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The word "Inflow" is misnomer as IPR analysis is applicable for both producers and injectors.
The most general proxy-model is given by LIT (Laminar Inertial Turbulent) IPR model:
| LaTeX Math Block |
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|
a \, q + b \, q^2 = \Psi(p_r) - \Psi(p_{wf}) |
where
| static wellbore pressure |
| laminar flow coefficient |
| turbulent flow coefficient |
| pseudo-pressure function specific to fluid type |
It needs well tests at least three different rates to assess
| LaTeX Math Inline |
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| body | --uriencoded--\%7B a \, , \, b, \, p_r \%7D |
|---|
|
but obviously more tests will make assessment more accurate.
The IPR analysis is closely related to well Productivity Index (PI)
which is defined as below:
...
For a single layer formation with low-compressibility fluid (water or dead oil) the PI does not depend on drawdown (or flowrate)
and
IPR plot is
reperented represented by a straight line (
Fig. 2)
...
This is a typical IPR plot for water supply wells, water injectors and dead oil producers.
The For the oil/water production the PI can be estimated using the Darcy equation Dupuit PI @model:
| LaTeX Math Block |
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J_s = \frac{2 \pi \sigma}{ \ln \frac{r_e}{r_w} + \epsilon+ S} |
where
| LaTeX Math Inline |
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| body | \sigma = \Big \langle \frac{k} {\mu} \Big \rangle \, h = k \, h\, \Big[ \frac{k_{rw}}{\mu_w} + \frac{k_{ro}}{\mu_o} \Big] |
|---|
|
– water-based or water-oil-based
transmissbility transmissibility above bubble point
| LaTeX Math Block Reference |
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| anchor | Perrine2phase_alpha |
|---|
| page | Linear Perrine multi-phase diffusion @model |
|---|
|
,
...
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 |
|---|
|
a \, q + b \, q^2 = \Psi(p_r) - \Psi(p_{wf}) |
where
– is pseudo-pressure function specific to a certain gas PVT model, is laminar flow
coefficient and is turbulent flow coefficient.
It needs two well tests at two different rates to assess
| LaTeX Math Inline |
|---|
| body | \{ q_{max} \, , \, n \} |
|---|
|
or . But obviously more tests will make assessment more accruate.
Saturated Oil IPR
...
For saturated oil reservoir the free gas flow inflict the downward trend of IPR plot similar to dry gas (Fig. 4).
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[ Vogel IPR @model ] [ Richardson and Shaw IPR @ model ] [ Wiggins IPR @ model ][ LIT IPR @ model ][ PADE IPR @ model ]
[ Dual-layer IPR][ Multi-layer IPR ] [ Dual-layer IPR with dynamic fracture ]
Reference
...
Gilbert, W.E.: "Flowing and Gas-Lift Well Performance," Drill. and Prod. Prac.
, API (1954) 126.
...
