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The IPR analysis is closely related to well PI – Productivity Index
which is defined as below:
| LaTeX Math Block |
|---|
| J_s(q_{\rm liq}) = \frac{q_{\rm liq}}{p_R-p_{wf}} |
|
for oil producer with surface liquid production (water and oil) |
| LaTeX Math Block |
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| J_s(q_g) = \frac{q_g}{p_R-p_{wf}} |
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for gas producer |
| LaTeX Math Block |
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| J_s(q_g) = \frac{q_g}{p_{wf}-p_R} |
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for gas injector |
| LaTeX Math Block |
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| J_s(q_w) = \frac{q_w}{p_R-p_{wf}} |
|
for water injector |
where
| water, oil, gas flow rates at separator |
| field-average formation pressure withing the drainage area of a given well: | LaTeX Math Inline |
|---|
| body | p_R = \frac{1}{V_e} \, \int_{V_e} \, p(t, {\bf r}) \, dV |
|---|
|
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Based on these notions the general WFP – Well Flow Performance can be wirtten in univseral universal form:
| LaTeX Math Block |
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|
p_{wf} = p_R - \frac{q}{J_s(q)} |
providing that
has a specific meaning and sign as per the table below:
| for producer |
| for injector |
| LaTeX Math Inline |
|---|
| body | q=q_{\rm liq}=q_o+q_w |
|---|
|
| for oil producer |
| for gas producer or injector |
| for water injector or water-supply producer |
For a single - layer formation with low-compressibility fluid (like water) the PI does not depend on flowrate drwadown (or flowrate)
and
WFP – Well Flow Performance plot is reperented by a straight line (Fig. 1)
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It can be interpreted as deterioration of near-reservoir zone permeability with fluid velocity growthis growing.
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In general case of saturated oil, the PI
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features a complex dependance on bottom-hole pressure ...
( or flowrate ) which can be etstablished based on numerical simulations of multiphase formation flow.But when field-average formation pressure is above bubble-point as a function of
: (which means that most parts of the drainage area are saturated oil) the PI can be farily approximated by some analytical correlations.
| Note |
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Despite of terminological similarity there is a big difference in the way WFP and Well Testing deal with formation pressure and flowrates which results in a big difference in productivity index definition and corresponding analysis. This difference is summarized in the table below:
| WFP | Well Testing |
|---|
| Formation pressure | – field-average pressure within the drainage area
| – pressure value at boudary of the drainage area
| | Flow rate | | LaTeX Math Inline |
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| body | q_{\rm liq}=q_oO+q_wW |
|---|
|
– surface liquid rate | | LaTeX Math Inline |
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| body | q_t = B_w \, q_W + \frac{B_o - R_s B_g}{1 - R_v R_s} \, q_O + \frac{B_g - R_v B_o}{1 - R_v R_s} \, q_G |
|---|
|
– total flowrate at sandface | | Prroducivity Index | | LaTeX Math Inline |
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| body | J = \frac{q_{\rm liq}}{p_R - p_{wf}} |
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|
| LaTeX Math Inline |
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| body | J_g = \frac{q_g}{p_R - p_{wf}} |
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|
| | LaTeX Math Inline |
|---|
| body | J = \frac{q_t}{p_e - p_{wf}} |
|---|
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