Page tree

Versions Compared

Key

  • This line was added.
  • This line was removed.
  • Formatting was changed.


LaTeX Math Block
anchor1
alignmentleft
J = \frac{q}{|p_e - p_{wf}|}

where

LaTeX Math Inline
bodyq

flowrate (the specification of which may differ, see below)

LaTeX Math Inline
bodyp_e

formation pressure

LaTeX Math Inline
bodyp_{wf}

bottom hole pressure at sandface


The definition of flowrate 

LaTeX Math Inline
bodyq
 and formation pressure 
LaTeX Math Inline
bodyp_e
 may vary depending on application.


Overall concept is applicable to both producers and injectors but can be split into specific definitions:

Productivity Index of producerInjectivity Index of injector


LaTeX Math Block
anchor1
alignmentleft
J^{\uparrow} = \frac{q^{\uparrow}}{p_e - p_{wf}}



LaTeX Math Block
anchor1
alignmentleft
J^{\downarrow} = \frac{q^{\downarrow}}{p_{wf} - p_e}


LaTeX Math Inline
bodyq^{\uparrow}

production rate

LaTeX Math Inline
bodyq^{\downarrow}

injection rate


The PI concept also applies to aquifer expansion:

LaTeX Math Block
anchorQJPUF
alignmentleft
J^{\downarrow} = \frac{q^{\downarrow}}{p(t) - p_{AQ}(t)}

where

LaTeX Math Inline
bodyq

volumetric water inflow rate from aquifer into hydrocarbon reservoir

LaTeX Math Inline
bodyp(t)

formation pressure in hydrocarbon reservoir

LaTeX Math Inline
bodyp_{AQ}(t)

formation pressure in aquifer



See Also


Petroleum Industry / Upstream / Production / Subsurface Production / Subsurface E&P Disciplines / Production Technology 

Definition specifics on formation pressure and productivity index  ] [ Sandface Productivity Index ] [ Surface Productivity Index ] [ Specific Productivity Index ] [ Injectivity Index ]