Differential hydrostatic pressure between cement in the annulus and mud inside the casing

Input(s)

$\mathrm{h}_{\mathrm{w}}$: Well Depth (ft)

$\mathrm{h}_{\mathrm{f}}$: Float Collar (Feet Number Above the Shoe) (ft)

$\mathrm{h}_1$: Lead Slurry Depth (ft)

$\mathrm{h}_{\mathrm{t}}$: Tail Slurry Depth (ft)

$\mathrm{w}_{\mathrm{m}}$: Mud Weight (lb/gal)

$\mathrm{w}_{\mathrm{l}}$: Lead Slurry Weight (lb/gal)

$\mathrm{w}_{\mathrm{t}}$: Tail Slurry Weight (lb/gal)

Output(s)

$\mathrm{P}_{\mathrm{a}}$: Total Pressure in Annulus (psi)

$\mathrm{P}_{\mathrm{c}}$: Total Pressure in Casing (psi)

$\mathrm{P}_{\mathrm{d}}$: Total Pressure Differential (psi)

Formula(s)

$$ \begin{gathered} \mathrm{P}_{\mathrm{a}}=0.052 *\left(\mathrm{w}_{\mathrm{l}} * \mathrm{~h}_{\mathrm{l}}+\mathrm{w}_{\mathrm{t}} * \mathrm{~h}_{\mathrm{t}}+\mathrm{w}_{\mathrm{m}} *\left(\mathrm{~h}_{\mathrm{w}}-\mathrm{h}_{\mathrm{l}}-\mathrm{h}_{\mathrm{t}}\right)\right) \\ \mathrm{P}_{\mathrm{c}}=0.052 *\left(\mathrm{w}_{\mathrm{m}} *\left(\mathrm{~h}_{\mathrm{w}}-\mathrm{h}_{\mathrm{f}}\right)+\mathrm{w}_{\mathrm{t}} * \mathrm{~h}_{\mathrm{f}}\right) \\ \mathrm{P}_{\mathrm{d}}=\mathrm{P}_{\mathrm{a}}-\mathrm{P}_{\mathrm{c}} \end{gathered} $$

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: 84.