# 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.