# 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.

## Related

### Difference in pressure gradient between the cement and mud

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