Difference between the actual wellbore pressure and a pressure Normalized dimensionless difference between the sandface bottomhole pressure (BHP)
and a reservoir pressure of a reference model of a full-entry vertical well with homogeneous
reservoir and non-damaged
near-well reservoir zone estimated at wellbore radius :
LaTeX Math Block |
---|
|
S = \frac{2 \pi \sigma }{q_t} \, \delta p |
By definition the skin-factor is a pressure adjustment at the well wall and does not affect pressure distribution in reservoir away from wellbore.
Dimensionless value characterising permeability change in a thin layer around the well cased by stimulations or deteriorations, represented by Hawkins' equation:
{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:
LaTeX Math Block |
---|
LaTeX Math Block |
---|
anchor | TI84W |
---|
|
S = \left[ ( \frac{k}{k_s} - 1 \right ) \ \ln \left ( \frac{r_s}{r_w} \right ) |
Motivation
...
...
...
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
...
...
.
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:
LaTeX Math Block |
---|
|
S_T = S_G + \frac{A_w}{A_{wrc}} \cdot S_M |
where
Based on definition the wellbore pressure dynamics
В зависимости от типа коллектора и технологии бурения и освоения скважины проницаемость призабойной зоны
может оказаться как лучше так и хуже удаленной зоны пласта : .В общем случае, для учета этого явления при расчете динамики давления пласта необходимо применять радиально-композитную фильтрационную модель: внутреннее кольцо пораженного пласта + внешнее кольцо невредимого пласта.
Однако, если кольцевая зона поражения пласта намного меньше радиуса дренирования
LaTeX Math Block |
---|
anchor | rsrwre |
---|
alignment | left |
---|
|
r_s - r_w \ll r_e \rm \, , |
...
...
...
of the well with skin-factor can be writen as: LaTeX Math Block |
---|
anchor | P_wf_skin |
---|
|
p_{wf}(t) = p^o_{wf}(t)| - \frac{q_t}{2 \pi \sigma} \ Sгде – дебит скважины в пластовых условиях, – гидропроводность дальней зоны пласта, – скин-фактор – безразмерная характеристика повреждения призабойной зоны: LaTeX Math Block |
---|
| S = \bigg ( \frac{k}{k_s} - 1 \bigg ) \ \ln \big ( \frac{r_s}{r_w} \big ) |
Из определения видно, что ухудшенная призабойная зона , S + p_{\rm ref}(t,r_w) |
where
...
...
...
...
...
...
...
...
LaTeX Math Block Reference |
---|
|
...
На практике, наиболее популярные значения скин-фактора лежат в интервале
. В частности, однофазная радиальная фильтрация в однородном бесконечном пласте, вскрытым скважиной со скин-фактором
приводит к следующей формуле для забойного давления: LaTeX Math Block |
---|
|
p_{wf}(t) = p(t,r_w) = p_i + \frac{q_t}{4 \pi \sigma} \, \bigg[ - 2S + {\rm Ei} \bigg( - \frac{r_w^2}{4 \chi t} \bigg) \bigg] |
...
...
LaTeX Math Block Reference |
---|
page | 1DR Line Source Solution (LSS) @model |
---|
|
...
| 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
[ Well & Reservoir Surveillance ]
[ Skin-factor (geometrical) ][ Skin-factor (mechanical) ]