...
The EUR during the natural oil depletion can be assessed with the following formulaequation (see NDR @model for derivation):
LaTeX Math Block | ||||
---|---|---|---|---|
| ||||
{\rm EUR}_{\rm NDR}O = \frac{Q_oO}{V_oO} = \frac{ (p_i - p_{wf}) \, c_t}{(1-s_{wi})\, B_o} = \frac{ (p_i - p_{wf}) }{(1-s_{wi})\, B_o} \, \big( c_r + s_{wi} c_w + (1-s_{wi})c_o \big) |
where
|
---|
...
minimal flowing bottom-hole pressure |
...
|
---|
...
initial formation pressure |
...
|
---|
...
formation volume factor for oil, |
...
|
---|
...
cumulative oil production |
...
|
---|
...
STOIIP |
...
|
---|
...
initial water saturation in oil pay |
...
title | EUR Deduction |
---|
...
|
---|
...
LaTeX Math Block | ||||
---|---|---|---|---|
| ||||
V_O = V_o/B_o = s_o \, V_\phi = (1-s_{wi}) \, V_\phi |
so that
LaTeX Math Block | ||||
---|---|---|---|---|
| ||||
V_\phi = \frac{B_o \, Q_O}{(1-s_{wi})} |
The pore volume reduction due to offtakes is:
LaTeX Math Block | ||||
---|---|---|---|---|
| ||||
\delta V_\phi = Q_O \, B_o |
thus leading to
...
...
|
---|
...
where
...
anchor | 1 |
---|---|
alignment | left |
...
...
...
...
\delta p = p_i - p_{wf}
pressure reduction due to pore volume reduction caused by offtakes.
For
...
the
...
LaTeX Math Inline | ||
---|---|---|
|
...
LaTeX Math Block Reference | ||
---|---|---|
|
...
LaTeX Math Block | ||||
---|---|---|---|---|
| ||||
\frac{1-s_{wi}}{\delta p} \cdot {\rm EUR_O} = c_t \, (p_i - p_{wf \, min}) |
and
LaTeX Math Block | ||||
---|---|---|---|---|
| ||||
{\rm EUR}_{\rm NDR} = \frac{Q_o}{V_o} = \frac{ (p_i - p_{wf \, min}) \, c_t}{(1-s_{wi})\, B_o} |
For the naturally flowing wells the bottom hole pressure under flowing conditions can be roughly assed by homogeneous multiphase pipe flow model assessed as:
...
Petroleum Industry / Upstream / Production / Field Development Plan / Recovery Methods
[ NDR @model ]