The plot of. WOR (along y-axis) against the inverse oil production rate (along x-axis) (see Fig. 1).
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 |
|---|
| WOR = \frac{q_W}{q_O} = a + b \cdot q^{-1}_O |
| | LaTeX Math Block |
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| a = J^{-1}_{1O} \cdot ( J_{1W} + J_{2W}) |
| | LaTeX Math Block |
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| 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 |
|---|
|
<WOR> =\frac{<q_W>}{<q_O>} = a + b \cdot <q_O^{-1}> |
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
References
Chan, K. S. (1995, January 1). Water Control Diagnostic Plots. Society of Petroleum Engineers. doi:10.2118/30775-MS
