...
providing that
has a specific meaning and sign as per the table below:
| for producer |
| for injector |
| LaTeX Math Inline |
|---|
| body | q=q_{\rm liq}=q_o+q_w |
|---|
|
| for oil producer |
| for gas producer or injector |
| for water injector or water-supply producer |
The Productivity Index can be constant or dependent on bottom-hole pressure
or equivalently on flowrate
.
...
The popular dry gas IPR correlation is Rawlins and Shellhardt:
| LaTeX Math Block |
|---|
| anchor | IPRGas |
|---|
| alignment | left |
|---|
|
\frac{q}{q_{max}} = \Bigg[ \, 1- \Bigg( \frac{p_{wf}}{p_R} \Bigg)^2 \, \Bigg]^n |
where
is the turbulent flow exponent, equal to 0.5 for fully turbulent flow and equal to 1 for laminar flow.
The more accurate approximation is given by LIT (Laminar Inertial Turbulent) IPR model:
| LaTeX Math Block |
|---|
|
q \, q + b \, q^2 = \Psi(p_R) - \Psi(p_{wf}) |
where
– is pseudo-pressure function, is laminar flow coefficient and is turbulent flow coefficient.
Saturated Oil IPR
...
For 2-phase oil-gas formation flow below bubble point
the free gas slippage effects inflicting the downward trend at the right side of
WFP – Well Flow Performance plot (Fig. 3).
...
