Calculations required for spotting pills

Input(s)

hd: Diameter of Hole (in.)

pd: Diameter of Drill Pipe (in.)

cd: Diameter of Drill Collar (in.)

$\mathrm{L}_{\mathrm{s}}$ : Length of Section $(\mathrm{ft})$

$\mathrm{L}_{\mathrm{e}}$ : Length Above the Collar (ft)

WF: Washout Factor (fraction)

$\mathrm{V}_{\mathrm{ds}}$ : Volume Left in Drill String (bbl)

$\mathrm{C}_{\mathrm{dc}}$ : Drill Collar Capacity (bbl/ft)

$\mathrm{C}_{\mathrm{dp}}$ : Drill Pipe Capacity (bbl/ft)

L: Length ( $\mathrm{ft}$ )

PO: Pump Output (bbl/stroke)

$\mathrm{S}_{\mathrm{ds}}$ : Strokes of Drill Pipe (fraction)

$\mathrm{AC}_{\mathrm{dc}}$ : Annular Capacity of Drill Collar (bbl/ft)

$\mathrm{AC}_{\mathrm{dp}}$ : Annular Capacity of Drill Pipe (bbl/ft)

$\mathrm{V}_{\mathrm{dc}}$ : Volume in Drill Collar (bbl)

$\mathrm{V}_{\mathrm{dp}}$ : Volume in Drill Pipe (bbl)

$\mathrm{V}_{\mathrm{a}}$ : Volume of Pill Required in Annulus (bbl)

$\mathrm{V}_{\mathrm{ts}}$ : Total Volume of Pill Required (bbl)

$\mathrm{C}_{\mathrm{t}}$ : Total Capacity of Drill String (bbl)

$\mathrm{S}_{\mathrm{pp}}$ : Strokes for Pump Pill (no.)

$\mathrm{V}_{\mathrm{cp}}$ : Volume Req for Chase Pill (bbl)

$\mathrm{S}_{\mathrm{cp}}$ : Strokes for Chase Pill (no.)

$\mathrm{S}_{\mathrm{t}}$ : Total Strokes to Spot the Pill (no.)

\begin{gathered} \mathrm{AC}_{\mathrm{dc}}=\frac{(\mathrm{hd})^{2}-(\mathrm{cd})^{2}}{1029.4} \\ \mathrm{AC}_{\mathrm{dp}}=\frac{(\mathrm{hd})^{2}-(\mathrm{pd})^{2}}{1029.4} \\ \mathrm{~V}_{\mathrm{dc}}=\mathrm{AC}_{\mathrm{dc}} * \mathrm{~L}_{\mathrm{s}} * \mathrm{WF} \\ \mathrm{V}_{\mathrm{dp}}=\mathrm{AC}_{\mathrm{dp}} * \mathrm{~L}_{\mathrm{e}} * \mathrm{WF} \\ \mathrm{V}_{\mathrm{a}}=\mathrm{V}_{\mathrm{dc}}+\mathrm{V}_{\mathrm{dp}} \\ \mathrm{V}_{\mathrm{ts}}=\mathrm{V}_{\mathrm{a}}+\mathrm{V}_{\mathrm{ds}} \\ \mathrm{C}_{\mathrm{t}}=\left(\mathrm{C}_{\mathrm{dc}}\right) * \mathrm{~L}_{\mathrm{s}}+\left(\mathrm{C}_{\mathrm{dp}}\right) * \mathrm{~L} \\ \mathrm{~S}_{\mathrm{pp}}=\frac{\mathrm{V}_{\mathrm{ts}}}{\mathrm{PO}} \\ \mathrm{V}_{\mathrm{cp}}=\mathrm{C}_{\mathrm{t}}-\mathrm{V}_{\mathrm{ds}} \\ \mathrm{S}_{\mathrm{cp}}=\left(\frac{\mathrm{V}_{\mathrm{cp}}}{\mathrm{PO}}\right)+\mathrm{S}_{\mathrm{ds}} \\ \mathrm{S}_{\mathrm{t}}=\left(\mathrm{S}_{\mathrm{pp}}\right)+\left(\mathrm{S}_{\mathrm{cp}}\right) \end{gathered}

Lapeyrouse, N. J., 2002, Formulas and Calculations for Drilling, Production and Workover, Second Edition, Gulf Professional Publishin, Page: 75.