# Viscous shear stress at the outer mudcake boundary

## Input(s)

$$R_{c}$$: Radius from the Center of Drillpipe to the beginning of Mudcake (in.)

$$R_{p}$$: Radius from the Center to the Inner Boundary of the Drillpipe (in.)

$$v_{z}$$: Axial Velocity Parallel to the Wellbore Axis (in/s)

$$x_{f}$$: Transient Invasion Front (in.)

$$x_{f, o}$$: Initial Displacement, i.e., Spurt (in.)

$$\frac{d p}{d z}$$: Pressure change with $$\mathrm{Z}$$ direction that is parallel to the Wellbore Axis (psi/in.)

$$\mu$$: Viscosity $$(\mathrm{cP})$$

## Output(s)

$$\tau_{(R c)}$$: Viscous Shear Stress at the outer Mudcake boundary (lb/in. $${ }^{2}$$ )

## Formula(s)

$\begin{gathered} \tau_{(R c)}=\mu\left(d v_{z} / d r\right)_{(R c)} \\ \tau_{(R c)}=\frac{1}{4}\left[2 R_{c}+\left\{\left(R_{c}^{2}-R_{p}^{2}\right) /\left(R_{c} \log \left(R_{p} / R_{c}\right)\right)\right\}\right] \frac{d p}{d z} \end{gathered}$

## Reference(s)

Chin, W. C. (1995). Formation Invasion, Page: 59.

An unhandled error has occurred. Reload 🗙