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.