One of the Productivity Diagnostics methods based on relation between the bottom-hole pressure
and surface flow rate
during the
stabilised formation flow (see
the reference to original paper of Gilbert):
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p_{wf} = p_{wf}(q) |
One of the two key concepts of Well Flow Performance analysis along with Vertical Lift Performance (VLP).
The word "Inflow" is misnomer as Inflow Performance Relationship (IPR) analysis is applicable for both producers and injectors.
The Inflow Performance Relationship (IPR) analysis is closely related to well Productivity Index (PI)
which is defined as below:
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In general case of multiphase flow the PI
features a complex dependance on bottom-hole pressure
(or equivalently on flowrate
) which can be etstablished based on numerical simulations of multiphase formation flow.
For undersaturated reservoir the numerically-simulated Inflow Performance Relationship (IPR)s have been approximated by analytical models and some of them are brought below.
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These correaltions should be calibrated to the available well test data to set a up a customised IPR model for a given formation.
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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 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 PI can be estimated using the Darcy equation:
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The alternative form of the constant Productivity Index IPR is given by:
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\frac{q}{q_{max}} = 1 -\frac{p_{wf}}{p_r} |
where
is the maximum reservoir deliverability when the bottom-hole is at atmospheric pressure and also called
Absolute Open Flow (AOF).
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For gas producers, the fluid compressibility is high and formation flow is essentially non-linear, inflicting the downward trend on the whole IPR plot (Fig. 3).
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But obviously more tests will make assessment more accruate.
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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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For undersaturated oil reservoir
the behavior of
IPR model will vary on whether the bottom-hole pressure is above or below bubble point.
When it is higher than bubble point
then formation flow will be single-phase oil and production will follow the constant
Inflow Performance Relationship (IPR).
When bottom-hole pressure goes below bubble point
the near-reservoir zone free gas slippage also inflicts the downward trend at the right side of
IPR plot (
Fig. 5).
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q_{max} = q_b \, \Big[1 + \frac{1}{1.8} \frac{p_b}{(p_r - p_b)} \Big] |
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For saturated 3-phase water-oil-gas reservoir the IPR analysis is represented by oil and water components separately (see Fig. 6.1 and Fig. 6.2).
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\frac{q_w}{q_{w, \, max}} = 1 - 0.72 \, \frac{p_{wf}}{p_r} - 0.28 \Bigg(\frac{p_{wf}}{p_r} \Bigg)^2 |
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For undersaturated 3-phase water-oil-gas reservoir the IPR analysis is represented by oil and water components separately (see Fig. 7.1 and Fig. 7.2).
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The analytical correlation for saturated 3-phase oil flow is given by Wiggins model: | LaTeX Math Block |
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| \frac{q_o}{q_{o, \, max}} = 1 - 0.52 \, \frac{p_{wf}}{p_r} - 0.48 \Bigg(\frac{p_{wf}}{p_r} \Bigg)^2 |
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| \frac{q_w}{q_{w, \, max}} = 1 - 0.72 \, \frac{p_{wf}}{p_r} - 0.28 \Bigg(\frac{p_{wf}}{p_r} \Bigg)^2 |
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Petroleum Industry / Upstream / Production / Subsurface Production / Subsurface E&P Disciplines / Field Study & Modelling / Production Analysis / Productivity Diagnostics
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[ Vogel IPR @model ] [ Richardson and Shaw IPR @ model ] [ Wiggins IPR @ model ]
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Gilbert, W.E.: "Flowing and Gas-Lift Well Performance," Drill. and Prod. Prac.
, API (1954) 126.
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