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LaTeX Math Block
anchorBHP_PROD
alignmentleft
p^{\uparrow}_{wf, k}(t) = p(t) - {J^{\uparrow}_k}^{-1} \cdot \frac{dQ^{\uparrow}_k}{dt}



LaTeX Math Block
anchorBHP_INJ
alignmentleft
p^{\downarrow}_{wf, \, j}(t) = p(t) -  {J^{\downarrow}_j}^{-1} \cdot \frac{dQ^{\downarrow}_j}{dt}


wherewhere

LaTeX Math Inline
bodyp^{\uparrow}_{wf, \, k}(t)
\,

BHP in

LaTeX Math Inline
bodyk
-th producer

LaTeX Math Inline
bodyp^{\downarrow}_{wf, \, j}(t)

BHP in

LaTeX Math Inline
bodyj
-th injector

LaTeX Math Inline
bodyQ^{\uparrow}_k(t)

cumulative offtakes from

LaTeX Math Inline
bodyk
-th producer by the time moment
LaTeX Math Inline
bodyt

LaTeX Math Inline
bodyQ^{\downarrow}_j(t)

cumulative intakes to

LaTeX Math Inline
bodyj
-th injector by the time moment
LaTeX Math Inline
bodyt

LaTeX Math Inline
bodyJ^{\uparrow}_k

productivity index of

LaTeX Math Inline
bodyk
-th producer

LaTeX Math Inline
bodyJ^{\downarrow}_j

injectivity Index of

LaTeX Math Inline
bodyj
-th injector

...