Pump Output / Stroke Volume Calculator

    Calculate pump output and stroke volume for triplex and duplex mud pumps with support for efficiency factors and multiple units.

    Calculation Inputs

    Select the type of mud pump

    Pump liner inside diameter

    Length of pump stroke

    Typical values: 85-100% (100% for theoretical)

    What Is Pump Output?

    Pump output is the volume of drilling fluid displaced by the mud pump per stroke. When multiplied by pump strokes per minute, it determines the actual circulating flow rate in the well. Because the pump drives the entire hydraulics system, an accurate pump output value is essential for calculating annular velocity, hydraulic horsepower, bit nozzle performance, ECD, and standpipe pressure.

    Mud pumps used in drilling are typically either triplex(three pistons) or duplex double-acting pumps. Each pump type has its own displacement formula, based on piston diameter, liner diameter, stroke length, and rod diameter (for duplex). The calculator uses industry-standard field-unit constants to convert piston geometry into barrels per stroke (bbl/stk).

    Pump output is a theoretical maximum. Actual flow rate is usually lower due to volumetric efficiency losses, valve leakage, liner wear, and fluid compressibility. The efficiency (%) input allows you to adjust the theoretical value to reflect expected real-world performance.

    Pump Output Formulas

    The formulas used in this calculator match the standard field-unit conversions found in the IADC Drilling Manual and common pump charts:

    Triplex: Outputbbl/stk = 0.000243 × D² × S

    Where D = liner (piston) diameter in inches and S = stroke length in inches. Constant 0.000243 converts in³ per stroke into barrels.

    Duplex: Outputbbl/stk = 0.000162 × S × (2D² − d²)

    Where D = liner diameter, d = rod diameter. Duplex pumps displace fluid on both forward and return strokes, but rod volume reduces total output.

    Key variables:

    • D — liner/piston diameter (in)
    • d — rod diameter (in, duplex only)
    • S — stroke length (in)
    • Eff% — volumetric efficiency (%)
    • bbl/stk — barrels per stroke
    • bbl/min — bbl/stroke × strokes/minute
    • gpm — bbl/min × 42

    Example Pump Output Calculation

    Consider a triplex pump with a 6.5 in liner, 12 in stroke length, and operating at 100 strokes per minute. Assume 90% volumetric efficiency.

    Outputbbl/stk = 0.000243 × 6.5² × 12 = 0.000243 × 42.25 × 12 ≈ 0.123 bbl/stk

    Flowbbl/min = 0.123 × 100 = 12.3 bbl/min

    Efficiency-adjusted flow = 12.3 × 0.90 = 11.07 bbl/min

    Flowgpm = 11.07 × 42 ≈ 465 gpm

    This example shows how pump geometry directly affects the achievable flow rate. Larger liners and longer strokes increase displacement, but efficiency losses can significantly reduce the real output seen on flow meters.

    Why Pump Output Matters

    • Hydraulics design:Accurate pump output determines annular velocity, bit nozzle sizing, hydraulic horsepower, and pressure-loss predictions.
    • Hole cleaning:Minimum flow requirements depend on AV in the annulus; pump output directly controls this.
    • Standpipe pressure:Pump displacement sets the actual circulating rate, which drives friction losses throughout the system.
    • Well control operations:During circulation and kill procedures, predictable pump output is essential for calculating SICP trends, kill mud rates, and dynamic pressures.
    • Equipment limits:Exceeding pump stroke speed or operating outside ideal liner/rod sizes can overheat equipment, increase wear, and reduce volumetric efficiency.

    Triplex Pump:

    Output = 0.000243 × D² × S

    Output in bbl/stk, D in inches, S in inches

    Duplex Pump:

    Output = 0.000162 × S × [2D² - d²]

    D = liner diameter, S = stroke length, d = rod diameter

    D: Liner Diameter (inches)
    S: Stroke Length (inches)
    d: Rod Diameter (inches, duplex only)
    Efficiency: Multiply result by efficiency % to get actual output

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