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Well

LaTeX Math Inline
bodyq

total subsurface flowrate of the well

LaTeX Math Inline
bodyJ

total well productivity Index

LaTeX Math Inline
bodyp_e

apparent formation pressure of dual-layer formation
Layer #1

LaTeX Math Inline
body--uriencoded--p_%7Bwf%7D = p_%7Bwf, 1%7D

bottom-hole pressure at Layer #1 top

LaTeX Math Inline
bodyq_1

total subsurface flowrate of the Layer #1

LaTeX Math Inline
bodyp_1

formation pressure of the Layer #1

LaTeX Math Inline
bodyJ_1

productivity Index of the Layer #1
Layer #2

LaTeX Math Inline
body--uriencoded--p_%7Bwf2%7D = p_%7Bwf%7D + \delta p_2

bottom-hole pr4essure at Layer #2 top

LaTeX Math Inline
body \delta p_2

wellbore pressure loss between the tips of two layers

LaTeX Math Inline
bodyq_2

total subsurface flowrate of the Layer #2

LaTeX Math Inline
bodyp_2

formation pressure of the Layer #2

LaTeX Math Inline
bodyJ_2

productivity Index of the Layer #2


In many practical cases one can safely assume:

LaTeX Math Block
anchordpk
alignmentleft
\delta p_2 = \rho \, g \, h

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