 inch hole, a 4 inch drill pipe OD, plastic viscosity of 15 cP, mud weight of 10 ppg, a cutting diameter of 0.20 inch, and a cutting density of 20 ppg, annular velocity works out to about 310.3 ft/min and cutting slip velocity to about 35.0 ft/min. That gives a net rise velocity around 275 ft/min and a transport ratio near 89 percent, comfortably in the good hole cleaning range since annular velocity is far greater than slip velocity.

Why it matters

Poor hole cleaning is one of the most common contributors to stuck pipe, especially in deviated and horizontal sections where cuttings can settle on the low side of the hole rather than being suspended in the flow. Checking annular velocity against slip velocity before increasing rate of penetration, or before tripping, gives an early warning that pump rate, mud rheology, or rotation may need adjusting to keep the hole clean.

Hole Cleaning / Cuttings Transport Calculator

Related Calculator and Reference

For pump pressure losses in the same circulating system, see the Drilling Hydraulics Pump Pressure Loss Calculator. Formula reference: DrillingFormulas.com, Cutting Slip Velocity Calculation Method 1.