The near reservir zone across the well penetration is subject to damage under anthropogenic activity (like drilling or various types of reservoir invasion and treatment).

The extension of damaged zone is characterized by the damade radius $\begin{array}{l}r_s\end{array}$ :

(1)	$\begin{array}{l}\displaystyle r_w < r < r_s\end{array}$

where

$\begin{array}{l}r_w\end{array}$

well radius

The typical extension of the damage zone around wellbore is $\begin{array}{l}0.1 \, \mbox{m} \leq r_s - r_w \leq 1 \, \mbox{m}\end{array}$ .

The permeability of the damaged zone $\begin{array}{l}k_s\end{array}$ can show an improvement $\begin{array}{l}k_s > k\end{array}$ or deterioration $\begin{array}{l}k_s < k\end{array}$ against the permeability of the far reservoir zone $\begin{array}{l}k\end{array}$ :

(2)	$\begin{array}{l}{\rm Permeability} = \begin{cases} k_s, & \mbox{if } r_w \leq r \leq r_s \\ k, & \mbox{if } r> r_s \end{cases}\end{array}$

This leads to adjustment to the pressure drop comparing to the case when the near-reservoir zone stays undamaged which is called Mechanical Skin.

In general case to account for the effects of Mechanical Skin one has to perform a proper simulation of pressure drop against the damaged zone.

But in many practical cases the problem can be simplified by the radial composite approximation.

The pressure drop in radial flow across reservoir rim $\begin{array}{l}r_1 \leq r \leq r_2\end{array}$ is:

(3)	$\begin{array}{l}\displaystyle \Delta p = \frac{q}{2\pi\sigma}\ln\frac{r_2}{r_1}\end{array}$

where

$\begin{array}{l}q\end{array}$	volumetric flowrate
$\begin{array}{l}\sigma = \frac{k \cdot h}{\mu}\end{array}$	reservoir transmissibility

The pressure drop $\begin{array}{l}\Delta p = p_e - p_{wf}\end{array}$ between wellbore pressure $\begin{array}{l}p_{wf}\end{array}$ and formation pressure at the boundary of the drainage area $\begin{array}{l}p_e\end{array}$ is the sum of pressure drops inside and outside the damaged zone:

(4)	$\begin{array}{l}\displaystyle \Delta p = p_e - p_{wf} = (p_e - p_s) + (p_s - p_{wf}) = \frac{q}{2\pi\sigma_s}\ln\frac{r_s}{r_w} + \frac{q}{2\pi\sigma}\ln\frac{r_e}{r_s}\end{array}$

The same pressure drop $\begin{array}{l}\Delta p = p_e - p_{wf}\end{array}$ can be expressed through the definition of mechanical skin-factor (Skin-factor (mechanical):1)as:

(5)	$\begin{array}{l}\displaystyle \Delta p = p_e - p_{wf} = \frac{q}{2\pi\sigma} \left( \ln\frac{r_e}{r_w} + S \right)\end{array}$

Comparing (4) and (5):

(6)	$\begin{array}{l}\displaystyle \frac{q}{2\pi\sigma} \left( \ln\frac{r_e}{r_w} + S \right) = \frac{q}{2\pi\sigma_s}\ln\frac{r_s}{r_w} + \frac{q}{2\pi\sigma}\ln\frac{r_e}{r_s}\end{array}$

which leads to

(7)	$\begin{array}{l}\displaystyle \frac{1}{k} \left( \ln\frac{r_e}{r_w} + S \right) = \frac{1}{k_s}\ln\frac{r_s}{r_w} + \frac{1}{k}\ln\frac{r_e}{r_s}\end{array}$

(8)	$\begin{array}{l}\displaystyle \ln\frac{r_e}{r_w} + S = \frac{k}{k_s}\ln\frac{r_s}{r_w} + \ln\frac{r_e}{r_s}\end{array}$

(9)	$\begin{array}{l}\displaystyle S = \frac{k}{k_s}\ln\frac{r_s}{r_w} + \ln\frac{r_w}{r_s} =\left( \frac{k}{k_s} - 1 \right) \ln\frac{r_s}{r_w}\end{array}$

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Hawkins equation for mechanical skin-factor @model

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