Drilling guides › Mud pump output, strokes to bit and bottoms-up time
Mud pump output, strokes to bit and bottoms-up time
Pump output turns volumes into strokes and minutes. It sets the strokes on the kill sheet and the time to circulate bottoms-up before a trip or a connection gas check. Because the stroke counter is often the only flow measurement the driller has during a kill, an output figure that is a few percent wrong puts every point on the pressure schedule in the wrong place.
Triplex pump (single-acting)
The constant comes from three cylinders of π/4 × D² × S cubic inches each, divided by 9,702 cubic inches per barrel. Use a volumetric efficiency of about 95–97 % for a well-maintained triplex, or the value measured on your rig.
Each piston sweeps a cylinder of liner bore by stroke length once per stroke and pushes mud only on the forward stroke, which is what single-acting means. A "stroke" on the counter is one turn of the crankshaft, so all three pistons have fired once.
Worked example
6 in liners, 12 in stroke, 97 % efficiency:
At 100 strokes per minute: 0.1018 × 100 = 10.18 bbl/min, or 10.18 × 42 = 428 gpm.
Worked example: larger liners
The same pump fitted with 6½ in liners for a 12¼ in section, at 95 % efficiency and 110 spm:
Larger liners give more flow per stroke but a lower pressure rating, so check the liner chart on the pump before changing them.
Metric output
For the 6 in × 12 in pump (152.4 mm × 304.8 mm): 0.002356 × 152.4² × 304.8 ÷ 1,000 ≈ 16.68 L/stk at 100 %, or 16.18 L/stk at 97 %. That is the same 0.1018 bbl/stk, since one barrel is 158.99 litres.
Duplex pump (double-acting)
A duplex pumps on both sides of the piston, so the rod's volume is taken off the back stroke. Example: 6½ in liners, 2½ in rod, 16 in stroke, 90 %: 0.000162 × 16 × (2 × 42.25 − 6.25) × 0.90 = 0.1825 bbl/stk.
Duplex pumps are now mostly found on older and smaller rigs, but the formula still turns up in exams and on workover units.
Volumetric efficiency
Real pumps deliver less than the swept volume. Valves close a fraction late, seals and liners wear, and air or gas in the suction mud compresses instead of moving. Poor suction (a low pit level, a blocked screen or a weak charge pump) can drop efficiency sharply. The figure on the data sheet is a starting point; a measured value is better.
Worked example: measuring efficiency
With the pump lined up to a calibrated tank, 300 strokes move 29.4 bbl.
Using 97 % in this case would overstate the flow by about 4 %, which over a 1,788-stroke kill is roughly 70 strokes of error.
Strokes and time
Worked example
Using the 178 bbl string and 459 bbl annulus from the hole volume guide and the 0.1018 bbl/stk pump above:
A full circulation of the hole plus 600 bbl of active surface pits is (178 + 459 + 600) ÷ 0.1018 ≈ 12,151 strokes, or just over two hours at 100 spm. That is the time it takes for every barrel in the system to pass the bit once, which matters when you treat or weight up the whole system.
Where the numbers are used
- Kill sheets: strokes to bit and bottoms-up strokes set the pressure schedule and tell you when kill mud should reach surface.
- Lag time: mud loggers use bottoms-up time to match cuttings and gas to the depth they came from.
- Hole cleaning: flow rate sets the annular velocity, and companies often require several bottoms-up before a trip in deviated hole.
- Pills and slugs: strokes to place a pill at the bit or a slug at the top of the string.
Choosing a kill rate
Kill rates are much slower than drilling rates, often a third to a half. A slow rate keeps the annular friction small, so the extra pressure on the shoe during a kill is low; it gives the choke operator time to follow the schedule; and it stays inside what the mud-gas separator and choke manifold can handle when gas reaches surface. The cost is time: halving the rate doubles the time to circulate the kick out. Most crews record SCRs at two rates so there is a choice on the day.
Reading pump pressure at a steady rate
At a fixed stroke rate, standpipe pressure should stay steady while the mud and the depth stay the same. A slow fall over minutes or hours, with the strokes unchanged, often means a washout in the string or a worn pump; a sudden rise can mean a plugged nozzle or packing-off around the BHA. A sudden drop with the strokes rising can mean a twist-off. Stopping to check the cause is cheaper than fishing.
Common mistakes
- Leaving out efficiency, or using 100 % because it is simpler.
- Using the liner's outside size or the part number instead of the bore.
- Running two pumps with different liners and multiplying one output by two.
- Trusting a stroke counter that has not been checked since the last rig move.
Good practice
- Record the liner size and the measured efficiency for each pump on the kill sheet, and recheck after changing liners or valves.
- Reset the stroke counter at the moment kill mud enters the string, not when the pump starts.
- Compare calculated and real bottoms-up whenever a clear marker comes back, and adjust efficiency or hole size assumptions to match.