Volume of fluid displaced for duplex pumps

Input(s)

$\mathrm{D}_{\mathrm{L}}$: Piston Diameter (in.) $\mathrm{D}_{\mathrm{r}}$: Rod Diameter (in.)

$\mathrm{L}_{\mathrm{S}}$: Stroke Length (in.)

$\mathrm{N}_{\mathrm{C}}$: Number of Cylinders (unitless)

$\mathrm{n}_{\mathrm{v}}$: Volumetric Efficiency (unitless)

Output(s)

$\mathrm{V}_{\mathrm{t}}$: Volume of Fluid Displaced (bbl/stroke)

Formula(s)

$$ \mathrm{V}_{\mathrm{t}}=\frac{\mathrm{N}_{\mathrm{C}} * \mathrm{~L}_{\mathrm{S}} *\left(\left(2 * \mathrm{D}_{\mathrm{L}}^{2}\right)-\mathrm{D}_{\mathrm{r}}^{2}\right) * \mathrm{n}_{\mathrm{v}}}{42 * 294} $$

Reference(s)

Samuel. E Robello. 501 Solved Problems and Calculations for Drilling Operations. Sigma Quadrant. 2015. Houston, Texas, Page: 49.