Annular Velocity

BH07 Annular Velocity

A useful velocity calculation starts with a defined airflow, a defined passage and a stated operating condition.

Annular velocity describes flow through the space around the drill string. In conventional direct-circulation air drilling, this return passage is part of the route used to bring cuttings towards the surface. A calculated velocity helps describe the air duty, but its meaning depends on how the flow and area were defined.

A number presented simply as “metres per second” can conceal a major distinction: it may be a reference-volume calculation used by a drilling manual, or an estimate of actual gas velocity at a particular location. Those results cannot be compared indiscriminately.

This guide explains the calculation, demonstrates that distinction and sets out what a reviewer needs before using a result for equipment selection.

Establish what the result represents

Use a clear description alongside every calculated value.

The last distinction matters when applying a simple air calculation to a wet or solids-laden return. The full annulus is not necessarily available to gas alone. A gas-only example cannot establish the transport behaviour of that mixture.

The basic equation and its units

For an ideal circular hole surrounding circular drill pipe:

• A = π × (D² − d²) ÷ 4
• v = Q ÷ A

Here, A is annular area, D is hole diameter, d is pipe outside diameter and Q is volumetric flow on the stated basis. The resulting v retains that flow basis.

With Q in m³/min, divide Q/A by 60 to obtain m/s. Convert millimetres to metres before squaring the diameters if the required area unit is m².

For diameters in inches and flow in ft³/min, the equivalent expression is:

v in ft/min = 183.35 × Q ÷ (D² − d²).

The rounded factor includes both circular geometry and the conversion from square inches to square feet. Using 144 alone in that expression would omit the π/4 area factor.

These equations describe an average over the stated section. They do not resolve the velocity distribution around an eccentric string or through local changes in the assembly.

Worked example: one geometry, two different meanings

Consider a hypothetical circular passage with a 203 mm hole and 114 mm pipe outside diameter. Assume an air quantity expressed as 24.0 m³/min at an explicitly chosen reference condition of 1.00 bar absolute and 293.15 K. This reference is chosen for the example; it is not asserted to be the default definition of FAD or standard air.

The area is:

A = π/4 × (0.203² − 0.114²) = 0.0221584 m².

Using the reference-volume flow:

v(reference basis) = 24.0 ÷ 0.0221584 = 1,083.1 m/min = 18.05 m/s.

The arithmetic is valid, but 18.05 m/s is not yet an actual downhole velocity. It is the result obtained using the specified reference-volume airflow.

Now consider a hypothetical location where the gas is at 3.00 bar absolute, at the same temperature. Assume steady ideal-gas flow, unchanged gas composition, no leakage or gas addition, and no liquid or solids occupying the passage. For the same mass flow, the local volume is one-third of the reference volume:

Q(local) = 24.0 × 1.00/3.00 = 8.00 m³/min.

The corresponding ideal local mean velocity is:

v(local) = 8.00 ÷ 0.0221584 ÷ 60 = 6.02 m/s.

The difference comes from the volume basis. Neither result is a recommended cleaning velocity, an approved drilling duty or a measured field condition. The assumed local pressure is not a compressor setpoint and is not inferred from a drilling depth.

Correcting a reference volume to local conditions

For the same steady mass flow of an ideal gas with unchanged composition:

Q(local) = Q(reference) × [p(reference)/p(local)] × [T(local)/T(reference)].

Use absolute pressures in consistent units and temperatures in kelvin. Gauge pressure cannot be inserted directly into the ratio. Celsius values cannot be used as the temperature ratio.

The expression is a simplified gas-state conversion. It does not calculate the local pressure or temperature for you. Those inputs need a defensible measurement or engineering basis. Real-gas behaviour, changing moisture content, losses or additional gas require further treatment where material.

Keep this calculation separate from compressor performance. Converting a flow between conditions does not demonstrate that a particular compressor can deliver the required mass flow at its operating pressure.

Match the assessment method before judging the result

Some DTH manuals define bailing velocity using an atmospheric/reference-volume convention and exclude bottom-hole pressure from that calculation. Apply any associated guidance on its stated basis. Comparing such a threshold with a pressure-corrected local velocity changes the method.

A value found in rotary blasthole guidance also needs its application checked before use in DTH work. Published ranges are not interchangeable merely because their units match.

Before accepting a target, retain its source, applicable drilling method, equipment scope, flow definition and qualifications. Confirm whether it covers the proposed water or injection conditions. Where the method is unclear, seek clarification before assigning a pass or fail.

Make the calculation reviewable

A useful calculation sheet should allow another person to reconstruct the result without guessing what an input means.

A correctly evaluated formula may still contain uncertain inputs. Show those uncertainties beside the result. Extra decimal places cannot improve an assumed hole size or an unverified flow figure.

Questions that deserve a technical review

If the return area changes along the hole, a single-section calculation is incomplete. If pressure and temperature change, actual gas volume can change even when mass flow is conserved. If the hole contains significant water or cuttings, the simple gas-only interpretation no longer describes the whole return stream.

These are reasons to review the operating case, rather than to increase compressor capacity by an arbitrary percentage. Avoid changing tooling or hammer settings solely to achieve a target spreadsheet value. Equipment compatibility and manufacturer operating requirements remain part of the decision.

Frequently asked questions

Is annular velocity the same as cuttings velocity?

No. A calculated gas velocity is not a measurement of particle movement. Cuttings transport requires an assessment of the material and flow conditions; the arithmetic here does not predict a particle lifting rate.

Can I use the CFM printed on the compressor?

Only after establishing its reference basis, applicable pressure and relevance to the assessed operating case. A nominal product label does not, by itself, establish flow through the selected return section.

Is a higher calculated value always better?

A larger number alone is not an acceptance criterion. Use applicable equipment guidance and a compatible calculation method; consider operating limitations as well as cleaning requirements.

Does a satisfactory result prove drilling performance?

No. It is one part of the technical assessment. It does not establish penetration rate, hole stability, achieved depth or satisfactory material removal under changing conditions.

Bring a defined air duty to the equipment discussion

For a compressor purchase or rental enquiry, send Reddy Compressors the calculation basis, bore-section details, tooling identification and proposed operating conditions. Include the source of any specified velocity requirement. Equipment suitability and availability can then be considered against the documented duty, with high-pressure supply subject to confirmation.

Related pages: Borewell Compressors Parts and Lifecycle Support · DTH Compressor Sizing and Duty Confirmation · Borewell Project Enquiry Brief