The plot of water production rate(along y-axis) against the oil production rate (along x-axis).
It can be used for express Watercut Diagnostics of thief water production.
The mathematical model of the thief water production from aquifer is based on the following equation:
| LaTeX Math Block |
|---|
| q_W = a \, \cdot q_O + b |
| | LaTeX Math Block |
|---|
| a = J^{-1}_{1O} \cdot ( J_{1W} + J_{2W}) |
| | LaTeX Math Block |
|---|
| b = J_{2W} \cdot (p^*_2 - p^*_1) |
|
where
For the case of aquifer pressure is higher than that of petroleum reservoir:
| LaTeX Math Inline |
|---|
| body | --uriencoded--b > 0 \Leftrightarrow p%5e*_2 > p%5e*_1 |
|---|
|
For the case of aquifer pressure is lower than that of petroleum reservoir:
| LaTeX Math Inline |
|---|
| body | --uriencoded--b < 0 \Leftrightarrow p%5e*_2 < p%5e*_1 |
|---|
|
In practical applications, the equation
| LaTeX Math Block Reference |
|---|
|
is often considered through the
weighted average values:
| LaTeX Math Block |
|---|
|
<q_W> = a \, \cdot <q_O> + \, b |
where
| are weighted average of and |
There are different ways to calculate weighted average of the dynamic variable, for example:
| |
|---|
| LaTeX Math Block |
|---|
| < A >_t \ = \frac{1}{t} \int_o^t A(t) \, dt |
| | LaTeX Math Block |
|---|
| <A>_q \ = \frac{1}{Q(t)} \int_o^t A(t) \, q(t) \, dt |
|
See Also
Petroleum Industry / Upstream / Production / Subsurface Production / Field Study & Modelling / Production Analysis / Watercut Diagnostics
