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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:
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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 |
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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:
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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)
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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:
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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] |
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– water-based or water-oil-based
transmissbility transmissibility above bubble point
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anchor | Perrine2phase_alpha |
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page | Linear Perrine multi-phase diffusion @model |
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,
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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 |
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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 |
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body | \{ q_{max} \, , \, n \} |
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or .
But obviously more tests will make assessment more accruate.
Saturated Oil IPR
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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 ]
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