Drill String/Annular Volumes, Strokes to Bit, and Circulating Times

Drill String/Annular Volumes, Strokes to Bit, and Circulating Times

A critical element of maintaining control during a kill operation is knowing exactly where the fluids are within the wellbore at any given moment. Because we cannot see the fluids thousands of feet underground, we rely on the mud pump as a sophisticated metering device. By calculating system volumes and dividing them by the pump's output, we convert volume into pump strokes and time.

Calculating Capacities and Volumes

The internal and annular capacities of the wellbore tubulars (drill pipe, heavy weight drill pipe, drill collars, and casing/open hole) are calculated using fundamental geometry formulas adapted for oilfield units (inches and barrels).

Internal Capacity Formula

The capacity inside the drill string is given by:

$\text{Internal Capacity (bbl/ft)} = \frac{ID^2}{1029.4}$

Where:

• ID is the Internal Diameter of the pipe in inches.
• 1029.4 is a constant that converts square inches into barrels per foot.

Annular Capacity Formula

The capacity of the space between the outside of the pipe and the wall of the hole (or casing) is given by:

$\text{Annular Capacity (bbl/ft)} = \frac{D_{\text{hole}}^2 - OD_{\text{pipe}}^2}{1029.4}$

Where:

• $D_{\text{hole}}$ is the diameter of the open hole or the ID of the casing.
• $OD_{\text{pipe}}$ is the Outside Diameter of the drill pipe or drill collars.

To find the volume for any section, simply multiply the capacity (bbl/ft) by the length of that section in feet:

$\text{Volume (bbl)} = \text{Capacity (bbl/ft)} \times \text{Length (ft)}$

Complete System Volume Table

To manage a complete well kill, drillers must construct a comprehensive volume table dividing the wellbore into distinct sections. Each section represents a different geometry, requiring separate capacity and volume calculations. Below is a representative system volume table:

Strokes to Bit and Bottoms-Up

Once the volumes are tabulated, they must be converted into operational metrics: strokes and minutes.

Strokes to Bit (Surface to Bit, STB)

Strokes to Bit estimates the delivered stroke count needed to displace the internal string volume. With the stated route, verified output and ideal front assumption, kill fluid then reaches the bit and the fixed-rate drillpipe target reaches FCP. Mixing, compressibility, losses or changed flow paths can make the actual transition differ; track observations against the prediction.

$\text{STB} = \frac{\text{Total Drill String Volume (bbl)}}{\text{Pump Output (bbl/stroke)}}$

Strokes Bottoms-Up (Bit to Surface, BTS)

The Strokes Bottoms-Up indicates how many strokes are required to circulate fluid from the bit up the annulus and back to the surface. When using the Wait and Weight method, pumping this volume ensures the Kill Mud has fully displaced the annulus, effectively killing the well.

$\text{BTS} = \frac{\text{Total Annular Volume (bbl)}}{\text{Pump Output (bbl/stroke)}}$

Total System Circulation Strokes and Time

The Total Strokes required to complete the entire kill process is simply the sum of the STB and BTS.

$\text{Total Strokes} = \text{STB} + \text{BTS}$

By dividing these stroke counts by the chosen Slow Circulating Rate (in Strokes Per Minute, SPM), you calculate the circulation times:

$\text{Circulating Time (min)} = \frac{\text{Strokes}}{\text{SPM}}$

Worked Example at Different Pump Rates

Let's calculate the operational timelines utilizing the System Volume Table above. Assume the rig's pump output is 0.115 bbl/stk.

Step 1: Calculate Total Strokes

• Strokes to Bit (STB) = $167.8 \text{ bbl} / 0.115 \text{ bbl/stk} = 1,459 \text{ strokes}$
• Strokes Bottoms-Up (BTS) = $487.45 \text{ bbl} / 0.115 \text{ bbl/stk} = 4,239 \text{ strokes}$
• Total Kill Strokes = $1,459 + 4,239 = 5,698 \text{ strokes}$

Step 2: Calculate Times at 30 SPM vs. 40 SPM

If the driller decides to kill the well at a Slow Circulating Rate of 30 SPM:

• Time to Bit = $1,459 / 30 = 48.6 \text{ minutes}$
• Time Bottoms-Up = $4,239 / 30 = 141.3 \text{ minutes}$
• Total Kill Time = $5,698 / 30 = 189.9 \text{ minutes (3 hours, 10 minutes)}$

If the driller selects a slightly faster SCR of 40 SPM:

• Time to Bit = $1,459 / 40 = 36.5 \text{ minutes}$
• Time Bottoms-Up = $4,239 / 40 = 106.0 \text{ minutes}$
• Total Kill Time = $5,698 / 40 = 142.5 \text{ minutes (2 hours, 22 minutes)}$

While 40 SPM completes the job nearly 50 minutes faster, the driller must weigh this time saving against the higher annular friction (ECD) generated by the faster rate, which could exceed MAASP and fracture the formation. Precision in calculating these volumes ensures safe decision-making.

A complete pre-tour example including surface equipment

Use a separate simplified training circuit to check all required outputs: string volume 150 bbl, bit-to-shoe annulus 100 bbl, shoe-to-surface annulus 200 bbl, surface equipment 20 bbl and verified output 0.10 bbl/stroke. At 30 spm, rate is 3.0 bbl/min. Surface-to-bit requires 1,500 strokes and 50 minutes; bit-to-shoe requires 1,000 strokes and 33.333 minutes; bottoms-up through the annulus requires 3,000 strokes and 100 minutes. Full circuit including the 20 bbl surface volume is 470 bbl, 4,700 strokes and 156.667 minutes. Record which starting and finishing points define each time so a surface delay is neither omitted nor counted twice.

For a separate subsea line inventory, a 3,000 ft riser with effective annular capacity 0.30 bbl/ft contains 900 bbl. A 3,000 ft choke line of 0.009 bbl/ft contains 27 bbl, and an identical kill line contains another 27 bbl. Their combined volume is 954 bbl, but each line requires its own verified displacement route. At a verified 3 bbl/min, the riser volume alone corresponds to 300 minutes, excluding transfer-line volumes and any different permitted displacement rate. Do not use this inventory as a prescription to circulate every line simultaneously.

The pre-tour record also identifies current MD and TVD, shoe TVD, fluid densities in the well and associated lines, accepted integrity data, the calculated MAASP, pumps/rates and pressure-loss records. Capacities and measured lengths produce volumes; TVD produces hydrostatic head. Compare totals with the official surface or subsea kill-sheet layout and have missing or uncertain data resolved before it is needed. Strokes indicate a calculated front location; mixing, slip and pump efficiency can make the actual arrival differ. Verify it through the planned observations rather than declaring the well dead solely because the counter reached its target.