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Fig. 1. Dual-layer well schematic



(1) q = \sum_{k=1}^N q_k
(2) p_{wf} = p_e - q/J
(3) J = \sum_{k=1}^N J_k
(4) p_e = J^{-1} \cdot \sum_{k=1}^N J_k \, (p_k- \rho \, g \, h_k)

where

q

total subsurface flowrate of the well

J

total well productivity Index

p_e

apparent formation pressure of dual-layer formation

h

true vertical height between the layers tops

\rho

wellbore fuid density

g

gravity constant

p_{wf}

bottom-hole pressure at the top of the reference layer

p_{wf,k} = p_{wf} +\rho \, g\, h_k

bottom-hole pressure at the top of the k-th layer

q_k

total subsurface flowrate of the  k-th layer

p_k

formation pressure of the  k-th layer

J_k

productivity Index of the  k-th layer


The above equations are valid for both producers and injectors.

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]

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