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| field-average formation pressure within the drainage area of a given well: | LaTeX Math Inline |
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| body | p_R = \frac{1}{V_e} \, \int_{V_e} \, p(t, {\bf r}) \, dV |
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Based on above defintions the general general WFP – Well Flow Performance can be wirtten in a general form:
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providing that
has a specific meaning and sign as per the table below:
| for producer |
| for injector |
| LaTeX Math Inline |
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| body | q=q_{\rm liq}=q_o+q_w |
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| 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 pressure
or equivalently on flowrate .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.Some analytical correlations can be used to approximate the numerical solutions and some of them are brought below.
They are very helpful in practise to design a proper well flow optimization procedure.
These correaltions should be calibrated to the available well test data to set a up a customized WFP – Well Flow Performance model for a given formation.
Water and Dead Oil IPR
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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
WFP – Well Flow Performance plot is reperented by a straight line (Fig. 1)
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For gas producers, the fluid compressibility is high and formation flow in well vicinity becomes flow is essentially non-linear (deviating from Darcy) fot high flowrates, inflicting the downward trend on on the whole WFP – Well Flow Performance plot (Fig. 2).
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In general case of saturated oil, the PI
features a complex dependance on bottom-hole pressure ( or flowrate ) which can be etstablished based on numerical simulations of multiphase formation flow....
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Saturated Oil IPR
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For 2-phase oil-gas formation flow below bubble point
the free gas slippage effects
inflict inflicting the downward trend
on at the right side of WFP – Well Flow Performance plot (Fig. 3).
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But when field-average formation pressure is above bubble-point (which means that most parts of the drainage area are saturated oil) the PI can be farily approximated by some analytical correlations.
Multiphase IPR
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For 3-phase water-oil-gas flow the IPR analysis is perfomed on oil and watr components (see Fig. 4.1 and Fig. 4.2).
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