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| Fig. 1. Multi-layer well schematic |
| LaTeX Math Block |
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| q = \sum_{k=1}^N q_k |
| | 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 = \sum_{k=1}^N J_k |
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| LaTeX Math Block |
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| p_e = J^{-1} \cdot \sum_{k=1}^N J_k \, (p_k- \delta p_k) |
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where
| 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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| LaTeX Math Inline |
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| body | --uriencoded--p_%7Bwf%7D = p_%7Bwf, k_%7Bref%7D%7D |
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| bottom-hole pressure at the top of the reference layer | LaTeX Math Inline |
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| body | --uriencoded--k_%7Breff%7D |
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| LaTeX Math Inline |
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| body | --uriencoded--p_%7Bwf,k%7D = p_%7Bwf%7D +\delta p_k |
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| bottom-hole pressure at the top of the -th layer |
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| wellbore pressure loss between -th layer and reference layer | LaTeX Math Inline |
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| body | --uriencoded--k_%7Breff%7D |
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| total subsurface flowrate of the -th layer |
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| formation pressure of the -th layer |
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| productivity Index of the -th layer |
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The above equations are valid for both producers and injectors.
In many practical cases:
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\delta p_k = \rho \, g \, h_k |
where
| wellbore fuid density |
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| gravity constant |
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| LaTeX Math Inline |
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| body | --uriencoded--h_k = TVDS_k - TVDS_%7Bk_%7Bref%7D%7D |
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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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See Also
Petroleum Industry / Upstream / Production / Subsurface Production / Subsurface E&P Disciplines / Field Study & Modelling / Production Analysis / Productivity Diagnostics
[ Production Technology / Well Flow Performance ]
[ Formation pressure (Pe) ] [ Dual-layer IPR]
