Critical annular velocity and critical flow rate

Input(s)

0600: 600 Viscometer Dial Reading (dimensionless)

0300: 300 Viscometer Dial Reading (dimensionless)

Dh: Diameter of Hole (in.)

Dp: Diameter of Drill Pipe (in.)

MW: Mud Weight in Use (ppg)

Output(s)

n: Power Constant (dimensionless)

$\mathrm{K}$: Constant (dimensionless)

$\mathrm{x}$: Constant (dimensionless)

AVc: Critical Annular Velocity (ppg)

GPMc: Critical Flow Rate (ppg)

Formula(s)

$$ \begin{gathered} \mathrm{n}=3.32 * \log \left(\frac{\theta 600}{\theta 300}\right) \\ \mathrm{K}=\frac{\theta 600}{1022^{\mathrm{n}}} \\ \mathrm{x}=81600 * \mathrm{~K} * \frac{(\mathrm{n})^{0.387}}{\left((\mathrm{Dh}-\mathrm{Dp})^{\mathrm{n}}\right) * \mathrm{MW}} \\ \mathrm{AVc}=\mathrm{x}^{\frac{1}{2-(\mathrm{n})}} \\ \mathrm{GPMc}=\mathrm{AVc} * \frac{\mathrm{Dh}^{2}-\mathrm{Dp}^{2}}{24.5} \end{gathered} $$

Reference(s)

Lyons, W. C., Carter, T., and Lapeyrouse, N. J., 2012, Formulas and Calculations for Drilling, Production and Workover, Third Edition, Gulf Professional Publishing, Page: 212.