Normalized dimensionless difference between the sandface bottomhole pressure (BHP) p_{wf}(t) and a reservoir pressure p_{\rm ref}(t,r) of a reference model of a full-entry vertical well with homogeneous and non-damaged near-well reservoir zone estimated at wellbore radius r_w:
| S = \frac{p_{\rm ref}(t, r_w) - p_{wf}(t)}{ \left[ r \cdot \frac{\partial p_{\rm ref}}{\partial r} \right]_{r=r_w} } |
It can be interpreted as the dimensionless ratio of linear-average pressure gradient between wellbore axis and wellbore radius to the actual pressure gradient at wellbore radius:
| S = \left[ \frac{p_{\rm ref}(t, r_w) - p_{wf}(t)}{ r_w } \right] \Big/ { \left[ \frac{ \partial p_{\rm ref}}{\partial r} \right]_{r=r_w}} |
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_w.
This means that skin-based pressure calculations in the damaged or in non-homogenous and non-radial-flow area around a well may become a bit inaccurate.
Nevertheless the size of a damaged area is usually much smaller than a drainage area during the well testing () the skin-factor concept works just fine for the most practical well tests applications.
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_{\rm ref}(t,r_w) |
where
q_t | total sandface rate |
\sigma | formation transmissibility outside the damaged reservoir zone A_s |
p_{\rm ref}(t,r) | a reference model of a full-entry vertical well with homogeneous reservoir and non-damaged near-reservoir zone |
See Also
Petroleum Industry / Upstream / Subsurface E&P Disciplines / Well Testing / Pressure Testing