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The Inflow Performance Relation (IPR) analysis is closely related to well Productivity Index (PI)
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| for gas producer with gas flowrate
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| for gas injector with injection rate
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| for water injector with injection rate
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where
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Based on above defintions the aribitrary IPR can be wirtten in a general form:
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providing that
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| for water injector or water producer or water production from oil producer |
See more on the variations of PI definition between Dynamic Modelling, Well Flow Performance and Well Testing.
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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)
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| Fig.1. IPR plot for constant productivity (water and dead oil) |
This is a typical IPR plot for water supply wells, water injectors and dead oil producers.
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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. 2).
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Fig. 2. IPR for dry gas producer or gas injector into a gas formation |
The popular dry gas IPR correlation is Rawlins and Shellhardt:
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For saturated oil reservoir the free gas flow inflict the downward trend of IPR plot similar to dry gas (Fig. 3).
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Fig. 3. IPR for 2-phase oil+gas production below and above bubble point |
The analytical correlation for saturted oil flow is given by Vogel model:
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\frac{q}{q_{max}} = 1 - 0.2 \, \frac{p_{wf}}{p_r} - 0.8 \Bigg(\frac{p_{wf}}{p_r} \Bigg)^2 \quad , \quad p_b > p_r > p_{wf} |
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It can be interpreted as deterioration of near-reservoir zone permeability when the fluid velocity is high and approximated by rate-dependant skin-factor.
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Fig. 3. IPR for 2-phase oil+gas production below and above bubble point |
The analytical correlation for undersaturated oil flow is given by modified Vogel model:
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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. 4.1 and Fig. 4.2).
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Fig. 4.1. Oil IPR for saturated 3-phase (water + oil + gas) formation flow | Fig. 4.2. Water IPR for saturated 3-phase (water + oil + gas) formation flow |
The analytical correlation for saturated 3-phase oil flow is given by Wiggins model:
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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. 4.1 and Fig. 4.2).
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Fig. 4.1. Oil IPR for udersaturated 3-phase (water + oil + gas) formation flow | Fig. 4.2. Water IPR for undersaturated 3-phase (water + oil + gas) formation flow |
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The analytical correlation for saturated 3-phase oil flow is given by Wiggins model:
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