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 :

r_w < r < r_s

where

well radius

The typical extension of the damage zone around wellbore is .

The permeability of the damaged zone can show an improvement or deterioration against the permeability of the far reservoir zone :

{\rm Permeability} = \begin{cases} 
k_s, & \mbox{if } r_w \leq r \leq r_s
\\ 
k, & \mbox{if } r> r_s
\end{cases}

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 is:

\Delta p = \frac{q}{2\pi\sigma}\ln\frac{r_2}{r_1}

where

	volumetric flowrate
	reservoir transmissibility

The pressure drop between wellbore pressure and formation pressure at the boundary of the drainage area is the sum of pressure drops inside and outside the damaged zone:

\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}

The same pressure drop can be expressed through the definition of mechanical skin-factor as:

\Delta p = p_e - p_{wf} = \frac{q}{2\pi\sigma} \left( \ln\frac{r_e}{r_w} + S \right)

Comparing and :

\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}

which leads to

\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}

 \ln\frac{r_e}{r_w} + S = \frac{k}{k_s}\ln\frac{r_s}{r_w} + \ln\frac{r_e}{r_s}

  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}

See Also