Normalised dimensionless difference between the sandface bottomhole pressure (BHP) p_{wf}(t) and a model of a full-entry vertical well with homogeneous reservoir and non-damaged near-well reservoir zone p^*_{wf}(t):
| S = \frac{p_{wf}(t) - p(t, r_w)}{r_w \cdot \frac{\partial p}{\partial r} \Bigg|_{r=r_w} } |
where
q_t | total sandface rate |
\sigma | formation transmissibility outside the damaged reservoir zone A_s |
By definition the skin-factor is a pressure adjustment at the well-reservoir contact and does not affect pressure distribution in reservoir away from wellbore r > r_s.
The total skin is usually decomposed into a sum of two components:
| S_T = S_G + \frac{A_w}{A_{wrc}} \cdot S_M |
where
S_G | Geometrical skin, related to deviation of the well-reservoir contact from the simplest model |
S_M | Mechanical skin, related to pressure drop caused by the near-reservoir zone formation damage |
A_w | borehole flow area |
A_{wrc} | well-reservoir contact area |
Based on definition the wellbore pressure dynamics p_{wf}(t) of the well with skin-factor can be writen as:
| p_{wf}(t) = \frac{q_t}{2 \pi \sigma} \, S + p^*_{wf}(t) |
where p^*_{wf}(t) is a model of a full-entry vertical well with homogeneous reservoir and non-damaged near-reservoir zone.