Normalised dimensionless difference between the sandface bottomhole pressure (BHP) $\begin{array}{l}p_{wf}(t)\end{array}$ and the sandface reservoir pressure $\begin{array}{l}\displaystyle p({\bf r}, t) |_{{\bf r} \in \Gamma_s}\end{array}$ at the boundary $\begin{array}{l}\Gamma_s\end{array}$ of damaged reservoir zone $\begin{array}{l}A_s\end{array}$ :

(1)	$\begin{array}{l}\displaystyle S_M = \frac{2 \pi \sigma}{q_t} \cdot \left[ p_{wf}(t) - p({\bf r}, t) \|_{{\bf r} \in \Gamma_s} \right]\end{array}$

where

$\begin{array}{l}q_t\end{array}$	total sandface rate
$\begin{array}{l}\sigma\end{array}$	formation transmissibility at the boundary $\begin{array}{l}\Gamma_s\end{array}$ of the damaged reservoir zone $\begin{array}{l}A_s\end{array}$
$\begin{array}{l}A_s\end{array}$	damaged reservoir zone
$\begin{array}{l}\Gamma_s\end{array}$	boundary of damaged reservoir zone

The (1) can be re-wrriten as:

(2)	$\begin{array}{l}\displaystyle p_{wf}(t) = p^o_{wf}(t)\| - \frac{q_t}{2 \pi \sigma} \ S_M\end{array}$

with the meaning that near-reservoir damage is resulting in additional pressure drop quantified by the value of mechanical skin-factor $\begin{array}{l}S_M\end{array}$

It quantitatively characterises permeability change in a thin layer (usually < 1 m) around the well or around the fracture plane, caused by stimulation or deterioration during the reservoir invasion under drilling or well intervention or under routine production or injection.

It contributes to the total skin estimated in transient well testing.

For the radial-symmetric permeability change around the well it can be estimated by means of Hawkins equation:

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

where

$\begin{array}{l}r_w\end{array}$	well radius from drilling
$\begin{array}{l}r_s\end{array}$	damaged reservoir ( $\begin{array}{l}k_s \neq k\end{array}$ ) radius: $\begin{array}{l}r_s > r_w\end{array}$ ( the most typical range is: $\begin{array}{l}r_w < r_s < 1\end{array}$ m )
$\begin{array}{l}k\end{array}$	absolute formation permeability in the undamaged reservoir zone away from well location
$\begin{array}{l}k_s\end{array}$	absolute formation permeability in the damaged near-well reservoir zone

The definition of $\begin{array}{l}S_M\end{array}$ in (3) suggests that:

deteriorated permeability of the near-well reservoir zone $\begin{array}{l}k_s < k\end{array}$ is characterised by a positive skin-factor $\begin{array}{l}S>0\end{array}$ ,
improved permeability of the near-well reservoir zone $\begin{array}{l}k_s > k\end{array}$ is characterised by a negative skin-factor $\begin{array}{l}S< 0\end{array}$ .

The most popular practical range of skin-factor variation is $\begin{array}{l}-5 < S_M < 8\end{array}$ with upper limit may sometimes extend further up.

For the negative skin-factor values there is a natural limitation from below caused by the Mechanical Skin concept itself.

The Mechanical Skin concept is trying to approximate the true inhomogeneity of the near and far reservoir zones with homogenous far reservoir model and additional pressure drop at the well wall.

In case of high permeability

The values of $\begin{array}{l}S_M < -5\end{array}$ are usually not supported by the majority of commercial simulators as these values assume almost infinite permeability in the 10 m area around the well see (4) below:

(4)	$\begin{array}{l}\displaystyle k_s = k \cdot \left[ 1+\frac{S_M}{ \ln \frac{r_s}{r_w}} \right]^{-1} \rightarrow \infty \, \mbox{ when } S_M \rightarrow -5\end{array}$

In other words, the highly negative skin-factor $\begin{array}{l}S_M < -5\end{array}$ should be modelled as composite area around near-reservoir zones rather than using the concept of Mechanical Skin.

For horizontal wells the lower practical limit when Mechanical Skin concept can be applied is even lower and usually assumed as 0.

Page tree

See Also

Page tree

Skin-factor (mechanical)

See Also