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LaTeX Math Block |
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| q = q_1 + q_2 |
| LaTeX Math Block |
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| p_{wf} = p_e - q/J |
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LaTeX Math Block |
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| J = J_1 + J_2 |
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LaTeX Math Block |
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| p_e = \frac{J_1 \cdot p_1 + J_2 \cdot (p_2- \rho \, g \, hdelta p_2)}{J_1 + J_2} |
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where
Well |
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| | total subsurface flowrate of the well |
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| | total well productivity Index |
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| | apparent formation pressure of dual-layer formation |
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| | wellbore pressure loss between the tips of two layers |
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| | true vertical height between the layers tops |
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| | wellbore fuid density |
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| | gravity constant |
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Layer #1 |
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| LaTeX Math Inline |
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body | --uriencoded--p_%7Bwf%7D |
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| bottom-hole pr4essure at Layer #1 top |
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| | total subsurface flowrate of the Layer #1 |
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| | formation pressure of the Layer #1 |
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| | productivity Index of the Layer #1 |
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Layer #2 |
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| LaTeX Math Inline |
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body | --uriencoded--p_%7Bwf2%7D = p_%7Bwf%7D + \rho \, g\, hdelta p_2 |
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| bottom-hole pr4essure at Layer #2 top |
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| | total subsurface flowrate of the Layer #2 |
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| | formation pressure of the Layer #2 |
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| | productivity Index of the Layer #2 |
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In many practical cases:
LaTeX Math Block |
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\delta p_2 = \rho \, g \, h |
where
| wellbore fuid density |
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| gravity constant |
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LaTeX Math Inline |
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body | h = TVDSS_1 - TVDSS_2 |
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| true vertical height between -th layer and reference layer LaTeX Math Inline |
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body | --uriencoded--k_%7Breff%7D |
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The above equations are valid for both producers and injectors.
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Panel |
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borderColor | wheat |
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bgColor | mintcream |
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borderWidth | 7 |
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LaTeX Math Block |
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| p_{wf} = p_1 - q_1/J_1 |
LaTeX Math Block |
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| p_{wf,2} = p_2 - q_2/J_2 |
LaTeX Math Block |
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| p_{wf2} = p_{wf} + \delta p_2 |
This leads to LaTeX Math Block |
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| p_1 - q_1/J_1 = p_2 - \delta p_2 - q_2/J_2 |
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See Also
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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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